Advances in Multiphase Modeling 2019 R1

Jay Sanyal, Vinay Gupta, Markus Braun

1 Major Focus Areas (1)

• Mixture Multiphase Numerics ‐ Explicit VOF formulation ‐ Surface tension modeling • Generalized turbulence dispersion for N-phases • Semi-Mechanistic Boiling Model • Generic file read capability to specify Relative Permeability and Capillary Pressure in a tabular format Major Focus Areas (2)

• Fluent/CFX cross-model assessment – comparison of drag, virtual mass, lift and turbulent forces • Robust TUI for multiphase materials • Extend heat/mass/IAD models to N-phase framework • New Multiphase GUI (In progress) • EWF partial wetting model Mixture Multiphase Additions Mixture Multiphase vs VOF • VOF : For modeling sharp interfaces • Addition of dispersive characteristics such as diffusion in volume fraction: Counter- intuitive • Mixture: For modeling dispersed interfaces • Add flexibility for modeling sharp/dispersed interfaces • Supports turbulent diffusion (counter-active for VOF)

Mixture Multiphase extension

• Surface tension modeling support • Compatibility with NITA (beta) • Explicit volume fraction formulation support (VOF solved once per time step) • Accurate than Implicit formulation for Courant based time step size • Accurate for more than two phase flow due to explicit accounting of mass errors • Errors due to limiting and normalization of volume fraction • Implicit requires deeper convergence • Stable for compressible and surface tension dominated flow • Run time calculation of forces based on evolving vof field might be unstable Mixture Multiphase Additions (2) Slug Flow – Mixture Model Mixture/Drift-Flux + ITA/NITA + Explicit/Implicit + Surface Tension evaluation Case Study-1: Pressure rise in static drop

Pressure Water velocity vectors Mixture + Implicit : ITA Drift-Flux + Explicit – ITA

Air velocity vectors Mixture + Implicit : NITA Drift-Flux + Explicit – NITA Case Study-2: Slug Flow (Drift-Flux + Implicit + ITA + Surface Tension)

Volume Fraction: water Water velocity vectors Air velocity vectors

Case Study-3: Thermal induced Marangoni instability (Mixture + ITA/NITA + Surface Tension)

ITA NITA Case Study-4: Drift-Flux + Granular Flow ( Implicit/Explicit)

Implicit Explicit Case study: Static drop : Effect of Patch/Smoothing

Legacy patch option

Patch reconstruction + smoothing (0.25)

Initial vof Final vof (100 time-steps) Static pressure in the drop (100 time- steps) Generalized Turbulent Diffusion for Cavitating Flow Turbulent Diffusion : Diffusion in VOF equation Spreading of dispersed phase due to turbulent motion

- Default for Cavitating Flow from both physical and Numerical considerations - Driving vapor away from the wall in cavitating flow - Numerical -Interfacial diffusion adds to solution stability

Generalized treatment for turbulent diffusion

Old Issues: - It was a default treatment for cavitating flow, which had following issues - Only two-phase specific treatment which has been generalized for N-phase flow. - Earlier turbulent diffusion used to get activated for all phase pairs, which is now limited to only cavitating phase pair. - Treatment was dependent on the order of phases. - Had issues with energy imbalance Old issues Secondary phase-1

For Cavitating Flow, Primary Phase - Secondary-Primary interaction was active by default for all possible Secondary phase-2 phase-pairs. - No Secondary-Secondary interaction, even if desirable

Secondary phase-n Air Vapor Water Water Air Vapor Water-Vapor Open Channel Flow Air Diesel Current treatment activates the turbulent Diesel-Vapor diffusion for cavitating phase pair Diesel Fuel Injector Air Calculation of Mass diffusion coefficients 1 휇 Γ = 푡,푚 휌 푑 푆푐 휌 푑 Γ푑 = 퐷휌푑 휇 = 푀𝑖푥푡푢푟푒 푇푢푟푏푢푙푒푛푡 푉𝑖푠푐표푠𝑖푡푦 푡 푚 휇 푡,푚 D = 푡,푚 휌푚 휌푚 = 푀𝑖푥푡푢푟푒 퐷푒푛푠𝑖푡푦 1 휇푡,푚 휌푑 = 퐷𝑖푠푝푒푟푠푒푑 푃ℎ푎푠푒 퐷푒푛푠𝑖푡푦 Γ푐 = 휌푐 Γ푐 = 퐷휌푐 푆푐푡 휌푚 Specific Diffusion 휌푐 = 퐶표푛푡𝑖푛푢표푢푠 푃ℎ푎푠푒 퐷푒푛푠𝑖푡푦 Coefficient

