solving engineering problems

Contents

Solving Engineering Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

1 Simulating Engineering Tasks with Flow Simulation . . . . . . . . . . . . . . . 1-4Selecting Geometrical and Physical Features of the Task . . . . . . . . . . . . . . . . . . . . 1-4Creating the Model and the Flow Simulation Project. . . . . . . . . . . . . . . . . . . . . . . 1-5

2 Solving Engineering Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6Strategy of Solving the Engineering Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6Settings for Resolving the Geometrical Features of the Model and for Obtaining the Required Solution Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7Monitoring the Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-9Viewing and Analyzing the Obtained Solution. . . . . . . . . . . . . . . . . . . . . . . . . . 1-10Estimating the Reliability and Adequacy of the Obtained Solution. . . . . . . . . . . . . 1-10

3 Frequent Errors and Improper Actions . . . . . . . . . . . . . . . . . . . . . . . . . . 1-11

Advanced Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

1 Mesh - Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1Types of Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1Mesh Construction Stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3Basic Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4Control Planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5Resolving Small Features by Using the Control Planes . . . . . . . . . . . . . . . . . . . . . 2-5Contracting the Basic Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5Resolving Small Solid Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7Curvature Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7

Solving Engineering Problems with Flow Simulation 2012 i

Tolerance Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-9Narrow Channel Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-10Local Mesh Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12

Recommendations for Creating the Computational Mesh. . . . . . . . . . . . . . . . . . . 2-132 Mesh-associated Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-14

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-14Visualizing the Basic Mesh Before Constructing the Initial Mesh . . . . . . . . . . . . . 2-14Enhanced Capabilities of the Results Loading . . . . . . . . . . . . . . . . . . . . . . . . . . 2-14Viewing the Initial Computational Mesh Saved in the .cpt Files . . . . . . . . . . . . . . 2-16Viewing the Computational Mesh Cells with the Mesh Option . . . . . . . . . . . . . . . 2-16Visualizing the Real Computational Geometry . . . . . . . . . . . . . . . . . . . . . . . . . 2-17Switching off the Interpolation and Extrapolation of Calculation Results . . . . . . . . 2-19Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-20

3 Meshing - Additional Insight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-20Initial Mesh Generation Stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-21

Basic Mesh Generation and Resolving the Interface . . . . . . . . . . . . . . . . . . . . 2-21Narrow Channel Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-23Thin walls resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-25Square Difference Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-26Mesh Diagnostic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-28

Refinements at Interfaces Between Substances . . . . . . . . . . . . . . . . . . . . . . . . . 2-28Small Solid Features Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-28Curvature Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-29SSFRL or CRL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-30Tolerance Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-31

Local Mesh Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-31The "Optimize thin walls resolution" option . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-32Postamble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-33Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-33

4 Calculation Control Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-33Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-33Finishing the Calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-34Refinement of the Computational Mesh During Calculation . . . . . . . . . . . . . . . . . 2-36

5 Flow Freezing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-38What is Flow Freezing? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-38How It Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-38

Flow Freezing in a Permanent Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-39Flow Freezing in a Periodic Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-40

Advanced Features Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1

1 Cavitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1Physical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2

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Engineering Cavitation Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2Isothermal Cavitation Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2

Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3

Examples of use. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-8

2 Steam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9Physical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9Interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9Example of use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10

3 Humidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-11Physical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-11Interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-12Example of use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-14Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-14

4 Real Gases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-15Physical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-15Interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-16Example of use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-18Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-19References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-19

5 Rotation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-20Physical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-20

Local Rotating Regions - Additional Information. . . . . . . . . . . . . . . . . . . . . . . 3-21Interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-22

Global Rotating Reference Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-22Local Rotating Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-23

Examples of Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-24Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-26

Solving Engineering Problems with Flow Simulation 2012 iii

1

Solving Engineering Problems

Introduction

Engineering problem is them problem connected with designing certain object or system.

There are three general approaches to solveing engineering problems:

• an experimental approach: a hardware rig or prototype, i.e., the full-scale object and/or its model, is manufactured and the experiments needed for designing the object are conducted with this hardware;

• a computational approach: the computations needed for designing the object are performed and their results are directly used for designing the object, without conducting any experiments;

• a computational-experimental approach combines computations and experiments (with the manufactured full-scale object and/or its model) needed for designing the object, their sequence and contents depending on the solved problem, e.g. iterative procedures may be run.

Each of the first two approaches has advantages and disadvantages.

The purely experimental approach, being properly conducted, does not require additional validations of the obtained results, but it is very expensive, even if it is realized on the object models, since testing facilities and hardware are required anyway. Moreover, if the object models are tested, the obtained results must be scaled to the full-scale object, so some computations are required anyway.

Solving Engineering Problems with Flow Simulation 2012 1-1


The purely computational approach, being properly performed, is substantially less expensive than the experimental one, both in terms of finances and time, but it requires assurance in adequacy of the obtained computational results. Naturally, such assurance must be based on numerous verifications and validations of the used computational codes, both from mathematical and physical viewpoints, i.e., both on the mathematical accuracy of the obtained results (the results’ adequacy to the used mathematical model) and on the adequacy of the used mathematical model to the governing physical processes, that is validated by comparing the computations with the available experimental data.

The third approach, if it combines experiments and computations reasonably, joins the advantages of both of the first two above-mentioned approaches and avoids their disadvantages. Complex engineering problems are solved mainly in this way. A computational code validated on available experimental data allows of quickly selecting the optimal object design and/or its optimal operating mode. Then necessary experiments are conducted to verify the selection.

When selecting from the world market a computational code that is most suitable for solving your problems, it is necessary to take into account the following suggestions. Any computational code is based, firstly, on a mathematical model of the governing physical processes (expressed in the form of a set of differential and/or integral equations derived from physical laws, and include, if necessary, semi-empirical and empirical constants and/or relationships) and, secondly, a method of solving these equations. Since the equations of the mathematical model cannot be solved analytically, they are solved in a discrete form on a computational mesh, so the solution of the mathematical problem is obtained with a certain degree of accuracy. Naturally, the accuracy of the solution of the mathematical problem depends on both the method of discretising the differential and/or integral equations and on the method of solving the obtained discrete equations. Once these methods have been selected, the accuracy of solution of the mathematical problem depends on how well the computational mesh resolves the problem regions of non-linear behavior. To provide good accuracy, the mesh has to be rather fine in these regions. Moreover, a usual way of estimating the accuracy of solution of the mathematical problem consists of obtaining solutions on several different meshes, from coarser to finer. So, if beginning from some mesh in this set, the difference in the interesting physical parameters between the solutions obtained on the finer and coarser meshes becomes negligible from the viewpoint of the engineering problem, i.e., the solution flattens, then the accuracy of solution of the mathematical problem required for solving this engineering problem is considered to be attained, since the so-called solution mesh convergence is attained. Naturally, the solution of the mathematical problem can differ from the experimental values (i.e., from the solution of the physical problem, if it is known), and this difference depends, firstly, from the conformity of the mathematical model and the simulated physical processes, and, secondly, on the error, which these experimental values have been measured with and which are known and tend to decrease upon increasing the number of tests peroformed to measure them.

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Correspondingly, the computational codes presented on the market differ from each other not only in their cost, but also in accuracy of mathematical simulation of the physical problems, as well as in the procedure of specifying the initial data, in the amount of user’s time needed for this specification, in the procedure of solving a problem and the computer memory and CPU time needed for obtaining a solution of the required accuracy, and at last in the procedures of processing and visualization of the obtained results and the user’s time needed for that.

Naturally, a highly accurate solution requires a fine computational mesh, and consequently rather substantial computer memory and CPU time, as well as, in some cases, increased user time and efforts for specifying the initial data for the calculation. As a result, if the time needed to solve an engineering problem with a computational code exceeds some threshold time, then either the engineering problem becomes irrelevant, e.g. because your competitors have out-distanced you by this time, or alternative approaches, which may be not so accurate, but are surely faster, are used instead in order to solve this problem at given time span.

Before getting acquainted with the recommended procedure of obtaining a reliable and rather accurate solution of an engineering problem with Flow Simulation, it is expedient to consider Flow Simulation features governing the below-described strategy of solving engineering problems with Flow Simulation.

Since Flow Simulation is based on solving time-dependent Navier-Stokes equations, steady-state problems are solved through a steady-state approach. To obtain the steady-state solution quicker, a method of local time stepping is employed over the computational domain considered. A multigrid method is used for accelerating the solution convergence and suppressing parasitic oscillations. The computational domain is designed as a parallelepiped enveloping the model with planes orthogonal to the axes of the SolidWorks model’s Cartesian Global coordinate system. The computational mesh is built by dividing the computational domain into parallelepiped cells with its sides orthogonal to the Global coordinate system axes. (The cells lying outside the fluid-filled regions and outside solids with heat conduction inside do not participate in the subsequent calculations). Procedures of the computational mesh refinement (splitting) are used to resolve the model features better, such as high-curvature surfaces in contact with fluid, thin walls surrounded by fluid, narrow flow passages (gaps), and the specified insulators’ boundaries. During the subsequent calculations during the solving of the problem the computational mesh can be refined additionally (if that is allowed by the user-defined settings) to better resolve the high-gradient flow and solid regions revealed in these calculations (Solution-Adaptive Meshing).



Since steady-state problems are solved in Flow Simulation through the steady-state approach, it is necessary to determine the termination moment for the calculation properly. If the calculation is finished too early, i.e., when the steady state solution has not been attained yet, then the obtained solution can depend on the specified initial conditions and so be not very reliable. On the contrary, if the calculation is finished too late, then some time has been wasted uselessly. To optimize the termination moment for the calculation and to determine physical parameters of interest (e.g. a force acting on a model surface, or a model hydraulic resistance) with a sufficient degree of accuracy, you can specify them as the calculation goals.

The way to simulate an engineering problem with SolidWorks+Flow Simulation correctly and adequately from the physical viewpoint, i.e. to state the corresponding model problem, and to solve this model problem properly and reliably with Flow Simulation, is described in the chapters Simulating Engineering Tasks with Flow Simulation and Solving Engineering Tasks.

1 Simulating Engineering Tasks with Flow Simulation

It is necessary to remember that a fast but inaccurate beginning will cost you more efforts and time spent not only for specifying the initial data, but, even worse, for the subsequent calculations, until they finally become reliable. Therefore, we strongly recommend that you carefully read this section.

Selecting Geometrical and Physical Features of the Task

Before you start to create a SolidWorks model and a Flow Simulation project, it is necessary to select the engineering problem’s geometrical and physical features that most substantially influence this problem’s solution - first of all, those, which are important for estimating the possibility of solving this problem with Flow Simulation. For example,

• if the problem contains movable parts, then it is necessary to estimate the importance of taking into account their motions when solving the problem, and, if these motions are important, to estimate the possibility of solving this problem with a quasi-stationary approach, since model parts’ motions during a calculation are not considered in Flow Simulation (however, you may specify a translational and/or rotational motion of the specific wall or a rotating reference frame),

• if the problem includes several fluids, or fluid and solid, then it is necessary to estimate the importance of chemical reactions between them for the problem’s solution, and, if the reactions are important, i.e., the reactions rates are rather high and the reacting fluids are intensely mixed with each other under the problem’s conditions, then to estimate a possibility of introducing the reaction products as an additional fluid when solving this problem, since chemical reactions are not

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considered in Flow Simulation,

• if the problem includes fluids of different types (for example, a gas and a liquid), and there is an interface between them or these fluids are mixing, then it is

necessary to estimate the importance of taking this into account, since Flow Simulation does not consider a free fluid surface, or mixing of fluids of different types.

We can present other examples of an clear impossibility of solving some engineering problems with Flow Simulation, as well as of simplifying the engineering problems for solving them with Flow Simulation, but it is impossible to envision and describe all the possible situations in the present document, so that on each particular case you will have to make decision by yourself.

Creating the Model and the Flow Simulation Project

If the SolidWorks model has already been created when designing the object, i.e. it is fully adequate to the object, then, to solve the engineering problem with Flow Simulation, it may be required:

• to simplify the model by removing the parts, which do not influence the problem’s solution, but consume computer resources, i.e. memory and CPU time. For example, a corrugated model surface which will result in an exceedingly large number of mesh cells required to resolve it can be specified instead as smooth surface with equivalent wall roughness. If a model has narrow fluid-filled blind holes whose influence on the overall flow pattern is, by rough estimate, barely perceptible, it would be better to remove these features in order to avoid the excessive mesh splitting around them.

• to add auxiliary parts to the model, e.g. inlet and outlet tubes for stabilization of the flow, lids to cover the inlet and outlet openings, and parts to denote rotating regions, local initial meshes or other areas where special conditions are applied.

Both these actions, being executed properly, can be very pivotal in obtaining a reliable and accurate solution. Naturally, adding the auxiliary parts to a model will inevitably cause an increase of the computational mesh cells and, consequently, the required computer memory and CPU time, therefore these parts’ dimensions must be adequate to the stated problem.

If a model has not been created yet, it is expedient to take all the above-mentioned factors into account when creating it.

If all effects of these actions are not clear enough, it may be worthwhile to vary the model parts and/or their dimensions in a series of calculations in order to determine their influence on the obtained solution.

Then, in accordance with the problem’s physical features revealed and adapted to Flow Simulation capabilities, the basic part of the Flow Simulation project is specified, i.e., the problem type (internal or external), fluids and solids involved in the problem, physical features taken into account (e.g. heat conduction in solids, time-dependent analysis,


gravitational effects, etc.), boundaries of the calculation domain, initial and boundary conditions, and, if necessary, fluid subdomains, rotating regions, volume and/or surface heat sources, fans and other features and conditions.


The specified boundary conditions, as well as heat sources, fans, and other conditions and features must correspond to the problem’s physical statement and not conflict with each other.

Eventually, you specify the physical parameters of interest as the Flow Simulation project goals. They can be local or integral, defined within the whole computational domain or a certain volume, on a surface or a point. The parameters determined over some region are expressed in the form of their minimum, or maximum, average, or bulk average values. This allows you to increase substantially reliability and accuracy of determination of these parameters, since their behavior is saved on each iteration during the calculation and can be analyzed later. On the contrary, the convergence behavior of the parameters not specified as goals can not be analyzed afterwards, as they are saved only at the last iteration and, optionally, at the user-specified iterations.

2 Solving Engineering Tasks

As soon as you have specified the basic part of the Flow Simulation project that is unlikely to be changed in the subsequent calculations, the next step is to select the strategy of solving the engineering problem with Flow Simulation, i.e., obtaining the reliable and accurate solution of the problem.

