Verification, Validation & Uncertainty Quantification

1. Verification, Validation & Uncertainty Quantification

2. Verification StrategySanjivaLele, ParvizMoin, Ali Mani (Stanford)Iain Boyd (Univ. Michigan), Krishnan Mahesh (Univ. Minnesota), James Glimm (SUNY)

3. Verification • Target application involves multi-way coupling between particles, turbulent flow and thermal radiation • In addition to the low-M variable density Navier-Stokes, thermal energy and radiative transfer the simulations will use physical models and numerical models for: • Momentum exchange between particles and flow • Thermal exchange between particles and flow • Inter-particle interactions • Particle-wall interactions • Radiation coupling

4. Verification • Target application involves multi-way coupling between particles, turbulent flow and thermal radiation • In addition to the low-M variable density Navier-Stokes, thermal energy and radiative transfer the simulations will use physical models and numerical models for: • [Physical models] • Numerical treatment of two-way and four-way coupling • Point-approximation in particle-laden turbulent flow • Integration of radiation transport and coupling

5. Verification Target application involves multi-way coupling between particles, turbulent flow and thermal radiation In addition to the low-M variable density Navier-Stokes, thermal energy and radiative transfer the simulations will use physical models and numerical models for: [Physical models] [Numerical models] This is about correctness of the implementations

6. “Multilevel” Modeling

7. “Multilevel” Verification

8. “Multilevel” Verification … more in Swetava’s poster

9. Verification – Test Problems Extensions required to Lagrangian tracking and radiation Analytical and semi-analytical solutions Special limiting cases Simplified regimes (various decoupling, fully coupled 1-D, transient, etc.) Manufactured solutions Variable density flow with radiation Eulerian-Lagrangian model with particles

10. Verification – Approaches Space/Time Discretization - Convergence Tests Solution Sensitivity - Correctness Tests Partition Independence Initial condition Independence ….

11. Verification – Approaches Lagrangian/Eulerian Numerical Methods introduce additional challenges Capecelatro, Desjardin JCP 2012 Particle/Gas Energy Coupling Term Space/Time Discretization - Convergence Tests Solution Sensitivity - Correctness Tests Partition Independence Initial condition Independence ….

12. Verification – Approaches Initial extension to particle-laden turbulence • Intrusive Approach - Explicit Filtering • Introduce a numerical length scale independent of the grid size to achieve formal convergence • Differentiable filters and grid-independent LES developed at Stanford

13. Verification – Approaches Particle clusters (PDF of particle TKE) at late time are statistically stationary • Intrusive Approach - Explicit Filtering • Introduce a numerical length scale independent of the grid size to achieve formal convergence • Non-Intrusive Approach – W* (Young Measure) Convergence • introduce coarse grained subdomain (or supercells). Supercells provide spatial localization, sufficient if the statistical flow description is slowly varying in space.

14. Verification – Approaches … more in Javier’s poster … more in Vinay’s poster Particle clusters (PDF of particle TKE) at late time are statistically stationary • Intrusive Approach - Explicit Filtering • Introduce a numerical length scale independent of the grid size to achieve formal convergence • Non-Intrusive Approach – W* (Young Measure) Convergence • introduce coarse grained subdomain (or supercells). Supercells provide spatial localization, sufficient if the statistical flow description is slowly varying in space.

15. Verification Plan • Short Term (1-2 yrs) – Develop a suite of verification test cases for single physics, two-way coupling, and all-way coupling – used by both p-code and c-code • Analytical & Semi-analytical • Manufactured Solutions • Long Term (2-4yrs) – Demonstrate verification approaches on integrated problem using p-code • Explicit Filtering • W* • Further Opportunities – Integrate verification strategy and code correctness/resiliency

16. Validation ExperimentsJohn Eaton, Chris Elkins, Andrew Banko (Stanford)FilippoColetti (Univ. Minnesota)

17. Validation Experiments • Data in the literature • Reduced coupling: no radiation • No granularity in measurements • Limited information on losses and boundary conditions • Single parameter experiments

18. Validation Experiments • Data in the literature • Reduced coupling: no radiation • No granularity in measurements • Limited information on losses and boundary conditions • Single parameter experiments • Opportunity • Build on established collaboration during PSAAP • Leverage investments in particle-laden turbulence

