numerical simulation of flow in lid-driven cavity using openfoam · 2018-10-12 · flows and roll...

INSTITUTE OF TECHNOLOGY, NIRMA UNIVERSITY, AHMEDABAD – 382 481, 08-10 DECEMBER, 2011 1

Abstract-- In recent years OpenFOAM solvers have attracted

great attention of the academia and industrial practitioners.

Principal potentialities of this software are full access to the

code, easy solver generation, modification and a huge and open

users community among others. The isothermal flow patterns in

lid-driven cavity for three different geometric configurations of

the cavity are obtained using OpenFOAM solvers. These

configurations include the square cavity, skewed cavity and

trapezoidal cavity. The steady flow patterns obtained by

OpenFOAM for different Reynolds numbers (Re) ranging from

100 to 3200 are compared with the benchmark published results

of Ghia et al. The isothermal flow in all the three cavities are

discussed in detail for varying Reynolds numbers.

Keywords--OpenFOAM, icoFoam, Lid-driven cavities, Stream

function, Vorticity.

I. INTRODUCTION

avity flows such as lid-driven cavity has served over and

over again as a model problem for testing and evaluating

numerical techniques. Lid driven cavity flows are

important in many industrial processing applications such as

short-dwell and flexible blade coaters. They also provide a

model for understanding more complex flows with closed

recirculation regions, such as flow over a slit, contraction

flows and roll coating flows. Cavity flows contain a full

range of flow types from pure rotation near the center of the

recirculation region to strong extension near the edges of the

lid. Numerical simulations of the 2D lid-driven cavity flow

are performed for a wide range of Reynolds numbers.

Accurate benchmark results are provided for steady solutions

as well as for periodic solutions around the critical Reynolds

number. The laminar incompressible flow in square, skewed

and trapezoidal cavities whose top wall (lid) moves with a

uniform velocity is studied here for Reynolds number range

of 100 to 3200. Results are available in the literature for this

problem using variety of solution methods [1]. The present

study of lid driven cavity for different geometric

configurations is mainly aimed to demonstrate the utility of

OpenFOAM CFD solver. The procedure to use OpenFOAM

for solution of isothermal flow in variety of geometric

configurations is demonstrated in this work.

II. OPENFOAM SOLVER

PENFOAM (Open Field Operation and Manipulation)

CFD Toolbox is a free, open source CFD software

package produced by a commercial company; OpenCFD

Ltd. OpenFOAM is a free source CFD package written in

C++ which uses classes and templates to manipulate and

operate scalar, vectorial and tensorial fields[2]. Thus,

OpenFOAM can interpret the true meaning of a field,

encapsulating the idea of magnitude and direction of a vector.

Combined with implementations of adequate numerical

methods to the discretization of partial differential equations

and to the solution of the resulting linear systems,

OpenFOAM is a good choice to handle CFD problems. Besides, its open-source characteristic is an advantage in the

implementation of any addition or modification in the code.

OpenFOAM gives a flexible framework which combines all

the required tools for solving any CFD problem. This

framework consists of enormous groups of libraries for

different mathematical, numerical and physical models.

Linking the mathematical and numerical tools with the

physical models in a main C++ function produces different

solvers and utilities. It has a large user base across most areas

of engineering and science, from both commercial and

academic organizations. The discretization of the flow

governing equations in OpenFOAM is based on the finite

volume method (FVM) formulated with collocated variable

arrangement, with pressure and velocity solved by segregated

methods. SIMPLE (Semi-implicit Method for Pressure

Linked Equations) or PISO (Pressure Implicit Splitting of

Operators) are used for pressure–velocity coupling. SIMPLE,

SIMPLER, SIMPLEC, and PISO are the most widely used

algorithms to pressure–velocity coupling. The software also

offers a wide range of interpolation schemes, solvers and pre-

conditioners for the discretized algebraic equation system.

OpenFOAM has an extensive range of features to solve

anything from complex fluid flows involving chemical

reactions, turbulence and heat transfer, to solid dynamics and

electromagnetic. Almost everything (including meshing, and

pre- and post-processing) runs in parallel as standard.

