Numerical prediction of the flow around a marine propeller

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1 Numerical prediction of the flow around a marine propeller Mitja Morgut Department of Naval Architecture, Ocean and Environmental Engineering, DINMA University of Trieste Trieste, Italy September 14, 2009

2 Outline 1 Road Map 2 Numerical Method Computational Domains Results simplesrffoam 3 Full Cavitation Model 4

3 Road Map

4 Road Map Road Map

5 Numerical Method Computational Domains Results simplesrffoam

6 Numerical Method Numerical Method Computational Domains Results simplesrffoam The developed CFD procedure: considers only one passage blade employs a MFR (Multiple Frame of Reference) approach meshes are generated using ANSYS ICEM CFD 11 calculations are performed with MRFSimpleFOAM turbulence is modelled using SpalartAllmaras model

Numerical Method Computational Domains Results simplesrffoam Computational Domains In this case simulations were performed using two different computational domains: Hmid Lmid L1 L2

7 Numerical Method Computational Domains Results simplesrffoam Computational Domains In this case simulations were performed using two different computational domains: Hmid Lmid L1 L2 H2 DOMAIN A Rotating Fixed 0.17D 0.76D 1.5D 5D 1.38D Hmid Lmid L1 L2 H2 DOMAIN B Rotating Fixed 0.17D 0.76D 1.5D 5D 4.3D D = Diameter of the Propeller Lmid = Length of part Rotating

Propeller E779a Numerical Method Computational Domains Results simplesrffoam 1.0 10

8 Propeller E779a Numerical Method Computational Domains Results simplesrffoam K Q Exp. Data MRF Domain A MRF Domain B K T, 10K Q 0.5 K T J ɛ(k T )% = K T,NUM K T,EXP K T,EXP 100 ɛ(k Q )% = K Q,NUM K Q,EXP K Q,EXP 100 Domain A Domain B J ɛk T (%) ɛk Q (%) ɛk T (%) ɛ(k Q )(%) The INSEAN E779A Propeller Dataset, INSEAN Propulsion and Cavitation Laboratory, 2006

9 SimpleSRFFoam Numerical Method Computational Domains Results simplesrffoam Simulation on Domain A Suction Side Pressure Side Comment: Pressure distribution completely wrong. (J=0.695) Simulation on Domain B Under Investigation

10 Full Cavitation Model

11 Full Cavitation Model In momentum equation, subgrid viscosity (µ S ) replaced by turbulent viscosity (µ t ) interphasechangefoam surfacescalarfield muf = twophaseproperties->muf() + fvc::interpolate(rho*turbulence->nusgs()); fvvectormatrix UEqn ( fvm::ddt(rho, U) + fvm::div(rhophi, U) - fvm::sp(fvc::ddt(rho) + fvc::div(rhophi), U) - fvm::laplacian(muf, U) - (fvc::grad(u) & fvc::grad(muf)) ); surfacescalarfield mueff = ( mueff, twophaseproperties->muf() + fvc::interpolate(rho*turbulence->nut()) ); fvvectormatrix UEqn ( fvm::ddt(rho, U) + fvm::div(rhophi, U) - fvm::sp(fvc::ddt(rho) + fvc::div(rhophi), U) - fvm::laplacian(mueff, U) - (fvc::grad(u) & fvc::grad(mueff)) );

12 Full Cavitation Model, Theory The momentum conservation equation for the mixture is: Full Cavitation Model t (ρm v m) + (ρ m vm v m) = p + [µ m( v m + v T m )] + ρm g + F (1) The mass conservation equation for the mixture t (ρm) + (ρm v m) = 0 (2) The ρ m f v (Mixture density - vapour mass fraction) relationship The vapour phase (α v ) volume fraction 1 ρ m = fv ρ v + 1 fv ρ l (3) α v = f v ρ m ρ v = 0 (4)

13 Full Cavitation Model, Theory Full Cavitation Model The trasport equation for the vapour mass fraction f v t (ρmfv ) + (ρm v mf v ) = (Γ f v ) + R e R c (5) The source terms: 8 >< >: q V R e = C ch e γ ρ l ρ 2 p v p v (1 f 3 ρ v ), when p < p v l q V R c = C ch c γ ρ l ρ 2 p p v l f 3 ρ v, when p > pv l (6) V ch = k, C e = 0.02, C c = 0.01 (7) Singhal, A.K., et. al., 2002, Mathematical Basis and Validation of the Full Cavitation Model, J. Fluids Eng., 124, pp

14 Full Cavitation Model Full Cavitation Model, Implementation, MyFCM In the solver interfoam, the GammaEqn.H was replaced by the trasport equation for the vapour mass fraction, (Eqn. (2)). The mixture density is computed using Eqn. (3). fvscalarmatrix feqn ( fvm::ddt(rho, f) + fvm::div(rhophi, f) - fvm::laplacian(mueff, f) + fvm::sp(spcoeff,f) - ScCoeff ); solve ( feqn ); rho=scalar(1)/((f/rho2)+((1-f)/rho1)); rhophi=phi*fvc::interpolate(rho);

15 Venturi Type Section Full Cavitation Model Ventury-type section 1 σ = 2.4, V ref = 7.2m/s MyFCM [1] Coutier-Delgosha, O., et. al, 2003, Evaluation of the Turbulence Model Influence on the Numerical Simulations of Unsteady Cavitation, J. Fluids Eng., 125, pp

16 Naca 0015 Full Cavitation Model Contours of the Vapour Volume Fraction MyFCM Vin = 6m/s α = 8 o Re = σ = 1.2

18 What I have achieved: Procedure for the prediction of the flow around a marine propeller working in uniform flow and non cavitating conditions What I am planning to do: Investigate the influence of the turbulent model on the prediction of the performances of the propeller working in uniform flow Validate the cavitating flow solver Improve the cavitating flow solver MyFCM Develop a procedure for the prediction of the flow around a marine propeller working in uniform flow and cavitating conditions

CAVITATION PREDICTION IN A KAPLAN TURBINE USING STANDARD AND OPTIMIZED MODEL PARAMETERS

6 th IAHR International Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, September 9-11, 2015, Ljubljana, Slovenia CAVITATION PREDICTION IN A KAPLAN TURBINE