Search NASA⌕ Search

SEARCH · Search NASA

Results for “Entropy Viscosity Method”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

RELAP-7 Numerical Stabilization: Entropy Viscosity Method

The RELAP-7 code is the next generation nuclear reactor system safety analysis code being developed at the Idaho National Laboratory (INL). The code is based on the INL's modern scientific software development framework, MOOSE (Multi-Physics Object Oriented Simulation Environment). The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical integration methods, and physical models. The end result will be a reactor systems analysis capability that retains and improves upon RELAP5's capability and extends the analysis capability for all reactor system simulation scenarios. RELAP-7 utilizes a single phase and a novel seven-equation two-phase flow models as described in the RELAP-7 Theory Manual (INL/EXT-14-31366). The basic equation systems are hyperbolic, which generally require some type of stabilization (or artificial viscosity) to capture nonlinear discontinuities and to suppress advection-caused oscillations. This report documents one of the available options for this stabilization in RELAP-7 -- a new and novel approach known as the entropy viscosity method. Because the code is an ongoing development effort in which the physical sub models, numerics, and coding are evolving, so too must the specific details of the entropy viscosity stabilization method. Here the fundamentals of the method in their current state are presented.

42 ENGINEERING↗
DOE OSTI2015

Entropy–viscosity method for the single material Euler equations in Lagrangian frame

In this work, a new finite element method for solving the Euler equations in Lagrangian coordinates is proposed. The method is stabilized by adding artificial diffusion terms compatible with positivity of mass and internal energy, a minimum principle on the specific entropy, and all generalized entropy inequalities. Two options of first-order artificial diffusion are considered. One is in the spirit of the Eulerian based method (Guermond et al., 2011 [23, 22]; Zingan et al., 2013) and the other is similar to existing viscosity stabilizations in Lagrangian frame, e.g., Dobrev et al. (2012). The method is verified to be high-order for smooth solutions even with active viscosity terms. This is achieved by using high-order finite element spaces and an entropy-based viscosity stabilization that degenerates the first-order viscous terms. This stabilization automatically distinguishes smooth and singular regions. The formal accuracy and convergence properties of the proposed methods are tested on a series of benchmark problems. This is the first result extending the entropy–viscosity methodology to the Lagrangian hydrodynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Simulations of single- and two-phase shock tubes and gravity-driven wave problems with the RELAP-7 nuclear reactor system analysis code

Propagation of pressure waves in single and two-phase flows is of key interest for nuclear safety analyses, reactor design, construction and life extension of nuclear reactors. In this work, we assess the capabilities of RELAP-7, the next-generation nuclear reactor system code, to solve single- and two-phase flows developing pressure waves. RELAP-7 is based on a 7-equation, two-phase flow model, with distinct phasic pressures. It is well established that these hyperbolic conservation laws can develop shocks and discontinuities and thus, require a stabilization numerical method. The all-Mach flow Entropy Viscosity Method (EVM) is now employed in RELAP-7 as a viscous stabilization approach. In this paper, we briefly describe the implementation of the EVM and use open-literature test cases that exhibit pressure waves to show that the entropy viscosity method performs adequately for these single- and two-phase cases.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2015

Entropy-based viscous regularization for the multi-dimensional Euler equations in low-Mach and transonic flows

We present a new version of the entropy viscosity method, a viscous regularization technique for hyperbolic conservation laws, that is well-suited for low-Mach flows. By means of a low-Mach asymptotic study, new expressions for the entropy viscosity coefficients are derived. These definitions are valid for a wide range of Mach numbers, from subsonic flows (with very low Mach numbers) to supersonic flows, and no longer depend on an analytical expression for the entropy function. In addition, the entropy viscosity method is extended to Euler equations with variable area for nozzle flow problems. The effectiveness of the method is demonstrated using various 1-D and 2-D benchmark tests: flow in a converging–diverging nozzle; Leblanc shock tube; slow moving shock; strong shock for liquid phase; low-Mach flows around a cylinder and over a circular hump; and supersonic flow in a compression corner. Convergence studies are performed for smooth solutions and solutions with shocks present.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2017

Preliminary Study on the Suitability of a Second-Order Reconstructed Discontinuous Galerkin Method for RELAP-7 Thermal-Hydraulic Modeling

This document presents a preliminary study on the suitability of a second-order reconstructed discontinuous Galerkin (rDG) method for RELAP-7 thermal-hydraulic modeling. The document begins with a brief description of the governing equations for compressible, two-phase vapor and liquid flow, with a presentation of the seven-equation formulation details. A comparative study between the second-order rDG method and the RELAP-7's finite element method (FEM) with a entropy viscosity method (EVM) based numerical stabilization scheme (namely FEM-EVM) over a series of benchmark test problems is demonstrated. The intent for this suite of test problems is to provide baseline comparison data that demonstrate the performance of 1) the rDG solution and 2) the RELAP-7's FEM-EVM solution (with RELAP-7 code version dated August 15, 2017), on problems from single- to specific, limited two-phase flows. For all the test problems in this document, the rDG solutions were obtained with a second-order, two-step, explicit strong stability preserving Runge-Kutta time integration method. The computational results clearly indicate that the performance of the rDG method is superior to that of the RELAP-7's FEM-EVM method in all the test problems presented. Therefore, as far as the test problems in this document are considered, the second-order rDG method is recommended as an improved solution method option for RELAP-7.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Viscous regularization of the full set of nonequilibrium-diffusion Grey Radiation-Hydrodynamic equations

