cfd supercritical airfoils

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CFD ANALYSIS OF SUPERCRITICAL AIRFOIL OVER SIMPLE AIRFOIL

A Thesis Submitted in Partial Fulfilment of the

Requirements for the Degree

By

Shantanu Khanna

(R180207050)

Under the Guidence of

Dr. Ugur Guven

Professor of Aerospace Engineering (Ph.D)

Nuclear Science and Technology Engineer (M.sc)

College of Engineering

University of Petroleum and Energy Studies,

Dehradun

May, 2011

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A Thesis Submitted in Partial Fulfilment of the

Requirements for the Degree

By

Shantanu Khanna

(R180207050)

Under the Guidence of

Dr. Ugur Guven

Professor of Aerospace Engineering (Ph.D)

Nuclear Science and Technology Engineer (M.sc)

Approved

.......................................

Dean

College of Engineering

University of Petroleum and Energy Studies,

Dehradun

May, 2011

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CERTIFICATE

This is to certify that the work contained in this thesis titled “CFD Analysis of Supercritical Airfoil over Simple Airfoil” has been carried out by Shantanu Khanna under my supervision and has not been submitted elsewhere for a degree.

Dr.UGUR GUVEN

Professor of aerospace engineering

(April 15 2011)

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UNIVERSITY OF PETROLIUM AND ENTEGY STUDIES


Major Project by

Shantanu Khanna

Project Supervisor: Prof. Dr.Ugur GUVEN

Department: ASE

Program: B.Tech

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Forward I would like to express my deep appreciation and thanks for my advisor. This work is supported by Prof. Dr. Ugur GUVEN

April 2011

Shantanu Khanna

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Table of Contents

S.no Page no.

List of Tables.....................................................................................................3

List of Figures....................................................................................................4

Abstract..............................................................................................................6

Chapter 1: Introduction....................................................................................7

1.1 Supercritical Airfoil........................................................................................7

1.2 Features of Supercritical Airfoil.....................................................................8

1.2.1 Trailing Edge Thickness..................................................................8

1.2.2 Maximum Thickness.......................................................................8

1.2.3 Aft upper surface curvature.............................................................8

1.3 Airfoil Data....................................................................................................8

Chapter 2: CFD Literature.............................................................................10

2.1. CFD (Computational Fluid Dynamics).......................................................10

2.1.1. Discretization Methods in CFD ...................................................10

2.1.1.1. Finite difference method (FDM)...................................10

2.1.1.2. Finite volume method (FVM).......................................11

2.1.1.3. Finite element method (FEM).......................................11

2.1.2. How does a CFD code work? ......................................................12

2.1.2.1. Pre-Processing ..............................................................13

2.1.2.2. Solver ...........................................................................16

2.1.2.3 Post-Processing: ............................................................17

2.1.3. Advantages of CFD......................................................................17

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Chapter 3: Analysing flow in CFD...................................................................19

3.1 Create geometry in Gambit............................................................................19

3.1.1 Import edge.....................................................................................19

3.1.2 Crete Farfield Boundary.................................................................19

3.1.3 Create Face.....................................................................................20

3.2 Mesh geometry in Gambit............................................................................20

3.2.1 Mesh Edges...................................................................................20

3.2.2 Mesh Face.....................................................................................21

3.3 Specify Boundary Types in Gambit............................................................21

3.3.1 Define Boundary Types................................................................21

3.4 Set up problem in Fluent.............................................................................21

3.5 Solve...........................................................................................................24

Chapter 4: Analysis........................................................................................25

Chapter 5: Conclusion...................................................................................46

5.1 Pressure drag……………………………………………………………..46

5.2 Shock wave strength..................................................................................46

REFRENCE...................................................................................................47

APPENDIX....................................................................................................48

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List of Table

S.no Page no

Table 1.1: Specification of NACA SC(2) 0714.....................................................8

Table 1.2 : Specifications of NACA 4412 airfoil..................................................9

Table 5.1; Pressure Drag.....................................................................................46

Table 5.2: Strength of Shockwave......................................................................46

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List of Figures

S.no Page no.

