MODELLING OF MULTIPHASE FLOWS
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1 MODELLING OF MULTIPHASE FLOWS FROM MICRO-SCALE TO MACRO-SCALE Department of Applied Mechanics, University of Technology, Gothenburg, Sweden. Siamuf Seminar October 2006
2 OUTLINE 1 GROUP PHILOSOPHY 2 PROJECTS AND PEOPLE 3 MULTIFLOW Theory Status Examples 4 PHD STUDENTS Rasmus Hemph Vinay Gopala Aldo Benavides Andreas Mark José Oliveira 5 CONCLUSIONS
3 GROUP PHILOSOPHY Understanding physical behaviour at various scales. Combining knowledge obtained at one scale to improve modelling at another. Combination of fundamental projects and applied projects. Employ (inhouse code), OpenFoam (Open Source), Fluent, CFX.
4 VARIOUS LENGTH AND TIME SCALES eddy particle wake cluster turbulence interaction big clusters meso scale turbulent structures micro scale meso scale macro scale
5 PROJECTS AND PEOPLE Model and Solver Development - Berend van Wachem Particle packing for Chromatography - Rasmus Hemph Modeling and validation of Liquid-Liquid flows - Vinay Gopala Numerical simulation of turbulent gas-solid two-phase flows - Aldo Benavides Direct numerical simulation of gas-solid flows - Andreas Mark Direct numerical simulation around objects - José Oliveira
6 Theory Status Examples MODEL AND SOLVER DEVELOPMENT: MULTIFLOW is a fully coupled, parallel code for various sets of governing equations describing multiphase flows: Eulerian-Lagrangian particle modelling. Volume of Fluid modelling. Direct Numerical Simulation around objects (IBM). Eulerian-Eulerian is underway. Most algorithms employed to solve multiphase governing equations are based on single phase ideas and are therefore time-consuming. employs analytical weighting of the momentum equations at cell faces. The resulting equations are employed to solve the continuity equation.
7 MULTIFLOW APPROACH I Theory Status Examples The approach is shown on single phase type equations, for example, used for VOF modelling. EQUATIONS ρ uj t x i ui = 0 + ρ x i ( u i u j) = p x j + τ ij x i Ru j S j
8 MULTIFLOW APPROACH II Theory Status Examples DISCRETIZED EQUATIONS By discretizing these equations, we can determine analytical expressions for the variables at both cell centers as well as face centers. uf i si f = 0 faces [ ] 1 + c e d (uj ) e u j e = ũj e ) d(uj e ] [ p x j + c e d (uj) e u j,o e e
9 MULTIFLOW APPROACH III Theory Status Examples SOLVER The complete set of equations are put into matrix form, and the inverse of this matrix determines the solution u 1 RH u u 2 RH u u p = RH u3 RH p α RH α Solution is directly presented in unknowns; velocity, pressure, volume fraction, etc.
10 STATUS OF MULTIFLOW Theory Status Examples VOF, Levelset FCT, Youngs, PLIC, CICSAM, Inter Gamma Mass transfer, Improve model for surface tension Eulerian-Lagrangian Size distributions, LES, drag models Non-spherical objects, attrition, agglomeration. Immersed Boundary Method Arbitrary shapes, non-stationairy bodies Deformable bodies, LES/RANS(?) Eulerian-Eulerian Kinetic Theory, Turbulence Modulation
11 LID DRIVEN CAVITY Group Philosophy Theory Status Examples To validate the approach, the solver is compared with the lid driven cavity data of Ghia et al (1982) (Results of José) Re=100 Re=400
12 Theory Status Examples FLOW AROUND OBJECTS: IBM METHOD
13 Theory Status Examples LARGE-SCALE LAGRANGIAN PARTICLE MODELLING Particles and gas velocity Particles and averaged volume fraction
14 FLUIDIZED BED MODELLING Theory Status Examples U = 2U mf, N P = 50, 000, t = s
15 PARTICLE FLOW MODELLING Theory Status Examples Fluidized Bed 3Umf WursterBed1 WursterBed2 Fines Particle flow through tubes
16 VOF MODELLING (VINAY) Theory Status Examples t = 0 t = 1 4 P t = 5 8 P 0.06 PLIC Theoretical 0.02 PLIC Height at the left face (m) Error (%) t = P Time (s) Period Time(s) Error
17 Rasmus Hemph Vinay Gopala Aldo Benavides Andreas Mark José Oliveira PARTICLE PACKING FOR CHROMATOGRAPHY OpenFoam simulations of the emptying of a 3 dimensional hopper.