19. Experimental Apparatus PIV/LDA seed Sealed, pressurized screw feeder 200 x 200 mm2 0.45 m Nickel seeding Acrylic 0.19 m 3 screens/grids Flow conditioning 0.2 m 25:1 contraction (5th order poly.) Honeycomb + mesh Development length 40 x 40 mm2 Cyclone separator Development length (one shown) Aluminum 2 m Valve Test section(s) Blower Flow meter Filter Flow meter Valve

20. Experiment Overview Nominal Conditions 40 mm square channel Fully developed turbulent inflow Uniform mean particle loading Particles smaller than all turb. scales Uniform near-infrared illumination in two test region Measurements Upstream, middle, downstream Integral and model support measurements Parameter variations to test sensitivity

21. Measurements Phase 1: Integral measurements: yrs 1 -3 Phase 2: Physics/model support: yrs 2-5

22. Tight Coupling to Simulation • Experiment >>> Simulation • Validation including parameter variation • Physical understanding and model guidance • Simulation >>> Experiment • 1D/Homogeneous models give starting parameter sets • Particle selection from Mie scattering model • Simple fully coupled models show problems (e.g. turbophoresis) • UQ calculations inform measurement fidelity requirements • Specification of inlet particle uniformity • Documentation of radiation uniformity • Individual particle properties

23. 1-D Models H H L Flow direction

24. Nominal Case (Low Power)

25. High Loading, High Power

26. Illumination System • (directivity of lamps exaggerated in the picture for illustration purposes) • 12 x 1.6 kW IR lamps • back side gold-plated for frontward emission • individually rotated for maximum homogeneity of radiation density • Polished aluminum mirrors to concentrate radiation towards test section • Small but non-negligible radiation absorbed by the mirror (≈3-5% absorptivity)

27. Illumination Uncertainties • Characterization of the lamps (wavelenghtl) • Losses through walls, absorption at mirrors, misalignment, etc.

28. Illumination Uncertainties • Characterization of the lamps (wavelenghtl) • Losses through walls, absorption at mirrors, misalignment, etc. • Particle properties (shape, size, absorption, …) • How to select particle?

29. Particle Selection • Constraints • Safety: size, toxicity, flammability • Dynamics: St, Bi, Qabs • Ease of use • Consistency: aerodynamic sorting • Cost, reusability • Status • Nickel particles • Small scale experiment planning to quantify absorption

30. Particle-Radiation Test • Goal: test radiation-particle interaction without significant air flow • Solar simulator: Xenon lamps, heat flux up to 8 MW/m2 • Calorimeter + thermocouple in particle stream • Scale to measure settling rate w/ and w/o radiation • Parameterstovary: • particlesize • particle mass flux • radiationintensity screw feeder quartz window calorimeter scale Xenon lamps

31. Risks and Mitigation • Safety risks: hot section and particle inhalation • Rapid cold air dilution • Sealed closed loop apparatus + protective breathing apparatus • Aerodynamically remove fines prior to experiments • Something unexpected (explosion, high reflectivity) when particles exposed to high radiation • Preliminary open experiment • Start channel experiments at low loading • Homogeneous flow models • Turbophoresis makes difficult inlet condition • Point-particle channel flow simulation • Roughness in development duct to enhance dispersion

32. Risks and Mitigation (2) • No effect of radiation on particle distribution • Homogeneous flow simulations for particle selection • Wide range of parameters (Re/mass loading)in single apparatus • Integral measurements can’t discriminate between models. • Experiments designed for low and well-understood uncertainty • Early computational UQ on simple channel flow models • Detailed measurements add another level of discrimination • Non uniformity of illumination dominates • Early UQ of fully coupled system and non-uniform illumination • Rough uniformity documentation using transient, thin plate calorimeter • Adjustable illumination system

33. Risks and Mitigation (2) … more in Andrew’s poster • No effect of radiation on particle distribution • Homogeneous flow simulations for particle selection • Wide range of parameters (Re/mass loading)in single apparatus • Integral measurements can’t discriminate between models. • Experiments designed for low and well-understood uncertainty • Early computational UQ on simple channel flow models • Detailed measurements add another level of discrimination • Non uniformity of illumination dominates • Early UQ of fully coupled system and non-uniform illumination • Rough uniformity documentation using transient, thin plate calorimeter • Adjustable illumination system

