Application of discrete adjoint method to sensitivity and uncertainty analysis in steady-state two-phase flow simulations

Guojun Hu, Tomasz Kozlowski

Research output: Contribution to journalArticle

Abstract

Adjoint method is efficient for computing sensitivities of a response to a large number of input parameters; however, a successful application of adjoint method to sensitivity analysis in two-phase flow simulations is rare. In this article, a discrete adjoint sensitivity analysis framework is developed for steady-state two-phase flow problems. The new framework is based on a new implicit forward solver. The residual function of the discretized forward governing equation is used to formulate the adjoint problem. The framework is verified with the faucet flow problem and the Boiling Water Reactor Full-size Fine-mesh Bundle Test (BFBT) benchmark. For the faucet flow problem, adjoint sensitivities are shown to match analytical sensitivities very well. For the BFBT benchmark, the adjoint sensitivities are shown to match the sensitivities calculated with a perturbation equation. The adjoint sensitivities are also used to propagate uncertainties in input parameters to the uncertainty in the response. The uncertainty propagation with the adjoint method is verified with the Monte Carlo method and is shown to be accurate and efficient.

Original languageEnglish (US)
Pages (from-to)122-132
Number of pages11
JournalAnnals of Nuclear Energy
Volume126
DOIs
StatePublished - Apr 2019

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Uncertainty analysis
Flow simulation
Two phase flow
Sensitivity analysis
Boiling water reactors
Monte Carlo methods
Uncertainty

Keywords

  • Adjoint sensitivity analysis
  • Boiling pipe
  • Two-phase flow
  • Uncertainty analysis

ASJC Scopus subject areas

  • Nuclear Energy and Engineering

Cite this

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abstract = "Adjoint method is efficient for computing sensitivities of a response to a large number of input parameters; however, a successful application of adjoint method to sensitivity analysis in two-phase flow simulations is rare. In this article, a discrete adjoint sensitivity analysis framework is developed for steady-state two-phase flow problems. The new framework is based on a new implicit forward solver. The residual function of the discretized forward governing equation is used to formulate the adjoint problem. The framework is verified with the faucet flow problem and the Boiling Water Reactor Full-size Fine-mesh Bundle Test (BFBT) benchmark. For the faucet flow problem, adjoint sensitivities are shown to match analytical sensitivities very well. For the BFBT benchmark, the adjoint sensitivities are shown to match the sensitivities calculated with a perturbation equation. The adjoint sensitivities are also used to propagate uncertainties in input parameters to the uncertainty in the response. The uncertainty propagation with the adjoint method is verified with the Monte Carlo method and is shown to be accurate and efficient.",
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N2 - Adjoint method is efficient for computing sensitivities of a response to a large number of input parameters; however, a successful application of adjoint method to sensitivity analysis in two-phase flow simulations is rare. In this article, a discrete adjoint sensitivity analysis framework is developed for steady-state two-phase flow problems. The new framework is based on a new implicit forward solver. The residual function of the discretized forward governing equation is used to formulate the adjoint problem. The framework is verified with the faucet flow problem and the Boiling Water Reactor Full-size Fine-mesh Bundle Test (BFBT) benchmark. For the faucet flow problem, adjoint sensitivities are shown to match analytical sensitivities very well. For the BFBT benchmark, the adjoint sensitivities are shown to match the sensitivities calculated with a perturbation equation. The adjoint sensitivities are also used to propagate uncertainties in input parameters to the uncertainty in the response. The uncertainty propagation with the adjoint method is verified with the Monte Carlo method and is shown to be accurate and efficient.

AB - Adjoint method is efficient for computing sensitivities of a response to a large number of input parameters; however, a successful application of adjoint method to sensitivity analysis in two-phase flow simulations is rare. In this article, a discrete adjoint sensitivity analysis framework is developed for steady-state two-phase flow problems. The new framework is based on a new implicit forward solver. The residual function of the discretized forward governing equation is used to formulate the adjoint problem. The framework is verified with the faucet flow problem and the Boiling Water Reactor Full-size Fine-mesh Bundle Test (BFBT) benchmark. For the faucet flow problem, adjoint sensitivities are shown to match analytical sensitivities very well. For the BFBT benchmark, the adjoint sensitivities are shown to match the sensitivities calculated with a perturbation equation. The adjoint sensitivities are also used to propagate uncertainties in input parameters to the uncertainty in the response. The uncertainty propagation with the adjoint method is verified with the Monte Carlo method and is shown to be accurate and efficient.

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