Generalized Treatment for any phase pair

Legacy treatment 푆푑 = 훻. Γ푑 훼푐 훻훼푑 − 훼푑 훻훼푐 푆푑 = 훻. Γ푑훻훼푑 푆 = 훻. Γ 훻훼 푆푐 = 훻. Γ푐 훼푑 훻훼푐 − 훼푐 훻훼푑 푐 푐 푐

N-phase Flow 2-phase Flow Cavitation : 2 Phase Flow (Water, Water-Vapor)

With Turbulent diffusion

Without Turbulent diffusion Cavitating Flow : With and Without Energy Treatment (Independent of phase reversal)

T

Without Energy Treatment

T

With Energy Treatment Diesel Fuel Cavitation in a Planar Injection Nozzle (Hydraulic Flip) Mixture Multiphase: - Compressive Scheme for sharp/dispersed interface modelling - Surface tension force modelling

• 3-phase flow: Diesel liquid - Diesel vapor - Air • Phase transition due to cavitation: o Diesel liquid – Diesel vapor: Zwart-Gerber-Belamri cavitation model • Phase pairs without mass transfer: o Diesel liquid – air o Diesel vapor – air Air Diesel liquid Diesel vapor • Density (kg/m3) 1.225 830 1 • Viscosity (kg/m s) 1.7e-6 0.00223 7 e-6

Diesel liquid /Air Air / Diesel vapor Diesel liquid /Diesel vapor • Surface tension(N/m) 0.026 0 0.026 Turbulent diffusion treatment : Legacy (secondary-primary) vs New (cavitating phase pair) Fuel Injector : Cavitation + Hydraulic Flip

P = 200 KPa P = 350 KPa P = 200 KPa P = 350 KPa Legacy : New : Turbulent dispersion gets activated between all Turbulent dispersion gets activated only between cavitating secondary-primary phase pairs. phase pair. Po @ 130kpa Po @ 190kpa Po @ 210kpa Po @ 300kpa Po @ 330kpa Po @ 400kpa

Comparison with experimental result: Mass flow rate vs Injection pressure Boiling models used for automotive applications

• Simplified approach to boiling simulation • Based on homogeneous multiphase flow • Mixture multiphase flow model in ANSYS Fluent • Any boiling model must address following two aspects of boiling: – Heat transfer augmentation at the wall • Use 1D empirical correlations to calculate boiling at the wall – Chen correlation (superposition of single-phase heat flux + nucleate boiling heat flux) – Volumetric phase change • Use simplified approach to calculate volumetric phase change – Evaporation-Condensation model in ANSYS Fluent SBM GUI Validation Case : Water Pure Water: P = 2 bar, Tin = 95C, Tsat = 121C

V = 0.2 m/s • Horizontal Nucleate boiling with 2 bar operating pressure

• The channel dimensions are 10 mm X 16 mm X 241 mm • Heated plate dimensions are 10 mm X 50 mm V = 0.39 m/s • Material : water • Heated wall temperature is varied for different – Operating Pressure – Inlet Velocity – Inlet Sub-cooling Implementing a new TUI hierarchy for multiphase flow

• Until R-19.2, the TUI for a number of FLUENT features has been organized in a sequence of queries. Whenever a new sub-model or parameters/data of a sub-model changes, this sequence will be changed and the TUI will break.

• Among other objectives, this new feature provides a text user interface that allows compatibility with old scripts whenever new properties are added.

• A new TUI hierarchy has been implemented, which allows changing the sequence of settings into separate TUI commands that can be applied in an arbitrary order (as long as they do not depend on each other).

• Extra measures have been taken in order to maintain compatibility with the old TUI menu hierarchy and commands. This allows user to transition on their own peace to the NEW TUI hierarchy without breaking current clients’ journals.

• This new TUI implementation have been extensively studied with a number of different multiphase flow cases (eulerian, vof, mixture, etc.), and a number of cases from the test matrix have been modified and automatized using this new TUI hierarchy. Implementing a new TUI hierarchy for multiphase flow • New text user interface (TUI) commands to set properties for individual phases and define their interaction have been added under the new: define/phases/set-domain-properties text command menu.