Figure 1.1: Supercritical Airfoil..........................................................................7

Figure 2.1: Algorithm of numerical approach used by simulation softwares.......15

Figure 3.1: Import Edges......................................................................................19

Figure 3.2: Meshing..............................................................................................21

Figure 3.2: Model Solver......................................................................................23

Figure 3.4: Model Viscous...................................................................................24

Figure 3.5: Defining Boundary condition............................................................25

Figure 4.1: Contours of static pressure.................................................................25

Figure 4.2: Contours of dynamic pressure............................................................26

Figure 4.3: Contours of total pressure..................................................................26

Figure 4.4: Contours of static temperature...........................................................27

Figure 4.5: Contours of total temperature............................................................27

Figure 4.6: Contours of velocity magnitude........................................................28

Figure 4.7: Velocity vectors.................................................................................28


Figure 4.9: Contours of dynamic pressure...........................................................29

Figure 4.10: Contours of total pressure...............................................................30

Figure 4.11: Contours of static temperature........................................................30

Figure 4.12: Contours of total temperature.........................................................31

Figure 4.13: Contours of velocity magnitude.....................................................31

Figure 4.14: Velocity vectors..............................................................................32

Figure 4.15: Contours of static pressure..............................................................32

Figure 4.16: Contours of dynamic pressure.........................................................33

Figure 4.17: Contours of total pressure................................................................33

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Figure 4.18: Contours of static temperature.........................................................34

Figure 4.19: Contours of total temperature..........................................................34

Figure 4.20: Contours of velocity magnitude.......................................................35

Figure 4.21: Velocity vectors................................................................................35

Figure 4.22: Contours of static pressure................................................................36

Figure 4.23: Contours of dynamic pressure...........................................................36

Figure 4.24: Contours of total pressure.................................................................37

Figure 4.25: Contours of static temperature..........................................................37

Figure 4.26: Contours of total temperature............................................................38

Figure 4.27: Contours of velocity magnitude........................................................38

Figure 4.28: Velocity vectors.................................................................................39


Figure 4.30: Contours of dynamic pressure............................................................40

Figure 4.31: Contours of total pressure...................................................................40

Figure 4.32: Contours of static temperature............................................................41

Figure 4.33: Contours of total temperature..............................................................41

Figure 4.34: Contours of velocity magnitude...........................................................42

Figure 4.35: Velocity vectors...................................................................................42

Figure 4.36: Contours of static pressure...................................................................43

Figure 4.37: Contours of dynamic pressure..............................................................43

Figure 4.38: Contours of total pressure.....................................................................44

Figure 4.39: Contours of static temperature..............................................................44

Figure 4.40: Contours of total temperature...............................................................45

Figure 4.41: Contours of velocity magnitude............................................................45

Figure 4.42: Velocity vectors......................................................................................46

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ABSTRACT

In this project flow over supercritical airfoil and conventional airfoil is compared at

Mach number 0.6. Parameters which are observed are Pressure drag and Strength of

shockwave as they are one of the parameters which are prominent in transonic speed.

Software tools used are GAMBIT and FLUENT. Gambit is used for preparing the

geometry and meshing and FLUENT is used for analysing the flow. Computational

fluid dynamics is used because preparing a model of airfoil is a lengthy and difficult

process and wind tunnel capable of 0.6 Mach number is not available. CFD gives

99% accurate results.

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Chapter 1: INTRODUCTION

1.1 Supercritical Airfoil

Transonic Jet aircrafts fly at speed of .8-.9 Mach number. At these speeds speed of

air reaches speed of sound somewhere over the wing and compressibility effects start

to show up. The free stream Mach number at which local sonic velocities develop is

called critical Mach number. It is always better to increase the critical mach number

so that formation of shockwaves can be delayed. This can be done either by

sweeping the wings but high sweep is not recommended in passenger aircrafts as

there is loss in lift in subsonic speed and difficulties during constructions. So

engineers thought of developing an airfoil which can perform this task without loss

in lift and increase in drag. They increased the thickness of the leading edge and

made the upper surface flat so that there is no formation of strong shockwave and

curved trailing edge lower surface which increases the pressure at lower surface and

accounts’ for lift.

Figure 1.1: Supercritical Airfoil.

1.2 Features of Supercritical Airfoil

1.2.1 Trailing Edge Thickness

The design philosophy of the supercritical airfoil required that the trailing-edge

slopes of the upper and lower surfaces be equal. This requirement served to retard

flow separation by reducing the pressure recovery gradient on the upper surface so

that the pressure coefficients recovered to only slightly positive values at the trailing

edge. Increasing the trailing-edge thickness of an interim ll-percent-thick

supercritical airfoil from 0 to 1.0 percent of the chord resulted in a significant

decrease in wave drag at transonic Mach numbers; however, this decrease was

achieved at the expense of higher drag at subcritical Mach numbers.

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1.2.2 Maximum Thickness

For the thinner airfoil, the onset of trailing-edge separation began at an

approximately 0.1 higher normal-force coefficient at the higher test Mach numbers,

and the drag divergence Mach number at a normal-force coefficient of 0.7 was 0.01

higher. Both effects were associated with lower induced velocities over the thinner

airfoil.

1.2.3 Aft upper surface curvature

The rear upper surface of the supercritical airfoil is shaped to accelerate the flow

following the shock wave in order to produce a near-sonic plateau at design

conditions.