OpenFOAM offers complete freedom to customise and

extend its existing functionality and gives support from

OpenCFD. It follows a highly modular code design in which

collections of functionality (e.g. numerical methods, meshing,

physical models) are each compiled into their own shared

library. Executable applications are then created that are

simply linked to the library functionality. There are many

recent contributions in implementing different solvers and

physical models in OpenFOAM. OpenFOAM, undoubtedly,

opens new horizons for CFD community for efficient models

devolving, allowing the industrial sectors to be updated with

Numerical Simulation of Flow in Lid-driven

Cavity using OpenFOAM

A. Jignesh P. Thaker and B. Jyotirmay Banerjee

A. M.Tech (Turbomachines), Department of Mechanical Engineering, SVNIT, Surat.

B. Associate Professor, Department of Mechanical Engineering, SVNIT, Surat.

C

O

INTERNATIONAL CONFERENCE ON CURRENT TRENDS IN TECHNOLOGY, ‘NUiCONE – 2011’ 2

all new models without any delay for waiting the new models

to be implemented in the commercial CFD codes.

OpenFOAM includes over 80 solver applications that

simulate specific problems in engineering mechanics and

over 170 utility applications that perform pre- and post-

processing tasks, e.g. meshing, data visualisation, etc. One of

the strengths of OpenFOAM is that new solvers and utilities

can be created by its users with some pre-requisite knowledge

of the underlying method, physics and programming

techniques involved. OpenFOAM is supplied with pre- and

post-processing environments. The interface to the pre- and

post-processing are themselves OpenFOAM utilities, thereby

ensuring consistent data handling across all environments.

The overall structure of OpenFOAM is shown in Fig.1.

Fig.1. Overview of OpenFOAM structure.

III. PROCEDURE FOR SOLUTION OF DIFFERENT CAVITIES IN

OPENFOAM

The present section is a discussion on how to pre-process,

run and post-process the isothermal, incompressible flow in a

two dimensional square domain using OpenFOAM. The three

geometric configurations considered for simulation in this

work are shown in Fig.2.[6] For square cavity, all the

boundaries of the square are walls. The top wall moves in the

x-direction at a constant speed while the other 3 are

stationary. The flow is assumed to be laminar and is solved

on a uniform mesh using the icoFoam solver for laminar,

isothermal, incompressible flow.

Fig.2. Geometry of square, skewed and trapezoidal cavity.

The whole process is categorised in three steps.

1) Pre-processing

First a directory is created for this case and given a name

as square cavity in the directory of OpenFOAM. It needs

three directories; initialize, constant and system. In initialize

the starting condition for properties of the fluid are provided.

In constant directory there are two subdirectory; polyMesh

and transport properties. PolyMesh contains blockMesh and

boundary case files. Now the code for geometry of square

lead driven cavity in OpenFOAM need to be written and

saved in to blockMesh file. Editing of files is possible in

OpenFOAM. OpenFOAM always operates in a 3 dimensional

Cartesian coordinate system and all geometries are generated

in 3 dimensions. OpenFOAM solves the case in 3 dimensions

by default but can be instructed to solve in 2 dimensions by

specifying a ‘special’ empty boundary condition on

boundaries normal to the (3rd) dimension for which no

solution is required. In OpenFOAM this data is stored in a set

of files within a case directory rather than in a single case

file. This code being simulated involves data for mesh, fields,

properties, control parameters, etc.

For generating mesh it should have command of

blockMesh. Run blockMesh command in terminal window so

OpenFOAM created mesh in square domain. Any mistakes in

the blockMeshDict file are picked up by blockMesh and the

resulting error message directs to the line in the file where the

problem occurred. There should be no error messages at this

stage. For checking mesh it is required to write the command

checkMesh in terminal window. Then it shows mesh size,

number of cells, number of faces, patches, etc. Once the mesh

generation is complete, then look at this initial fields set up

for this case. The case is set up to start at time t = 0, so the

initial field data is stored in a initialise directory means 0 sub-

directory of the cavity directory. The 0 sub-directory contains

2 files, p and U, one for each of the pressure (p) and velocity

(U) fields whose initial values and boundary conditions must

be set.

