Extension of the OpenFOAM CFD tool set for modelling multiphase flow

Transcription

1 Extension of the OpenFOAM CFD tool set for modelling multiphase flow Ridhwaan Suliman Johan Heyns Oliver Oxtoby Advanced Computational Methods Research Group, CSIR South Africa CHPC National Meeting, Durban, 5-7 December 2012

2 Overview

3 Applications Energy Process Casting analysis Microfluidics Naval Hydro

4 OpenFOAM Open source CFD tool set Modular (OOP C++ with templates) Extensive set of libraries Large community Problem Extended software Solution Modified problem Existing software Modified solution

5 Free surface modelling In two-fluid flow governing equations ρu i t u i x i = 0 α t + (αu x i ) i = 0 + x j ( ρui u j ) p x i = Improvements/Extensions: Surface capturing Non-isothermal Heat and mass transfer Chemical reactions Surface tension x j ( µ u ) i + ρg x i j

6 Volume-of-fluid Navier-Stokes with volume fraction α(x i,t) = Mixture properties ρ = αρ l + (1 α)ρ g µ = αµ l + (1 α)µ g { 1 for the point (xi,t) in the liquid 0 for the point (x i,t) in the gas αu x2+ x x 1 gas αu x1 x 2 αu x1+ x x 2 δx2 Advantages Conservative Merging and breakup of free-surface Arbitrary unstructured 3D (parallel) liquid αu x2 x 1 δx1

7 Higher-resolution artificial compressive scheme (HiRAC) α n+1 α n = 1 [ (ui α) n+1 t 2 x + (u i α) n ] i x [u c i x i α(1 α)] n+1 i Temporal discretisation: 2 nd order Crank-Nicolson Spacial discretisation: Blended higher-resolution TVD slope limiting Artifical compressive term: Normal to interface ψ 2 1 First order downwinding CBC Central differencing 1 2 TVD κ-scheme Second order upwinding First order upwinding r

8 Violent sloshing Experimental MULES CICSAM HiRAC vlc.png Pressure t (s)

9 Liquid rocket fuel sloshing High fidelity numerical sloshing code Low cost alternative Various geometrical and loading conditions Automated pre- and post-processing Compare with linear wave sloshing experiments Case study: Space vehicle entering jet stream Sharp lateral loading Characterise realistic non-linear sloshing in tank

10 Linear wave sloshing Cylindrical tank, no baffles

11 Linear wave sloshing Cylindrical tank with baffle

12 Non-linear violent sloshing vlc.png vlc.png vlc.png No baffles S/R = 0.1, W/R = 0.1 S/R = 0.1, W/R = 0.2

13 Non-linear violent sloshing induced forces on the tank: No baffles S1W1 S1W No baffles S1W1 S1W2 Forces in x direction, Fx (N) Forces in Y direction, Fy (N) Time, t (s) Lateral direction Time, t (s) Vertical direction

14 Assumptions In fluid - density variations negligible except in buoyancy term Immiscible fluids Averaged VOF energy equation T ρ k c p t + ρ T kc p u j ( ) T k m x j x j x j Boussinesq approximation = 0 ρ k = 1 β(t T ref )

15 1D heat transfer

16 Non-isothermal multiphase flow ρ b >> ρ t ρ b > ρ t ρ b ρ t

17 Model High density ratios Low Mach number flows Large pressure variations Existing FSM solvers In Compressible Full set of equations Long wave acoustics

18 Assumptions Homogeneous flow (u g = u l, p g = p l ) Low mach number flow Isothermal Non-dimensional analysis (ρu i ) t Ideal gas law α t + (αu j ) = 0 x j (1 α) ρ g ρ g t + (ρu i u j ) + p = x j x i = u j x j x j ρ g ρ g o = 1 cg 2 (p p o ) ( µ u i x j ) + αρ l g i

19 Validation: vlc.png

20 Validation: Absolute Relative

21 Non-isothermal and weakly flows Assumptions Low mach number flow Large density ratios (liquid-gas) Non-dimensional analysis α t + (αu j ) = 0 x j (1 α) 1 P ρ g RT t (1 α) 1 T T t (ρu i ) + (ρu i u j ) + p = t x j x i T t + u T j ( ) T k m = x j x j x j Equations of state = u j x j x j ρ g = P RT ; ρ l = 1 β(t T ref ) ( µ u i x j ) + ρ k g i 1 D(1 α)p ρ k c p Dt

22 Non-isothermal compression vlc

23 OpenFOAM tool set Modular, easily extensible Large community Multiphase modelling applications Violent sloshing of fuel in aircraft and rockets Non-isothermal flows formulation Low Mach number multiphase flows with heat transfer