Implementing Vortex Lattice Representation of Propeller Sections - - PowerPoint PPT Presentation

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Implementing Vortex Lattice Representation of Propeller Sections - - PowerPoint PPT Presentation

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CFD with OpenSource Software 2014 Implementing Vortex Lattice Representation of Propeller Sections Developed for OpenFOAM-2.3.x Surya Kiran Peravali Chalmers University of Technology, Gothenburg, Sweden . December 1, 2014 11/30/14 Surya

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Implementing Vortex Lattice Representation of Propeller Sections

Surya Kiran Peravali CFD with OpenSource Software 2014 December 1, 2014 Developed for OpenFOAM-2.3.x Chalmers University of Technology, Gothenburg, Sweden.

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  • Resolving the flow around a ship including

a rotating propeller with high-fidelity simulation tools is always very demanding.

  • Propeller has different inflow parameters

for different flow regimes.

  • Vortex Lattice Method evaluates the basic

performance of the propeller accounting the geometry of the propeller, cross section

  • f the blade and local in flow around the

ship. Basic Idea

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Evaluating The Performance

  • Actuator

disk theory, simulating the propeller by an infinitely thin disk which adds momentum to the fluid.

  • Actuator Line Models
  • Lifting Line Method
  • Vortex lattice method
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The Lifting Line class:

  • Base class for Vortex lattice class.
  • Uses the concept of circulation
  • Replace the propeller by a single line in span

wise direction with an peace wise constant circulation.

  • Lift is calculated from kutta-joukowski theorem

from the given circulation values.

  • The induced velocities are calculated using

circulation.

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Layout:

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The Vortex Lattice Theory

  • Superimpose a finite number of horse

vortex of different strength Гij on the wing surface.

  • We apply Biot-Savart law and flow-

tangency condition to obtain a system

  • f simultaneous algebraic equations,

which can be solved for the unknown Гij .

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Aerofoil theory Cosine spacing:

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The vertical velocity induced at the nth control point by mth point vortex is: Total vertical velocity is thus,

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Introducing vector notation; Matrix of influence coefficients; From kutta joukowski theorem

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Applying Vortex Lattice method to propellers:

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Introducing solidity σ, radial coordinate x=r/R and slope of CL vs α

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What we have now,

  • V* is calculated
  • α is calculated
  • The camber slope(dy/dx) will ve provided as an input (depends on type of

aerorfoil used). Blade forces The final lift force Fi on a single 2D blade section is calculated according to Kutta-Joukowski theorem. The final drag force Fv is calculated with a given blade section drag coefficient Cd and the profile chord length c and aligned with the total inflow velocity V.

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Body Forces: Momentum Equation: The body forces are projected onto the volume grid utilizing Gaussian Projection: is the point force at radius i. fi (r) is the body force projected. r is the distance between control point i and a grid cell. ε is a control parameter for the projection.

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Features:

  • Model the propeller forces in a transient simulations, accounting for
  • changes 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.
  • Effect of Blade twist.
  • Account for the cross sectional properties (aerofoil, camber, chord etc.)
  • Shape of Blade ( accounts for scewness).
  • Circulation distribution need not be specified.
  • Pitch can be varied.
  • Works also for off design conditions (contra rotating).
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Limitations

  • +x must be east, +y must be north and +z must be up.
  • The propeller geometry has to be specified.
  • There is no hub-effect taken into account.
  • Accounting for cross flow parameters.
  • The interpolation for the outermost vertex radii needs to be improved.
  • Only for convention propellers.
  • No output plots regarding performance such a efficiency , Thrust etc.
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Implementation

  • The model is implemented as a class and can be an object of any solver.
  • In case we implement with pisoFoam.