For this case of cavity, the boundary consists of walls only,

split into two patches named: fixedWalls for the fixed sides

and base of the cavity; movingWall for the moving top of the

cavity. As walls, both are given a zeroGradient boundary

condition for p, meaning “the normal gradient of pressure is

zero”. The frontAndBack patch represents the front and back

planes of the 2D case and therefore must be set as empty. In

this case, the initial fields are set to be uniform. Here the

pressure is kinematic, and as an incompressible case, its

absolute value is not relevant, so is set to uniform 0 for

convenience. The boundary field for velocity requires the

same boundary condition for the front and Back patch. The

other patches are walls: a no-slip condition is assumed on the

fixed Walls, hence a fixedValue condition with a value of

uniform (0 0 0). The top surface moves at a speed of 1 m/s in

the x-direction so requires a fixedValue condition also but

with uniform (1 0 0).

The physical properties for the case are stored in

dictionaries. For an icoFoam case, the only property that must

be specified is the kinematic viscosity which is stored from

the transport Properties dictionary. Check that the kinematic

viscosity is set correctly by opening the transport Properties

dictionary to view or edit its entries. The keyword for

kinematic viscosity is nu, the phonetic label for the Greek

symbol by which it is represented in equations. Initially this

case is run with a Reynolds number of 100, where the

Reynolds number is defined as,


where d and U are the characteristic length and velocity

respectively and is the kinematic viscosity.

Input data relating to the control of time are read from the

control dictionary. For viewing this file; as a case control file,

it is located in the system directory. The start and stop times

and the time step for the run must be set. OpenFOAM offers

great flexibility with time. To start the run from time t=0

means OpenFOAM needs to read field data from a directory

named 0. Therefore it is required to set the startFrom

keyword to startTime and then specify the startTime keyword

to be 0. The end time is to reach the steady state solution. As

a general rule, the fluid should pass through the domain 10

times to reach steady state in laminar flow. In this case the

flow does not pass through this domain as there is no inlet or

outlet, so instead the end time can be set to the time taken for

the lid to travel ten times across the cavity. In fact, with

hindsight, we discover that 15 s is sufficient so adopt this

value. To specify this end time, it must specify the stopAt

keyword as endTime and then set the endTime keyword to

15. Now it needs to set the time step, represented by the

keyword deltaT. To achieve temporal accuracy and numerical

stability when running icoFoam, a Courant number of less

than 1 is required. The Courant number ( is defined for

one cell as:

where δt is the time step, |U| is the magnitude of the velocity

through that cell and δx is the cell size in the direction of the

velocity.

The flow velocity varies across the domain and it must

ensure Co < 1 everywhere. Therefore choose δt based on the

worst case: the maximum Co corresponding to the combined

effect of a large flow velocity and small cell size. Here, the

cell size is fixed across the domain so the maximum Co will

occur next to the lid where the velocity approaches 1 ms−1.

The cell size is:

Here for this geometry d=1 and number of grids are

129x129. Thus δx becomes 0.007752 and δt becomes

0.007752 by Courant number definition. The δt is take as

0.005 for stability in these computations. As the simulation

progresses to write results at certain interval of time that can

later be view with a post-processing package, the

writeControl keyword presents several options for setting the

time at which the results are written. Here it is required to

select the timeStep option which specifies that results are

written every nth time step where the value n is specified

under the writeInterval keyword.

Now it is required to specify the choice of finite volume

discretisation schemes in the fvSchemes dictionary in the

system directory. The specification of the linear equation

solvers, tolerances and other algorithm controls is made in the

fvSolution dictionary, similar to the in the system directory.

In a closed incompressible system such as the cavity, pressure

is relative: it is the pressure range that matters not the

absolute values. In cases such as this, the solver sets a

reference level by pRefValue in cell pRefCell.[2] In this

example both are set to 0. Changing either of these values

will change the absolute pressure field, but not, of course, the

relative pressures or velocity field.

