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Verification, Validation & Uncertainty Quantification. Verification Strategy Sanjiva Lele , Parviz Moin , Ali Mani (Stanford) Iain Boyd (Univ. Michigan), Krishnan Mahesh (Univ. Minnesota), James Glimm (SUNY). Verification.

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Verification, Validation & Uncertainty Quantification

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Verification validation uncertainty quantification

Verification, Validation & Uncertainty Quantification


Verification validation uncertainty quantification

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


Verification

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


Verification1

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


Verification2

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


Multilevel modeling

“Multilevel” Modeling


Multilevel verification

“Multilevel” Verification


Multilevel verification1

“Multilevel” Verification

… more in Swetava’s poster


Verification test problems

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


Verification approaches

Verification – Approaches

Space/Time Discretization - Convergence Tests

Solution Sensitivity - Correctness Tests

Partition Independence

Initial condition Independence

….


Verification approaches1

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

….


Verification approaches2

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


Verification approaches3

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.


Verification approaches4

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.


Verification plan

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


Validation experiments john eaton chris elkins andrew banko stanford filippo coletti univ minnesota

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


Validation experiments

Validation Experiments

  • Data in the literature

    • Reduced coupling: no radiation

    • No granularity in measurements

    • Limited information on losses and boundary conditions

    • Single parameter experiments


Validation experiments1

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


Experimental apparatus

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


Experiment overview

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


Measurements

Measurements

Phase 1: Integral measurements: yrs 1 -3

Phase 2: Physics/model support: yrs 2-5


Tight coupling to simulation

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


1 d models

1-D Models

H

H

L

Flow direction


Nominal case low power

Nominal Case (Low Power)


High loading high power

High Loading, High Power


Verification validation uncertainty quantification

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)


Verification validation uncertainty quantification

Illumination Uncertainties

  • Characterization of the lamps (wavelenghtl)

  • Losses through walls, absorption at mirrors, misalignment, etc.


Verification validation uncertainty quantification

Illumination Uncertainties

  • Characterization of the lamps (wavelenghtl)

  • Losses through walls, absorption at mirrors, misalignment, etc.

  • Particle properties (shape, size, absorption, …)

  • How to select particle?


Particle selection

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


Particle radiation test

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


Risks and mitigation

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


Risks and mitigation 2

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


Risks and mitigation 21

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


Validation experiment plan

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


Verification validation uncertainty quantification

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


Sources of uncertainty

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


  • Sources of uncertainty1

    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


    How many uncertainties

    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


    Initial steps

    Initial Steps

    • 1D-1D model (stochastic)

    • Perturbation in Dp

    • Solved using Collocation

    DT = Tp-Tg

    1D model (deterministic)

    • ODEs for momentum/energy


    Initial steps ii

    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…


    Uq approach

    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


    Uq approach1

    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


    Uq propagation

    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


    Uq plan

    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


    Summary

    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


    Vvuq more today

    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


    Discussion comments

    Discussion & Comments


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