Strategy of Solving the Engineering Tasks

As it has been mentioned in Introduction, by performing a series of calculations on a set of computational meshes ranging from coarser to finer ones, we can estimate the accuracy of solution of the mathematical problem. As soon as the calculation on a finer mesh does not yield a noticeably different (from the engineering problem’s viewpoint) solution, i.e. the solution flattens with respect to the mesh cells’ number, we can conclude that the solution of the mathematical problem has achieved mesh convergence, i.e., the required mathematical solution accuracy is attained. Naturally, first you must determine the threshold for a solution-vs.-mesh change, so that the change smaller than this threshold will be considered as negligible. Since the determination of this threshold is possible only in relation with some physical parameter, it is natural to connect it with the physical parameters of interest of the engineering problem in question, in particular, with the admissible determination errors of these physical parameters. Moreover, since steady-state problems are solved with Flow Simulation through the steady-state approach, the supervision for a behavior of the calculation goals during the calculation (i.e., in iterations) can serve two purposes. Firstly, if these parameters oscillate during the solution, it will allow you to determine their values and observation errors more accurately by averaging them over a number of iterations and determining their deviation from this average value. Secondly, you may want to intervene in the calculation process by finishing the calculation manually if you see that either the calculation is unacceptable for you by

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some reasons, or, vice versa, if the solution has actually already converged, so that there is no reason to calculate any further.

Therefore, the strategy of solving an engineering problem with Flow Simulation consists, first of all, in performing several calculations on the same basic project (i.e., with the same model, inside the same computational domain, and with similar boundary and initial conditions) varying only the computational mesh. Since the computational mesh is built automatically in Flow Simulation, it may be varied by varying the project parameters that govern its design (the initial computational mesh on which the calculation starts, and maybe its refinement during the calculation): Result Resolution Level, Minimum Gap Size, Minimum Wall Thickness.

An additional item of this strategy of solving an engineering problem with Flow Simulation consists in varying the auxiliary elements added to the model as needed to solve the problem with Flow Simulation (e.g. inlet and outlet tubes attached to the inlet and outlet openings, for internal problems), the dimensions of which are questionable from the viewpoint of their necessity and sufficiency. Those physical parameters of the engineering problem whose values are not known exactly and which, in your opinion, can influence the problem solution, must be varied also. When performing these calculations, there is no need to investigate the solution-vs.-mesh convergence again, since it has been already achieved before. It is enough to just perform these calculations with the project mesh settings that provided the solution with satisfactory accuracy during the solution-vs.-mesh convergence investigation. The same applies also to the parametric engineering calculations while you are changing the model parts and/or flow parameters. However, you must keep in mind the potential necessity for checking the solution-vs.-mesh convergence, because in doubtful cases it must be checked again.

In spite of the apparent simplicity of the proposed strategy, its full realization is usually troublesome due to the substantial difficulties including, first of all, a dramatic increase of the requirements for computer memory and CPU time when you are substantially increasing the number of cells in the computational mesh. Since both the computer memory and the time for which the engineering problem must be solved are usually restricted, the specific realization of this strategy eventually governs the accuracy of the problem solution, whether it will be satisfactory or not. Perhaps, a further simplification of the model and/or reducing the computational domain will be required.

Some specific description of this strategy is presented in the next sections of this document.

Settings for Resolving the Geometrical Features of the Model and for Obtaining the Required Solution Accuracy

The computational mesh variation described in Section 2.1 is the key item of the proposed strategy of solving engineering problems with Flow Simulation.

The result resolution level specified in the Wizard governs the number of basic mesh cells, the criteria for refinement (splitting) of the basic mesh to resolve the model geometry, i.e.,


creating the initial mesh, as well as the criteria for refinement (splitting) of the initial mesh during the problem solution. The Result Resolution specified in the Wizard defines the following parameters in the created project: the Level of initial mesh and the Results


resolution level. The Level of initial mesh governs only the initial mesh and is accessible (after the Wizard has been finished) from the Initial Mesh dialog box. The Results resolution level is accessible from the Calculation Control Options dialog box and controls the refinement of computational mesh during calculation and the calculation finishing conditions. The Geometry Resolution options that also influence the initial mesh may be changed on the Automatic Settings tab of the the Initial Mesh dialog box. Their effects can be altered on the other tabs of the Initial Mesh dialog box or in the Local Initial Mesh dialog box.

Before creating the initial mesh, Flow Simulation automatically determines the minimum gap size and the minimum wall thickness for the walls which are in contact with a fluid on both sides. That is required for resolving the geometrical features of the model with Flow Simulation computational mesh. So, when creating the initial mesh, it is taken into account that the number of the mesh cells along the normal to the model surface must not be less than a certain number if the distance along this normal from this surface to the opposite wall is not less than the minimum gap size. Depending on the mesh cell arrangement, the model flow passages not resolved with the computational mesh either are automatically replaced with a wall, or increased up to the mesh cell size. In the automatic mode these mesh parameters are determined from dimensions of the surfaces on which boundary conditions have been specified, e.g. the model inlet and outlet openings in an internal analysis, as well as those surfaces and volumes on or in which heat sources, local initial conditions, surface and/or volume goals and some of the other conditions and features. Before the calculation, you can see the minimum gap size and the minimum wall thickness that are determined in such a way. If these values cannot provide an adequate resolution of the model geometry, you can specify them manually. At that, it is necessary to take into account that the number of the computational mesh cells generated to resolve the model geometrical features depends on the specified result resolution level.

Evidently, when creating a Flow Simulation project it is necessary to make sure that both the minimum gap size and the minimum wall thickness are relevant to the model geometry. However, if the model geometry is complicated (e.g. there are non-circular flow passages, sharp edges protruding into the stream, etc.), it can be difficult to determine these parameters unambiguously. In this case it may be useful to perform several calculations by varying these parameters within a reasonable range in order to reveal their influence on the problem solution. In accordance with the strategy of solving engineering problems, these calculations must be performed at different result resolution levels.

The initial mesh created at result resolution levels of 3…5 is not changed during the solving of a problem, i.e. is not adapted to the solution being obtained. Result resolution levels of 5…7 yield the same initial mesh, but at result resolution levels of 6 and 7 the mesh is refined during the calculations in the regions of increased physical parameters gradients. At level 8, a finer initial mesh is generated and refinements during calculation take place.

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It makes sense to perform calculations at the result resolution level of 3 if both the model geometry and the flow field are relatively smooth. For more complex problems we recommend first of all to perform the calculation at the result resolution level of 4 or 5

(naturally, with specifying explicitly the minimum gap size and minimum wall thickness). After that, if the calculation at the result resolution level of 5 has been performed, we recommend, in order to ascertain the mesh convergence, to perform the calculation at the result resolution level of 7 and, if the computer resources allow you to do this, at the result resolution level of 8.

Monitoring the Calculation

Monitoring the calculation, i.e., at least, monitoring behavior of the physical parameters specified by you as the project goals (you can inspect also physical parameters fields at the specified planar cross-sections) is useful for the following reasons:

• you can intervene in the process of calculation, i.e., manually finish the calculation before it finishes automatically, if you see that either the calculation is unacceptable for you for some reasons (e.g. if Flow Simulation has generated warnings making clear that the sequential calculation is senseless), or, vice versa, when solving a steady-state problem (that concerns some time-dependent problems also), the solution has already converged, so that there is no reason to continue the calculation;

• if a steady-state problem is solved, and the physical parameters specified by you as the project goals oscillate during the iterations, then inspecting these parameters’ behavior during the calculation will allow you to determine their values and determination errors more accurately by averaging their values over the iterations and determining their deviations from these average values;

• if the physical parameters of interest do not change substantially during the calculation, you can obtain their intermediate (preliminary) values beforehand, and in the subsequent iterations they will be refined finally;

• if you solve a time-dependent problem, you can see the calculation results obtained at the current physical time moment before the calculation is finished.

The first above-mentioned reason is especially useful since it allows you to substantially reduce the CPU time in some cases. For example, if you do not specify the high Mach number gas flow in the project settings, whereas in fact the flow becomes supersonic, or if Flow Simulation warns you about a vortex at the model outlet, that substantially reduces the calculation accuracy, making it necessary to change some of the problem settings (i.e. specify high Mach number flow for the first case or lengthen the model outlet tube for the second one). If you solve a steady-state problem at the result resolution level of 7 or 8 and you see that the computational mesh refinements performed during the calculation do not increase the number of cells in the mesh and, therefore, do not noticeably improve the problem solution (the values of the project goals does not change), you can finish the calculation relatively early (say, after 1…2 travels have been performed).



Viewing and Analyzing the Obtained Solution

When viewing and analyzing the obtained solution after finishing the calculation, it is recommended to plot the evolutions of the project goals during the calculation, if you did not monitor them directly as the calculation went on. If a steady-state problem is solved, and you have specified the physical parameter of interest as the project goal, then, if this parameter has oscillated during the calculation, you can determine its value more accurately by averaging it over the last iterations interval, in which its steady-state oscillation is seen. This wayt you also determine the variance of this goal, i.e., its deviation from the average value, that characterizes the goal determination error in the obtained solution.

It is also useful to check for vortices at the model outlet, as well as to see the flow pattern in the model and, if heat transfer in solids has been calculated, the temperature distribution over the solid parts of the model. Naturally, first of all it is expedient to see the obtained field of the physical parameter you are interesting in, not only in the region of interest, but also in a broader area, in order to check this field for apparently incosistent results.

It is also worthwhile to examine the obtained fields of other physical parameters related to the one you are interested in. For example, if you are interested in the total pressure loss, you may want to see the velocity field, whereas if you are interested in the temperature of solid, a picture of the fluid-to-solid heat flux field is also useful.

Estimating the Reliability and Adequacy of the Obtained Solution

In accordance with the general approach to estimating reliability and accuracy of the engineering problem solution obtained with a computational code, this estimation consists of the following two parts: an estimation of how accurate is the solution of the mathematical problem corresponding to the mathematical model of the physical process, and an estimation of accuracy of simulating the physical process with the given mathematical model.

The accuracy of solution of the mathematical problem is determined by mathematical methods, independently of the consistency of the model to the physical process under consideration. In our case, this accuracy estimation is based on analyzing the mesh convergence of the problem solutions obtained on different computational meshes (See Section 2.2). Then, since steady-state problems are solved with Flow Simulation via a steady-state approach by employing local time steps, it is useful to verify additionally the accuracy of the obtained solution by solving the similar time-dependent problem not employing local time steps.

As soon as the mathematical problem solution of a satisfactory accuracy has been obtained, the next step consists of estimating the accuracy of simulating the physical process under consideration with the mathematical model employed in the computational code. To do this, the obtained solution is compared with the available experimental data

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(taking into account their errors which consist of measurement errors and experimental errors arising from possible spurious influences). Naturally, since experimental data are always restricted, for this validation it is desirable to select the data which are as close to

the engineering problem being solved as possible. To validate the computational code on the available experimental data, you have to solve the corresponding test problem in addition to the engineering problem being solved (preferably before you start to solve the engineering problem following the above-mentioned strategy), but this operation increases the reliability of estimating the obtained solution of the engineering problem so substantially that the required additional time and efforts will be fully paid back later on, in particular when solving similar engineering problems.

If after solving the test problem you see that accuracy of its solution obtained with Flow Simulation is not satisfactory from your viewpoint, check to see that you have properly specified the Flow Simulation project, that all substantial features of the engineering problem have been taken into account, and, finally, that Flow Simulation restrictions do not impede solving this engineering problem.

3 Frequent Errors and Improper Actions

Let us consider errors and improper actions frequently done when solving engineering problems with Flow Simulation.

When Specifying Initial Data:

• not taking into account physical features which are important for the engineering problem under consideration: e.g. high Mach number gas flow (should be taken into account if M>3 for steady-state or M>1 for transient tasks or supersonic flow occurs in about a half of the computational domain or greater), gravitational effects (must be taken into account if either the fluid velocity is small, the fluid density is temperature-dependent, and a heat source is considered, or several fluids having substantially different densities are considered in a gravitational field), necessity of the time-dependent analysis (e.g. at the moderate Reynolds numbers, when unsteady vortices are generated);

• incorrectly specifying symmetry planes as the computational domain boundaries (e.g. at the moderate Reynolds numbers, when unsteady vortices are generated; you should keep in mind that the symmetry of model geometry and initial and boundary conditions does not guarantee you the symmetry of flow field);

• if symmetry planes have been specified and you click Reset at the Size tab of the Computational Domain dialog box, please do not forget to replace Symmetry by Default at the Boundary Condition tab;

• if you have specified symmetry planes and intend to specify a mass or volume flow rate at a model inlet or outlet opening, please do not forget to specify only the fraction of total flow rate proportional to the fraction of the opening area laying inside the computational domain, instead of specifying the total flow rate;

• if you specify integral boundary or volume conditions (heat transfer rates, heat


generation rates, etc.), please remember that their values specified in the Flow Simulation dialog boxes correspond to the fraction of area or volume laying inside the computational domain;


• if you specify a flow swirl on a model inlet or outlet openings (in the Fans or Boundary Conditions dialog boxes), please do not forget to properly specify their swirl axes and the coordinate system in the Definition tab;

• if you specify a Unidirectional or Orthotropic porous medium, please do not forget to specify their directions;

• please do not forget that the specified boundary conditions must not conflict with each other. For example, if you deal with gas flows and the model inlet flow is subsonic, whereas the flow inside the model becomes supersonic, it is incorrect to specify flow velocity or volume flow rate as a boundary condition at the model inlet, since they are fully determined by the geometry of the model flow passage and the fluid’s specific heat ratio;

• if you solve a time-dependent problem, and this problem has cyclic-in-time boundary conditions, thus leading to a steady-state cyclic-in-time solution, to obtain which you have to calculate the flow several times in cycle, every time specifying the solution from the previous calculation as the initial condition for the next calculation, there is no need to specify the boundary conditions for several cycles. Instead it is more convenient to specify them for a cycle and perform a series of calculations, running each calculation with selected Take previous results check box in the Run dialog box;

• when specifying Surface Goals, Volume Goals, Point Goals or Equation Goals, it is better to give them sensible names to identify these goals unambiguously, instead of selecting them in the tree and looking for the respective places at the model in the SolidWorks graphics area;

• if you want to monitor the intermediate calculation results at certain sections of the model during the calculation, it is better to determine these sections’ positions in the Global coordinate system beforehand, i.e. before actually running the calculation, since during the calculation it is a bit more difficult and you may be literally ’late’ in terms of the problem’s physical time;

When Monitoring a Calculation:

• when monitoring intermediate calculation results during a calculation, please do not forget the spatial nature of the problem being solved (of course, if the problem itself is not 2D). To take a look at the full pattern it is expedient to see the results at least in 2 or 3 intersecting planes;

When Viewing the Obtained Solution after Finishing a Calculation:

• please take into account that all settings made in the View Settings dialog box concern all Cut Plots, 3D Plots, Surface Plots, Flow Trajectories, Isosurfaces, which are active in the SolidWorks graphicsarea, therefore:

• your will not be able to open the Flow Trajectories dialog box if a parameter defined only on wall surfaces or in solid has been selected on the Contours

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tab and the Use from contours option has been selected at the Flow Trajectories tab of the View Settings dialog box;

• to view different result features in different panes simultaneously, you can split the SolidWorks graphics area into 2 or 4 panes and build different result features in different graphical areas through their individual Cut Plots, 3D Plots, Surface Plots, Flow Trajectories, Isosurfaces defined in these areas;

• if you intend to see integral physical parameters (e.g. area, mass or volume flow rates, heat generation rates, forces, etc.) with the Surface Parameters dialog box, please remember that:

• their shown values are determined over the parts of the surface that belong to the computational domain;

• their determination errors include errors of representing these surfaces in SolidWorks and Flow Simulation, the latter depends on the computational mesh;

• if you want to see the computational mesh in Cut Plots and/or Surface Plots, make sure that the Display mesh is enabled under Tools, Options, Third Party Options, otherwise the Mesh button in the Cut Plots and Surface Plots PropertyManagers will be unavailable.