To see the mesh of square domain then before the case is

run it is a good idea to view the mesh to check for any errors.

The mesh is viewed in paraFoam, the post-processing tool

supplied with OpenFOAM. The paraFoam post-processing is

started by typing in the terminal from within the case

directory paraFoam. This launches paraview window and in

that see the domain how it looks and also see the mesh.

2) Processing

OpenFOAM applications can be run in two ways: as a

foreground process, i.e. one in which the shell waits until the

command has finished before giving a command prompt; as a

background process, one which does not have to be

completed before the shell accepts additional commands.

Here, it is required run icoFoam in the foreground. The

icoFoam solver is executed by entering the case directory and

typing icoFoam in the terminal window. It tells the current

time, maximum Courant number, initial and final residuals

for all fields in terminal window. It should also calculate the

stream function and vorticity values at each and every time

steps.

3) Post-processing

As soon as results are written to time directories, they can

be viewed using paraFoam. One should return to the

paraFoam window and select the Properties panel for the

cavity. OpenFOAM case module. In paraView the pressure,

velocity, stream function and vorticity contours can be

visualised.

IV. RESULTS AND DISCUSSION

The numerical simulations for isothermal flow for square,

skewed and trapezoidal cavity are carried out using the CFD

solver OpenFOAM. Results are generated for various

Reynolds number to observe the influence on stream line and

vorticity patterns in the cavity. The influence of grid size on

flow distribution is also discussed. In this section first the

validation of the numerical results are depicted. This is

followed by discussion on flow inside the square cavity. The

influence of Reynolds number on flow is elaborated. The

flow pattern in the skew cavity and the trapezoidal cavity are

discussed then for varying values of Reynolds number.

1) Validation

First, the results obtained by OpenFOAM solver are

compared with the benchmark results for square cavity

presented by Ghia et al. [1]. Fig. 3 and Fig.4 show the

contours of streamline and vorticity generated by

OpenFOAM for square cavity for a grid size 129x129 for

Re=100. These results are compared benchmark result

obtained by of Ghia et al.[1] . The figures on the left are

results obtained by OpenFOAM and those on the right are

from Ghia et al. [1]. The values of the stream function and

vorticity obtained by OpenFOAM are exactly comparable to

results obtained by Ghia et al. [1]. To get a better picture

Table I and II provides the exact values of stream function

(ψ) and vorticity [5].


Fig.3. Comparison of streamline values for Re=100 with results of Ghia at

al.[1] (129x129)

TABLE I

VALUES OF STREAMLINES CONTOURS FOR SQUARE CAVITY

Fig.4. Comparison of vorticity values for Re=100 with results of Ghia at

al.[1] (129x129). TABLE II

VALUES OF VORTICITY FOR ALL CAVITIES

Fig.5. Streamlines and vorticity contours for Re=400 (129x129) of square

cavity plotted with OpenFOAM.








2) Square Cavity

The influence on lid motion to the flow pattern in the

cavity for lid-driven square cavity is discussed in this sub-

section. Fig 3, 5, 6and 7 show the contours of streamlines and

vorticity for Re=100, 400, 1000 and 3200 inside the lid

driven square cavity. It is observed that as Re increases from

100 to 3200, the secondary vortices start developing and

getting larger in magnitude. The center of the primary vortex

is towards the top right corner for lower values of Reynolds

number. It moves towards the geometric center of the cavity

with the increase in Re. All secondary vortices appear

initially very near the corners and its center shifts towards the

cavity center as Re increases. As Re increases, several

regions of high velocity gradients, indicated by concentration

of the vorticity contours, appear within the cavity. It is

observed that these regions are not aligned with the geometric

boundaries of the cavity. At a very high Reynolds number

secondary vortices are observed even at the upper left corner

Figure 7 shows the stream lines and vorticity contours

observed for Re=3200. Figure 8 shows the influence of grid

size on the flow pattern distribution for Re=400.