18 Rasmus Hemph Vinay Gopala Aldo Benavides Andreas Mark José Oliveira PARTICLE PACKING FOR CHROMATOGRAPHY Particle packing due to flow and gravity in a 5 mm wide column.
19 Rasmus Hemph Vinay Gopala Aldo Benavides Andreas Mark José Oliveira MODELLING OF INTERFACIAL FLOWS Youngs Method (*) Flux Corrected Transport Lagrangian PLIC (*) CICSAM Inter-Gamma Scheme Experimental result
20 Rasmus Hemph Vinay Gopala Aldo Benavides Andreas Mark José Oliveira RAYLEIGH-TAYLOR INSTABILITY t = 0s t = 0.2s t = 0.4s t = 0.6s t = 0.8s t = 0.95s, CICSAM
21 Rasmus Hemph Vinay Gopala Aldo Benavides Andreas Mark José Oliveira IMPROVING COALESCENCE MODELS
22 Rasmus Hemph Vinay Gopala Aldo Benavides Andreas Mark José Oliveira TURBULENT GAS-SOLID FLOWS A carrier fluid (gas-phase) which is loaded with particles (solid-phase) An turbulent interstitial fluid is present. Applications: fluidized beds, inhalers, pneumatic transport of powders, dispersion of pollutants, so forth Need to model the interaction (including turbulence) between phases
23 Rasmus Hemph Vinay Gopala Aldo Benavides Andreas Mark José Oliveira EULERIAN OR TWO-FLUID MODEL EQUATION SET α k = 1 α ) k + (α kuk t ) ) (ρ k α kuk + (ρ k α kuk Uk t t (ρ kα k K k ) + k = 0 = [α k ( T k + Rk )] + α k P + M k + ρ k α kbk ) (ρ k α kuk K k = [α k Jk ] + α k (P k ǫ k ) + E k
24 Rasmus Hemph Vinay Gopala Aldo Benavides Andreas Mark José Oliveira FULLY DEVELOPED TURBULENT PIPE FLOW z 1.4 Normalized mean velocity profiles, comparison with Tsuji et al. data V U g 0.8 R r dp dz Gas Solids Gas (experiments) Clear gas r R
25 SECOND ORDER IMPLICIT IBM Rasmus Hemph Vinay Gopala Aldo Benavides Andreas Mark José Oliveira The IB is a triangulation of an arbitrary surface Reversed velocity field over the IB An implicit immersed boundary condition constrains the velocity of the fluid to the IB velocity exactly at the IB Implemented for both moving and stationairy IBs with three way coupling
26 SECOND ORDER IMPLICIT IBM Rasmus Hemph Vinay Gopala Aldo Benavides Andreas Mark José Oliveira Separation, Re= spheres interacting with the flow
27 SECOND ORDER IMPLICIT IBM Rasmus Hemph Vinay Gopala Aldo Benavides Andreas Mark José Oliveira Cd value for medium Re Immersed Flow 1 Immersed Flow 2 Stoke Drag Shiller and Naumann Lapple Langmuir and Blodgett 10 2 C d Re Drag coefficient for a sphere Flow around a non-spherical object
28 Rasmus Hemph Vinay Gopala Aldo Benavides Andreas Mark José Oliveira FULLY IMPLICIT IBM: FLOW AROUND PARTICLES Solution after 1 iteration!
29 CONCLUSIONS : approach at various scales. Couple the knowledge obtained at the various scales. Work on physical modelling from a fundamental and an applied viewpoint. Modelling work done in, OpenFoam, Fluent, CFX. Development of novel solver and physics:.
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