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2

Advanced Knowledge

Introduction

The present document supplies you with our experience of employing the advanced Flow Simulation capabilities, organized in the following topics:

Manual adjustment of the initial computational mesh settings

Mesh-associated tools (viewing the mesh before and after the calculation and advanced post-processing tools)

Calculation control options (refinement of the computational mesh during calculation, conditions of finishing the calculation)

Flow freezing

1 Mesh - Introduction

This chapter provides the fundamentals of working with the Flow Simulation computational mesh, describes the mesh generation procedure and explains the use of parameters governing both automatically and manually controlled meshes.

First, let us introduce a set of definitions.

Types of Cells

Any Flow Simulation calculation is performed in a rectangular parallelepiped-shaped computational domain which boundaries are orthogonal to the axes of the Cartesian Global Coordinate System. A computational mesh splits the computational domain with a


set of planes orthogonal to the Cartesian Global Coordinate System's axes to form rectangular parallelepipeds called cells. The resulting computational mesh consists of cells of the following four types:

Advanced Knowledge

• Fluid cells are the cells located entirely in the fluid.

• Solid cells are the cells located entirely in the solid.

• Partial cells are the cells which are partly in the solid and partly in the fluid. For each partial cells the following information is kept: coordinates of intersections of the cell edges with the solid surface and normal to the solid surface within the cell.

As an illustration let us look at the original model (Fig.1.1) and the generated computational mesh (Fig.1.2).

Fig.1.1 The original model.

Fig.1.2 The computational mesh cells of different types

Zero level cell (basic cell)

Solid cell

Partial cell

First level cellFluid cell

Partial cell

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Mesh Construction Stages

Refinement is a process of splitting a rectangular computational mesh cell into eight cells by three orthogonal planes that divide the cell's edges in halves. The non-split initial cells that compose the basic mesh are called basic cells or zero level cells. Cells obtained by the first splitting of the basic cells are called first level cells, the next splitting produces second level cells, and so on. The maximum level of splitting is seven. A seventh level cell is 87 times smaller in volume than the basic cell.

The following rule is applied to the processes of refinement and merging: the levels of two neighboring cells can only be the same or differ by one, so that, say, a fifth level cell can have only neighboring cells of fourth, fifth, or sixth level.

The mesh is constructed in the following steps:

Construction of the basic mesh taking into account the Control Planes and the respective values of cells number and cell size ratios.

Resolving of the interface between substances, including refinement of the basic mesh at the solid/fluid and solid/solid boundaries to resolve the relatively small solid features and solid/solid interface, tolerance and curvature refinement of the mesh at a solid/fluid, solid/porous and a fluid/porous boundaries to resolve the interface curvature (e.g. small-radius surfaces of revolution, etc).

Narrow channels refinement, that is the refinement of the mesh in narrow channels taking into account the respective user-specified settings.

Refinement of all fluid, and/or solid, and/or partial mesh cells up to the user-specified level.

Mesh conservation, i.e. a set of control procedures, including check for the difference in area of cell facets common for the adjacent cells of different levels.

After each of these stages is passed, the number of cells is increased to some extent.

In Flow Simulation you can control the following parameters and options which govern the computational mesh:

1 Nx, the number of basic mesh cells (zero level cells) along the X axis of the Global Coordinate System. 1 ≤ Nx ≤ 1000

2 Ny, the number of basic mesh cells (zero level cells) along the Y axis of the Global

During the solution-adaptive meshing the cells can be refined and merged. See ”Refinement of the Computational Mesh During Calculation’ on page 36.

If you switch on or off heat conduction in solids, or add/move insulators, you should rebuild the mesh.


Coordinate System. 1 ≤ Ny ≤ 1000.

3 Nz, the number of basic mesh cells (zero level cells) along the Z axis of the Global Coordinate System. 1 ≤ Nz ≤ 1000.

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4 Control planes. By adding and relocating them you can contract and/or stretch the basic mesh in the specified directions and regions. Six control planes coincident with the computational domain's boundaries are always present in any project.

5 Small solid features refinement level (Lb). 0 ≤ Lb ≤ 7.

6 Curvature refinement level (Lcur). 0 ≤ Lcur ≤ 7.

7 Curvature refinement criterion (Ccur). 0 ≤ Ccur ≤ π.

8 Tolerance refinement level (Ltol). 0 ≤ Ltol ≤ 7.

9 Tolerance refinement criterion (Ctol). 0 ≤ C tol.

10 Narrow channels refinement: Characteristic number of cells across a narrow channel, Narrow channels refinement level, The minimum and maximum height of narrow channels to be refined.

These options are described in more detail below in this chapter.

Basic Mesh

The basic mesh is a mesh of zero level cells. In case of 2D calculation (i.e. if you select the 2D plane flow option in the Computational Domain dialog box) only one basic mesh cell is generated automatically along the eliminated direction. By default Flow Simulation constructs each cell as close to cubic shape as possible.

The number of basic mesh cells could be one or two less than the user-defined number (Nx, Ny, Nz). There is no limitation on a cell oblongness or aspect ratio, but you should carefully check the calculation results in all cases for the absence of too oblong or stretched cells.

Fig.1.3 Basic mesh examples.

a) 10x12x1 b) 40x36x1

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Control Planes

The Control Planes option is a powerful tool for creating an optimal computational mesh, and the user should certainly become acquainted with this tool if he is interested in optimal meshes resulting in higher accuracy and decreasing the CPU time and required computer memory. Control planes allow you to resolve small features, contract the basic mesh locally to resolve a particular region by a denser mesh and stretch the basic mesh to avoid excessively dense meshes.

Resolving Small Features by Using the Control Planes

If the level of splitting is not high enough, small solid features may be not resolved properly. In this case, two methods can be used to improve the mesh:

• increase the level of splitting. However, this may result in unnecessary increase of the number of cells in other regions, creating a non-optimal mesh, or

• set a control plane crossing the relevant small feature (e.g. a solid's sharp edge). This will allow you to resolve this feature better without creating an excessively dense mesh elsewhere. It is especially convenient in cases of sharp edges oriented along the Global Coordinate System axes.

Contracting the Basic Mesh

Using control planes you may contract the basic mesh in the regions of interest. To do this, you need to set control planes surrounding the region and assign the proper Ratio values to the respective intervals. The cell sizes on the interval are changed gradually so that the proportion between the first and the last cells of the interval is close (but not necessarily equal) to the entered Ratio value. Negative values of the ratio correspond to the reverse order of cell size increase. Alternatively, you may explicitly set the Number of cells for each interval, in which case the Ratio value becomes mandatory. For example, assume that there are two control planes Plane1 and Plane2 (see Fig.1.4) and the ratio on the interval between them is set to 2. Then the basic mesh cells adjacent to the Plane1 will be approximately two times longer than the basic mesh cells adjacent to the Plane2.

It is recommended that you place a control plane slightly submerged into the solid, and avoid placing it coincident with the solid surface.


Advanced Knowledge

Use of control planes is especially recommended for external analyses, where the computational domain may be substantially larger than the model.

Fig.1.5 Default control planes. Fig.1.6 Two custom control planes.

Fig.1.4 Specifying custom control planes.

Default control plane

Default control plane

Custom control plane

Custom control plane

Interval 3:number of cells=3 (automatic)ratio=1

Interval 2:number of cells=12 (manual)ratio=1

Interval 1:number of cells=12 (automatic)ratio=2

Plane 4

Plane 3

Plane 2

Plane 1

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In the Fig.1.6 two custom control planes are set through the center of the body with the ratio set to 5 and -5, respectively, on the intervals to the both sides of each plane.

Resolving Small Solid Features

The procedure of resolving small solid features refines only the cells where the solid/fluid (solid/solid, solid/porous as well as fluid/porous) interface curvature is too high: the maximum angle between the normals to a solid surface inside the cell exceeds 120°, i.e. the solid surface has a protrusion within the cell.

Such cells are split until the the Small solid features refinement level of splitting mesh cells is achieved.

Curvature Refinement

The curvature refinement level is the maximum level to which the cells will be split during refinement of the computational mesh until the curvature of the solid/fluid or fluid/porous interface within the cell becomes lower than the specified curvature criterion (Ccur).

The curvature refinement procedure has the following stages:

1 Each solid surface is triangulated: Flow Simulation gets triangles that make up the SolidWorks surfaces.

2 A local (for each cell) interface curvature is determined as the maximum angle between the normals to the triangles within the cell.

3 If this angle exceeds the specified Ccur, and the curvature refinement level is not reached then the cell is split.

The performance settings do not govern the triangulation performance.


Advanced Knowledge

The curvature refinement is a powerful tool, so that the competent usage of it allows you to obtain proper and optimal computational mesh. Look at the following illustrations to the curvature refinement by the example of a sphere.

Fig.1.7 Curvature refinement level is 0;Total number of cells is 64.

Fig.1.8 Curvature refinement level is 1;Total number of cells is 120.

Fig.1.9 Curvature refinement level is 2; Curvature criterion is 0.317;Total number of cells is 120.

Fig.1.10 Curvature refinement level is 2; Curvature criterion is 0.1;Total number of cells is 148.

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Tolerance Refinement

Tolerance refinement allows you to control how well (with what tolerance) mesh polygons approximate the real interface. The tolerance refinement may affect the same cells that were affected by the small solid features refinement and the curvature refinement. It resolves the interface's curvature more effectively than the small solid features refinement, and, in contrast to the curvature refinement, discerns small and large features of equal curvature, thus avoiding refinements in regions of less importance (see images below).

Any surface is approximated by a set of polygons which vertices are surface's intersection points with the cells' edges. This approach accurately represents flat faces though curvature surfaces are approximated with some deviations (e.g. a circle can be approximated by a polygon). The tolerance refinement criterion controls this deviation. A cell will be split if the distance (h, see below) between the outermost interface's point within the cell and the polygon approximating this interface is larger than the specified criterion value.

Fig.1.11 Curvature refinement level is 3; Curvature criterion is 0.1;

Fig.1.12 Tolerance refinement level is 3; Tolerance criterion is 0.1 mm;


Advanced Knowledge

Narrow Channel Refinement

The narrow channel refinement is applied to each flow passage within the computational domain (or a region, in case that local mesh settings are specified) unless you specify for Flow Simulation to ignore passages of a specified height. The Narrow Channels term is conventional and used for the definition of the flow passages of the model in the direction normal to the solid/fluid interface.

The basic concept of narrow channel refinement is to resolve the narrow channels with a sufficient number of cells to provide a reasonable level of solution accuracy. It is especially important to have narrow channels resolved in analyses of low Reynolds numbers or analyses with long channels, i.e. in such analyses where the boundary layer thickness becomes comparable to the size of the partial cells where the layer is developed.

The narrow channel settings available in Flow Simulation are the following:

• Narrow channels refinement level – the maximum level of cells refinement in narrow channels with respect to the basic mesh cell.

• Characteristic number of cell across a narrow channel – the number of cells (including partial cells) that Flow Simulation will attempt to set across the model flow passages in the direction normal to the solid/fluid interface. If possible, the number of cells across narrow channels will be equal to the specified characteristic number, otherwise it will be as close to it as possible. The Characteristic number of cells across a narrow channel (let us denote it as Nc) and the Narrow channels refinement level (let us denote it as L) both influence the mesh in narrow channels in the following manner: the basic mesh in narrow channels will be split to have Nc number per channel, if the resulting cells satisfy the specified L. In other words, whatever the specified Nc, the smallest possible cell in a narrow channel is 8L times smaller in volume (or 2L times smaller in each linear dimension) than the basic mesh cell. This is necessary to avoid undesirable mesh splitting in very fine channels that may cause the number of cells to increase to an unreasonable value.

• The minimum height of narrow channels, The maximum height of narrow channels – the minimum and maximum bounds for the height outside of which a flow passage will not be considered as a narrow channel and thus will not be refined by the narrow channel resolution procedure.

For example, if you specify the minimum and maximum height of narrow channels, the cells will be split only in those fluid regions where the distance between the opposite walls of the flow passage in the direction normal to wall lies between the specified minimum and maximum heights.

The narrow channel refinement operates as follows: the normal to the solid surface for each partial cell is extended up to the next solid surface, which will be considered to be the opposite wall of the flow passage. If the number of cells per this normal-to-wall direction is less than the specified N , the cells will be split to satisfy the narrow channel settings as

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cdescribed above.

Although the settings that produce an optimal mesh depends on a particular task, here are some ’rule-of-thumb’ recommendations for narrow channel settings:

1 Set the number of cells across narrow channel to a minimum of 5.

2 Use the minimum and maximum heights of narrow channels to concentrate on the regions of interest.

3 If possible, avoid setting high values for the narrow channels refinement level, since it may cause a significant increase in the number of cells where it is not necessary.