1.3 Airfoil Data

There are two airfoils chosen for this analysis one is supercritical and other is

conventional airfoil. Super critical airfoil chosen for this project is NACA SC(2)

0714 and NACA 4412 which is conventional airfoil.

Table 1.1: Specification of NACA SC(2) 0714

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Table 1.2 : Specifications of NACA 4412 airfoil

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Chapter 2: CFD Literature

2.1. CFD (Computational Fluid Dynamics)

CFD is one of the branches of fluid mechanics that uses numerical methods and

algorithms to solve and analyze problems that involve fluid flows. Computers are

used to perform the millions of calculations required to simulate the interaction of

fluids and gases with the complex surfaces used in engineering. However, even with

simplified equations and high speed supercomputers, only approximate solutions can

be achieved in many cases. More accurate codes that can accurately and quickly

simulate even complex scenarios such as supersonic or turbulent flows are an

ongoing area of research.

2.1.1. Discretization Methods in CFD

There are three discretization methods in CFD:

1. Finite difference method (FDM)

2. Finite volume method (FVM)

3. Finite element method (FEM)

2.1.1.1. Finite difference method (FDM)

A finite difference method (FDM) discretization is based upon the differential form

of the PDE to be solved. Each derivative is replaced with an approximate difference

formula (that can generally be derived from a Taylor series expansion). The

computational domain is usually divided into hexahedral cells (the grid), and the

solution will be obtained at each nodal point. The FDM is easiest to understand when

the physical grid is Cartesian, but through the use of curvilinear transforms the

method can be extended to domains that are not easily represented by brick-shaped

elements. The Discretization results in a system of equation of the variable at nodal

points, and once a solution is found, then we have a discrete representation of the

solution.

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2.1.1.2. Finite volume method (FVM)

A finite volume method (FVM) discretization is based upon an integral form of the

PDE to be solved (e.g. conservation of mass, momentum, or energy). The PDE is

written in a form which can be solved for a given finite volume (or cell). The

computational domain is discretized into finite volumes and then for every volume

the 12 governing equations are solved. The resulting system of equations usually

involves fluxes of the conserved variable, and thus the calculation of fluxes is very

important in FVM. The basic advantage of this method over FDM is it does not

require the use of structured grids, and the effort to convert the given mesh in to

structured numerical grid internally is completely avoided. As with FDM, the

resulting approximate solution is a discrete, but the variables are typically placed at

cell centers rather than at nodal points. This is not always true, as there are also face-

centered finite volume methods. In any case, the values of field variables at non-

storage locations (e.g. vertices) are obtained using interpolation.

2.1.1.3. Finite element method (FEM)

A finite element method (FEM) discretization is based upon a piecewise

representation of the solution in terms of specified basis functions. The

computational domain is divided up into smaller domains (finite elements) and the

solution in each element is constructed from the basis functions. The actual equations

that are solved are typically obtained by restating the conservation equation in weak

form: the field variables are written in terms of the basis functions, the equation is

multiplied by appropriate test functions, and then integrated over an element. Since

the FEM solution is in terms of specific basis functions, a great deal more is known

about the solution than for either FDM or FVM. This can be a double-edged sword,

as the choice of basis functions is very important and boundary conditions may be

more difficult to formulate. Again, a system of equations is obtained (usually for

nodal values) that must be solved to obtain a solution.

Comparison of the three methods is difficult, primarily due to the many variations of

all three methods. FVM and FDM provide discrete solutions, while FEM provides a

continuous (up to a point) solution. FVM and FDM are generally considered easier to

program than FEM, but opinions vary on this point. FVM are generally expected to

provide better conservation properties, but opinions vary on this point also.

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2.1.2. How does a CFD code work?

CFD codes are structured around the numerical algorithms that can be tackle fluid

problems. In order to provide easy access to their solving power all commercial CFD

packages include sophisticated user interfaces input problem parameters and to

examine the results. Hence all codes contain three main elements: 13

1. Pre-processing.

2. Solver

3. Post-processing.

2.1.2.1. Pre-Processing

This is the first step in building and analyzing a flow model. Preprocessor consist of

input of a flow problem by means of an operator –friendly interface and subsequent

transformation of this input into form of suitable for the use by the solver. The user

activities at the Pre-processing stage involve:

• Definition of the geometry of the region: The computational domain.

• Grid generation the subdivision of the domain into a number of smaller, non-

overlapping sub domains (or control volumes or elements Selection of physical or

chemical phenomena that need to be modeled).

• Definition of fluid properties

• Specification of appropriate boundary conditions at cells, which coincide with or

touch the boundary. The solution of a flow problem (velocity, pressure, temperature

etc.) is defined at nodes inside each cell. The accuracy of CFD solutions is governed

by number of cells in the grid. In general, the larger numbers of cells better the

solution accuracy. Both the accuracy of the solution & its cost in terms of necessary

computer hardware & calculation time are dependent on the fineness of the grid.

