cwk_aerofoil

8/6/2019 cwk_aerofoil

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CFD Aerofoil Example - 1 David Apsley

AEROFOIL SPRING 2011

1. Notes on the program

2. Assigned exercises

1. NOTES ON THE PROGRAM

1.1 Accessing and Running the Program

The following files must be downloaded from the CFD web pages:

aerofoil.exe (user interface)streamaero.exe (CFD solver)gridaero.exe (grid-generator)

Start by double-clicking the graphical user interface. All files will be saved in the folder fromwhich you run the program.

1.2 Flow ConsideredThe program simulates 2-d, incompressible, laminar or turbulent flow around an aerofoil. The

approach-flow velocity U0 is uniform. The angle of attack may be varied.

camberthickness

chord, c

U0

x

y

The aerofoil section may be any member of the NACA 4-digit series

NACA mpth

where

m = maximum camber in percentage of chordp = position of maximum camber in tenths of chord

th = maximum thickness in percentage of chord

The default profile is the symmetric NACA 0009 aerofoil.

1.3 Non-Dimensionalisation

All variables are non-dimensionalised using the approach-flow velocity U0 and the aerofoil

chord c. The Reynolds number is defined as /Re 0cU= .


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1.4 Output to the Screen

The program outputs to screen the equation residuals and, at both backup and completion:

the upstream stagnation point and any separation or reattachment points;

minimum and maximumy+

values (see the lectures on turbulence modelling);

drag and lift coefficients, based on force components (per unit span) parallel andperpendicular to the approach flow:

cU

dragcD 2

021

= ,cU

liftcL 2

021

=

1.5 Main ButtonsGrid

[Set up laminar] set grid and aerofoil parameters for the default laminar flow

[Set up turbulent] set grid and aerofoil parameters for the default turbulent flow[Edit parameters] edit grid and aerofoil parameters

[Run] run the grid-generator

Case

[Set up] set default flow, transition and flow-specific plot parameters

[Edit parameters] edit case parameters (including angle of attack)

Solver

[Set up laminar] set parameters for a default laminar-flow calculation (Re = 103)

[Set up turbulent] set parameters for a default turbulent-flow calculation (Re = 106)

[Edit parameters] edit individual solver parameters[Run] run the CFD solver

Plots

[Set near] set parameters for a default plot focused on the aerofoil

[Set far] set parameters for a default plot showing the whole domain

[Edit parameters] edit general plot parameters

[Grid] plot the grid

[Streamlines] plot streamlines

[Pressure] plot pressure contours

[Turbulent KE] plot turbulent-kinetic-energy contours

[Vectors (all)] plot mean-velocity vectors at all nodes

[Vectors (regular)] plot interpolated mean-velocity vectors on a regular grid (**)

[Profiles] plot streamwise-mean-velocity profiles along the aerofoil (**)

(**) Regular-grid velocities and profiles are only output at the end of a flow calculation.

Graphs

[cp] plot a graph of pressure coefficient

[cf] plot a graph of skin-friction coefficient

Hard copy

[File] save the current plot as a picture file (type .png)


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1.6 User-Defined ParametersThe [Edit parameters] buttons launch menus for grid, case, solver and plot parameters. The

program carries out some checks to exclude unreasonable values, but it is not foolproof.

Grid Parameters

Aerofoil parameters

m maximum camber in percentage of chord

p position of maximum camber in tenths of chord

th maximum thickness in percentage of chord

Size of domain

xMax downstream extent of grid

Radius upstream extent of grid from leading edge

Numbers of cells

NChord number of cells along the chord of the aerofoil

NWake number of cells downstream of the aerofoil

NRadius number of cells in a radial direction

Minimum cell dimensions

Dx1 nominal width of the cell at the upstream end of the aerofoil

Dx2 nominal width of the cell at the downstream end of the aerofoil

Dy1 nominal depth of cells adjacent to the aerofoil

Elliptic-grid-generator parametersMaximum number of iterations

Tolerance for convergence of the grid generator

Over-relaxation parameter

There are hard-coded limits in the flow solver for the maximum numbers of cells.

Case Parameters

Angle of attack, .

Laminar-to-turbulent transition points on the aerofoil surface (as percentage of chord).

Free-stream turbulence intensity and turbulent-to-molecular viscosity ratio.

Presentation grid (regular rectangular array for interpolated velocity vectors); specify

the first and last coordinates and the number of points in each directions.

The length of the lines along which velocity profiles are computed.

Parameters for the pressure-coefficient (cp) and skin-friction-coefficient (cf) graphs.

Solver and Plot Parameters

There are many of these. Hopefully, the menus are self-explanatory.