3) Skewed Cavity

The procedure mentioned above is followed for obtaining

the isothermal flow inside the skewed cavity. The skewed

cavity is inclined at 45º with respect to x-axis [6]. Length L1

and L2 are the dimensions of the skewed cavities, and β =45º

is the skew angle as shown in Fig2. The variation of

streamlines and vorticity contours due to the inclination are

discussed in this section.

Fig.9. Streamlines and vorticity contours for Re=100 of skewed cavity

plotted with OpenFOAM.

Fig.10. Streamlines and vorticity contours for Re=1000 (of skewed cavity


Fig.9 and Fig.10 show the streamlines and vorticity

contour plots inside the skewed cavity at Re=100 and 1000

respectively. As Re increases from 100 to 1000, the

secondary vortices start developing at left corner of the cavity

and grow larger in magnitude. All secondary vortices appear

initially very near the left corners but when Re increases

vortices shifts towards the cavity center. To get a better

picture Table III provides the exact values of stream function

(ψ) for skewed cavity. TABLE III

VALUES OF STREAMLINES CONTOURS FOR SKEWED CAVITY

4) Trapezoidal Cavity

A trapezoidal cavity of general shape is given by the

location of the vertices and is represented here by E( ),

F(( , G( ) and H( ), Where =

and as shown in Fig.2.[6].

Fig.11. Streamlines and vorticity contours for Re=100 of trapezoidal cavity



Fig.12. Streamlines and vorticity contours for Re=400 of trapezoidal cavity


Fig.11 and Fig.12 depict the streamlines and vorticity

contour plots inside the trapezoidal cavity for Re=100 and

400 respectively. As Re increases from 100 to 400, the

secondary vortices start developing from bottom of the cavity

and grow larger in magnitude and shifts towards the cavity

center. The values of the stream function (ψ) in the cavity are

tabulated in Table IV. TABLE IV

VALUES OF STREAMLINES CONTOURS FOR TRAPEZOIDAL CAVITY

V. CONCLUSION

Steady flow analysis of the lid-driven square cavity shows

the existence of secondary vortices at the corners of the

cavity. The strength of the vortices increases as Reynolds

number increases. The obtained results from OpenFOAM

solver compared with available results of Ghia et al. [1]. The

steady state results of lid-driven square cavity are obtained

for Re = 100, 400, 1000 and 3200 using OpenFOAM. Also

the isothermal flow inside lid-driven skewed and trapezoidal

cavities for Re = 100, 400 and 1000 are discussed in terms of

streamline patterns and vorticity contours.

VI. REFERENCES

[1] U.Ghia, K. N. Ghia, and C. T. Shin, “High-Re Solutions for

Incompressible Flow Using the Navier-Stokes Equations and a

Multigrid Method”, Journal of Computational Physics, vol. 48, pp. 387-

411, January 1982.

[2] OpenFOAM, OpenFOAM user guide, 2010.

[3] W. D. McQuain, C. J. Ribbens, C. Y. Wang, and L. T. Watson, Steady

Viscous Flow in a Trapezoidal Cavity, Comput. Fluids, vol. 23, pp.

613–626, 1994.

[4] A. Sharma and V. Eswaran, A Finite Volume Method, in K. Muralidhar

and T.Sundararajan (eds.), Computational Fluid Flow and Heat

Transfer, chap. 12, Narosa, New Delhi, 2003.

[5] O. Bottela and R. Peyret, “Benchmark spectral results on the Lid-

Driven Cavity flow”, Computers & Fluids, vol.27, No.4, pp. 421-433,

1998.

[6] Sachin B. Paramane and Atul Sharma, “Consistent Implementation and

Comparison of FOU, CD, SOU, and QUICK Convection Schemes on

Square, Skew, Trapezoidal, and Triangular Lid-Driven Cavity Flow”,

Numerical Heat Transfer, Part B, vol.54, pp. 84-102,2008.

numerical simulation of flow in lid-driven cavity using openfoam · 2018-10-12 · flows and roll...

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