CFD with OpenSource software A course at Chalmers University of Technology Taught by HÅKAN NILSSON. Project work: intersettlingfoam

Transcription

1 Taught by HÅKAN NILSSON Project work: intersettlingfoa Developed for OpenFOAM Author: Pedra Rain Deceber, /21/2014 1

2 Presentation Outline: The objective of this presentation Introduction to settlingfoa Set up the case Introduction to interfoa Set up the case intersettlingfoa Final result 2/21/2014 2

3 objective this presentation In this work two solvers settlingfoa and interfoa are cobined together to predict the flow otion at the free surface of the water phase while the settling of the dispersed phase in the water phase is also considered. 2/21/2014 3

4 Drift Flux Model Field Equations The ixture of ass ixture velocity diffusion velocity settlingfoam v = α 1ρ 1 v 1 + α 2 ρ 2 v 2 ρ v 2 = α 1ρ 1 α 2 ρ 2 v 2 = α 1ρ 1 ρ v 1 v 2 ) diffusion velocities fro the drift velocity v 2 = ρ 1 ρ 2 v 2j = α 1ρ 1 α 2 ρ v 1j strea line and velocity relationship in two-phase flow Brennan 2001) 2/21/2014 4

5 settlingfoa Governing equations the continuity equations for each phase are added together to yield a ixture continuity equation t t u. u ) 0. u u the oentu equations are added to yield a single ixture continuity equation. ). P. t d c d. v v ) g M dj dj 1 d Diffusion stress Tensor flux: viscous stress Turbulent stress inter-facial oentu transfer ters, to couple the two phases together The distribution of the dispersed phase within the ixture is odelled by a convection diffusion equation derived fro the dispersed phase continuity equation. d d c. v ). v ). d dj d t 2/21/2014 5

6 Initial and boundary conditions Solver setting U P_rgh Alpha diensions [ ] [ ] [ ] Internal field Unifor 0 0 0) Unifor 0 0 0) Unifor 0 inlet type fixedvalue zerogradient fixedvalue value unifor ) unifor 0.01 outlet type pressureinletoutletvelocity fixedvalue zerogradient value unifor 0 0 0) unifor 0 walldiffuser type fixedvalue zerogradient zerogradient value unifor 0 0 0) U P_rgh alpha k epsilon Solver PBiCG PCG PBiCG PBiCG PBiCG Tolerance 1e-07 1e-07 1e-07 1e-07 1e-07 Relaxation factor Control variable value Maxiu Corrant nuber 0.5 Delta T 0.1 Maxiu delta T 1 endtie /21/2014 6

7 Mesh generation The Mesh is based on the O grid ethod for the pipe cross section //Plane A: ) // Vertex A0 = 0 //Plane B: ) // Vertex B0 = 8. // Defining blocks: blocks //Blocks between plane A and plane B: // block0 - positive x O-grid block hex ) AB ) siplegrading 5 1 1) 2/21/2014 7

8 edges //Plane A: arc ) arc ) //Plane B: arc ) arc ) // Defining patches: patches patch inlet ) ) ) ) ) ) patch outlet ) ) ) ) ) ) wall walldiffuser ) ) ) ) ) ); Radius 0.13 Length 2 Nuber of cells in radial direction 6 Nuber of cells in tangential direction 10 Nuber of cells in longitudinal direction 40 Expansion ratio in radial direction 4 2/21/2014 8

9 Dispersed phase fraction and flow field in pipe 2/21/2014 9

10 Liquid phase fraction Indicator function and phase fraction: interfoam interfoa applies the Volue of Fluid VOF) ethod which uses the volue fraction α as an indicator to indicate which portion of the corresponding cell is occupied by the fluid phase Face f whose owner is P and neighbor N conservation of ass: α 1 t +. U 1α 1 = 0 Constraint: discontinuous nature of the liquid fraction odifying the advection ter 2/21/

11 interfoa Governing equations: The oentu equation ρu t +. ρuu = P +. τ + ρg + F F σκ α P = P ρg. x. τ =. μ u + u) T Pressure-Velocity solution loop Piple) Moentu Predictor: using previous pressure filed to solve the seidescritized oentu equation a P U P = H u Pressure Solution: first estiation of the new pressure fields by using the velocity profile calculated earlier Pressure Poisson Equation) Velocity Correction: calculating velocity explicitly P g. x ρ + σκ α a P 1 P f =. a P 1 H u g. x ρ + σκ α f U P = a P 1 H u P g. x ρ + σκ α 2/21/

12 Mesh generation As previous case The Mesh is based on the O grid ethod for the pipe cross section setfield: defaultfieldvalues volscalarfieldvalue alpha1 0 ); regions boxtocell box ) ) fieldvalues volscalarfieldvalue alpha1 1 ); ); 2/21/

