Post on 01-Mar-2022
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Development of a Validation and Uncertainty Quantification Framework for Closure Models in Multiphase CFD Solver
Yang Liu and Nam Dinh
Multi-Physics Model Validation WorkshopJune/28/2017
Multiphase Flow and boiling
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Multiphase Flow and boiling involves multi-scale phenomena with different physics
• Flow regime (cm)
• Bubble behavior, interfacial exchange (mm)
• Turbulence and nucleation (μm)
Eulerian-Eulerian two-fluid-model: closure dependent averaged conservative equations
Condensation&Evaporation
Turbulence
Interfacial forces
Condensation&Evaporation
Turbulence
Mass
Momentum
Energy
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Wall boiling Interfacial forcesTurbulence model
Active nucleation site density
Evaporation heat transfer
Single-phase convective
heat transfer
Quenching heat transfer
Near wall heat transfer and evaporation
Bubble induced turbulence
Wall function
Turbulent viscosity
Turbulent heat fluxTurbulent viscosity
Momentum exchange
Interfacialcondensation
Drag forceBubble size
Turbulence viscosity
force
Wall lubrication
force
Lift force
Bubble departure diameter
Bubble departure frequency
Condensation
U α h α
Uh
Nucleation
Bubble breakup
Bubble coalesce
Heat transfer partition
Closure Structure in MCFD Solver
• Wall boiling• Heat partitioning, nucleation
• Interfacial momentum
• Interfacial mass/heat transfer
• Bubble size
• Turbulence• Bubble induced turbulence
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?)
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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 workDAKOTADRAMPython scikit-learnQUESO
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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
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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
– Collect, document, qualify, structure, format, integrate and manage data and information in various forms and from various sources
Credit: Dr. W.Ren, ORNL
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NE-KAMSKnowledge
Base
Validation Experiment
V&V and UQ Guidelines
V&V and UQStandards and Requirements
V&V & UQ Assessments
Computation
M&SActivities
Data management : Database example
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Data Source: Prof. Buongiorno group, MITData are automatically processed and stored in two scales
[F1] General information NoteSource Synthetic CRUD Test (MIT) Details can be found in[ref][F2] System configurationGeometry Vertical flow in rectangular
channelFluid materials water liquid/vaporHeater materials ITO sapphire heater with
synthetic CRUD[F3] Test programFlow conditions 500 kg/m2
Heat configurations 2um thick CRUD with10um diameter chimneyson a 45um pitch
Heat flux 1400 kW/m2
[F4] Data[D0] raw data IR counts distribution[D1] primary data temperature/heat flux
distributionUsed to current VUQ workin current practice
[D2] secondary data ensemble averagedtemperature, heat flux andnucleation information
Used to current VUQ workin current practice
[D3] ternary data Nucleation sites location/interaction etc.