Efforts are underway to develop CFD codes with a (self) adaptive meshing

capability. Ultimately such programs will automatically refine the grid in areas of

rapid variation.

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GAMBIT (CFD PREPROCESSOR) GAMBIT is a state-of-the-art preprocessor

for engineering analysis. With advanced geometry and meshing tools in a powerful,

flexible, tightly-integrated, and easy-to use interface, GAMBIT can dramatically

reduce preprocessing times for many applications. Complex models can be built

directly within GAMBIT‘s solid geometry modeler, or imported from any major

CAD/CAE system. Using a virtual geometry overlay and advanced cleanup tools,

imported geometries are quickly converted into suitable flow domains. A

comprehensive set of highly-automated and size function driven meshing tools

ensures that the best mesh can be generated, whether structured, multiblock,

unstructured, or hybrid. 14

2.1.2.2. Solver

The CFD solver does the flow calculations and produces the results. FLUENT,

FloWizard, FIDAP, CFX and POLYFLOW are some of the types of solvers.

FLUENT is used in most industries. FloWizard is the first general-purpose rapid

flow modeling tool for design and process engineers built by Fluent. POLYFLOW

(and FIDAP) are also used in a wide range of fields, with emphasis on the materials

processing industries. FLUENT and CFX two solvers were developed independently

by ANSYS and have a number of things in common, but they also have some

significant differences. Both are control-volume based for high accuracy and rely

heavily on a pressure-based solution technique for broad applicability. They differ

mainly in the way they integrate the fluid flow equations and in their equation

solution strategies. The CFX solver uses finite elements (cell vertex numerics),

similar to those used in mechanical analysis, to discretize the domain. In contrast, the

FLUENT solver uses finite volumes (cell centered numerics). CFX software focuses

on one approach to solve the governing equations of motion (coupled algebraic

multigrid), while the FLUENT product offers several solution approaches (density-,

segregated- and coupled-pressure-based methods)

The FLUENT CFD code has extensive interactivity, so we can make changes to the

analysis at any time during the process. This saves time and enables to refine designs

more efficiently. Graphical user interface (GUI) is intuitive, which helps to shorten

the learning curve and make the modeling process faster. In addition, FLUENT's

adaptive and dynamic mesh capability is unique and works with a wide range of

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physical models. This capability makes it possible and simple to model complex

moving objects in relation to flow. This solver provides the broadest range of

rigorous physical models that have been validated against industrial scale

applications, so we can accurately simulate real-world conditions, including

multiphase flows, reacting flows, rotating equipment, moving and deforming objects,

turbulence, radiation, acoustics and dynamic meshing. The FLUENT solver has

repeatedly proven to be fast and reliable for a wide range of CFD applications. The

speed to solution is faster because suite of software enables us to stay within one

interface from geometry building through the solution process, to post-processing

and final output. 15

The numerical solution of Navier–Stokes equations in CFD codes usually implies a

discretization method: it means that derivatives in partial differential equations are

approximated by algebraic expressions which can be alternatively obtained by means

of the finite-difference or the finite-element method. Otherwise, in a way that is

completely different from the previous one, the discretization equations can be

derived from the integral form of the conservation equations: this approach, known

as the finite volume method, is implemented in FLUENT (FLUENT user‘s guide,

vols. 1–5, Lebanon, 2001), because of its adaptability to a wide variety of grid

structures. The result is a set of algebraic equations through which mass, momentum,

and energy transport are predicted at discrete points in the domain. In the freeboard

model that is being described, the segregated solver has been chosen so the

governing equations are solved sequentially. Because the governing equations are

non-linear and coupled, several iterations of the solution loop must be performed

before a converged solution is obtained and each of the iteration is carried out as

follows:

(1) Fluid properties are updated in relation to the current solution; if the calculation is

at the first iteration, the fluid properties are updated consistent with the initialized

solution.

(2) The three momentum equations are solved consecutively using the current value

for pressure so as to update the velocity field.

(3) Since the velocities obtained in the previous step may not satisfy the continuity

equation, one more equation for the pressure correction is derived from the

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continuity equation and the linearized momentum equations: once solved, it gives the

correct pressure so that continuity is satisfied. The pressure–velocity coupling is

made by the SIMPLE algorithm, as in FLUENT default options.

(4) Other equations for scalar quantities such as turbulence, chemical species and

radiation are solved using the previously updated value of the other variables; when

inter-phase coupling is to be considered, the source terms in the appropriate

continuous phase equations have to be updated with a discrete phase trajectory

calculation.

