Development of a Validation and Uncertainty Quantification Framework for Closure Models in Multiphase CFD Solver Yang Liu and Nam Dinh Multi-Physics Model Validation Workshop June/28/2017 1
Multiphase Flow and boiling Multiphase Flow and boiling involves multi-scale phenomena with different physics Flow regime (cm) Bubble behavior, interfacial exchange (mm) Turbulence and nucleation (μm) 2
Eulerian-Eulerian two-fluid-model: closure dependent averaged conservative equations Mass Condensation & Evaporation Turbulence Momentum Interfacial forces Energy Turbulence Condensation & Evaporation
Closure Structure in MCFD Solver Wall boiling Heat partitioning, nucleation Interfacial momentum Interfacial mass/heat transfer Bubble size Turbulence Bubble induced turbulence Near wall heat transfer and evaporation Wall boiling Heat transfer partition Evaporation heat transfer Single-phase convective heat transfer Quenching heat transfer 4 Turbulent viscosity Turbulent heat flux Turbulence model Wall function Nucleation U α h α U h Bubble induced turbulence Turbulent viscosity Bubble departure frequency Bubble departure diameter Active nucleation site density Momentum exchange Drag force Turbulence viscosity force Wall lubrication force Lift force Interfacial forces Bubble breakup Bubble coalesce Condensation Interfacial condensation Bubble size
VUQ Framework for two-fluid model based solver For a solver that deal with Multi-physics & Multi-scale phenomena (e.g. MCFD or CTF), conservative variables are averaged and closure models are used for the missing information Empirical parameters exist in closures which are one of the major error/uncertainty source of the solver (another is numerical) Purpose: Given scenario, code, closure model, and available database, 1.What can we conclude on the uncertainty of the QoIs? 2.Is there model form inconsistency between closures? 3.What is the applicable space of the VUQ results? (how far can we extrapolate the VUQ work done under condition A to an unknown condition?) 4.What is the best option to improve the uncertainty? (which measurement can reduce uncertainty mostly?) 7/24/2017 5
VUQ workflow 7/24/2017 6
MCFD platform and VUQ tool boileulerfoam based on OpenFOAM Original developer: Dr. A.Bui and Prof. N.Dinh Major revision: C.Rollins and Prof. H.Luo (MAE, NCSU) Selected Model implementation: Y.Liu and Prof.N.Dinh VUQ tool used in this work DAKOTA DRAM Python scikit-learn QUESO 7
VUQ Framework for Multi-physics / Multi-scale solver Generalized workflow State of art tools Non-intrusive method Flexibility for method/algorithm selection Preparations Data management Validation metrics Model form inconsistency evaluation 7/24/2017 8
Data management: NEKAMS: Store and manage VUQ database NE-KAMS (Nuclear Energy Knowledge base for Advanced Modeling and Simulation) Enable knowledge base centric process for V&V, UQ and M&S activities Validation Experiment V&V and UQ Standards and Requirements Computation Collect, document, qualify, structure, format, integrate and manage data and information in various forms and from various sources V&V and UQ Guidelines NE-KAMS Knowledge Base M&S Activities Credit: Dr. W.Ren, ORNL V&V & UQ Assessments 7/24/2017 9
Data management : Database example Data Source: Prof. Buongiorno group, MIT Data are automatically processed and stored in two scales 7/24/2017 10 [F1] General information Note Source Synthetic CRUD Test (MIT) Details can be found in[ref] [F2] System configuration Geometry Vertical flow in rectangular channel Fluid materials water liquid/vapor Heater materials ITO sapphire heater with synthetic CRUD [F3] Test program Flow conditions 500 kg/m 2 Heat configurations 2um thick CRUD with 10um diameter chimneys on a 45um pitch Heat flux 1400 kw/m 2 [F4] Data [D0] raw data IR counts distribution [D1] primary data temperature/heat flux Used to current VUQ work distribution in current practice [D2] secondary data ensemble averaged Used to current VUQ work temperature, heat flux and in current practice nucleation information [D3] ternary data Nucleation sites location/ Used for a more detailed interaction etc. modeling approach [F5] Data characteristics Applicability boiling model VUQ for flow boiling on low pressure Quality Good High resolution data with designed surface
Validation Metrics: Evaluation of model uncertainty and model form inconsistency Confidence intervals There is a α% possibility that the true error between model and data are within the given interval EE = yy mm,oooooo 1 nn ii=1 ss = 1 nn nn 1 ii=1 nn yy ee ii yy ee ii yy ee,aaaaaa 2 1 2 Overlapping coefficient Simulation Data Experimental Data EE tt αα 2,vv ss nn, EE + tt αα 2,vv ss nn Overlapping Coefficient Response 7/24/2017 11