Fig.1.13 Small solid features refinement level is 3; Narrow channel refinement is disabled.

Fig.1.14 Small solid features refinement level is 3; Narrow channel refinement is on: 5 cells across narrow channels, Narrow channels refinement level is 2.


Advanced Knowledge

Local Mesh Settings

The local mesh settings option is one more tool to help create an optimal mesh. Use of local mesh settings is especially beneficial if you are interested in resolving a particular region within a complex model.

The local mesh settings can be applied to a component, face, edge or vertex. You can apply local mesh settings to fluid regions and solid bodies. To apply the local mesh settings to a fluid region you need to specify this region as a solid part or subassembly and then disable this component in the Component Control dialog box. The local mesh settings are applied to the cells intersected with the selected component, face, edge, or a cell enclosing the selected vertex. However, cells adjacent to the cell of the local region may be also affected due to the refinement rules described in the Mesh Construction Stages chapter.

Fig.1.15 Small solid features refinement level is 3; Narrow channel refinement is on: 5 cells across narrow channels, Narrow channels refinement level is 5.

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Recommendations for Creating the Computational Mesh1 At the beginning create the mesh using the default (automatic) mesh settings. Start

with the Level of initial mesh of 3. On this stage it is important to recognize the appropriate values of the minimum gap size and minimum wall thickness which will provide you with the suitable mesh. The default values of the minimum gap size and minimum wall thickness are calculated using information about the overall model dimensions, the Computational Domain size, and area of surfaces where conditions (boundary conditions, sources, etc.) and goals are specified. Don't switch off the Optimize thin walls resolution option, since it allows you to resolve the model's thin walls without the excessive mesh refinement.

2 Closely analyze the obtained automatic mesh, paying attention to the total numbers of cells, resolution of the regions of interest and narrow channels. If the automatic mesh does not satisfy you and changing of the minimum gap size and minimum wall thickness values do not give the desired effect you can proceed with the custom mesh.

3 Start to create your custom mesh with the disabled narrow channel refinement, while the Small solid features refinement level and the Curvature refinement level are both set to 0. This will produce only zero level cells (basic mesh only). Use control planes to optimize the basic mesh.

4 Next, adjust the basic mesh by step-by-step increase of the Small solid features refinement level and the Curvature refinement level. Then, enable the narrow channels refinement.

5 Finally, try to use the local mesh settings.

Fig.1.16 The local mesh settings used: Two narrow channels are refined to have 10 cells across them.


Advanced Knowledge

2 Mesh-associated Tools

Introduction

Since the mesh settings is an indirect way of constructing the computational mesh, to better visualize the resulting mesh various post-processing tools are offered by Flow Simulation. In particular, these tools allow to visualize the mesh in detail before the calculation, substantially reducing the CPU and user time.

The computational mesh constructed by Flow Simulation or other CFD codes cannot resolve the model geometry at the mesh cell level exactly. A discrepancy can lead to prediction errors. To facilitate an analysis of these errors and/or to avoid their appearance, Flow Simulation offers various options for visualizing the real computational geometry corresponding to the computational mesh used in the analysis.

Since the numerical solution is obtained inevitably in the discrete form, i.e., in the centers of computational mesh cells, it is interpolated and extrapolated by the post-processor to present the results in a smooth form, which is typically more convenient to the user. As a result, some prediction errors can stem from these interpolations and extrapolations. To facilitate an analysis of such errors and/or to prevent their appearance, Flow Simulation offers an option to visualize the physical parameters’ values calculated at the centers of computational mesh cells, so that when presenting results by coloring an area with a palette, the results are considered constant within each cell.

Visualizing the Basic Mesh Before Constructing the Initial Mesh

Using this option the user can inspect the Basic mesh and its Control planes corresponding to the mesh settings, which can be made manually or retained by default. The plot appears as soon as these settings have been made or changed, so you immediately see the resulting mesh. (See Help or User’s Guide defining the Basic mesh and its Control planes).

To enable this option, select the Show basic mesh option in the Flow Simulation, Project menu, or in the Initial Mesh dialog box. The option is accessible both before and after the calculation.

Using this option, you may shifting the Control planes to desired positions to assure that certain features of the model geometry are captured by the computational mesh.

Enhanced Capabilities of the Results Loading

Flow Simulation allows to view not only the calculation results and the current computational mesh, which they have been obtained on, but also the initial computational mesh (i.e., which the calculation begins on). The latter can be viewed either before or after the calculation, allowing the user to compare the initial and current (i.e., refined during the

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calculation) computational meshes.

To view various meshes, you must open the corresponding file via the Load results dialog box. The calculation results, including the current computational mesh, are saved in the .fld files, whereas the initial computational mesh is saved separately in the .cpt file. All these files are saved in the project folder, which name (a numeric string) is formed by Flow Simulation and must not be changed. The .cpt files and the final (i.e., with the solution obtained at the last iteration) .fld files have the name similar to that of the project folder, whereas the solutions obtained during the calculation at the previous iterations (corresponding to certain physical time moments, if the problem is time-dependent) are saved in the .fld files with names “r_<iteration number>”, e.g. the project initial data are saved in the r_000000.fld file.

Do not try to load the calculation results obtained in another project with a different geometry; the effect will be unpredictable.

Fig.2.1 The Basic mesh (left) and the Initial mesh (right).

Fig.2.2 The Load Results dialog box.


Advanced Knowledge

Viewing the Initial Computational Mesh Saved in the .cpt Files

To optimize the process of solving an engineering problem and to save time, in some cases it may be useful to view the initial computational mesh before performing the calculation, particularly to be sure that the model features are resolved well by this mesh. To view the initial computational mesh after loading the .cpt file, Flow Simulation offers you Cut Plots, Surface Plots, and the Mesh option (see below), which are also used for viewing the calculation results.

Viewing the Computational Mesh Cells with the Mesh Option

To view fluid cells of the computational mesh cells (i.e. the cells lying fully in the fluid), solid cells (lying fully in the solid), and partial cells lying partly in the fluid and partly in the solid, Flow Simulation offers you the Mesh option.

Different colors can be used to better differentiate between the computational mesh cells of each of the above-mentioned types. To see the cells in a certain parallelepiped region, the user must specify the coordinates of the region boundaries in the Global Coordinate System.

Using the Mesh option, you can also save the information concerning the mesh cells, including the physical parameters values obtained in their centers, in ASCII or Microsoft® Excel® files.

Visualization of a large amount of computational mesh cells (e.g. all fluid cells in the whole computational domain) may be impractical, since it could require substantial time and memory, and even then you might not be able to see all the visualized cells because the majority of them will likely be screened from view by other cells.

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Visualizing the Real Computational Geometry

Since the SolidWorks model geometry, especially its high-curvature parts, cannot be resolved exactly at the cell level by the rectangular (parallelepiped) computational mesh, the real computational geometry corresponding to the computational mesh used in the analysis can be viewed after the calculation to avoid or estimate the prediction errors stemming from this discrepancy. If no solution-adaptive meshing occurs during the calculation, the real computational geometry can be viewed just after the mesh generation. This option is employed by clearing the Use CAD geometry check box in Cut Plots, 3D Plots, Surface Plots, Flow Trajectories, Point Parameters and XY Plots. The result is especially clear when colored Contours are used to visualize a physical parameter values (see Fig.2.3).

This capability is especially useful for revealing important surface regions in the model, which are inadequately resolved by the computational mesh.

On the other hand, this option may be useful when creating Surface Plots for SolidWorks models containing rippled surfaces, where ripples, which are supposed to be not essential from the problem solution viewpoint, were not resolved by the computational mesh. In this case, coloring of the simplified solid/fluid interface instead of coloring the actual SolidWorks model faces can lead to substantial reduction of the CPU time and memory requirements.

Fig.2.3 Cut Plots around the SolidWorks model outer surface (left) and on its computational realization (right).


Advanced Knowledge

If the computational mesh has resolved the SolidWorks model well, so the obtained computational results are adequate, then enable the Use CAD geometry option before performing the final Cut Plots and Surface Plots to obtain smooth pictures which are more convenient for the analysis.Notice that when creating a Surface Plot with the Use CAD geometry option switched off, only the solid/fluid interfaces of partial cells within the computational mesh will be colored. When a Surface Plot is created in the Use all faces mode, solid/fluid interfaces of all partial cells will be colored. However, when a Surface Plot is created on a selected surface, the solid/fluid interfaces are colored only in the partial cells intersected by the SolidWorks model surface approximated by triangles inside SolidWorks, which may differ from the mesh-approximated surface of the model. Depending on the problem considered, there may be such cases when certain partial cells are not intersected by the triangulated surface and therefore the corresponding solid/fluid interfaces would not be colored. Naturally, this circumstance concerns visualization only and does not affect the calculation results.

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Switching off the Interpolation and Extrapolation of Calculation Results

Since the numerical solution is obtained inevitably in the discrete form, i.e., in the form of values in the centers of the computational mesh cells in Flow Simulation, it is interpolated and extrapolated by the post-processor to present the results in a smooth form, which is typically more convenient to the user. As a result, prediction errors can stem from and/or be hidden by such interpolation and extrapolation that smoothens the calculation results. To facilitate the revealing, analysis, and elimination of such errors, Flow Simulation offers an option to visualize the physical parameter values ’as is’, i.e. without interpolation, when presenting calculation results in Cut Plots and Surface Plots (other result features, namely, isolines, isosurfaces, flow streamlines and particle trajectories can not be built at all without interpolation), so when coloring a surface with a palette, the results are considered constant within the mesh cells (see Fig.2.4).

Since the mesh cells’ centers used in coloring the surface can lie at different distances from the surface, this can introduce an additional variegation into the picture, if the value of the displayed parameter depends noticeably on this distance (see Fig.2.4).

Fig.2.4 The fluid velocity Surface Plots in the near-wall region created with the interpolation of the calculation results (left) and without interolation (right).


Advanced Knowledge

Conclusion

The presented mesh-associated tools of Flow Simulation are additional tools for obtaining reliable and accurate results with this code. These tools are summarized in the table:

3 Meshing - Additional Insight

Flow Simulation considers the real model created in SolidWorks and generates a rectangular computational mesh automatically distinguishing the fluid and solid domains. The corresponding computational domain is generated in the form of a rectangular parallelepiped enclosing the model. In the mesh generation process, the computational domain is divided into uniform rectangular parallelepiped-shaped cells, which form a so-called basic mesh. Then, using information about the model geometry, Flow Simulation further constructs the mesh by means of various refinements, i.e. splitting of the basic mesh cells into smaller rectangular parallelepiped-shaped cells, thus better representing the model and fluid regions. The mesh, which the calculation starts from, so-called initial mesh, is fully defined by the generated basic mesh and the refinement

Option

Application

ReasonBasic mesh

Initial mesh

After the calculation

Visualizing the Basic mesh

+ + + To inspect the Basic mesh and setting its Control planes

Widened capabilities of loading the results

+ + To view the Initial mesh and the calculation results

Viewing the Initial mesh

+ + To analyze the Initial mesh

Viewing mesh cells of different type

+ + To view mesh cells and save the respective physical parameters values

Visualizing the computational geometry

+ + For analysis of inadequate results and quick post-processing of the results of complicated models

Switching off the interpolation of results

+ For analysis of inadequate results

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settings.

Each refinement has its criterion and level. The refinement criterion denotes which cells have to be split, and the refinement level denotes the smallest size, which the cells can be split to. Regardless of the refinement considered, the smallest cell size is always defined with respect to the basic mesh cell size so the constructed basic mesh is of great importance for the resulting computational mesh.

The main types of refinements are:

Small Solid Features Refinement




Square Difference Refinement

In addition, the following two types of refinements can be invoked locally:

Cell Type Refinement

Solid Boundary Refinement

During the calculation, the initial mesh can be refined further using the

Solution-Adaptive Refinement.

Though it depends on a refinement which criterion or level is available for user control, we will consider all of them (except for the Solution-Adaptive Refinement) to give you a comprehensive understanding of how the Flow Simulation meshing works.

In the chapter below the most important conclusions are marked with the blue italic font. For abbreviation list refer to the Glossary paragraph.

Initial Mesh Generation Stages

Basic Mesh Generation and Resolving the Interface

1 Create basic mesh cells which sizes are governed by the computational domain size, the user-specified Control Planes and the number of the basic mesh cells. [Nx, Ny, Nz, Control Planes. Parameters which act on each stage are summarized in square brackets at the end of the stage.]

2 Analyze triangulation in each basic mesh cell at the interfaces between different substances (such as solid/fluid, solid/porous, solid/solid and porous/fluid interfaces) in order to find the maximum angle between normals to the triangles which compose the interface within the cell.

3 Depending on the maximum angle found, the decision whether to split the cell or not is


made in accordance with the specified Small solid features refinement level (SSFRL), Narrow channel refinement level (NCRL), Curvature refinement level (CRL) and Curvature criterion (CRC), Tolerance refinement level (TRL) and Tolerance

Advanced Knowledge

Refinement Criterion (TRC) (see the Refinements at Interfaces Between Substances paragraph). [SSFRL, NCRL, CRL and CRC].

4 If a basic mesh cell is split, the resulting child cells are analyzed as described in items 2 and 3, and split further, if necessary. The cell splitting will proceed until the interface resolution satisfies the specified SSFR criterion, CRC and TRC, or the corresponding level of splitting reaches its specified value.

5 The operations 2 to 4 are applied for the next basic mesh cell and so on, taking into account the following Cell Mating rule: two neighboring cells (i.e. cells having a common face) can be only cells which levels are similar or differ by one. This rule has the highest priority as it is necessary for simplifying numerical algorithm in solver.

The mesh at this stage is called the primary mesh. The primary mesh implies the complete basic mesh with the resolution of the solid/fluid (as well as solid/solid, solid/porous, etc.) interface by the small solid features refinements and the curvature refinement also taking into account the local mesh settings.

If a cell belongs to a local initial mesh area, then the corresponding local refinement levels will be applied (see the Local Mesh Settings paragraph).

The specified levels of splitting denote the maximum admissible splitting, i.e. they show to which level a basic mesh cell can be split if it is required for resolving the solid/fluid interface within the cell.