(5) Finally, the convergence of the equations set is checked and all the procedure is

repeated until convergence criteria are met. (Ravelli et al., 2008) 16

Figure 2.1: Algorithm of numerical approach used by simulation softwares

The conservation equations are linearized according to the implicit scheme with

respect to the dependent variable: the result is a system of linear equations (with one

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equation for each cell in the domain) that can be solved simultaneously. Briefly, the

segregated implicit method calculates every single variable field considering all the

cells at the same time. The code stores discrete values of each scalar quantity at the

cell centre; the face values must be interpolated from the cell centre values. For all

the scalar quantities, the interpolation is carried out by the second order upwind

scheme with the purpose of achieving high order accuracy. The only exception is

represented by pressure interpolation, for which the standard method has been

chosen. Ravelli et al., 2008). 17

2.1.2.3 Post-Processing:

This is the final step in CFD analysis, and it involves the organization and

interpretation of the predicted flow data and the production of CFD images and

animations. Fluent's software includes full post processing capabilities. FLUENT

exports CFD's data to third-party post-processors and visualization tools such as

Ensight, Fieldview and TechPlot as well as to VRML formats. In addition, FLUENT

CFD solutions are easily coupled with structural codes such as ABAQUS, MSC and

ANSYS, as well as to other engineering process simulation tools.

Thus FLUENT is general-purpose computational fluid dynamics (CFD) software

ideally suited for incompressible and mildly compressible flows. Utilizing a

pressure-based segregated finite-volume method solver, FLUENT contains physical

models for a wide range of applications including turbulent flows, heat transfer,

reacting flows, chemical mixing, combustion, and multiphase flows. FLUENT

provides physical models on unstructured meshes, bringing you the benefits of easier

problem setup and greater accuracy using solution-adaptation of the mesh. FLUENT

is a computational fluid dynamics (CFD) software package to simulate fluid flow

problems. It uses the finite-volume method to solve the governing equations for a

fluid. It provides the capability to use different physical models such as

incompressible or compressible, inviscid or viscous, laminar or turbulent, etc.

Geometry and grid generation is done using GAMBIT which is the preprocessor

bundled with FLUENT. Owing to increased popularity of engineering work stations,

many of which has outstanding graphics capabilities, the leading CFD are now

equipped with versatile data visualization tools. These include

Domain geometry & Grid display.

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Vector plots.

Line & shaded contour plots.

2D & 3D surface plots.

Particle tracking.

View manipulation (translation, rotation, scaling etc.)

2.1.3. Advantages of CFD

Major advancements in the area of gas-solid multiphase flow modeling offer

substantial process improvements that have the potential to significantly improve

process plant operations. Prediction of gas solid flow fields, in processes such as

pneumatic transport lines, risers, 18

fluidized bed reactors, hoppers and precipitators are crucial to the operation of most

process plants. Up to now, the inability to accurately model these interactions has

limited the role that simulation could play in improving operations. In recent years,

computational fluid dynamics (CFD) software developers have focused on this area

to develop new modeling methods that can simulate gas-liquid-solid flows to a much

higher level of reliability. As a result, process industry engineers are beginning to

utilize these methods to make major improvements by evaluating alternatives that

would be, if not impossible, too expensive or time-consuming to trial on the plant

floor. Over the past few decades, CFD has been used to improve process design by

allowing engineers to simulate the performance of alternative configurations,

eliminating guesswork that would normally be used to establish equipment geometry

and process conditions. The use of CFD enables engineers to obtain solutions for

problems with complex geometry and boundary conditions. A CFD analysis yields

values for pressure, fluid velocity, temperature, and species or phase concentration

on a computational grid throughout the solution domain. Advantages of CFD can be

summarized as:

1. It provides the flexibility to change design parameters without the expense of

hardware changes. It therefore costs less than laboratory or field experiments,

allowing engineers to try more alternative designs than would be feasible otherwise.

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2. It has a faster turnaround time than experiments.

3. It guides the engineer to the root of problems, and is therefore well suited for

trouble-shooting.

4. It provides comprehensive information about a flow field, especially in regions

where measurements are either difficult or impossible to obtain.

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Chapter 3: Analysing flow in CFD

3.1 Create geometry in Gambit

3.1.1 Import edge

To specify the airfoil geometry we will import a file containing a list of vertices

along the surface and have GAMBIT join these vertices to create edge,

corresponding to the surface of the airfoil.

Main Menu >File >Input >ICEM input

Figure 3.1: Import Edges

3.1.2 Crete Farfield Boundary

We will create the farfield boundary by creating vertices and joining them

appropriately to form edges.

