B. Schmutz, le 9/3/06 tut PROFIL H105.fm

-1

A

CFD

GUIDLINETO

SIMULATE

THE

FLOW

AROUND

AN

AIRFOIL

1 Introduction

1.1 Objective

.

The main goal of this exercise is to give the cfd-newcomer the opportunity to simulate in an almost autonomous way the flow around an airfoil with cfd. To make so a minimum of indications will be imparted.

1.2 Procedure

.

look for profile coordinates and polar curve

.

import the profile coordinates into

Gambit

.

draw the 2D profile in its surrounding flow, and mesh this computational domain

.

simulate the incompressible, 2D and turbulent airflow around the airfoil with

Fluent

.

investigate pressure and velocity fields, flow trajectories, lift, drag and moment coefficients.

2 Profile data

2.1 downloading the profile coordinates

.

with your favourite browser go to:http://www.nasg.com/afdb/list-polar-e.phtml

.

check polar availabilitybrowse the list for your favourite profile e.g.

Speer H105

.

load profile coordinatesSearch -> Airfoil -> “H105”

“speer H105(...”

.

Save as .dat or .txt file

.

Prepare coordinates for

Gambit

open the .dat file into

Excel

DelimitedStart import at row 2 (where coord. begin),

Space delimited,

if column A is empty, remove itfill column C with 0be sure that the trail edge point appearonly one time (suppress redundant point where necessary)

save as Text (Tab delimited)

2.2 Read profile coordinates into

Gambit

.

File->Import->Vertex Data->Browse....Accept/Accept

.

Geom->Edge->Create Edge/NURBS

Proceed with several nurbs (6 to 8) containing a measured amount of vertex. Check that the

nurb

s are all “healthy” and connected

.

3 Geometry

.

Geom->Face->Form Face/Wireframe

Searchv ShowAirfoilContourData

vNext

v NextFinish

Yes

B. Schmutz, le 9/3/06 tut PROFIL H105.fm

-2

assemble all

Nurbs

into an airfoil-profile face

.

rotate the profile to the desired angle of attack:-3°, -1°, 1°, 2°, 3°, 4°, 6°, 8°, 10°, 12°

.

Create the computational domain with 2 rectangular faces

The dimensions of the computational domain should be at least 3 airfoil lengths in front of the airfoil, and 5 lengths behind. The displacement of the airfoil (thickness) should be not greater than 1-1.5% of the total cross sectional area. (This is not applicable if the domain boundaries represent the walls of a real wind-tunnel. In this case the simulation should take into account the related wall effects).In order to control the volume mesh near the airfoil, an “inner” box may be helpful. This box should extend about half a airfoil length in front, and to the sides, and about an airfoil length in the wake. This “inner-box” is not mandatory.

.

proceed by faces substraction

Be sure that the two boxes remain connected. If necessary:Geometry/Edge/connectand select the 4 outer edges of the inner box together with the 4 inner edges of the outer box and connect them

.

Choose the right solver (

Fluent

5/6)

4 Mesh

.

Determine the thickness of the first cells near the profile wall. For external flow, let:

.

; with

and

kg·m

-3

;

kg

·m

-1

·s

-1

m

1

·s

-1

for this exercise, a coarse value of 400 should be sufficient. Cell length should not exceed 2 to 3 times

.

Create a boundary layer all around the profile with about 10 layers and a growth factor of about 1.1 to 1.15

.

Create a fixed size function (Tools/Size Function) attached to the inner box with the airfoil edges as sourcesstart size = 2 to 3 times ; end size = 50 , growth factor 1.1

outer box

airfoil

velocity inlet

wall (symmetry)

pressure outlet

inner box

edges to be connected

Y P9 L!ReL---------- y+!" 30 y+ 500# #

$ 1.15= % 1.73 10 5–!= c& 55.56=

Y P

Y P Y P

B. Schmutz, le 9/3/06 tut PROFIL H105.fm

-3

.

Create a fixed size function attached to the outer box with the inner box outer edges as sourcesstart size 50 ; end size = 200 ; growth factor 1.1

.

mesh successively the inner and the outer box with tri-elements

.

visualize the mesh, check it for skewness; smooth it or move some nodes where necessary

.

Define the boundaries, pay attention to separate the airfoil wall from the other walls

.

Export the 2d Mesh

.

leave

gambit

to unlock licenses

5 Case setting in

Fluent

5.1 Verifying and visualizing the mesh

.

Read and Check the grid

5.2 Define the physical model

Solver

.

Segregated

continuity equation is first solved for all cells, then Momentum and then turbulence. This works well for incompressible and moderate compressible flow

.

Implicit

(each equation is solved for all cells together with actual data. The implicit solver brings faster convergence)

.

2D; Steady

(airfoil velocity will be constant and we don’t expect instabili-ties. Nevertheless, it could be possible that by some angle of attack, an unsteady wake appears.)

Viscous

.

k-epsilon

a robust and efficient turbulent model which gives good results in most cases where turbulence have an isotropic repartition

.

to begin with: Standard

exaggerate wall viscosity effects and delays boundary layer sep-aration, but very robust in term of convergence

.

then Realizable

gives better results by positive pressure gradient in the flow direction and when it is not clear where flow separation should take place.

.

to begin with Standard Wall Functions

velocity profiles from experiments will be paste onto the sub-boundary-layers. This allows the relative coarse mesh that we build.

.

then Non Equilibrium Standard Wall Functions

better by curvature or pressure gradient in the flow direction

.