13 flow field in open surface U P_rgh diensions [ ] [ ] Internal field Unifor ) Unifor 0 0 0) inlet type fixedvalue zerogradient value unifor ) outlet type zerogradient fixedvalue unifor 0 wall type fixedvalue zerogradient value unifor 0 0 0) atosphere type pressureinletoutletvelocity TotalPressure Value Value unifor 0 0 0) P0 unifor 0 U U phi phi rho rho Psi none Gaa 1 Control variable value Maxiu Corrant nuber 0.5 Delta T 0.1 Maxiu delta T 1 MaxCO 0.5 endtie 1 2/21/

14 intersettlingfoa Following odification needs to be done creatfield.h The inforation related to what new variables will be solved needs to be odified Adding necessary transport properties: diensionedscalar rhodtransportproperties.lookup"rhod")); diensionedscalar uctransportproperties.lookup"uc")); diensionedscalar umaxtransportproperties.lookup"umax") ); Adding new the coefficients: diensionedvector V0VdjModelCoeffs.lookup"V0")); diensionedscalar avdjmodelcoeffs.lookup"a")); diensionedscalar a1vdjmodelcoeffs.lookup"a1")); diensionedscalar alphaminvdjmodelcoeffs.lookup"alphamin")); the dictionary file has to be edited to reflect the changes: Info<< "Initialising field Vdj\n" << endl; volvectorfield Vdj IOobject "Vdj", runtie.tienae), esh, IOobject::NO_READ, IOobject::AUTO_WRITE ), esh, diensionedvector"0.0", U.diensions), vector::zero), U.boundaryField).types) ); volscalarfield alphas IOobject "alphas", runtie.tienae), esh, IOobject::NO_READ, IOobject::AUTO_WRITE ), rho*alphas/rhod ); 2/21/

15 interfoa.c The drift equation only reads the velocity and does not play an active role in PIMPO loop. Info<< "Tie = " << runtie.tienae) << nl << endl; twophaseproperties.correct); #include "alphaeqnsubcycle.h" interface.correct); // adding new line #include "alphaseqn.h" // done adding the new line // --- Pressure-velocity PIMPLE corrector loop while piple.loop)) #include "UEqn.H" // --- Pressure corrector loop while piple.correct)) #include "peqn.h" if piple.turbcorr)) turbulence->correct); 2/21/

16 transportproperties Adding the value for the new paraeters umax umax [ ] 10.0; uc uc [ ] ; rhod rhod [ ] 1996; siplecoeffs V0 V0 [ ] ); a a [ ] ; a1 a1 [ ] 0; alphamin alphamin [ ] 0; FvSchees discretization schee to apply to the equation divschees divphialphas,alphas) Gauss upwind; // divphivdj,vdj) Gauss linear;// 2/21/

17 alphaeqn surfacescalarfield phialpha IOobject "phialpha", runtie.tienae), esh ), phi + rhoc*esh.sf) & fvc::interpolatevdj)) ); FvScalarMatrix AlphaEqn fv::ddtrho, Alpha) + fv::divphialpha, Alpha) - fv::laplacianut, Alpha) ); Info<< "Solid phase fraction = " << Alpha.weightedAverageesh.V)).value) << " MinAlpha) = " << inalpha).value) << " MaxAlpha) = " << axalpha).value) << endl; Alpha.in1.0); Alpha.ax0.0); rho == rhoc/scalar1) + rhoc/rhod - 1.0)*Alpha); alpha == rho*alpha/rhod; t d. d v ) d. c v dj ). d 2/21/

18 fvsolution Initial and boundary condition AlphaS AlphaSFinal solver BICCG; preconditioner DILU; tolerance 1e-7; reltol 0; solver BICCG; preconditioner DILU; tolerance 1e-7; reltol 0; diensions [ ]; internalfield unifor 0; boundaryfield inlet type fixedvalue; value unifor 0.01; walls type zerogradient; outlet type zerogradient; atosphere type inletoutlet; inletvalue unifor 0; value unifor 0; 2/21/

19 intersettlingfoa initial and boundary condition U P_rgh AlphaS diensions [ ] [ [ ] 0] Internal field Unifor 0 0 2) Unifor 0 0 Unifor 0 0) inlet type fixedvalue zerogradient fixedvalue value unifor 0 0 2) unifor 0.1 outlet type zerogradient fixedvalue zerogradient unifor 0 wall type fixedvalue zerogradient zerogradient value unifor 0 0 0) atosphere type pressureinletoutletvelocity TotalPressure inletoutlet Value Value unifor 0 0 0) P0 unifor inletvalue unifor 0 0 Value unifor 0 U U phi phi rho rho Psi none Gaa 1 Control variable value Maxiu Corrant nuber 0.5 Delta T 0.1 Maxiu delta T 1 MaxCO 0.5 endtie 200 2/21/

20 intersettlingfoa Final result 2/21/

21 Thanks for your attention 2/21/