34. Validation Experiment Plan • Phase 1 (1-3 yrs) – Set-up the apparatus and perform integral measurements • Power absorption • Mean temperatures • Uncertainty analysis (includes no-flow tests) • Phase 2 (2-5yrs) – Physics/model support • Fluid mean velocities and fluctuations • Particle concentration, velocity, spectra • Temperature spectra • Uncertainty analysis • Further Steps – Detailed characterization of inflow and BCs

35. Uncertainty Quantification Gianluca Iaccarino, George Papanicolaou (Stanford)AlirezaDoostan (Univ. Colorado, Boulder), James Glimm (SUNY)

36. Sources of Uncertainty Lycopodium, Eaton’s Lab • How to characterize them? • Use a combination of data in literature data and dedicated experiments (binning, no-flow tests, etc.) • Use initial UQ analysis to identify what is important Sandia Report 1999 Naturally occurring (AUQ) • Particle size/property variability • Radiation forcing • Losses through walls • Inflow/Injection conditions … • Mathematical models • Particle physics • Radiation/particle coupling • Airflow/particle interactions …

37. Sources of Uncertainty A – Reflection B – Refraction C – Internal reflection/refraction D – Diffraction • How to characterize them? • Simplified unit problems • Hierarchy of models Introduced by physical models (EUQ) • Particle physics • Radiation/particle coupling • Airflow/particle interactions …

38. How many uncertainties? All formally independent random quantities Random Fields Particles • Moderate mass loading: 10M • Diameters, eccentricity • Absorptivity, emissivity, conductivity … Radiation • IR lamp wavelength • Losses, distortion …

39. Initial Steps • 1D-1D model (stochastic) • Perturbation in Dp • Solved using Collocation DT = Tp-Tg 1D model (deterministic) • ODEs for momentum/energy

40. Initial Steps, II DT = Tp-Tg … more in Gianluca’s poster 1D-MultiD model (random field) • Spatial (x) variability in Dp, heat losses and radiation intensity • Stochastic collocation & ANOVA • 10K solutions…

41. UQ Approach Particle/Gas Energy Coupling Term • Need to compute sensitivities and uncertainty ranking efficiently with 1000s of inputs • Black-box vs. Clear-box approach …

42. UQ Approach Particle/Gas Energy Coupling Term Uncertainties in particle size, shape, properties, etc. Particle Transport Gas Momentum/Energy “local” effect Uncertainties in lighting uniformity, wavelength, etc. feedback … more in Akshay’s poster • Need to compute sensitivities and uncertainty ranking efficiently with 1000s of inputs • Black-box vs. Clear-box approach …

43. UQ Propagation • “Extreme” high dimensionality poses challanges • MLMC considers a decomposition of solution on a set of nested grids with the hope that variability of solution difference on consecutive grids becomes smaller. • Demonstrated on model problems, needs considerable extensions • Opportunities • Can we “telescope” on particles? • On supercells? , i.e. multiple small • particle-laden turbulence boxes • Combine with fault-tolerance … more in Alireza’s poster

44. UQ Plan • Phase 1 (1-3 yrs) – provide simulation support for estimating uncertainties, sensitivities and ranking • Simplified 1D,2D stochastic models • Intrusive and Semi-intrusive multi-physics decoupling • Multi Level Monte Carlo customization • Phase 2 (2-5yrs) – expand on numerical techniques and stochastic computation framework and focus on physical-model uncertainty • (Coupled) MLMC and decoupling techniques for large-scale parallelism • Epistemic uncertainty induced by physical models, following perturbation ideas introduced in PSAAP • Probabilistic DSL

45. Summary • VVUQ is a critical, foundational component of the Center • Verification • Experience with MMS and unit problems • New Challenges because of the Eulerian/Lagrangian nature of the problem • Intrusive & Non-Intrusive Approaches • Validation • Designed a tailored experimental campaign • Multiple prediction targets (integral, local) • Strong interaction between computations & experiments • Uncertainty Quantification • # of uncertainties is overwhelming • Aleatory and epistemic sources • Both intrusive and non-intrusive approaches

46. VVUQ – More Today Ari Frankel/HadiPouransari– Presentation on p-code SwetavaGanguli/SanjivaLele– Verification Strategy Javier Urzay/ParvizMoin– SGS of particle-laden turbulence VinayMahadeo/James Glimm– W* Convergence Andrew Banko/John Eaton – Validation Experiment Gianluca Geraci– UQ of the 1D model Akshay Mittal – Multiphysics (de)coupling for UQ AlirezaDoostan– MLMC

47. Discussion & Comments

48. Uo Io (x) Uo Io (x)