The fourth-level red cells appearing after resolving the cog cause the neighboring cells to be split up to third level (yellow cells), that, in turn, causes the subsequent refinement producing second level cells (green cells) and first level cells (blue cells). The white zero level cell (basic mesh cell) remains unsplit since it borders on first level cells only, thus satisfying the rule.

The Cell Mating rule is strict and has higher priority than the other cell operations. The rule is also enforced for the cells that are entirely in a solid.

Fig.3.1Fluid cell refinement due to the Cell Mating rule.

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After the primary mesh has been created, the narrow channel refinement is put in action. The Narrow Channels term is conventional and used for the definition of the model flow passages which are ’narrow’ in the direction normal to the solid/fluid interface.

Regardless of the real solid curvature, the mesh approximation is that the solid boundary is always represented by a set of flat elements, which nodes are the points where the model intersects with the cell edges. Thus, whatever the model geometry, there is always a flat element within a partial cell and the normal to this element denotes the direction normal to the solid/fluid interface for this partial cell.

The narrow channel refinement operates as follows:

1 For each partial cell Flow Simulation calculates the “local” narrow channel width as the distance between this partial cell and the next partial cell found on the line normal to the solid/fluid interface of this cell (i.e. normal to the flat surface element located in the cell).

2 If the distance value falls within the range defined by the Minimum height of narrow channel (NCHmin) and Maximum height of narrow channel (NCHmax) options, the number of cells per this interval is calculated including both partial cells and taking into account which portion of each partial cell is in fluid. [NCHmin, NCHmax].

3 More precisely, the number of cells across the channel (i.e. on the interval between the two partial cells) is calculated as N = Nf + np1 + np2, where Nf is the number of fluid cells on the interval, and np1 and np2 are the fluid portions of the both partial cells. This value is compared with the specified Characteristic number of cells across a narrow channel (CNC). If N is less than the specified CNC then the cells on this interval are split. For example, on Fig.3.2 Nf = 2, np1 = np2 = 0.4, and N = 2+0.4+0.4 = 2.8 which is less than the criterion. On Fig.3.3 the partial cells are split, so that the fluid portions of the newly-formed partial cells are np1 = np2 = 9/10, and the criterion is satisfied (N > CNC).

If the line normal to the solid/fluid interface crosses a local initial mesh area, then the corresponding local narrow channel refinement settings is applied to the cells in this direction.

Fig.3.2 Fig.3.3


NCRL = 2; CNC = 3;N = 2.8 < CNC

NCRL = 3; CNC = 3;N = 3.8 > CNC

Advanced Knowledge

The narrow channel refinement is symmetrical with respect to the midpoint of the interval and proceeds from the both ending partial cells towards the midpoint. [CNC, NCRL].

In Fig.3.4, the specified Characteristic number of cells across a channel is 5 but only two cells were generated since the maximum refinement level of one allows only basic mesh cells and first-level cells to be generated.

In Fig.3.5, the specified Narrow channel refinement level is high enough to allow five cells to be placed across the channel.

5 Next, for all the fluid cells within the entire computational domain the following Fluid Cell Leveling procedure is applied: if a fluid cell is located between two cells of higher level, it is split to be equalized with the level of neighboring smaller cells.

Like in the other refinements, the Narrow channel refinement level (NCRL) denotes the maximum level to which the cells can be split to satisfy the CNC criterion. The NCRL has higher priority than the CNC, so the refinement will proceed until the CNC criterion is satisfied or all the cells reach the Narrow channel resolution level.

Fig.3.4CNC = 5; NCRL = 1

Fig.3.5CNC = 5; NCRL = 3

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Thin walls resolution

In contrast to the narrow channels, thin walls can be resolved without the mesh refinement inside the wall, since the both sides of the thin wall may reside in the same cell. Therefore, the amount of cells needed to resolve a thin wall is generally lower than the number of cells needed to properly resolve a channel of the same width. See Fig.3.6 - 3.8 illustrating the thin walls resolution technology and its limitations.

Fig.3.6One mesh cell can contain more than one fluid and/or solid volume; during calculation each volume has an individual set of parameters depending on its type (fluid or solid).

Solid 1

Solid 2 Fluid 1

Fluid 2

Fig.3.7If the wall thickness is greater than the basic mesh cell's size across the wall or if the

wall creates only one fluid volume in the cell, then the opposite sides of the wall will not lay within the same cell. Such walls are resolved with two or more cells across.


Advanced Knowledge

Square Difference Refinement

The Square Difference Refinement checks the neighboring partial cells of different levels for the difference between their fluid passage areas. If the difference between the fluid passage area of the higher-level cell and the total fluid passage areas of the adjacent lower-lever cells exceeds the Square Difference Refinement Criterion (SDRC) then the greater-level cell is split to the level of adjacent cells in order to equalize the fluid passage areas (see Fig.3.9). The Square Difference Refinement is always enabled and cannot be disabled since it is a strict solver requirement. As with the Cell Mating rule, this is another condition imposed by the solver to provide stability for the convergence processes.

Though you cannot turn off the Square Difference Refinement, you can control its criterion, which is directly proportional to the Curvature refinement criterion. [CRC].

Fig.3.9Two adjacent partial cells of

different levels at the cylinder surface.

Fig.3.10Cut plot of the cylinder. The concerned cells are blue.

SSFRL = 2; CRL = 0; CRC = 3.14; NCRL = 1.

Fig.3.8The edges of thin walls ending within a mesh cell may be trimmed in certain cases. These mesh cells

are called Trimmed cells.

Model geometry Meshed geometry

Trimmed edge

Trimmed cell

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Fig.3.9 shows neighboring partial cells of different levels at the cylinder's solid/fluid interface. The fluid passage area of the higher-level cell is the ABDE polygon. The total fluid passage area of the lower-level cells is the ABCDE polygon, so the difference between the fluid passages is the yellow BCD triangle. In this example we have increased the curvature refinement criterion to π, thereby increasing the Square Difference Refinement Criterion so that the fluid passage difference (BCD) is smaller than the criterion, and thus, there is no need to split the higher-level cell.

Note that the Square Difference Refinement may cause a domino effect when one splitting produces cells which become lower-level cells for the next adjacent cell causing it to split too, and so on, resulting in an increased number of cells.

In the Fig.3.11 the total number of cells is nearly 20% more than in the Fig.3.12 in spite of the fact that the Curvature refinement is disabled (CRL = 0) in the first case. Here, the model geometry is similar and before the Square Difference Refinement the mesh is practically the same in both cases and mostly governed by the Small Solid Features Refinement when the SSFRL exceeds the CRL, i.e. changing the CRL from 0 to 3 would not change substantially the number of cells. However, in the first case the curvature criterion is lower, resulting in a more stringent criterion of the Square Difference Refinement. So the smaller Square Difference Refinement criterion leads to a greater number of cells subject to the Square Difference Refinement. In the Fig.3.11 you can see a stripe of the third level cells along the cylinder. This is the result of the Square Difference Refinement and the domino effect when a cell on the cylinder edge involves the neighboring cell in the refinement procedure and so forth along the cylinder.

Fig.3.11SSFRL = 3, CRL = 0; CRC = 0.45

Total cells = 49391.

Fig.3.12SSFRL = 3, CRL = 2; CRC = 0.50;

Total cells = 41376.

Increase of the curvature criterion will increase the Square Difference Refinement Criterion, and, in turn, decrease the number of cells in both cases.


If in the first case we specify the same CRC as in the second case (0.5054 rad), the total number of cells decreases to 40963.

Advanced Knowledge

Mesh Diagnostic

The mesh diagnostic is intended to inspect the resulting initial mesh but not to change the total number of cells.

Refinements at Interfaces Between Substances

Different interface types (solid/fluid, solid1/solid2, solid/porous or porous/fluid) are checked on different refinement criteria, namely: small solid features criterion, curvature refinement criterion, tolerance refinement criterion and narrow channel refinement criterion for solid/fluid and solid/porous interfaces; small solid features criterion for solid1/solid2 interfaces; small solid features criterion and curvature refinement criterion for porous/fluid interfaces. Whereas the specified refinement levels are equally applied to any interface type.

Small Solid Features Refinement

The small solid features refinement acts on the cells where the maximum angle between normals to the surface-forming triangles is strictly greater than 120°. To make this 120-degree criterion easier to understand, let us consider simple small solid features of planar faces only. The normal to triangles that form the planar face is normal to the planar face too. Therefore, instead of considering the normals to the triangles we can consider normals to faces, or better the angle between faces.

In Fig.3.13 the cells with the cogs of 150 and 60 degrees were not split by the small solid features refinement because the maximum angles between the faces (i.e. between normals to the triangles enclosed by the cell) are 30° and 120°, respectively. If the angle between the normals becomes greater than 120° (121° for the 59°-cog) then the cell is split. The cell with the square spike surely has to be split because the lateral faces of the spike have their normals at the angle of 180°, thus satisfying the 120-degree criterion.

Note that rectangular corners (like in the rightmost cell) do not satisfy the criterion and therefore will not be resolved by the small solid features refinement.

Fig.3.13SSFRL = 1, CRL = 0, NCRL = 0

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From Fig.3.14 it is clear that the cells are split by the 120-degree criterion up to the first level, as defined by the narrow channel refinement level.

For the information about how the NCRL influences the narrow channel refinement see the Narrow Channel Refinement paragraph.


The curvature refinement works in the same manner as the small solid features refinement with the difference that the critical angle between the normals can be specified by the user (in radians) as curvature refinement criterion (CRC). Here, the smaller the criterion, the better resolution of the solid curvature. To give more precise and descriptive explanation, the following table presents several CRC values together with the corresponding angles between normals and the angles between planar faces.

Remember that if the Narrow channel refinement is enabled, the maximum level to which the small solid features refinement can split the cells is set as the maximum level from the specified SSFRL and Narrow channel refinement level (NCRL). In other words, if the Narrow channel refinement is enabled, the SSFRL has no effect if it is smaller than the NCRL.

Table 2.1: Influence of the curvature criterion on the solid curvature resolution.

Curvature criterion, rad 0.3176 0.4510 0.5548 0.6435 1.0472 1.5708 2.0944 3.1416

α' between normals, [degrees]

>19 >25 >31 >36 >60 >90 >120 180

α between faces, [degrees]

<161 <154 <148 <143 <120 <90 <60 0

Fig.3.14 SSFRL = 0, CRL = 0, NCRL = 1


Advanced Knowledge

The table states that if the CRC is equal to 0.4510 rad, then all the cells where the angle between normals to the surface-forming triangles is more than 25 degrees will be split.

You can see that the curvature criterion set to 0.4510 rad splits the cells with the 150-degrees cog.

However, the default curvature criterion values are small enough to resolve obtuse angles and curvature well. Increasing the curvature criterion is reasonable if you want to avoid superfluous refinement but it is recommended that you try different criteria to find the most appropriate one.

The curvature criterion also denotes the criterion of the Square Difference Refinement. The square difference refinement criterion is directly proportional to the CRC, so the smaller CRC, the smaller square difference refinement criterion, resulting in a greater number of cells appearing after the Square Difference Refinement.

SSFRL or CRL

Why is it necessary to have two criteria? As you can see, the curvature refinement has higher priority than the small solid features refinement if the curvature criterion is smaller than 2/3 π. Note that Flow Simulation-specified values of the curvature criterion are always smaller than 2/3 π.

Nevertheless, the advantage of the small solid features refinement is that being sensitive to relatively small geometry features it does not “notice” the large-scale curvatures, thus avoiding refinements in the entire computational domain but resolving only the areas of small features. At the same time, the curvature refinement can be used to resolve the large-scale curvatures. So both the refinements have their own coverage providing a

Fig.3.15 CRL = 1, CRC = 0.5548,SSFRL = 0, NCRL = 0

Fig.3.16 CRL = 1, CRC = 0.451,SSFRL = 0, NCRL = 0

Note that the curvature refinement works exactly as the small solid features refinement when the curvature criterion is equal to 2.0944 rad (2/3π).

In other words, if you did not set the CRC greater than 2/3 π and if the SSFRL and NCRL are smaller than the CRL, then the small solid feature refinement would be idle.

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flexible tool for creating an optimal mesh.


Any surface is approximated by a set of polygons which vertices are the points of intersection of this surface with the cells' edges. This approach accurately represents flat faces though curved surfaces are represented by some approximation (e.g. as a circle can be represented by a polygon). The tolerance refinement criterion controls the precision of this approximation. A cell will be split if the distance between the outermost point of the surface within the cell and the polygon approximating this surface is larger than the specified criterion value.

Local Mesh Settings

The local mesh settings influence only the initial mesh and do not affect the basic mesh in the local area, but are basic mesh sensitive in that all refinement levels are set with respect to the basic mesh cell.

The local mesh settings are applied to the cells intersected with the local mesh region which can be represented by a component, face, edge or vertex.

If a cell intersects with different local mesh setting regions, the refinement settings in this cell will be used to achieve the maximum refinement.

Cell Type Refinement. The refinement level of cells of a specific type (all cells, fluid and partial cells, solid and partial cells, or only partial cells) denotes the minimum level to

Small Solid Feature Refinement(refinement occurs regardless of the

feature’s size)


Tolerance criterion = 0.1Tolerance criterion

= 0.08

Curvature Refinement (refinement occurs regardless of the

curvature only)


Tolerance criterion = 0.1Refines cells only if the solid part cut by the polygon is large enough (h > 0.1)

Tolerance criterion = 0.03


which the corresponding cells must be split if it doesn’t contradict the Cell Mating rule.

Advanced Knowledge

If different cell types are to be refined, the refinement level of partial cells is set as the maximum level among all selected levels.

The local mesh settings have higher priority over the initial mesh settings. Therefore, the local mesh cells will be split to the specified local refinement levels regardless of the general SSFRL, CRL and NCRL (specified in the Initial Mesh dialog box). This, however, may cause refinement of cells located outside of the local region due to imposing the Cell Mating rule.

The "Optimize thin walls resolution" option

In the earlier versions of Flow Simulation refinement of the mesh around model's walls was needed to resolve thin walls properly, but it could also lead to increase in number of cells in adjacent fluid regions, especially in narrow channels between walls. If this additional mesh refinement is critical for obtaining proper results and you want to perform calculation on the same mesh as in the earlier version of Flow Simulation, clear the Optimize thin walls resolution check box. In this case the mesh will be almost the same as in the early versions. (see Fig.3.17).