• Commands under define/phases/set-domain-properties/phase-domains menu as an alternative to the existing text prompts under define/phases/phase-domain menu to set or edit each phase domain property individually.

• Commands in the define/phases/set-domain-properties/interaction-domain menu serve as an alternative to the existing text prompts under define/phases/interaction-domain menu to set or edit phase interaction settings.

• To change the phase name, the command under define/phases/set-domain-properties/change-phases-names? can be used. Extend heat/mass transfer/IAD models framework to N phases ● Scope ○ Removing further limitations of mass transfer mechanisms ○ Extend Thermal Phase Change and Lee model to N phase framework ○ Extend saturation temperature to N phase framework ○ Refactoring of GUI and TUI ○ Allow multiple selection of Evaporation/Condensation model ○ Extend IAD to all phase pairs

Old

New Extend heat/mass transfer/IAD models framework to N phases

GUI phase interaction panel for evaporation- condensation model

Allow multiple evap- cond model

Each evap-cond mechanism can have its own saturation temperature

New Old Data File Manager Ribbon Item Capillary Pressure Tabular Interface

Pick Tabular Input Columns Tabular Input for Vapor Pressure and Latent Heat as a function of T

P-T Table

P-T-L Table Provide a N phase framework for drag and other interfacial forces / Backward compatibility for the old Grace model • While working on the implementation of the new drag coefficients with swarm factor corrections, it was discovered that when a user is requested to introduced a coefficient value, using that model for more than one (1) pair of primary-secondary phases was not working as expected. Therefore, if a model such as Grace is used, then only the last defined coefficient will be taken into account for both interaction pairs. -> Note: This is an issue that was occurring only for cases with coefficient introduction by the users. Provide a N phase framework for drag and other interfacial forces / Backward compatibility for the old Grace model Thin Film Partial Wetting Model

• Film/Surface contact line defining wet and dry regions • Surface force at contact line limiting film spreading • Film fluid surface tension 

• For partial wetting fluids with fluid/surface contact angle w – Contact angle defines fluid ability of fluid to flood surface • Cause of partially wetting behaviour – Rivulets, dry spots, film rupture

• Surface force Fs as function of  and w (Young’s Law) • 푭풔 = 흈(ퟏ − 풄풐풔휽풘) (N/m) Thin Film Partial Wetting Model

• Surface Wet/Dry Regions • Represented by Wet Area Fraction (WAF) Function w(h) ퟎ, 풉 ≤ 풉 – 풘 풉 = ቊ 풄 ퟏ, 풉 > 풉풄

– h – film thickness; hc – critical film thickness (1.e-10 m)

• Surface Force Fs Applied as Shear Force s 2 • 흉풔 = 휷흈 ퟏ − 풄풐풔휽풘 훁풔풘 (N/m ) •  – empirical adjustment factor • Applied to film momentum equation Thin Film Partial Wetting Model

• Film Fluid Contact Angle w • As Constant • Sampled randomly from Gaussian distribution 휽 −휽 ퟐ ퟏ − 풘 풎 – 풇 휽 = 풆 ퟐ휹ퟐ 풘 ퟐ흅휹 – m – mean contact angle;  – standard deviation • Static spatial sampling over wall surface – Finer mesh → better representation Thin Film Partial Wetting Model

• Partial Wetting Model Setup (R19.2)

• Mean contact angle m – Constant – Profile (User Defined Function) • Standard deviation 

– Percentage of m – Zero gives uniform w = m • Empirical factor  – Case based EWF Partial Wetting Model Tests

• Film Flow Pattern  = 5°,  = 1, Coarse Mesh

G = 31 g/m/s G = 108 g/m/s G = 174 g/m/s G = 309 g/m/s EWF Partial Wetting Model Tests (2)

 = 5°, G = 100 g/m/s •  = 5°, G = 200 g/m/s Conclusions

• A large number of improvements in multiphase flow modeling were made in 2019 R1 • Improvements were made in both physical modeling, numerics and usability of the code • Several legacy limitations have been removed to make the code more generalized and intuitive • Most models were rigorously validated against experimental data

Acknowledgments : Gustavo Montoya, Bo Sun