Used for a more detailedmodeling approach
[F5] Data characteristicsApplicability boiling model VUQ for flow
boiling on low pressureQuality Good High resolution data with
designed surface
Validation Metrics: Evaluation of model uncertainty and model form inconsistency
• Confidence intervalsThere is a α% possibility that the true error between model and data are within the given interval
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�𝐄𝐄 − 𝑡𝑡 ⁄𝛼𝛼 2,𝑣𝑣 ⋅𝐬𝐬𝑛𝑛
, �𝐄𝐄 + 𝑡𝑡 ⁄𝛼𝛼 2,𝑣𝑣 ⋅𝐬𝐬𝑛𝑛
�𝐄𝐄 = �⃗�𝐲𝑚𝑚,𝑜𝑜𝑜𝑜𝑜𝑜 −1𝑛𝑛�𝑖𝑖=1
𝑛𝑛
�⃗�𝐲𝑒𝑒𝑖𝑖
𝐬𝐬 =1
𝑛𝑛 − 1�𝑖𝑖=1
𝑛𝑛
�⃗�𝐲𝑒𝑒𝑖𝑖 − �⃗�𝐲𝑒𝑒,𝑎𝑎𝑣𝑣𝑎𝑎2
⁄1 2
Experimental Data
Response
SimulationData
“Overlapping Coefficient”
Overlapping coefficient
Model form inconsistency evaluationTotal Data Model Integration
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'sin 1,2,inconsistency TDMI gleε
∞∝ −Y Y
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
Case Study I: interfacial momentum closure
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Expression Model
Drag Schiller-Naumman
Lift Tomiyama
Wall lubrication Antal
Turbulent dispersion Gosman
Virtual mass Rusche
Bubble size Anglart
3( )
4D Da b
s
C
Dρ α= − − −a b a bM U U U U
( ) ( )La L bC ρ α= − × ∇ ×a b aM U U U
21( )
2(y )WL
a WL b S rwC D xρ α= − ⋅a bM U U n
3
4
tTD bDa bt
s bt
C
D Pr
υρ α
σ= − − ∇a bM U U
1( )
2VM ba b vm
D D
Dt DtCρ α= − −aU U
M
ref,1 sub,2 ref,2 sub,1 sub
sub,1 sub,2
(T ) (T )subs
D T D TD
T T
− + −=
−
Case Study II: Wall heat transfer closures
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Kurul & Podowski(1991) : With different closure options (Version A & B) Shaver & Podowski(2014)
Surrogate construction
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CMFD solver Surrogate
Sampling +
Gaussian Process
I.C.B.C.
Closure parameter Closure parameter
QoIs QoIsI.C.B.C.
fixed fixed
Surrogate accuracy evaluation by cross validation
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QoI MaximumRMS
MaximumABS
Voidfraction 5.98e-3 3.98e-3
Gasvelocity 2.27e-3 1.70e-3
Relativevelocity 2.31e-3 1.66e-3
Low pressure adiabatic flow High pressure subcooled boiling flow
QoI Maximum RMS
Maximum ABS
Void fraction 2.37e-3 1.48e-3
Gas velocity 2.41e-3 1.54e-3
Relative velocity 5.81e-4 3.82e-4
Liquid Temperat
ure4.58e-2 2.70e-2
Global Sensitivity Analysis: Morris Measure and Sobol indices
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Interfacial momentum terms: interfacial forces and bubble size
Wall lubrication hasinfluence on all regions
Parameters have similarsensitivity in all regionsadiabatic flow, but havedifferent behavior inboiling flow
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Wall Boiling Model
8.55E-01Cwall3.70E-01C32.34E-02C2
-7.39E-03C1
-1.85E-03Prt
-8.06E-04vonKarman-6.12E-04yPlusSL
Comparison with Sobol indices
Global Sensitivity Analysis: Morris Measure and Sobol indices
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
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Parameter Selection: ad hoc approach
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• 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
Inverse Bayesian Inference using MCMC: Gen-I model, version B
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Check of convergence: Burn in pattern and autocorrelationJoint sampling of parameters
Bubble Effective area factor
Bubble diameter constant
Turbulent convective constant
One experiment, averaged over heater surface
Validation metrics example• One experiment, averaged over heater surface
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ConstructingConfidence intervals
Model form inconsistency identification:
One experiment, Distribution along heated wall
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Indication of model form inconsistency
Gen-I model, version A Shaver model
Issue identified
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Universal ‘optimal’ parameter estimates do not exist
Inference with datasets on all conditions simultaneously
Extrapolation can lead to large error
Inference with datasets on one condition, then apply parameter distribution to other conditions
A possible solution: gain knowledge from multiple validation results
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Test: infer posterior distribution through
interpolation and extrapolation
Desired future work• With many units, the desired data needs / best available model/parameter can be obtained and aid
decision making
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1 2 3
1 1 1
1 2 3
...
......
... ... ... ...
A A AB B BC C C
Closure options
Phenomena
IET .1
IET .2
SET .1SET .2
SET .3 SET .4
………. Micro-scale
Meso-scale
Macro-scaleValidation database Unit. A
Validation database Unit. B
……
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?
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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
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