The minimum level means the lower bound to which it is obligatory to split cells, though the cells can be split further if it is required to satisfy the other criteria such as Small solid features refinement, Curvature refinement, Narrow channels refinement or Solid Boundary Refinement.

Fig.3.17Mesh refinement around a thin wall: (a) the Optimize thin walls resolution option is switched

off, i.e. the mesh cells are split as in the previous versions of Flow Simulation; (b) the Optimize thin walls resolution option is selected (the default state), i.e. the mesh cells are not split.

(a) (b)

solid/fluidinterfaces

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Postamble

The problem of resolving a model with the computational mesh is always model-specific. In general, a denser mesh will provide better accuracy but you should tend to create an optimal mesh and to avoid redundant refinement.

When performing a calculation, try different mesh settings and analyze the obtained results carefully in order to understand whether it is necessary to refine the mesh or a coarser resolution is acceptable for the desired accuracy.

Glossary

Nx, Ny, Nz – Number of basic mesh cells per X, Y and Z directions, respectively.

SSFRL – Small solid features refinement level.

CRL – Curvature refinement level.

CRC – Curvature refinement criterion.

TRL – Tolerance refinement level.

TRC – Tolerance refinement criterion.

NCRL – Narrow channel refinement level.

CNC – Characteristic number of cells across a narrow channel.

NCHmin – The minimum height of narrow channels.

NCHmax – The maximum height of narrow channels.

SDRC – Square difference refinement criterion.

4 Calculation Control Options

Introduction

The Calculation Control Options dialog box introduced into Flow Simulation allows you to control:

• conditions of finishing the calculation,

• saving of the results during the calculation,


• refinement of the computational mesh during the calculation,

• freezing the flow calculation,

• time step for a time-dependent analysis,

Advanced Knowledge

• number of rays traced from the surface if radiating heat transfer is enabled.

This dialog box is accessible both before the calculation and during the calculation. In the last case the new-made settings are applied to the current calculation starting from the next iteration.

The main information on employing the options of Finishing the calculation and Refining the computational mesh during calculation is presented in this document.

Finishing the Calculation

Flow Simulation solves the time-dependent set of equations for all problems, including steady-state cases. For such cases it is necessary to recognize the moment when a steady-state solution is attained and therefore the calculation should be finished. A set of independent finishing conditions offered by Flow Simulation allow the user to select the most appropriate conditions and criteria on when to stop the calculation. The following finishing conditions are offered by Flow Simulation:

• maximum number of refinements;

• maximum number of iterations;

• maximum physical time (for time-dependent problems only);

• maximum CPU time;

• maximum number of travels;

• convergence of the Goals.

In Flow Simulation you can select the finishing conditions that are most appropriate from your viewpoint to solve the problem under consideration, and specify their values. For the latter two conditions (i.e., for the maximum number of travels and the Goals convergence settings) Flow Simulation presents their default values (details are described below). You can also select the superposition mode for multiple finishing conditions in the Finish Conditions value cell: either to finish the calculation when all the selected finishing conditions are satisfied or when at least one of them is satisfied.

In any case, information on the finishing conditions due to which the calculation has finished is shown in the Monitor’s Log box.

Travel is the number of iterations required for the propagation of a disturbance over the whole computational domain. Current number of iterations per one travel is presented in the Info box of the Calculation monitor.

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The Goals convergence finishing condition is complex since it consists of satisfying all the specified Goals criteria. A specified Goal criterion includes a specified dispersion, which is the difference between the maximum and minimum values of the Goal, and a specified analysis interval over which this difference (i.e., the dispersion) is determined. The interval is taken from the last iteration rearwards and is the same for all specified Goals. The analysis interval is applied after an automatically specified initial calculation period (in travels), and, if refinement of the computational mesh during calculation is enabled, after an automatically or manually specified relaxation period (in travels or in iterations) since the last mesh refinement is reached. As soon as the Goal dispersion obtained in the calculation becomes lower than the specified dispersion, the Goal is considered converged. As soon as all Goals included in the Goals convergence finishing condition (by selecting them in the On/Off column) have converged, this condition is considered satisfied. The Goals not included into the Goals convergence finishing condition are used for information only, i.e., with no influence on the calculation finishing conditions.

Let us consider the Flow Simulation default values for the maximum number of travels and the Goals convergence settings in detail. These default (recommended by Flow Simulation) values depend on the Result resolution level either specified in the Wizard or changed by pressing the Reset button in the Calculation Control Options dialog box. For higher Result resolution levels the finishing conditions are tighter.

The default maximum number of travels depends on

• the type of the specified Goal (i.e., dynamic or diffusive, see below);

• the specified Result resolution level;

• the problem's type (i.e., incompressible liquid or compressible gas, low or high Mach number gas flow, time-dependent or steady-state).

The default Goals convergence settings are the default analysis interval, which is shown in the Finish tab of the Calculation Control Options dialog box, and the default Goals criterion dispersion values, which are not shown in the Calculation Control Options dialog box, but, instead, are shown in the Monitor’s Goal Table or Goal Plot table (in the Criteria column), since they depend on the values of the Goal physical parameter calculated in the computational domain, and therefore are not known before the calculation and, moreover, can change during it. In contrast, the Goals criterion dispersion values specified manually do not change during the calculation.

The Dynamic goals are: Static Pressure, Dynamic Pressure, Total Pressure, Mass Flow Rate, Forces, Volume Flow Rate, and Velocity. The Diffusive goals are: Temperature, Density, Mass in Volume, Heat flux, Heat transfer rate, Concentrations, Mass Flow Rate of species, and Volume Flow Rate of species.


Advanced Knowledge

As for the automatically specified initial calculation period (measured in travels), it depends on the problem type, the Goal type, and the specified Result resolution level.

Refinement of the Computational Mesh During Calculation

Refinement of the computational mesh during calculation is a process of splitting or merging of the computational mesh cells in high-gradient flow areas. This option has the following governing parameters:

• refinement level,

• approximate maximum number of cells,

• strategy of refinements during the calculation.

The first two parameters are described in Flow Simulation Help. Here, let us consider the Refinement Strategy for transient analysis in detail. The following three strategies are available:

• Periodic refinement;

• Tabular Refinement;

• Manual Only refinement.

In the first two strategies the refinement moment is known beforehand. The solution gradients are analyzed over iterations belonging to the Relaxation interval, which is calculated from the current moment rearwards. As a result, only steady-state gradients are taken into account. The default length of the Relaxation interval can be adjusted manually. On the other hand, the analysis must not continue with the same relaxation interval defined from the start of the calculation, in order to avoid taking into account the

• the manually specified analysis interval for the Goals convergence finishing criteria must be substantially longer than the typical period of the flow field oscillation (if it occurs);

• the Goals determined on solid/fluid interfaces or model openings, as well as the Post-processor Surface Parameters, yield the most accurate and correct numerical information on flow or solid parameters, especially integral ones;

• Global Goals yield the most reliable information on flow or solid parameters, although they may be too general;

• the CPU time depends slightly on the number of the specified Goals, but, in some cases, vary substantially in the case of presence of a Surface Goal;

• Surface and Volume Goals provide exactly the same information that may be obtained via the Surface and Volume Parameters Post-processor features, respectively.

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initial highly unsteady period. Therefore, a period of at least two relaxation intervals is recommended before the first refinement. If the first assigned refinement is scheduled in a shorter term from the beginning, the period over which the gradients are analyzed is

shortened accordingly, so that in the extreme case it can be as short as one current iteration. If you initiate a refinement manually within this period, the gradients are analyzed in one current iteration only. Naturally, such a short period give not very reliable gradients and hence may result in an inadequate solution or excessive CPU time and memory requirements.

The figure below illustrates these concepts. Here, the letter r denotes the relaxation interval. This figure involves both Periodic and Tabular refinements. Case 1 is the recommended normal approach. In the Case 2 the first refinement is too close to the starting point of the calculation, so the gradients are analyzed over the shorter interval (which could even be reduced to only one current iteration in the extreme case). Case 3 is a particular case when a refinement is initiated manually just before a previously assigned refinement. As a result, the manual refinement is well-defined, since the gradients have been analyzed over almost the entire relaxation interval, but on the other hand, the previously assigned refinement is performed on the substantially shorter interval, and therefore its action can be incorrect. Case 3 demonstrates the possible error of performing manual and previously assigned refinements concurrently.

Fig.4.1 Refinement strategy.

Collecting of the statistics is prohibited

Statistics are collectedRefinement

Case 1

Auto ref.

0

0

Ref. point 1 Ref. point 2

Case 2 Case 3

Ref. point 1

r1

Manual ref.

r2rr

rr


Advanced Knowledge

5 Flow Freezing

What is Flow Freezing?

Sometimes it is necessary to solve a problem that deals with different processes developing at substantially different rates. If the difference in rates is substantial (10 times or higher) then the CPU time required to solve the problem is governed almost exclusively by the slower process. To reduce the CPU time, a reasonable approach is to stop the calculation of the fastest process (which is fully developed by that time and does not change further) and use its results to continue the calculation of the slower processes. Such an approach is called “freezing”.

In the case of problems solved with Flow Simulation the processes of convective mass, momentum, and energy transport are the fastest processes to develop and to converge, whereas the processes of mass, momentum, and energy transfer by diffusion are the slowest ones. Accordingly, Flow Simulation offers the “Flow Freezing” option that allow you to freeze, or fix, the pressure and velocity field while continuing the calculation of temperature and composition. This option is especially useful in solving steady-state problems involving diffusion processes that are important from the user’s viewpoint, e.g. species or heat propagation in dead zones of the flow. Time-dependent analyses with nearly steady-state velocity fields and diffusion processes developing with time are also examples of this class of problems. As a result, the CPU time for solving such problems can be substantially reduced by applying the Flow Freezing option.

Flow Simulation treats Flow Freezing for the High Mach number flows differently. All flow parameters are frozen, but the temperature of the solid is calculated using these fixed parameters at the outer of the boundary layer and user defined time step. Temperature change on the solid's surface and relevant variation of the heat flows are accounted in the boundary layer only. It is impossible (and makes no sense) to use Flow Freezing for calculation of concentration propagation in the High Mach number flow. If custom time step is not specified, the steady-state temperature of solid will be reached in one time step assumed to be infinite.

How It Works

To access the Flow Freezing option, open the Calculation Control Options dialog box, then the Advanced tab. This option has three modes: Disabled (by default), Periodic, and Permanent.

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Flow Freezing in a Permanent Mode

As an example of applying the Flow Freezing option, let us consider a plane flow (2D) problem of heating the vortex core in a vessel (Fig.5.1).

At the beginning the entire fluid region is filled with a cold (T=300 K) liquid. A hot (T=400K) liquid enters the vessel through the lower channel (the upper channel is the exit). As a result, a vortex with a cold core is developed in the vessel. The vortex core temperature is changed mainly due to heat diffusion. To measure it, a small body is placed at the vortex center and disabled in the Component Control dialog box, so that it is treated by Flow Simulation as a fluid region. Its minimum temperature (i.e., the minimum fluid temperature in this region) is the Volume Goal of the calculation.

First of all, let us consider Flow Freezing operating in the Permanent mode. The only user-specified parameter in Permanent mode is the starting moment of enabling the Flow Freezing option. Until this moment the calculation runs in a usual manner. After this moment the fluid velocity field becomes frozen, i.e., it is no longer calculated, but is taken from the last iteration performed just before the Flow Freezing Start moment. For the remainder of the run only the equations’ terms concerning heat conduction and diffusion are calculated. As a result, the CPU time required per iteration is reduced.

The starting moment of the Flow Freezing option should be set not too early in order to let the flow field to fully develop. As a rule, an initial period of not less than 0.25 travels is required to satisfy this condition. In most problems the 0.5 travel initial period is sufficient, but there are problems that require a longer initial period.

The Flow Freezing Start moment, as well as other parameters of the Calculation Control Options dialog box can be changed during a calculation.

Fig.5.1 Heating the vortex core in a vessel.


Advanced Knowledge

When first solving the problem under consideration we set the maximum number of travels to 10. The calculation performed without applying the Flow Freezing option then required about 10 travels to reach the convergence of the project Goal (the steady-state minimum fluid temperature in the vortex core). However, the steady-state fluid velocity field was reached in about 0.5 travels, i.e., substantially earlier. So, by applying the Flow Freezing option in the Permanent mode (just after 0.5 travels) the same calculation requires substantially less time on the same computer to reach the convergence of the project Goal.

If it is necessary to perform several calculations with the same fluid velocity field, but different temperatures and/or species concentrations, it is expedient to first calculate this fluid velocity field without applying the Flow Freezing option. Then, clone the Flow Simulation project into several projects (including copying the calculation results), make the required changes to these projects, and perform the remaining calculations for these projects using the calculated results as initial conditions and applying the Flow Freezing option in the Permanent mode with a zero Start period.

Flow Freezing in a Periodic Mode

In some problems the flow field depends on temperature (or species concentrations), so both the velocity and the temperature (concentrations) change simultaneously throughout the calculation. Nevertheless, since they change in a different manner, i.e., the velocity field changes faster than the temperature (concentrations) field, therefore approaching its steady state solution earlier, the Flow Freezing option can be used in a Periodic mode to reduce the CPU time required for solving such problems. The Periodic mode of the Flow Freezing option consists of calculating the velocity field not in each of the iterations (time steps), but periodically for a number of iterations specified in No freezing (iterations)

As soon as the Flow Freezing option is invoked, only the slowest processes are calculated. As a result, the convergence and finishing criteria can become non-optimal. Therefore, to avoid obtaining incorrect results when enabling the Flow Freezing option, it is recommended to increase the maximum number of travels specified at the Finish tab of the Calculation Control Options dialog box by 1.5…5 times compared to the number that was set automatically or required for the calculation performed without the Flow Freezing option.

If you forget to use the calculated results as initial conditions, then the saved fluid velocity field will be lost in the cloned project, so the project must be created again. To use the calculated results as initial conditions for the current project, select the Transferred type of Parameter definition for the initial conditions in the General Settings dialog box.

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after a period of freezing specified in the Freezing (iterations) (see Fig.5.2) The

temperatures and concentrations are calculated in each iteration. Examples include channel flows with specified mass flow rates and pressures, so the fluid density and, therefore, velocity depend on the fluid temperature, or flows involving free convection, where due to the buoyancy the hot fluid rises, so the velocity field depends on the fluid temperature.