Spallart-Allmaras turbulence model has less physics inside, but is well tuned for aircraft aerodynamics thanks of years of experiments.

Energy

with normal sailplane-speed is ,so there are no notice-able compressible or heating effects to capture.

5.3 Operating conditions

.

precision will be enhance by calculating with relative pressure

.

there are no influence of gravity effects in such an air flow

5.4 material properties

.

air is considered as incompressible:

: kg·m

-3

.

Fluent

means dynamic viscosity: kg

·m

-1

·s

-1

5.5 boundary conditions

inlet

.

A turbulence Intensity of 0.5%, and a viscosity ratio of 5 should be representative of a wind tunnel flow, or calm atmospheric flight.

outlet

.

let have atmospheric pressure at the outlet; so type 0 Pa in the “Gauge pressure” field

. 2% in the “Backflow Turbulence-intensity”-field

. 20 for viscosity ratio

Y P Y P

Ma 0.3<

Ma 0.3< $ 1.15=% 1.73 10 5–!=

B. Schmutz, le 9/3/06 tut PROFIL H105.fm -4

so if there is a backflow through the outlet-edge, it will be mod-elled with more or less realistic values

top and bottom wall. with the very coarse mesh we made by the top and down walls, it is

impossible to capture a correct boundary layer on this walls, so we have to let the fluid glide on them (set shear stress to 0) or make them symmetry-plane.

airfoil profile. An airfoil surface is very smooth, no slip condition with a wall

roughness of 0 should be used

fluid. the air we defined

5.6 mathematical solver model. Solve -> Controls -> Solution

- let the standard relaxation factors for all variables- begin the solution with the most simple numeric scheme (1st. order)

5.7 Initialize the flow field. Initialize with the inlet flow values

This will attribute to all cells of the model, the velocity, pressure and turbulence values that we defined for the inlet. Those are not the correct values, but they are much better than “zero” and lead to a faster convergence to the “physically correct” values.

5.8 Various

Monitoring convergence. Enhance the plotting of the Residuals

So we will be able to follow the convergence of the solution on the monitor

References Values. Report->Reference values:

compute from inlet

An Area of 1 m2, a depth of 1m and a length of 1m are all coher-ent with our airfoil

Save the model caseUnder: h105_angleofattack_yourname,e.g.: “h105_3_bongg1”

6 Processing simulation

6.1 Calculate solution. Iterate with 1st order scheme until good tendency of convergence is shown. save case and data. Enable two monitors for lift and drag coefficients. Define monitor points for pressure or velocity at a particular point in the wake

region and enable its monitoring. switch to realisable model with non equilibrium wall functions. Iterate with 1st order scheme until good tendency to convergence is shown. ask for smaller convergence criterion (e.g. 10-5 for continuity). Iterate with 2nd order scheme. Carry on calculation until all monitors as well as

drag and lift coefficient show constancy

6.2 Occurrence of transient phenomena!. The development of an transient wake is physically possible. During the steady-

state solution process, time-dependence of the configuration can be detected by several criteria:

- Residuals especially for Reynolds Stresses don’t “come down” - Monitors for Drag and Lift are oscillating around a constant value - Solution process takes a long time in terms of number of itera-tions - Plot of Velocity Vectors in the wake of the airfoil, shows vari-ance during the iterative process, even if residuals are nearly constant (vectors can be displayed via the Animate Panel in Flu-ent 6, and one might display them every 250 iterations)

. If transient wake occurs estimate its frequency as follow

(6.a)

k '–

fSt c&!

l---------------=

B. Schmutz, le 9/3/06 tut PROFIL H105.fm -5

Strouhal Number characteristic length = profile thickness,The Frequency gives the number of periodical variations per sec-ond. Each variation should be resolved by at least 30 time steps, although 50 would be better. This gives the time-step for the cal-culation. The correctness of the time-step is verified if the conti-nuity residual drops about 2 orders of magnitude from the beginning of the time-step within 20 iterations. To obtain a meaningful solution for time averaging a periodical behaviour of the flow field has to appear. Therefore at least 10 (20 would be better) periods have to be calculated. Besides the transient parameters, the model set-up is the same as for steady-state sim-ulations.

7 Post-Processing

7.1 check . on the airfoil profile

7.2 Grid independence . By good cfd-practice, you should ensure that solution is grid-independent and

use grid adaption to modify the grid or create additional meshes for the grid-independence study. Anyhow, to save time, we will bypass this important step!

7.3 Visualise and analyse. pressure field. velocity field. turbulence kinetic energy , turbulence dissipation rates , vortricity . velocity vectors. passlines

. Checked to see that the solution makes sense based on engineering judgment. If flow features do not seem reasonable, you should reconsider your physical mod-els and boundary conditions. Reconsider the choice of the boundaries location (or the domain). An inadequate choice of domain (especially the outlet bound-ary) can significantly impact solution accuracy.

.

7.4 Calculate. Drag , Lift and Moments-factors ; compare with wind tunnel measure-

ments or third party simulation.Moments are measured at a quarter length of the airfoil, so set the Moment center to m and .

. Aerodynamic forces due to pressure and wall friction

7.5 Estimate. the boundary layer thickness and compare it with the one of the flat plate

8 Transmitting your results until 25.04.2006. Use Moodle. copy in there your following files

.jou .trn

.msh .cas

.dat and some nice plots your made

St 0.25(l

y+

k ' )

cd cl cM

x 0.25= y 0=