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AEROFOIL SPRING 2011
- Notes on the program
- 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 from which you run the program.
1.2 Flow Considered
The program simulates 2-d, incompressible, laminar or turbulent flow around an aerofoil. The approach-flow velocity U 0 is uniform. The angle of attack may be varied.
camber
thickness
chord, c
α
U 0
x
y
The aerofoil section may be any member of the NACA 4-digit series NACA mpth where m = maximum camber in percentage of chord p = 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 U 0 and the aerofoil chord c. The Reynolds number is defined as Re = U 0 c /.
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 maximum y +^ values (see the lectures on turbulence modelling);
- drag and lift coefficients, based on force components (per unit span) parallel and perpendicular to the approach flow:
U c
drag cD (^) 2 2 0
= 1 , (^) U c lift cL (^) 2 2 0
1.5 Main Buttons
Grid [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 = 10^3 ) [Set up turbulent] set parameters for a default turbulent-flow calculation (Re = 10^6 ) [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)
2. ASSIGNED EXERCISES
Laminar Flow
(L1) Grid Generation
Set up and generate the default grid for a laminar flow. 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 a flat plate of similar length:
Re
c (^) D = ( 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 estimated from 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 on the drag and lift coefficients and why?
(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 where x and y 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 2 0
1 U
p p c (^) p^ ∞
2 0
c (^) f = (^1) U
is the shear stress acting tangentially to the surface in the direction of x , which here corresponds to a clockwise 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 Flow
Set up the default grid parameters for a turbulent flow. Run the grid generator. Set up the default turbulent flow (Re = 10^6 ; 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): cL ≈ 2 sin
(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( c
h cL ≈ + ( h = maximum camber; angle in radians!)
AEROFOIL
x
y
A =( A x , Ay )=(−^ y ,^ x )
(Outward) area vector
τ