Copy the pisoFoam solver to your user directory for applications in the solvers for propulsion. cp -r $FOAM_APP/solvers/incompressible/pisoFoam \ $WM_PROJECT_USER_DIR/applications/solvers/propulsion Rename the pisoFoam solver to pisoFoamVLM2D and rename the solver code to pisoFoamVLM2D.C. cd $WM_PROJECT_USER_DIR/applications/solvers/propulsion/ mv pisoFoam pisoFoamVLM2D mv pisoFoamVLM2D/pisoFoam.C pisoFoamVLM2D/pisoFoamVLM2D.C

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In the createFields.H file in the pisoFoamVLM2D solver add the following lines to declare the object: propellerModels::openPropVLM2D propellers(U); Include the header file of the class (openPropVLM2D.H) in the pisoFoamVLM2D.C solver code: #include "openPropVLM2D.H" Now add the body force to the momentum equation: // Pressure-velocity PISO corrector // Momentum predictor fvVectorMatrix UEqn ( fvm::ddt(U) + fvm::div(phi, U) + turbulence->divDevReff(U)

  • propellers.force()

);

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Update the propeller models by adding propellers.update() function before runtime.write() in pisoFoamVLM2D.C. turbulence->correct(); Info<< "turbulence corrected" << endl; Info<< "start propeller update" << endl; //Update the propeller array. propellers.update(); runTime.write();

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The pisoFoamVLM2D solver is already provided in the files provided. Other alternative procedure is to directly extract VLM_tutorial.tar.gz to your user directory: tar -xvzf VLM_tutorial.tar.gz -C ~/OpenFOAM/$WM_PROJECT_USER_DIR Compilation For the compilation of the new solver we have to modify the files in

  • Makedirectory. Change Make/fies to:

pisoFoamVLM2D.C EXE = $(FOAM_USER_APPBIN)/pisoFoamVLM2D

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Change Make/options to: EXE_INC = \

  • I$(LIB_SRC)/turbulenceModels/incompressible/turbulenceModel \

. . .

  • I$(LIB_SRC)/finiteVolume/lnInclude \
  • I$(WM_PROJECT_USER_DIR)/src/propellerModels/lnInclude

EXE_LIBS = \

  • L$(FOAM_USER_LIBBIN) \
  • lincompressibleTurbulenceModel \
  • lincompressibleRASModels \
  • lincompressibleLESModels \
  • lincompressibleTransportModels \
  • lfiniteVolume \
  • lmeshTools \
  • luserPropellerModels
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First compile the class before compiling the solver: cd $WM_PROJECT_USER_DIR/src/propellerModels wmake libso Now compile the new solver: cd $WM_PROJECT_USER_DIR/applications/solver/propulsion/pisoFoamVLM2D wmake

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Test propeller N4148 The propeller specic data are provided in. constant/propellerProperties/n4148 NumBl 3; TipRad 0.5; HubRad 0.1; Js 0.833; Vs 1; CTPDES 0.5505; OverHang 0.01; Baseline2Shft 0.5; ShftTilt 0.0; Rake (0 0 0); YawRate 0.0; SpeedControllerType "none"; YawControllerType "none"; sectionPoints 10; meanADchord 0.1763; a0 1; BladeData ( // r/R c/D Cd Pitch(P/D) ( 0.200 0.1600 0.08 0.9921 ) ( 0.300 0.1818 0.08 0.9967 ) . . camberSlope (.7223 0.1953 0.1069 0.0427 0.0075 -0.0739 -0.1081 -0.1158

  • 0.1089 -1.2228);
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Openwater

  • Test case of propeller N4148 working in a

box with undisturbed inflow.

  • The set up is essentially taken from the

pisoFoam tutorial for a RASModel.

  • The initial conditions for the k- ε

turbulence model are taken from the LiftingLine tutorial.

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One propeller is included in the domain ts position is given in constant/propellerArrayProperties The simulation starts at 0 time step and runs for 20 seconds blockMesh pisoFoamVLM2D propeller0 { propellerType "n4148"; baseLocation (3.0 1 0.5); numBladePoints 10; pointDistType "uniform"; epsilon 1; smearRadius 0.25; sphereRadiusScalar 1.1; tipRootLossCorrType "none"; rotationDir "cw"; Azimuth 0.0; RotSpeed 72.02; NacYaw 270.0; }

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Openwater Result

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Wake

  • Test case of the same propeller in a box with

some blockage to simulate roughly a some wake.

  • Non-uniform force generation.
  • Implement parallel computation.

blockMesh decomposePar mpirun -np 4 pisoFoamVLM2D -parallel reconstructPar

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Fully Developed Flow:

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Comparison with MPUF 3A code:

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Chord wise properties:

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Future Work

  • Creating an 3D model and testing with variable cross

section.

  • Introduce the effect due to Hub.
  • Improvising the mesh and capture the tip vortices.
  • Applying to non- conventional propellers.
  • Introduce model to real ship wake.