Operation Toolpad >Geometry Command Button >Vertex Command Button >Create

Vertex

Label X Y Z

A -12 12 0

B 12 12 0

C 12 -12 0

D -12 -12 0

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Operation Toolpad >Geometry Command Button >Edge Command Button >Create

Edge

Create edges AB, BC, CD, DA by selecting the vertices

3.1.3 Create Face

We will create the face by selecting the edges AB, BC, CD, DA naming the face

Farfield.

Operation Toolpad >Geometry Command Button >Face Command Button >Form

Face

By selecting the airfoil edges make an airfoil face naming Airfoil.

Before proceeding to the next step we will subtract the faces, subtracting face Airfoil

from Farfield.

Operation Toolpad >Geometry Command Button >Face Command Button

Click on the Boolean Operations Button and select Subtract Face Box select Farfield

in upper box and Airfoil in lower box click apply.

3.2 Mesh geometry in Gambit

3.2.1 Mesh Edges

Operation Toolpad >Mesh Command Button >Edge Command Button >Mesh Edges

Taking interval count 50 we mesh the edges AB, BC, CD, DA.

3.2.2 Mesh Face

Operation Toolpad >Mesh Command Button >Face Command Button >Mesh Faces

Taking interval count 100 we mesh the face Farfield

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Figure 3.2: Meshing

3.3 Specify Boundary Types in Gambit

3.3.1 Define Boundary Types

Operation Toolpad >Zone Command Button >Specify Boundary Types

Under entity select Edges and select AB, CD as Prssure_Farfield, DA as

Velocity_Inlet, BC as Peassure_Outlet.

Save the work and Export Mesh.

Main Menu >File >Save

Main Menu >File >Export >Mesh

3.4 Set up problem in Fluent

Import File

Main Menu >File >Read Case

Check Grid

Main Menu >Grid >Check

Define Properties

Define >Model >Solver

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Figure 3.2: Model Solver

Under Solver select Density based Solver and in Gradient option select Green-Gause

node based.

Define >Model >Viscous

Under Viscous select K-epsilon

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Figure 3.4: Model Viscous

Define >Model >Energy

Turn On the Energy equation

Define >Materials

Make sure that air is selected under Fluid Material and set Density to Ideal Gas

Define >Operating Conditions

Set Operating Pressure to be 101325 Pascal

Define >Boundary Conditions

Set the Velocity Magnitude to be 250 m/sec i.e around 0.6 Mach

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Figure 3.5: Defining Boundary condition

3.5 Solve

Solve >Control >Solution

Set Discretization to be Second Order Upwind for Flow, Turbulent Kinetic Energy,

Turbulent Dissipation Rate

Solve >Initialize >Initialize

Set Velocity_Inlet under compute form

Main Menu >File >Write >Case

Solve Iterate

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Chapter 4: Analysis

Supercritical airfoil at Zero degree

Figure 4.1 shows static pressure contour at 0.6 Mach number. From figure 4.1 it can be observed that there is high pressure of 35100 Pascal and at trailing edge pressure is -18200 Pascal. Resultant pressure is 53300 Pascal.

Figure 4.1: Contours of static pressure

Figure 4.2 shows dynamic contour at 0.6 Mach number. From figure 4.2 it can be observed that a weak shock is formed near the trailing edge of the airfoil. And at the lower surface of the trailing edge high pressure region is there which compensates for lift loss due to flat upper surface.

Figure 4.2: Contours of dynamic pressure

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Figure 4.3: Contours of total pressure

Figure 4.3 and figure 4.4 shows contours of total pressure and static temperature their behaviour is same as static pressure and dynamic pressure.

Figure 4.4: Contours of static temperature

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Figure 4.5: Contours of total temperature

Figure 4.6: Contours of velocity magnitude

Figure 4.6 shows velocity magnitude and figure 4.5 shows contour of total temperature. Figure 4.7 shows the velocity vectors over supercritical airfoil.

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Figure 4.7: Velocity vectors

Supercritical airfoil at Fifteen degree



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Figure 4.10 shows contour of total pressure. Figure 4.11 and 4.12 shows contour of static temperature and total temperature the contours show same behaviour as static pressure and dynamic pressure.

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Figure 4.13 shows velocity magnitude and figure 4.14 shows velocity vectors. The contours behave same as contours of dynamic pressure.

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Figure 4.14: velocity vector

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Supercritical airfoil at Thirty degree





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Figure 4.17 shows contours of total pressure this contour shows combined effect of static pressure and dynamic pressure. Figure 4.18 shows effect on static temperature and it shows same result as static pressure. Formation of shockwave leads to rise in temperature and total temperature also increases as shown in figure 4.19.

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Figure 4.20 shows velocity magnitude and 4.21 shows direction of velocity vectors the contours behave same as plots of dynamic pressure.

