Multiphase Flow Developments in ANSYS CFX-12

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2 Outline Euler-Euler Wall Boiling Model Non-Drag Forces Euler-Lagrange Particle collision model Wall film Modeling Particle-Wall Interaction Other news/improvements 2008 ANSYS, Inc. All rights reserved. 2 ANSYS, Inc. Proprietary

3 RPI Wall Boiling Model Determines Heat Flux Partition at Wall: Q = Q c + Q q + Q e Q c = Convective Heat Transfer Determined by Turbulent Wall Function Q q = Quenching Heat Transfer Departure of a bubble from heated surface cooling of surface by fresh water. Q e = Evaporative Heat Transfer Determined by physical sub-models on the sub-grid scale. QQ QE QC G Qwall 2008 ANSYS, Inc. All rights reserved. 3 ANSYS, Inc. Proprietary

4 Wall Boiling Validation: Bartolomej Test Case MMT Validation Test Case Subcooled Boiling in Pipe with Heated Wall Bartolomej et al. (1967, 1982) (Conxita Lifante, 2008) large number of experimental testcase conditions with data steam-water pipe flow with wall boiling liquid sub-cooling defined to have steam inception always at the same wall height Different configurations were studied in the paper. Main parameters: Mass inflow rate Pressure Wall heat flux Pipe diameter 2008 ANSYS, Inc. All rights reserved. 4 ANSYS, Inc. Proprietary

Bartolomej Test Case: Description 2D axial symmetry, steady simulation 1 degree extrusion Specified heat flux at the wall Symmetry b.c. at planes and axis Inlet b.

5 Bartolomej Test Case: Description 2D axial symmetry, steady simulation 1 degree extrusion Specified heat flux at the wall Symmetry b.c. at planes and axis Inlet b.c. with given inlet mass flow Outlet b.c. with average static pressure X=X/100 R X=2m 2008 ANSYS, Inc. All rights reserved. 5 ANSYS, Inc. Proprietary

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Wall Boiling Verification: Rod Bundle Geometry 3 3 rod symmetry section from a nuclear reactor fuel assembly with guide vanes Periodic BC s at all sides Wall heat flux of q wall = 10 6 W/m 2

8 Wall Boiling Verification: Rod Bundle Geometry 3 3 rod symmetry section from a nuclear reactor fuel assembly with guide vanes Periodic BC s at all sides Wall heat flux of q wall = 10 6 W/m 2 Reference Pressure p = 15.7 MPa Water inlet temperature T Inlet = 607K FZ Dresden and Ansys Germany Validation with comparison to experimental data is work in progress 2008 ANSYS, Inc. All rights reserved. 8 ANSYS, Inc. Proprietary

9 Non-Drag Forces Motivation Bring to release excellent progress made in validation of non-drag force models in bubbly flow Joint work between Ansys and Forschungszentrum Dresden (FZD) Utilised in conjunction with wall boiling in most validation studies of boiling flow. Also make available well validated models for spherical solid and liquid droplet lift forces Numerics improvements to mitigate poor robustness of Virtual Mass Force implementation in previous releases (funded development) See later section on numerics improvements ANSYS, Inc. All rights reserved. 9 ANSYS, Inc. Proprietary

10 Non-drag Forces Mass weighted averaged conservation equations # # t # # t (! " ) + $ (! " U ) = 0 k k k k k (! " ) (! " ) " P (" k ) U + $ % U U = & $ & $ % ' + F + I k k k k k k k k k k k I = F + F { { L + F { WL + F { T + F { k D D VM drag lift wall turbulent lubrication dispersion virtual mass Turbulence models for each phase (k-ε, k-ω, SST, 0-eq. disperse phase turbulence model) Interfacial forces need empirical closure 2008 ANSYS, Inc. All rights reserved. 10 ANSYS, Inc. Proprietary

11 Non-Drag Forces: Lift Tomiyama Model Well validated model for bubbly flow. Takes into account change of sign of lift force due to change in bubble shape as bubble size increases. Depends on Eotvos number, hence requires specification of surface tension and gravitational force. Saffman Mei Applicable to rigid spheres. Generalises Saffman s anaytical model to extend applicability to higher particle Reynolds numbers. Legendre Magnaudet Applicable to liquid drops. Takes account of induced circulation inside drops ANSYS, Inc. All rights reserved. 11 ANSYS, Inc. Proprietary