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2. ASSIGNED EXERCISESLaminar Flow(L1) Grid Generation

Set up and generate the default grid for a laminarflow. Include suitable plots of the grid in

your report.

(L2) Symmetric Aerofoil

Set up the default case and laminar-flow parameters. Calculate the flow and include plots of

streamlines, shaded pressure contours, velocity profiles (not vectors) and the cp graph in your

report.

(L3) Aerofoil Drag

For the calculation above record the drag coefficient cD. Repeat grid and solver calculations

for a grid with double the number of grid cells in each direction (i.e., double NChord,

NWake and NRadius and re-run the grid generator and flow solver). Does your solution

give a satisfactorily grid-independent value for drag? Compare your results for drag

coefficient with the Blasius theory for aflat plate of similar length:

Re

33.1=Dc (per side)

Suggest reasons for any differences.

(L4) Angle of Attack

Returning to the default grid and aerofoil section and default laminar flow parameters (with

Re = 1000) compute the flow at angles of attack 3 and 6. In each case:

record drag and lift coefficients (as reported by the program);

record any separation point (as reported by the program);

plot streamlines, shaded pressure contours, velocity profiles and cp graphs.

Note that the program reports all points of flow reversal. You should exclude any

corresponding to stagnation or reattachment points.

Explain how flow separation can be identified from the skin-friction graph and how lift can

be estimatedfrom the pressure-coefficient graph. Why is this only an estimate?

(L5) Reynolds Number

With the default grid and aerofoil section calculate the flow around the aerofoil at an angle of

attack 6 with Reynolds numbers of 200 and 5000, recording drag and lift coefficients and

any separation point. What effects does the Reynolds number have on flow separation and onthe drag and lift coefficients and why?


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(L6) Camber and Thickness.

Generate the grid with default cell parameters but cambered aerofoil (NACA 2309). Compute

flow with Re = 1000 and angle of attack 3. Repeat for a thicker aerofoil (NACA 2312).

Record the drag and lift coefficients in each case and, by comparison with your earlier

symmetric-aerofoil calculations, comment on the effects of camber and thickness.

(L7) Lift and Drag

The code produces a data file surface.dat containing columns with the following data:

x/c y/c cp cf x/c y/c

wherex andy are cell-face-centre coordinates on the

surface of the aerofoil, and ( x, y) is the

corresponding surface line segment. cp and cf are

pressure and skin-friction coefficients defined by:

2

021 U

ppcp

= ,2

021 U

cf =

is the shear stress acting tangentially to the surface

in the direction of x, which here corresponds to aclockwise traversal of the aerofoil. For a NACA

2312 aerofoil, at Reynolds number 1000 and angle

of attack 3, show how to use this data to produce

drag and lift coefficients for the aerofoil, separating

each into pressure and viscous components.

Confirm that the overall drag and lift coefficients yield the values reported by the program.

Turbulent FlowSet up the default grid parameters for a turbulentflow. Run the grid generator. Set up the

default turbulent flow (Re = 106; Launder-Sharma turbulence model).

(T1) Lift as a Function of Angle of Attack

For the default symmetric aerofoil (NACA 0009) compute the flow for angles of attack

= 0, 3, 6, 9, 12. Plot graphs of lift and drag coefficients against angle of attack,

comparing your lift data with theory for a thin-chord symmetric aerofoil (White, Chapter 8):

sin2Lc

(T2) Effect of Camber

Repeat the calculations and graphs in T1 above for the cambered NACA 2309 aerofoil. This

time compare the computed lift coefficient with

)2

sin(2c

hcL + (h = maximum camber; angle in radians!)

AEROFOIL

x

y

)

,

(),( xyAA yx ==A

(Outward) area vector


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(T3) Turbulence Models

For the cambered NACA 2309 aerofoil and angle of attack 3 try computing the flow with the

following turbulence models (adjusting under-relaxation factors if necessary):

Linear eddy-viscosity models:

Launder-Sharma k- (the default); Menters SST k- model

Non-linear eddy-viscosity models:

Craft-Launder-Suga

Apsley-Leschziner

Reynolds-stress model Hanjalic and Jakirlic

In the last case you will have to reduce the turbulence under-relaxation factor (substantially).

If you wish to see all the equation residuals then you will also have to increase the width of

the command window showing these right-click on its header bar, then choose properties

and the layout tab.

For each turbulence model record results for drag and lift coefficients and plot velocity

profiles (not vectors). Comment on how these vary between turbulence models (if at all).

(T4) Transition

Using the aerofoil from T3 above, a 3 angle of attack and the Launder-Sharma model, set the

transition points at 40% chord on the lower (pressure) surface and 30% chord on the upper

(suction) surface of the aerofoil. Note and explain the effects (if any) on drag and lift.

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