Simplified flow around a propeller for the course CFD with ...hani/kurser/OS_CFD_2015/Gonzalo...NACA...

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Simplified flow around a propellerfor the course

CFD with OpenSource Software

Gonzalo Montero

Applied Mechanics/Fluid Dynamics,Chalmers University of Technology,

Gothenburg, Sweden

2015-12-08

Gonzalo Montero Simplified flow around a propeller 2015-12-08 1 / 37

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Contents

Introduction

Erik Svenning’s work

What can we do with propellerSimpleFoam?

Theoretical background

Mesh and m4

Xfoil

How to define a propeller

Seting up of a case

Some results and validation

Future work


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Introduction

An actuator disk is a simplification of a propeller that helps in seeing howit affects the surroundingsUseful when not to much detail is needed, can not see the flowAdd momentum directly to fluid flowing through the area it in


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Erik implemented an actuator disk model for OpenFOAM 1.5-dev.My implementation is built in top of that.


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Thrust and torque known and Goldstein optimum distribution


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What can we do with propellerSimpleFoam?

Take into account for the geometry of the propeller

Take into account the operating conditions

Analyze a propeller with different propeller sections

Obtained the polars automatically or define them


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Velocities are parametrized by ψ


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Ua = V + ua

Ut = Ωr − ut

U =√U2a + U2

t

Wa(ψ) = 0.5Ua + 0.5Usinψ

Wt(ψ) = 0.5Ut + 0.5Ucosψ

va(ψ) = Wa − Ua

vt(ψ) = Ut −Wt

α(ψ) = β − arctan(Wa/Wt)

W (ψ) =√W 2

a +W 2t

λw(ψ) =rWa

RWt

f(ψ) = 0.5B

(1− r

R

)1

λw

F (ψ) =2

πarccos(e−f )

Γ(ψ) = vt4πr

BF

√√√√1 +

(4λwR

πBr

)2

Γ =1

2Wccl


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The Newton update for psi then reads:

δψ = − R

dR/dψ

ψ ← ψ + δψ


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-15 -10 -5 0 5 10 15

α

-1.5

-1

-0.5

0

0.5

1

1.5

Cl

-1.5 -1 -0.5 0 0.5 1 1.5

Cl

0

0.02

0.04

0.06

0.08

0.1

0.12

Cd


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dT = B1

2ρW 2(cl cosφ− cd sinφ)c dr

dQ = B1

2ρW 2(cl sinφ+ cd cosφ)c r dr

Devide T with ρV nCellCirc and Q with ρV rnCellCircGonzalo Montero Simplified flow around a propeller 2015-12-08 11 / 37

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Mesh and m4


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Mesh and m4

m4 allows us to parametrize blockMeshDictvery easy to usem4 fileName.m4 > blockMeshDict


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Xfoil


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In fvSolution dictionaryTwo or three .txt files

geometry.txt

polarDistribution.txt

polarsData.txt (not compulsary)


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geometry.txt

10

0.3220 0.0568 15.8540

0.3626 0.0634 13.8499

0.3934 0.0682 12.1941

0.4450 0.0738 9.3355

0.5076 0.0761 6.3916

0.6230 0.0717 2.7624

0.7349 0.0625 0.4000

0.8468 0.0510 -1.4360

0.9586 0.0365 -3.0595

0.9900 0.0325 -3.5147


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polarsData.txt

2 //number of rows given for polar 1



-2 0.6648 0.0314 //point 1 of polar number 1

0 0.7890 0.0422 //point 2 of polar number 1







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polarDistribution.txt

10

0.382

0.3926

0.4334

0.445

0.5376

0.613

0.724

0.8558

0.9516

0.99


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Seting up of a case

OF24x

cd erikSvenning2.4/

cp -r cavityActuatorDisk $FOAM_RUN

cp cylindricalMesh.m4 $FOAM_RUN/cavityActuatorDisk/

constant/polyMesh

cp *.txt $FOAM_RUN/cavityActuatorDisk/

run

cd cavityActuatorDisk/constant/polymesh

(gedit cylindricalMesh.m4)

If wanted the mesh can be modified by cylindricalMesh.m4


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Seting up of a case

m4 cylindricalMesh.m4 > blockMeshDict

cd ../..

blockMesh

cd 0

gedit U


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Seting up of a case

internalField uniform (15 0 0);

boundaryField

inlet

type zeroGradient;

outlet

type zeroGradient;

walls

type slip;

gedit p


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Seting up of a case

internalField uniform 0;

boundaryField

inlet

type zeroGradient;

outlet

type zeroGradient;

walls

type zeroGradient;


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Seting up of a case

We have to initialize the volVectorField VolumeForce. For that lets make acopy of the U file and modify it.

cp U VolumeForce

Change the dimensions and the object to VolumeForce. The rest will beset as:

gedit VolumeForce

dimensions [0 1 -2 0 0 0 0];

internalField uniform (0 0 0);


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Seting up of a case

boundaryField

inlet

type fixedValue;

value uniform (0.0 0.0 0.0);

outlet

type fixedValue;


walls

type fixedValue;



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Seting up of a case

Now we need to create another one for the volScalarField xDimension, sosince it is a scalar this time we will copy and modify the pressure file:

cp p xDimension

gedit xDimension

Once again remember to change the dimension, in this case to meters andalso to change the object field to xDimension. Finally it should be like thisone:

dimensions [0 1 0 0 0 0 0];

internalField uniform 0;


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Seting up of a case

boundaryField

inlet

type fixedValue;

value uniform 0;

outlet

type fixedValue;

value uniform 0;

walls

type fixedValue;

value uniform 0;


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Seting up of a case

Now lets go on and modify the fvSolution dictionary.

cd ../system/

gedit fvSolution

In the SIMPLE subdictionary add:

pRefCell 0;

pRefValue 0;

Rename the actuatorDisk as propellerData. Add the missing fields so thatit ends up looking like this:


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Seting up of a case

propellerData

numberOfPolars 2;

flightSpeed 15;

deltaBeta 30;

centrePoint (15 0 0);

density 0.36518;

interiorRadius 0.49;

exteriorRadius 1.524;

rpm 500;

temperatureKelvin 216.86;

numberOfBlades 3;

dynamicViscosity 0.1433e-4;

ReRef 50000;

ReExp 0;


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Seting up of a case

In fvSolution create a subdictionary with the following structure andnamed polarsData.

polarsData

generatePolars 2;

type1 naca;

airfoilName1 2412;

type2 geometry;

airfoilName2 NACA0012.txt;

gedit fvSchemes


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Seting up of a case

and add the following change the divergence schemes so they look like:

default none;

div(phi,U) bounded Gauss upwind;

div(phi,k) bounded Gauss upwind;

div(phi,epsilon) bounded Gauss upwind;

div(phi,R) Gauss upwind;

div(R) Gauss linear;

div(phi,nuTilda) Gauss upwind;

div((nuEff*dev(grad(U).T()))) Gauss linear;

div((nuEff*dev(T(grad(U))))) Gauss linear;


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Seting up of a case

Now we are ready to run the case:

cd ..

propellerSimpleFoam


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0 0.5 1 1.5 2J

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18C

t

NACA report 640OpenFOAM


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Future work

Try to account for tip losses

Another model that allows highers speed flows

Solve the flow discretizing each blade

Compressible solver implementation


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