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Simple airfoil at Zero degree



41




Figure 4.24 shows contours of total pressure this contour shows combined effect of static pressure and dynamic pressure. Figure 4.25 shows effect on static temperature and it shows same result as static pressure. Figure 4.26 shows effect on dynamic temperature the formation of shockwave leads to rise in temperature and total temperature also increases as shown in figure 4.27.

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43


Figure 4.28: velocity magnitude

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Simple airfoil at Fifteen degree





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Figure 4.31 shows contours of total pressure this contour shows combined effect of static pressure and dynamic pressure. Figure 4.32 shows effect on static temperature and it shows same result as static pressure. The formation of shockwave leads to rise in temperature and total temperature also increases as shown in figure 4.33.


Figure 4.31 shows contours of total pressure this contour shows combined effect of static pressure and dynamic pressure. Figure 4.32 shows effect on static temperature and it shows same result as static pressure. Figure 4.33 shows effect on dynamic temperature the formation of shockwave leads to rise in temperature and total temperature also increases as shown in figure 4.34.


46




47


Simple airfoil at Thirty degree



48




Figure 4.38 shows contours of total pressure this contour shows combined effect of static pressure and dynamic pressure. Figure 4.39 shows effect on static temperature and it shows same result as static pressure. The formation of shockwave leads to rise in temperature and total temperature also increases as shown in figure 4.40.

49




50



51

Chapter 5: Conclusion

5.1 Pressure drag

Pressure Drag is calculated by taking difference in static pressure at leading edge and trailing edge. More difference means more pressure drag

Angle of Attack NACA 4412 NACA sc(2)0714

00 43130 Pascal 34995 Pascal

150 59600 Pascal 55400 Pascal

5.2 Shock wave strength

Strength of Shockwave is estimated by calculating the decrease in velocity.

Angle of Attack NACA 4412 NACA sc(2)0714

00 140 m/sec 113 m/sec

150 413 m/sec 148 m/sec

From above analysis I conclude that In case of Supercritical airfoil

at 00 angle of attack there is 18% decrement in pressure drag. at 150 angle of attack there is 7% decrement in pressure drag. at 00 angle of attack there is 19.2% decrement in strength of shockwave. at 150 angle of attack there is 64% decrement in strength of shockwave.

52

REFRENCE

Anderson, J.D(2001), Introduction to flight, New York, Tata Mc Grawhill

Anderson, J.D(2005), Introduction toAerodynamics, New York, Tata Mc Grawhill

URL:www.NASA.com

URL:www.cornelluniversitylectures.com

URL:www.aerospacelectures.co.cc

53

APPENDIX

A1: Airfoil data for NACA SC(2)0714

1.000000 -0.010400 0.990000 -0.007100 0.980000 -0.003900 0.970000 -0.000900 0.950000 0.004900 0.920000 0.013100 0.900000 0.018100 0.870000 0.025100 0.850000 0.029400 0.820000 0.035300 0.800000 0.038900 0.770000 0.043900 0.750000 0.046900 0.720000 0.050900 0.700000 0.053300 0.680000 0.055500 0.650000 0.058500 0.620000 0.061000 0.600000 0.062500 0.570000 0.064500 0.550000 0.065600 0.530000 0.066600 0.500000 0.067800 0.480000 0.068400

54

0.450000 0.069200 0.430000 0.069500 0.400000 0.069700 0.380000 0.069800 0.350000 0.069600 0.330000 0.069200 0.300000 0.068500 0.270000 0.067300 0.250000 0.066400 0.220000 0.064600 0.200000 0.063200 0.170000 0.060600 0.150000 0.058500 0.120000 0.054800 0.100000 0.051800 0.070000 0.046200 0.050000 0.041100 0.040000 0.038100 0.030000 0.034300 0.020000 0.029300 0.010000 0.021900 0.005000 0.015800 0.002000 0.009500 0.000000 0.000000 0.000000 0.000000

55

0.002000 -0.009300 0.005000 -0.016000 0.010000 -0.022100 0.020000 -0.029500 0.030000 -0.034400 0.040000 -0.038100 0.050000 -0.041200 0.070000 -0.046200 0.100000 -0.051700 0.120000 -0.054700 0.150000 -0.058500 0.170000 -0.060600 0.200000 -0.063300 0.220000 -0.064700 0.250000 -0.066600 0.280000 -0.068000 0.300000 -0.068700 0.320000 -0.069200 0.350000 -0.069600 0.370000 -0.069600 0.400000 -0.069200 0.420000 -0.068800 0.450000 -0.067600 0.480000 -0.065700 0.500000 -0.064400 0.530000 -0.061400