Model form inconsistency evaluation Total Data Model Integration Divide-and-Conquer Approach Model inconsistency in MCFD solver mainly stems from Potential conflict of assumptions between different closures Divide tightly coupled phenomena and treated them independently ' ε inconsistency Y TDMI Ysin gle 1,2, 7/24/2017 12
Case Study I: interfacial momentum closure Drag Lift Wall lubrication Turbulent dispersion Virtual mass Expression D 3 CD Ma = b ( ) 4 D ρα Ua Ub Ua Ub s L a L b M = C ρα( U U ) ( U ) a b a 1 M WL 2 = C (y ) ( ) a WL w ρ αd x b S U a U b n r 2 t M TD 3 D b a = C υ ρb 4 D t U α t a U b s σ Prb M 1 DUa DUb = ρ C α( ) 2 Dt Dt VM a b vm Model Schiller- Naumman Tomiyama Antal Gosman Rusche Bubble size Ds = Dref,1(T sub Tsub,2 ) + Dref,2 (T sub,1 Tsub ) Tsub,1 Tsub,2 Anglart 13
Case Study II: Wall heat transfer closures Kurul & Podowski(1991) : With different closure options (Version A & B) Shaver & Podowski(2014) 7/24/2017 14
Surrogate construction Sampling + Gaussian Process I.C. B.C. fixed CMFD solver QoIs I.C. B.C. fixed Surrogate QoIs Closure parameter Closure parameter 15
Surrogate accuracy evaluation by cross validation Low pressure adiabatic flow High pressure subcooled boiling flow QoI Void fraction Gas velocity Maximum RMS 5.98e-3 2.27e-3 Maximum ABS 3.98e-3 1.70e-3 QoI Void fraction Gas velocity Relative velocity Maximum RMS 2.37e-3 2.41e-3 5.81e-4 Maximum ABS 1.48e-3 1.54e-3 3.82e-4 Relative velocity 2.31e-3 1.66e-3 Liquid Temperat ure 4.58e-2 2.70e-2 16
Global Sensitivity Analysis: Morris Measure and Sobol indices Interfacial momentum terms: interfacial forces and bubble size Wall lubrication has influence on all regions Parameters have similar sensitivity in all regions adiabatic flow, but have different behavior in boiling flow 17
Global Sensitivity Analysis: Morris Measure and Sobol indices Wall Boiling Model Comparison with Sobol indices 8.55E-01Cwall 3.70E-01C3 2.34E-02C2-7.39E-03C1-1.85E-03Prt -8.06E-04vonKarman -6.12E-04yPlusSL 18
Parameter Selection Reason: parameter identifiability issue For complex non-linear model, there exists different combinations of parameters that fit the data equally well Thus the inverse Bayesian can be performed only on a subset of parameters without identifiability issue 19
Parameter Selection: ad hoc approach Check parameter identifiability among most important parameters Randomly get rid of one if identified Include parameter with intermediate importance one at a time, and check Do not include that one if identified Directly get rid of not important one 20
Inverse Bayesian Inference using MCMC: Gen-I model, version B One experiment, averaged over heater surface Joint sampling of parameters Check of convergence: Burn in pattern and autocorrelation Bubble Effective area factor Bubble diameter constant Turbulent convective constant 21
Validation metrics example One experiment, averaged over heater surface Constructing Confidence intervals 22
Model form inconsistency identification: One experiment, Distribution along heated wall Gen-I model, version A Shaver model Indication of model form inconsistency 23
Issue identified Extrapolation can lead to large error Inference with datasets on one condition, then apply parameter distribution to other conditions Universal optimal parameter estimates do not exist Inference with datasets on all conditions simultaneously 24
A possible solution: gain knowledge from multiple validation results Test: infer posterior distribution through interpolation and extrapolation 25
Desired future work With many units, the desired data needs / best available model/parameter can be obtained and aid decision making Validation database Unit. A Macro-scale Phenomena Closure options A1 A2 A3... B1 B1 B1... C1 C2 C3............... Validation database Unit. B IET.1 SET.1 SET.3 IET.2 SET.2 SET.4 Meso-scale. Micro-scale 7/24/2017 26
Summary: Current Achievement Purpose: Given scenario, code, closure model, and available database, 1.What can we conclude on the uncertainty of the QoIs? (Answered) 2.Is there model form inconsistency between closures? (Partially Answered) 3.What is the applicable range of the VUQ results? (can we extend the VUQ work done under condition A to B) (Partially Answered) 4.What is the best option to improve the uncertainty? 27
Summary: Current limitation Depends on multiple datasets with uncertainty known High fidelity data with thorough uncertainty analysis is desired Acquire more data sources from literature/high fidelity simulation Evaluating missing uncertainty information Parameter identifiability not fully resolved, the parameter selection depends on a lot trial and error Trying state-of-art mathematical methods, e.g. active subspace Simultaneous measurement of multiple physics is essential for a comprehensive evaluation of all closures (wall heat transfer behavior, near wall flow and bubble dynamics, bulk flow, etc.) However, those kind of measurements are currently not available 28