12 Non-Drag Forces: Wall Lubrication Tomiyama Like Tomiyama lift force, depends on Eotvos number, hence accounts for dependence of wall lubrication force on bubble shape. In conjunction with Tomiyama lift force, produces excellent results for bubble flow in vertical pipes. However, requires pipe diameter as input parameter, hence geometry dependent. Frank Generalises Tomiyama s model to be geometry independent. Model constants calibrated and validated for bubbly flow in vertical pipes ANSYS, Inc. All rights reserved. 12 ANSYS, Inc. Proprietary

13 Non-Drag Forces Validation: Bubbly Flow in Vertical Pipe Forschungszentrum Dresden (FZD) MT-Loop test facility. Wiremesh sensor with 24x24 electrodes. Database to test CFD predictions. Length, L = 4 m, Inner Diameter, D = 51.2 mm. Air-Water at atmospheric pressure, and 30 C. Measurements carried out for stationary flows of various superficial velocity ratios. 10 different cross sections located between L/ D = 0.6 and 59.2 from gas injection. Select test cases in bubbly flow regime with a near-wall peak in gas volume fraction ANSYS, Inc. All rights reserved. 13 ANSYS, Inc. Proprietary

16 Particle Collision Model - Conception Statistical collision model (Sommerfeld) Computational effort of simultaneously tracing all particles is not required Instead an iterative approach is used: Sequential calculation of particle trajectory Compute statistical particle properties (mean and standard deviation of droplet diameter and velocities) Creation of a virtual collision partner according to local statistical mean particle properties Random process decides whether or not a collision takes place 2008 ANSYS, Inc. All rights reserved. 16 ANSYS, Inc. Proprietary

17 Description of Validation Experiment Validation by experiment of Fohanno & Oesterlé Enforced crossing of trajectories Flow induced by gravitation Glass particles, d P = 3 mm ρ P = 2500 kg/m 3 Collision effects dominate 2008 ANSYS, Inc. All rights reserved. 17 ANSYS, Inc. Proprietary

Particle Trajectories Without / With Collision Model without collision model

19 Notes on Particle-Particle Collision Validation report available A stochastic particle-particle collision model for dense gas-particle flows implemented in the Lagrangian solver of ANSYS CFS and its validation, 6 th International Conference on Multiphase Flow, ICMF 2007, Leipzig, Germany, July 9-13, 2007, Paper No. 148, pp 1-16 This is an expensive model Particle integration time step may become very small compared to non-collision simulation (up to several (~2-4) orders of magnitude) 2008 ANSYS, Inc. All rights reserved. 19 ANSYS, Inc. Proprietary

20 Particle Wall Film Major physical phenomena Splashing Impinging Evaporatio n Convection External Forces Separation Conduction Film movement due to external forces is neglected for CFX 12 Still film can move if on a moving wall 2008 ANSYS, Inc. All rights reserved. 20 ANSYS, Inc. Proprietary

21 Wall Film Modeling Approach and Main Assumptions Modeling Approach Wall film is modeled using a Lagrangian approach I.e.: Wall film made of a special type of particles Wall particles Assumptions Thin film approach (no displacement effect) Neglect influence of film on fluid drag No film movement due to external forces Quasi Static Wall Film 2008 ANSYS, Inc. All rights reserved. 21 ANSYS, Inc. Proprietary

22 Wall Film Modeling Example: Evaporating Droplets Water droplets (T p = 293 K) hit a heated wall T wall = 350 [K] Q convective Assumptions: Droplets sticks to wall, i.e. no relative movement between particle and wall Q conduct Energy is transferred from wall/surrounding to film Film evaporates into ambient 2008 ANSYS, Inc. All rights reserved. 22 ANSYS, Inc. Proprietary

Wall Film Modeling Example: Evaporating Droplets (2) 2008

24 Particle-Wall Interaction Model Particle-Wall Interaction Model This model describes how particles interact with film covered walls and under which conditions a wall film is formed Prerequisite for wall film model Droplet-wall interaction is complex and not all aspects are well understood. Dimensional analysis shows that droplet-wall interaction depends on: Particle quantities (Weber Number), existence of a wall film, wall roughness, wall temperature (and much more) 2008 ANSYS, Inc. All rights reserved. 24 ANSYS, Inc. Proprietary