As an example, let us consider a 3D external problem of an air jet outflow from a body face into still air (see Fig.5.3, in which the jet outflow face is marked by a red line). Here, the wire frame is the computational domain. The other body seen in this figure is introduced and disabled in the Component Control dialog box (so it is a fluid region) in order to see the air temperature averaged over its face (the project Goal), depending on the air temperature specified at the jet outflow face.

This problem is solved in several stages. At the first stage, the calculation is performed for the cold (T = 300 K, which is equal to the environment temperature) air jet. Then we clone the project including copying the results. Next, we set the outlet air temperature to T = 400 K, specify the Periodic mode of the Flow Freezing option by its Start moment of 0.25 travels (in order for the heat to have time to propagate along the jet to the measuring face) and under Duration specify 10 as both the Freezing (iterations) and No freezing (iterations) values. Then perform the calculation on the same computational mesh with the Take previous results option in the Run box. As a result, the calculation with flow freezing takes less CPU time than the similar calculation without the Flow Freezing option enabled.

Fig.5.2

Start

Freezing

Iterations

No Freezing

Fig.5.3 Air jet outflow from a body face into a still air.


Advanced Knowledge

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3

Advanced Features Guide

This chapter gives an overview of the advanced physical simulation features available in Flow Simulation such as Cavitation, Steam, Humidity and Real Gases. The provided information includes a general description of the feature, the assumptions and limitations of the employed physical model, a full description of all interface options and settings you need to set to include the feature into the analysis, and some examples of the feature’s application for solving engineering problems.

1 Cavitation

Cavitation is a common problem for many engineering devices in which the fluid is in liquid state. The deleterious effects of cavitation include: lowered performance, load asymmetry, erosion and pitting of blade surfaces, vibration and noise, and reduction of the overall machine life. However, cavitation is also used in some industrial processes, such as the fuel spray formation in diesel and gasoline engines.

The following models of cavitation are available in Flow Simulation:

• Engineering cavitation model (for pre-defined water only):This model employs a homogeneous equilibrium approach and is available for pre-defined water only. It has the capability to account for the thermal effects.

• Isothermal cavitation model:This model is based on the approach considering isothermal two-phase flows. Fluid density is defined by the barotropic equation of state. The isothermal cavitation model is only available for user-defined incompressible liquids.



Physical model

Engineering Cavitation Model

The homogeneous equilibrium approach is employed. It is applicable for a variety of important industrial processes.

The fluid is assumed to be a homogeneous gas-liquid mixture with the gaseous phase consisting of the vapour and non-condensable (dissolved) gas. The vapour mass fraction is defined at the local equilibrium thermodynamic conditions. The dissolved gas mass fraction is a constant, which can be modified by user.

The model has the following limitations and/or assumptions:

• The properties of the dissolved non-condensable gas are set to be equal to those of air. By default, the mass fraction of the dissolved non-condensable gas is set to 10-4, but it can be modified by the user in the range of 10-3...10-5.

• The temperature and pressure ranges in the cavitation area must be within the following bounds:

280 < T < 583.15 K, 800 < P < 107 Pa.

• The velocities and temperatures of the gaseous (including vapour and non-condensable gas) and liquid phases are assumed to be the same.

• The model does not describe the detailed structure of the cavitation area, i.e parameters of individual vapour bubbles are not considered.

• For mixtures of different liquids the cavitation option cannot be selected.

• The volume fraction of vapour is limited by 0.95. The parameters of the flow at the inlet boundary conditions must satisfy this requirement.

Isothermal Cavitation Model

This model provides a capability to analyze two-phase flows of industrial liquids which thermophysical properties are not described in details.

In the isothermal cavitation model the following assumptions are made:

• The fluid temperature is constant and the thermal effects are not considered.

• The fluid density is defined by the barotropic equation of state.

• The liquid phase is an incompressible fluid.

• When liquid turns into vapour completely the vapour and non-condensable gas density is defined by the ideal gas law.

• The fluid contains non-condensable (dissolved) gas. One of the four gases can be used as dissolved gas: Air, Carbon dioxide, Helium and Methane. By default, the

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non-condensable gas is Air and the mass fraction is set to 10-4. This is a typical model value appropriated in most cases but it can be modified by the user in the

range of 10-2...10-6.

Interface

Isothermal cavitation model can be employed for any user-defined incompressible Liquid in the Engineering Database by selecting the Cavitation effect check box and specifying the Molar mass of the liquid and the Saturation pressure at the specific Temperature.

Engineering cavitation model becomes available when you select pre-defined Water as the project’s Default fluid.

Cavitation option in Flow Simulation is switched on by selecting the Cavitation check box under Flow Characteristic either in the Default Fluid dialog of the Wizard or the Fluids dialog of General Settings.



For a fluid subdomain the Cavitation option is switched on under Flow Characteristic of the Fluid Subdomain dialog.

Once enabled, the Cavitation option requires you to specify the Dissolved gas mass fraction.

For the pre-defined water the default value of this parameter is 10-4. This value is typical for air dissolved in water under normal conditions and therefore is appropriate for most cases. For a user-defined liquid the default Dissolved gas is Air and the default value of the Dissolved gas mass fraction is 10-4. This is a typical value under normal conditions and appropriate in most cases.

If needed, for the pre-defined water you can specify a different value of the Dissolved gas mass fraction in the range of 10-3...10-5 and for a user-defined liquid in the range of 10-2...10-6 for each gas which can be selected as the dissolved gas: Air, Carbon dioxide, Helium or Methane.

Cavitation is represented in the calculation results via the following parameters: Mass Fraction of Vapour and Volume Fraction of Vapour, which corresponds to the local mass or volume fraction of the vapour component. Make sure that those parameters are enabled in the Parameter list to make them available for selection in the View Settings dialog.

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Examples of use

Rotating impeller

Water flows through a rotating impeller with five blades of a curved shape, as shown on the picture. The aim of simulation is to predict the impeller characteristics.

Due to the pressure drop on the suction side of the impeller blades, a cavitation may develop in these areas, which cannot but affect the impeller performance.

The appearance of the calculated cavitation area in the form of isosurfaces is shown below on Fig.1.1.

Hydrofoil in a tunnel

A symmetric hydrofoil is placed with a non-zero angle of attack in a sufficiently wide water-filled tunnel. Obviously, water flow develops some pressure drop on the upper surface of the hydrofoil, which can lead to cavitation under certain conditions.

Fig.1.2 contains a representation of the calculated cavitation area visualized in terms of Volume Fraction of Vapour.

Fig.1.1 Isosurfaces for vapour volume fraction of 10%.


Fig.1.2 Calculated cavitation area.


Ball valve

Water flows inside an half-opened ball valve (see Fig.1.3) at the relatively low pressure and high velocity producing cavitation.

The results visualized in the form of Cut plot with Volume Fraction of Vapour as displayed parameter are presented on Fig.1.4. It is clearly seen that sudden expansion of the flow produces an area of strong cavitation.

Fig.1.3 Model of the ball valve.

Fig.1.4 Distribution of the vapour volume fraction.

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Throttle flow

Diesel fuel flows through a throttle (see Fig.1.5) under a relatively high difference between the injection pressure and back pressure.

When a high velocity fluid passes through a contraction like a nozzle, an area of low pressure is formed in the wake of its edge. In this wake the pressure can decrease below the saturation pressure, and thus cause the liquid to cavitate.

The results visualized in the form of Cut plot with Volume Fraction of Vapour as displayed parameter are presented on Fig.1.6. The red color indicates the region of high vapor fraction.

Fig.1.5 Model of the throttle.

Nozzle wall


Fig.1.6 Distribution of the vapour volume fraction.


Recommendations• If you analyze a flow of water in some points of which the local static pressure can

reach the saturation pressure at the local temperature causing cavitation or if a vaporization of water can occur in the water flow due to intense heating, it is recommended to use the Engineering cavitation model.

• Cavitation area growths slowly during calculation and there is a risk that the calculation will stop before the cavitation area develops completely. To avoid this, specify Global Goal of Average Density and increase the Analysis interval on the Finish tab of the Calculation Control Options dialog box. Also make sure that the other finish conditions do not cause the calculation to stop before goals are converged. The easiest way to ensure this is to select If all are satisfied in the Value cell for the Finish conditions on the Finish tab of the Calculation Control Options dialog box.

• The Cavitation option is not applicable if you calculate a flow in the model without flow openings (inlet and outlet).

• The fluid region where cavitation occurs must be well resolved by the computational mesh.

• Besides the Volume Fraction of Vapour you can also select Density as the visualization parameter to see the cavitation areas in your simulation.

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2 Steam

Physical model

Flow Simulation allows you to consider water steam among the project fluids. Like Humidity, the Steam option may be used to analyze engineering problems concerning water vapour and its volume condensation, along with the corresponding changes in the physical properties of the project fluid. Steam option in Flow Simulation describes the behavior of pure water steam or its mixtures with other gases.

Limitations and Assumptions


• Flow Simulation project may include pure Steam or its mixture with Gases (but not with Real gases).

• Thermodynamic parameters of steam should be contained within the following bounds:

283 < T < 610 K, P < 107 Pa.

• The volume fraction of condensed water should never exceed 5%.

• Steam option is incompatible with the High Mach number flow option, i.e. the two can not be employed simultaneously.

• The employed model of condensation is fully equilibrium and considers only volume condensation.

Interface

Steam is treated by Flow Simulation as a special kind of fluid and may be selected from the Engineering Database just like any other fluid.

Steam may be assigned for a fluid subdomain as well as for the whole project.

Steam may be mixed with any regular


Gases (but not with Real gases). In this case, its concentration in a form of mass or volume fraction must be specified in Initial conditions, as well as in all boundary conditions.


Steam content in the mixtures of water steam with other gases is represented in the calculation results via Mass Fraction of Water (that represent mass fraction of water wapour) and Relative Humidity (which is the ratio of the local partial density of water to the density of saturated water vapor under current conditions). The content of particular form of water, i.e. vapor or liquid, is represented via Mass Fraction of Condensate (that represents mass fraction of condensed steam in the fluid) and Moisture Content (that represents the fraction of condensed steam with respect to the overall content of steam). Note that you may need to check some of those parameters in the Parameter list to enable their selection in the View Settings window.

Example of use

Heat exchanger

Flow Simulation calculates the equilibrium condensation in water steam as steam flows through a cooled tube of a heat exchanger. Fig.2.1 shows cut plot of the condensate mass fraction parameter.

Recommendations• To avoid the risk of finishing the calculation before the condensation develops

completely, always specify some goal strongly dependent on condensation, for example Global Goal of Average Density, and make sure that the calculation will not stop before this goal is converged.

• To see the condensation areas, you may use Relative Humidity or the Condensate Mass Fraction as the parameter for visualization.

Fig.2.1 Cut plot showing the condensate mass fraction.

Inlet

Outlet

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3 Humidity

Physical model

Flow Simulation allows you to consider the relative humidity of the gas or mixture of gases. This allows you to analyze engineering problems where the condensation of water vapor contained in the air (or other gas), or, more generally speaking, where any differences in physical properties of wet and dry air play an important role. Examples may include air conditioning systems (especially in wet climate or in the places where relative humidity is very important, e.g. libraries, art museums, etc.), tank steamers, steam turbines and other kinds of industrial equipment. Flow Simulation can calculate equilibrium volume (but not surface) condensation of steam into water. As a result, the local fractions of gaseous and condensed steam are determined. In addition, the corresponding changes of the fluid temperature, density, enthalpy, specific heat, and sonic velocity are determined and taken into account.



• Humidity is currently available only in Gases (both in individual gases and in mixtures), but not in Real gases.

• Thermodynamic parameters in the fluid areas where humidity is considered should be contained within the following bounds:

283 < T < 610 K, P < 107 Pa.

• The volume fraction of condensed water should never exceed 5%.

• Humidity option is incompatible with the High Mach number flow option, i.e. the two can not be employed simultaneously.

• The model does not describe the condensation process in as subtle detail as the parameters of individual liquid droplets.

• Surface condensation, i.e. the formation of dew on solid surfaces, is not considered.

• The condensed steam has no history, since the employed condensation model is fully equilibrium. In other words, the state of condensed steam at given point is governed solely by the local conditions at this point.



Interface

Humidity option in Flow Simulation is switched on by checking the Humidity check box either in Wizard or in the General Settings window. This check box is present only if the current fluid type is set to Gases.

Once Humidity is switched on, the relative humidity of the gas becomes available to specify in the Initial conditions window. The relative humidity is defined as the ratio of the current water vapor density to that of saturated water vapor under current conditions.

Humidity can be assigned for a fluid subdomain as well as for the whole project by selecting the check box of the same name, and, once assigned, becomes available to specify in the Humidity Parameters group box.

The relative humidity must be specified within all boundary and initial conditions in contact with the fluid region for which the calculation of relative humidity is performed.

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Together with the humidity value for boundary and initial conditions you must also specify the values of Humidity reference pressure and Humidity reference temperature that describe the conditions under which the relative humidity has been determined, since these values may differ from the current pressure and temperature.

Humidity is represented in the calculation results via the following parameters: Mass Fraction of Water (that represent mass fraction of water wapour) and Relative Humidity (which is the ratio of the local partial density of water to the density of saturated water vapor under current conditions). The content of particular form of water, i.e. vapor or liquid, is represented via Mass Fraction of Condensate (that represents mass fraction of water condensate in the fluid) and Moisture Content (that represents the fraction of condensed water with respect to the overall content of water). Note that you may need to check some of those parameters in the Parameter list to enable their selection in the View Settings window.

Heat

Boundarycondition



Example of use

Aircraft

An air flow around an aircraft model can be simulated with the Humidity option selected. The examination of relative humidity distribution (Fig.3.1) reveals broad areas of more than 80% relative humidity from above of both wings. Naturally, these areas (together with smaller zones near the cockpit and the tail unit) are enriched with water condensate, as it may be seen on Fig.3.2.

Recommendations• If your analyze a flow of gas containing some amount of water vapor and the

conditions are likely to get over the dew point, it is recommended to consider humidity in the calculation as described in this chapter.

• To avoid the risk of finishing the calculation before the condensation develops completely, always specify some goal strongly dependent on condensation, for example Global Goal of Average Density, and make sure that the calculation will not stop before this goal is converged.

• To see the condensation areas, you may use Relative Humidity or the Condensate Mass Fraction as the parameter for visualization.

Fig.3.2 Isosurfaces of condensate mass fraction = 0.00015

Fig.3.1 Flow trajectories colored in accordance with relative humidity.