56

0.550000 -0.058800 0.580000 -0.054300 0.600000 -0.050900 0.630000 -0.045100 0.650000 -0.041000 0.680000 -0.034600 0.700000 -0.030200 0.730000 -0.023500 0.750000 -0.019200 0.770000 -0.015000 0.800000 -0.009300 0.830000 -0.004800 0.850000 -0.002400 0.870000 -0.001300 0.890000 -0.000800 0.920000 -0.001600 0.940000 -0.003500 0.950000 -0.004900 0.960000 -0.006600 0.970000 -0.008500 0.980000 -0.010900 0.990000 -0.013700 1.000000 -0.016300 A2: Airfoil data for NACA 4412

0.0000000 0.0000000 0

0.0005000 0.0023390 0

0.0010000 0.0037271 0

57

0.0020000 0.0058025 0

0.0040000 0.0089238 0

0.0080000 0.0137350 0

0.0120000 0.0178581 0

0.0200000 0.0253735 0

0.0300000 0.0330215 0

0.0400000 0.0391283 0

0.0500000 0.0442753 0

0.0600000 0.0487571 0

0.0800000 0.0564308 0

0.1000000 0.0629981 0

0.1200000 0.0686204 0

0.1400000 0.0734360 0

0.1600000 0.0775707 0

0.1800000 0.0810687 0

0.2000000 0.0839202 0

0.2200000 0.0861433 0

0.2400000 0.0878308 0

0.2600000 0.0890840 0

0.2800000 0.0900016 0

0.3000000 0.0906804 0

0.3200000 0.0911857 0

0.3400000 0.0915079 0

0.3600000 0.0916266 0

0.3800000 0.0915212 0

0.4000000 0.0911712 0

0.4200000 0.0905657 0

58

0.4400000 0.0897175 0

0.4600000 0.0886427 0

0.4800000 0.0873572 0

0.5000000 0.0858772 0

0.5200000 0.0842145 0

0.5400000 0.0823712 0

0.5600000 0.0803480 0

0.5800000 0.0781451 0

0.6000000 0.0757633 0

0.6200000 0.0732055 0

0.6400000 0.0704822 0

0.6600000 0.0676046 0

0.6800000 0.0645843 0

0.7000000 0.0614329 0

0.7200000 0.0581599 0

0.7400000 0.0547675 0

0.7600000 0.0512565 0

0.7800000 0.0476281 0

0.8000000 0.0438836 0

0.8200000 0.0400245 0

0.8400000 0.0360536 0

0.8600000 0.0319740 0

0.8800000 0.0277891 0

0.9000000 0.0235025 0

0.9200000 0.0191156 0

0.9400000 0.0146239 0

0.9600000 0.0100232 0

59

0.9700000 0.0076868 0

0.9800000 0.0053335 0

0.9900000 0.0029690 0

1.0000000 0 0

0.0000000 0.0000000 0

0.0005000 -.0046700 0

0.0010000 -.0059418 0

0.0020000 -.0078113 0

0.0040000 -.0105126 0

0.0080000 -.0142862 0

0.0120000 -.0169733 0

0.0200000 -.0202723 0

0.0300000 -.0226056 0

0.0400000 -.0245211 0

0.0500000 -.0260452 0

0.0600000 -.0271277 0

0.0800000 -.0284595 0

0.1000000 -.0293786 0

0.1200000 -.0299633 0

0.1400000 -.0302404 0

0.1600000 -.0302546 0

0.1800000 -.0300490 0

0.2000000 -.0296656 0

0.2200000 -.0291445 0

0.2400000 -.0285181 0

0.2600000 -.0278164 0

0.2800000 -.0270696 0

60

0.3000000 -.0263079 0

0.3200000 -.0255565 0

0.3400000 -.0248176 0

0.3600000 -.0240870 0

0.3800000 -.0233606 0

0.4000000 -.0226341 0

0.4200000 -.0219042 0

0.4400000 -.0211708 0

0.4600000 -.0204353 0

0.4800000 -.0196986 0

0.5000000 -.0189619 0

0.5200000 -.0182262 0

0.5400000 -.0174914 0

0.5600000 -.0167572 0

0.5800000 -.0160232 0

0.6000000 -.0152893 0

0.6200000 -.0145551 0

0.6400000 -.0138207 0

0.6600000 -.0130862 0

0.6800000 -.0123515 0

0.7000000 -.0116169 0

0.7200000 -.0108823 0

0.7400000 -.0101478 0

0.7600000 -.0094133 0

0.7800000 -.0086788 0

0.8000000 -.0079443 0

0.8200000 -.0072098 0

61

0.8400000 -.0064753 0

0.8600000 -.0057408 0

0.8800000 -.0050063 0

0.9000000 -.0042718 0

0.9200000 -.0035373 0

0.9400000 -.0028028 0

0.9600000 -.0020683 0

0.9700000 -.0017011 0

0.9800000 -.0013339 0

0.9900000 -.0009666 0

1.0000000 0 0

cfd supercritical airfoils

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