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Background Lifting Line Method Possibilities Limitations Implementation Compiling the code Test case Propeller Test case

Propller Lifting Line implementation

Florian Vesting

2012-10-18

Florian Vesting Propeller Lifting Line 2012-10-18 1 / 22


Basic idea

Resolving the flow around a shipincluding a rotating propellerwith high-fidelity simulationtools is always very demanding

Detailed flow analysis is oftenonly subject to academicresearch

Lifting Line Method in a hybridapproach can provide basicperformance of the propeller,while accounting for the localflow around a ship



What is available

Actuator disk theory, simulatingthe propeller by an infinitelythin disk which adds momentumto the fluid

Actuator line models

Vortex lattice methods,modeling a 3D propeller blade



Actuator Line Turbine Model

Basis for the propellerLiftingLineclass

Model wind turbine blades bysection wise constant airfoilproperties

Projects normalized forces backto the flow



General Layout



Theory

Mathematical model to predictlift

Uses the concept of circulation

Replace a propeller by a singleline in span-wise direction withpeace-wise constant circulation



Lift generation

Simple model for the flow abouta wing

Based in the superposition of afreestream flow and a vortex

According to theKutta-Joukowski Theorem is liftrelated to the inflow, the vortexand the density of the fluid

L = ρVΓ (1)



Lift generation

To account for a varying liftalong the blade, each sectionhas a different circulation

To satisfy the Helmhotztheorem at each section ofcirculation has to shed a vortexfilament down the flow with thestrength δΓ

Each section of constantcirculation form hence the socalled horse shoe

δΓ =

(dΓb

dr

)∆r (2)



Induced velocities

The free vortices of one boundvortex, however, effect the allneighboring section through theinduced velocities

The total (effected) inflowvelocity V∗ on one of the 2Dsections can be calculated

V∗ = (Va + u∗a) + (ωr + Vt + u∗

t) (3)



Induced velocities

The induced velocities at a control point of a discretized blade sectionm are computed by summing the induced velocities of each horseshoe vortex

u∗(m, i) is the velocity at control point m, by horse shoe vortex ofpanel i

In order to do this one uses formulas e.g. by Lerbs or Wrench

u∗(m) =

M∑i=1

Γ(i)u∗(m, i) (4)



Blade forces

The final lift force Fi on asingle 2D blade section iscalculated according toKutta-Joukowski theorem

The final drag force Fv iscalculated with a given bladesection drag coefficient Cd andthe profile chord length c andaligned with the total inflowvelocity V∗

Fi = ρV∗ × (Γer) (5)

Fv =1

2ρ (V ∗)2CDc (6)



Body forces

Body forces are projected onto the volume grid utilizing Gaussianprojection

fi(r) =FLiftingLinei

ε3π32

exp

[−(rε

)2](7)

FLiftingLinei is the point force at radius ifi(r) is the body force projectedr is the distance between the control point i and a grid cellε is a control parameter for the projection with



Possibilities

Model the propeller forces in a transient simulations, accounting forchanges in inflow

Non uniform thrust generation

Introduce forces back to the volume grid

Run in parallel disregarding the propeller position

Create several propellers within one domain



Limitations

+x must be east, +y must be north and +z must be up

The propeller geometry and circulation distribution has to be specified

There is no hub-effect taken into account

The interpolation for the outermost vertex radii needs to be improved

For the time being not output files with the propeller performance



Implementation

The model is implemented as a classCan be an object of any solver, the standard transient solverpisoFoam:

Add the object declaration to the createFields.HpropellerModels::openPropLiftingLine propellers(U);

Add the class header file to the solver code:#include "openPropLiftingLine.H"

Add the body force vectors to the momentum equation of the solver:// Pressure-velocity PISO corrector

{

fvVectorMatrix UEqn

(

fvm::ddt(U)

+ fvm::div(phi, U)

+ turbulence->divDevReff(U)

- propellers.force()

);

Add the class function update() somewhere at the end of the timelooppropellers.update();



Compile the code

Download the liftingLineTutotial.tar.gz from the course homepageand extract it into your openFOAM user directory e.g.tar -xvzf liftingLineTutotial.tar.gz -C ~/OpenFOAM/user-2.1.x

Compile the new class as a customer librarycd user-2.1.x/src/propellerModels

wmake libso

Compile the pisoFoam solvercd user-2.1.x/applications/solvers/propulsion/pisoFoamLLprop

wmake

Now you can run the test cases which are provided. You find them incd user-2.1.x/run



Test propeller 4118

Propeller 4118 is a typical test propeller withrather simple geometryThe propeller specific data are provided in.constant/propellerProperties/4118

NumBl 3 ;TipRad 0 . 5 ;HubRad 0 . 1 ;Vs 1 ;CTPDES 0 . 5505 ;OverHang 0 . 0 1 ;B a s e l i n e 2 Sh f t 0 . 5 ;S h f t T i l t 0 . 0 ;Rake (0 0 0 ) ;YawRate 0 . 0 ;SpeedCon t r o l l e rType ”none” ;YawContro l l e rType ”none” ;BladeData(// r c/D Gamma Cd( 0 .11 0 .3113 0 .1067 0 .08 )( 0 .1295 0 .3395 0 .1616 0 .08 ). . .) ;



Openwater

Test case of propeller 4118working in a box withundisturbed inflow

The set up is essentially takenfrom the pisoFoam tutorial for aRASModel

The initial conditions for the k-εturbulence model are taken fromthe actuatorDisk tutorial



Openwater

One propeller is included in the domainIts position is given inconstant/propellerArrayProperties

The simulation starts at 0 time step and runs for 20 secondsblockMesh

pisoFoamLLprop

p r o p e l l e r 0{

p r o p e l l e rT y p e ”4118” ;ba s eLoca t i on ( 5 . 0 1 0 . 5 ) ;numBladePoints 20 ;po i n tD i s tType ” un i fo rm ” ;e p s i l o n 1 ;smearRad ius 0 . 2 5 ;s p h e r eRad i u s S c a l a r 1 . 1 ;t i pRootLos sCor rType ”none” ;r o t a t i o nD i r ”cw” ;Azimuth 0 . 0 ;RotSpeed 7 2 . 0 2 ;NacYaw 270 . 0 ;

}



Openwater Result



Wake

Test case of the same propellerin a box with some blockage tosimulate roughly a ship wake

Shows the non-uniform forcegeneration

and parallel computation

blockMesh

decomposePar

mpirun -np 4 pisoFoamLLprop -parallel

reconstructPar



Wake results


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