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4 Real Gases

Physical model

Flow Simulation has an ability to consider real gases. A wide choice of predefined real gases is presented. The user may also create user-defined real gases by specifying their parameters. This option may be useful in the engineering problems concerning gases at nearly-condensation temperatures and/or at nearly-critical and supercritical pressures, i.e. at conditions where the behavior of the gas can no longer be represented adequately by the ideal-gas state equation.

The model of real gas implemented in Flow Simulation employs a custom modification of the Redlich-Kwong state equation. Naturally, the equation unavoidably has certain bounds of applicability, which are explained on the picture below:

The area of validity of the model includes zones 10, 11 and 12. (Each predefined real gas has its own values of Pmin, Pmax, Tmin, and Tmax, and those are also to be specified for a

user-defined real gas.) If the calculated pressure and/or temperature fall outside of this area, Flow Simulation issues a warning. The warning for zones 1 - 8 is: Real gas parameters (pressure and/or temperature) are outside the definitional domain of substance properties, with comment: P < Pmin, P > Pmax, T < Tmin, or T > Tmax,

depending on what has actually happen. The warning for zone 9 is: Phase transition in the Real gas may occur.

Supercritical

Vapor

Liquid





• Real gas may be used in a Flow Simulation project as pure fluid or in mixture with Gases (but not with other Real gases).

• Pressure and temperature of real gas should be contained within certain limits (those are specified individually for each of the predefined real gases).

• Real gas should not be put under conditions that cause its condensation into liquid.

• The use of real gas is incompatible with the High Mach number flow option.

• The precision of calculation of thermodynamic properties at nearly-critical temperatures and supercritical pressures may be lowered to some extent in comparison to other parameter ranges. The calculations involving user-defined real gases at supercritical pressures are not recommended.

• The copying of pre-defined real gases to user-defined folder is impossible since the employed models are not exactly similar.

Interface

Real gases are a special type of fluids and may be selected from the Engineering Database along with other fluids.

Real gas may be assigned for a fluid subdomain as well as for the whole project.

Real gases may be mixed with regular Gases (though not with each other). In this case, substance concentrations in a form of mass or volume fractions must be specified in Initial conditions, as well as in all boundary conditions.

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To create a user-defined real gas, the user must create a new item in the corresponding folder in the Engineering Database and specify the following parameters:

• Molar mass;

• Critical pressure pc;

• Critical temperature Tc;

• Critical compressibility factor Zc;

• Redlich-Kwong equation type that should be used, i.e. the original one or its modifications by Wilson, Barnes-King, or Soave;

• Acentric factor ω (if applicable);

• Minimum temperature, i.e. the lower margin of validity of the model;

• Maximum temperature, i.e. the corresponding upper margin;

• Order of ideal gas heat capacity polynomial, i.e. the order of polynomial function of temperature that defines the "ideal-gas" constituent of the real gas specific heat at constant pressure;

• Coefficients of ideal gas heat capacity polynomial, i.e. the coefficients of the aforementioned polynomial;

• Polarity (check if the gas in question has polar molecules);

• Vapor viscosity dependence on temperature, i.e. the coefficients a and n in the equation describing vapor viscosity as η = a·Tn;

• Vapor thermal conductivity dependence on temperature, which includes the coefficients a and n and the choice of dependency type between linear λ = a+n·T and power-law λ = a·Tn forms;

• Liquid viscosity dependence on temperature, which includes the coefficients a and n and the choice of dependency type between power-law η = a·Tn and exponential η = 10a(1/T-1/n) forms;



• Liquid thermal conductivity dependence on temperature, which includes the coefficients a and n and the choice of dependency type between linear λ = a+n·T and power-law λ = a·Tn forms;

The coefficients of the user-specified dependencies for thermophysical properties should be entered only in SI unit system, except those for the exponential form of dynamic viscosity of the liquid, which should be taken exclusively from Ref. 1.

Note that the foregoing dependencies for the specific heat and transport properties cover only the ’ideal-gas’ constituents of the corresponding properties, i.e. their values at low-pressure limit, and the actual formulae contain pressure-dependent corrections which are calculated automatically.

The post-processor display parameters concerning real gas includes its mass and volume fractions in a mixture (if it is not a sole component of the fluid) and the Real Gas State. The latter parameter represents the local phase state of real gas, which may be Vapor, Liquid, Supercritical, or Out of range. Once selected, it renders inaccessible the Palette and Min/Max settings within the Color Bar dialog and replaces the Color bar with the schematic phase diagram that provides an explanation of meaning of particular colors, as shown on the picture.

Example of use

Joule-Thomson effect

A flow of nitrogen through a tube containing narrow restriction is simulated. To reduce computation time, the tube was split in halves by a symmetry plane and Symmetry condition was applied to the corresponding boundary of the Computational Domain.

The calculation within ideal gas approximation, i.e. with nitrogen selected from Gases as the project fluid, results in the temperature distribution shown on Fig.4.1. It is clearly seen that the temperature of the gas, after undergoing a noticeable drop while passing through the hole, later reinstates its initial value. This is an expected behavior of an ideal gas, as its enthalpy does not depend on pressure.

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Fig.4.1 Field of temperatures for a flow of ideal gas.

The calculation was repeated with fluid changed to nitrogen selected from Real Gases and all other conditions similar. Now the gas temperature at outlet is different from that at inlet (see Fig.4.2).

Hence we may conclude that the real gas reveals a nonzero Joule-Thomson effect, as expected.

Recommendations• Minimum temperature for user-defined real gas should be set at least 5...10 K higher

than the triple point of the actual substance.

• Maximum temperature for user-defined real gas should be set so as to keep away from the area of dissociation of the gas.

• The user-specified dependencies for the specific heat and transport properties of the user-defined real gases should be valid in the whole temperature range from Tmin to Tmax (or, as for liquid, in the whole temperature range where the liquid exists).

References1 R.C. Reid, J.M. Prausnitz, B.E. Poling. The properties of gases and liquids, 4th edition,

McGraw-Hill Inc., NY, USA, 1987.

Fig.4.2 Field of temperatures for a flow of real gas.



5 Rotation

Physical model

Flow Simulation is capable of simulating rotation of model parts and components with the rotating reference frame approach. Depending on the model geometry, you can choose one of the following two options to simulate your rotating equipment:

• Global rotating reference frame. With this option the model and the global coordinate system are considered rotating with specified angular velocity. Global rotating reference frame is applicable when all non-rotating model components are axisymmetrical with respect to the selected rotation axis.

• Local regions of rotation. This option allows to specify multiple local rotating coordinate systems within the model. All model parts and components within the local rotating regions are considered rotating by default. With this option you can simulate rotation of specific model components and non-rotating model components outside rotating regions are not required to be axisymmetrical .

The rotating reference frame approach has the following prerequisites that must be satisfied in order to apply it successfully and obtain reliable results:

• the supposed inlet flow field at the rotating refrence frame boundaries must be axisymmetrical with respect to the rotation axis,

• the supposed outlet flow field at the rotating refrence frame boundaries must be as close to axisymmetrical with respect to the rotation axis as possible.

Please note that even in case of time-dependent (transient) analysis the flow parameters within a rotating referrence frame are calculated using a steady-state approach and averaged at the rotating refrence frame boundaries.

If you consider gravitational effects in your analysis, the rotation axis must be parallel to the gravity vector.

You can specify some model components within a global rotating reference frame or local rotating region as non-rotating by applying the Stator wall Boundary Condition to the components surfaces. All non-rotating components within a rotating reference frame must be axisymmetrical with respect to the selected rotation axis.

The rotating reference frame boundaries are the computational domain outer boundaries for the Global rotating option and the rotating region outer surface for Local regions option.

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Local Rotating Regions - Additional Information

In accordance with the employed approach, each rotating solid component is surrounded by an axisymmetrical Rotating region, which has its own coordinate system rotating together with the component. To connect solutions obtained within the rotating region and in non-rotating part of the computational domain, special internal boundary conditions are set automatically at the fluid boundaries of the rotating region. The rotating region’s boundaries are sliced into rings of equal width as shown on the Fig.5.1. Then the values of flow parameters transferred as boundary conditions from the adjacent fluid regions are averaged circumferentially over each of these rings.

Please note that even in the case of time-dependent (transient) analysis the flow parameters within the rotating regions are calculated using a steady-state approach and averaged on the rotating regions' boundaries as described above.

The rotating region option is not applicable for high Mach number flows.

A rotating region is defined by adding an auxiliary component representing the rotating region to the model and specifying the angular velocity. A component defining a rotating region must meet the following requirements:

• the rotating component must be fully enclosed by it and the rotating component walls must not contact or intersect the rotating region boundaries,

• it must be axisymmetrical (with respect to the rotating component's rotation axis),

• its intersections with other fluid and solid regions must be axisymmetrical too,

• the components defining different rotating regions must not intersect.

Computational domain or fluid subdomainFlow parameters are calculated in the inertial Global Coordinate System

Rotation axisFlow parameters areaveraged over these rings

Local rotating regionFlow parameters are calculatedin the local rotating coordinatesystem

Fig.5.1 Slicing of rotating region boundaries into rings.



Interface

The rotation type is specified in the Analysis Type dialog box of the Wizard or General Settings by selecting the Global rotating or Local region(s) option.

Global Rotating Reference Frame

For Global rotating reference frame specify Rotation axis and Angular velocity. These settings are applied to the entire computational domain.

To select the rotation axis for the Global

rotating reference frame, click and in the Rotation

Axis dialog box specify either a reference axis or axis of the reference coordinate system.

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Local Rotating Regions

In the Rotating Region dialog available under Flow Simulation, Insert, Rotating Region, you select the model component representing the volume, in which the local rotating reference frame is applied, and specify Angular velocity.

During the definition of rotating region in the graphics area you can see the green arrows denoting the rotation axis and direction, and the direction of the angular velocity vector considered as positive.

The following parameters, available in the results processing tools, are useful for analyzing the results of a calculation involving rotation:

• Axial velocity (m/s) is the fluid velocity component along the rotating coordinate system’s rotation axis, it can be determined both in the rotating coordinate system and in the absolute (i.e. non-rotating) one.

• Circumferential velocity (m/s) is the fluid velocity component along the rotating coordinate system’s peripheral velocity vector relative to the Z axis of the selected absolute (i.e. non-rotating) coordinate system.

• Circumferential velocity RRF (m/s) is the fluid velocity component along the peripheral velocity vector relative to the Z axis of the selected rotating coordinate system. Note that if rotation is considered in the project in the form of local rotating regions (i.e. not as the global rotating reference frame), the values of this parameter outside the rotating regions are determined in the absolute (i.e. non-rotating) coordinate system.


• Peripheral velocity (m/s) is the circumferential speed of the rotating coordinate system’s rotation: ω·r, where ω is the angular velocity at which the rotating


coordinate system rotates and r is the radius of the point under consideration in the cylindrical coordinate system corresponding to the rotating coordinate system.

• Velocity RRF (m/s) is the fluid velocity vector and/or its absolute value in the rotating coordinate system. Note that if rotation is considered in the project in the form of local rotating regions (i.e. not as the global rotating reference frame), the values of this parameter outside the rotating regions are determined in the absolute (i.e. non-rotating) coordinate system.

Note that you may need to Enable some of those parameters in the Parameter list to make them available for selection in the View Settings dialog.

Examples of Use

Rotating impeller

Flow through the rotating impeller of a centrifugal pump (Fig.5.2) can be simulated with the Global rotating refrence frame option since all non-rotating components of the pump are axisymmetrical with respect to the rotation axis. The static pressure distribution in the impeller flow passage midsection is shown on Fig.5.3.

Fig.5.2 Problem statement Fig.5.3 The static pressure distribution in the impeller flow passage midsection

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Axial fan

An air flow in an axial fan can be simulated with the Local rotating regions option (Fig.5.4). The rotating region encloses the fan and has a relatively simple shape.

The pressure and velocity vectors distributions are shown on Fig.5.5.

CPU cooler in external flow

An air flow around a CPU cooler is simulated with the Local rotating regions option. The external air flow from the chassis fan disturbs the flow over the CPU cooler. The resulting flow field at the boundaries of the rotating region enclosing the cooler fan is not axisymmetrical. However, this disturbance does not influence the CPU cooler performance much, and we can use the Local rotating region to simulate the rotation of the CPU cooler fan. The temperature and velocity vectors distributions are shown on Fig.5.6.

Fig.5.4 Problem statementFig.5.5 Pressure and velocity vectors distribution


Fig.5.6 Temperature and velocity vectors distributions.


Centrifugal pump

A water flow in a centrifugal pump can be simulated with the Local rotating region option (Fig.5.7). The centrifugal pump uses a rotating impeller to increase the pressure of the fluid to move the fluid through a piping system. The fluid enters the pump impeller near the rotation axis and is accelerated by the impeller, flowing radially outward into the volute chamber, from where it exits into the piping system downstream. The flow field at the boundaries of the rotating region enclosing the impeller is not completely axisymmetrical, but these deviations from axial symmetry are relatively small and do not influence the pump characteristics much.

The pressure and velocity vectors distributions are shown on Fig.5.8.

Recommendations• Choose such shape of the rotating region, that the flow direction will be as much

perpendicular to the rotating region boundary as possible.

• Local rotating region can be used to simulate rotation of a part or component even if the flow field at the local rotating region boundaries is not axisymmetrical, but you must consider how it can affect the device performance. If you solve a problem in which the flow symmetry directly influence the device characteristics, change the shape or position of the rotating region or make some other modifications, if possible, to ensure that the flow at the rotating region boundaries is axysimmetrical.

• Adjust the mesh settings to have at least 2 or 3 cells across the gaps between the rotating region boundary and the surface of the rotating component within the region.

Fig.5.8 Pressure and velocity vectors distribution

Fig.5.7 Problem statement

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• If the rotating model component is a body of revolution, use the Moving Wall boundary condition instead of a rotating reference frame to simulate rotation of such component.

• You can place rotating region boundary within a solid body instead of putting it into a narrow gap between the rotating component and non- rotating model geometry. This will allow you to reduce possible negative influence of the flow disturbances within the narrow gap on the calculation results.



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solving engineering problems

Documents

moderate reynolds numbers

velocity vectors distributions

velocity vectors distribution

rotating reference frame

heat generation rates

minimum gap size

solving engineering problems

entire computational domain