25 Notes on the Wall Interaction Models Elsässer Model Accounts for wall temperature effects, wall roughness and particle-wall material combination, Targeted towards IC-E applications (~ Gasoline injection) Stick to Wall Simplest possible model: all particles that hit a wall become part of the wall film 2008 ANSYS, Inc. All rights reserved. 25 ANSYS, Inc. Proprietary

Spin-off of Wall Interaction Extension Child droplet generation model Parent droplet can

27 Other Multiphase developments New Turbulence Induced Atomization Model Improvements / Added Functionality for Robustness of Coupled Volume Fraction for inhomogeneous multiphase flows Discretisation of Virtual Mass Force for more robustness More user control of Particles and Particle Output Particle Injection Options Secondary Break-Up Models 2008 ANSYS, Inc. All rights reserved. 27 ANSYS, Inc. Proprietary

29 Coupled Solver Simultaneous solution of the equations of a multiphase system would offer a more robust alternative to the segregated approach. The memory usage would be larger than the PC SIMPLE but the gains in convergence make this approach attractive for steady-state solution FLUENT has already an AMG coupled solver with ILU smoother used for single phase Description below uses velocity and pressure correction. Volume fraction is solved segregated Can be extended to volume fraction correction 2008 ANSYS, Inc. All rights reserved. 29 ANSYS, Inc. Proprietary

30 Validation IV Three-dimensional turbulent mixing tank, Montante and Bakker (2004). The system under investigation is a fourbaffled vessel with four Rushton turbines solved with the multiple reference model For a converged solution the CPU time ratio between the PC-SIMPLE solver and the coupled solver was about ANSYS, Inc. All rights reserved. 30 ANSYS, Inc. Proprietary

31 Multi-Fluid VOF Multi-Fluid VOF involves the following features: Interface sharpening schemes (such as Geo-Reconstruct, CICSAM, Modified HRIC) in the framework of Eulerian multiphase. This gives access to non-shared velocity and temperature fields for the problems involving sharp interface treatment. Variable time stepping for Explicit schemes in the framework of Eulerian multiphase. Modeling of Surface tension Wall adhesion Marangoni convection in the framework of Eulerian multiphase. Modeling of Anisotropic drag, especially for free surface flows. Compatibility of Explicit schemes with other models such as Turbulence, Energy, Species and Mass transfer, Dynamic mesh, Granular flow. Immiscible fluid option to model free surface flows. This option enables Geo-Reconstruct and CICSAM schemes for Explicit VOF. Drag law options with this model are Symmetric and Anisotropic ANSYS, Inc. All rights reserved. 31 ANSYS, Inc. Proprietary

32 Bubbles with Multi-Fluid VOF Bubbles rising through a slurry of granular solids in water. DPM is used to track the red particles with the granular phase velocity 2008 ANSYS, Inc. All rights reserved. 32 ANSYS, Inc. Proprietary

33 " = { 1, U, V, W, T, Yi, k,!...) Summary of Cavitation Models in FLUENT 12 Cavitation models developed under the general multiphase, pressure-based numerical framework Not available for the density-based solver The cavitation models can be applied to any geometric system, all grid types supported in FLUENT, non-conformal / sliding interfaces, and moving/deforming mesh The models have been extended to multiphase and multispecies systems The models can be solved with mixture (mixture model) or phase (Eulerian multifluid) temperature equations They are fully compatible with all the turbulence models in FLUENT, ranging from simple length scale models to LES Both liquid and vapor phase can be incompressible or compressible. The input material properties (vaporization pressure, density, viscosity, and etc.) can be constants or functions of temperature ANSYS, Inc. All rights reserved. 33 ANSYS, Inc. Proprietary

34 Dense Dispersed Particle Model The dense dispersed particle model (DPPM) is a Lagrangian technique to model particulate flows Provides an efficient treatment for size distributions in multiphase problems In FLUENT, this model is an extension from DPM to account for dense phase effects. Account for the effect of blockage on the fluid Introduce calculation of volume fraction Account for the effect of collisions on the motion of particles Use particle pressure and particle kinetic energy from Granular Kinetic Theory 2008 ANSYS, Inc. All rights reserved. 34 ANSYS, Inc. Proprietary

Calculate a solution using the pressure-based coupled solver.

Calculate a solution using the pressure-based coupled solver. Tutorial 19. Modeling Cavitation Introduction This tutorial examines the pressure-driven cavitating flow of water through a sharpedged orifice. This is a typical configuration in fuel injectors, and brings