A viscous regularization technique, based on the local entropy residual, was proposed by Delchini et al. (2015) to stabilize the nonequilibrium-diffusion Grey Radiation-Hydrodynamic equations using an artificial viscosity technique. This viscous regularization is modulated by the local entropy production and is consistent with the entropy minimum principle. However, Delchini et al. (2015) only based their work on the hyperbolic parts of the Grey Radiation-Hydrodynamic equations and thus omitted the relaxation and diffusion terms present in the material energy and radiation energy equations. Here in this paper, we extend the theoretical grounds for the method and derive an entropy minimum principle for the full set of nonequilibrium-diffusion Grey Radiation-Hydrodynamic equations. This further strengthens the applicability of the entropy viscosity method as a stabilization technique for radiation-hydrodynamic shock simulations. Radiative shock calculations using constant and temperature-dependent opacities are compared against semi-analytical reference solutions, and we present a procedure to perform spatial convergence studies of such simulations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

Entropy-based artificial viscosity stabilization for non-equilibrium Grey Radiation-Hydrodynamics

The entropy viscosity method is extended to the non-equilibrium Grey Radiation-Hydrodynamic equations. The method employs a viscous regularization to stabilize the numerical solution. The artificial viscosity coefficient is modulated by the entropy production and peaks at shock locations. The added dissipative terms are consistent with the entropy minimum principle. A new functional form of the entropy residual, suitable for the Radiation-Hydrodynamic equations, is derived. We demonstrate that the viscous regularization preserves the equilibrium diffusion limit. The equations are discretized with a standard Continuous Galerkin Finite Element Method and a fully implicit temporal integrator within the MOOSE multiphysics framework. The method of manufactured solutions is employed to demonstrate second-order accuracy in both the equilibrium diffusion and streaming limits. Several typical 1-D radiation-hydrodynamic test cases with shocks (from Mach 1.05 to Mach 50) are presented to establish the ability of the technique to capture and resolve shocks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A phase-field method for boiling heat transfer

Here we present a phase field method for heat transfer in two-phase flow with boiling. The vapor/liquid interface evolution is modeled by the Cahn-Hilliard equation. The phase change rate is determined by accounting for the heat conduction balance on either vapor or liquid side of the interfacial area, depending on which side the temperature is assumed to be maintained at the saturation temperature during boiling. The velocity correction scheme proposed by Dong & Shen [27] is extended to solve the Navier-Stokes equations for a non-solenoidal velocity field, and the entropy viscosity method is employed for stabilization. The phase change model is verified by two-dimensional simulations of a vapor bubble growing in super-heated liquid and in film boiling. In both cases, mesh independence of the results is systematically performed. Subsequently, the method is applied to predict the growth of three-dimensional vapor bubble in a rectangular microchannel with boiling flow, achieving good agreement with experimental measurements and available simulation results using the level-set method. The numerical experiments demonstrate that the required mesh resolution for the phase field method is comparable with that of volume of fluid (VoF) and level-set methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1988

An entropy and viscosity corrected potential method for rotor performance prediction

An unsteady Full-Potential Rotor code (FPR) has been enhanced with modifications directed at improving its drag prediction capability. The shock generated entropy has been included to provide solutions comparable to the Euler equations. A weakly interacted integral boundary layer has also been coupled to FPR in order to estimate skin-friction drag. Pressure distributions, shock positions, and drag comparisons are made with various data sets derived from two-dimensional airfoil, hovering, and advancing high speed rotor tests. In all these comparisons, the effect of the nonisentropic modification improves (i.e., weakens) the shock strength and wave drag. In addition, the boundary layer method yields reasonable estimates of skin-friction drag. Airfoil drag and hover torque data comparisons are excellent, as are predicted shock strength and positions for a high speed advancing rotor.

Bridgeman, John O.↗
DOE OSTI2016

Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization

Here we present a novel approach to the simulation of miscible displacement by employing adaptive enriched Galerkin finite element methods (EG) coupled with entropy residual stabilization for transport. In particular, numerical simulations of viscous fingering instabilities in heterogeneous porous media and Hele–Shaw cells are illustrated. EG is formulated by enriching the conforming continuous Galerkin finite element method (CG) with piecewise constant functions. The method provides locally and globally conservative fluxes, which are crucial for coupled flow and transport problems. Moreover, EG has fewer degrees of freedom in comparison with discontinuous Galerkin (DG) and an efficient flow solver has been derived which allows for higher order schemes. Dynamic adaptive mesh refinement is applied in order to reduce computational costs for large-scale three dimensional applications. In addition, entropy residual based stabilization for high order EG transport systems prevents spurious oscillations. Numerical tests are presented to show the capabilities of EG applied to flow and transport.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

RELAP-7 Progress Report. FY-2015 Optimization Activities Summary

This report summarily documents the optimization activities on RELAP-7 for FY-2015. It includes the migration from the analytical stiffened gas equation of state for both the vapor and liquid phases to accurate and efficient property evaluations for both equilibrium and metastable (nonequilibrium) states using the Spline-Based Table Look-up (SBTL) method with the IAPWS-95 properties for steam and water. It also includes the initiation of realistic closure models based, where appropriate, on the U.S. Nuclear Regulatory Commission’s TRACE code. It also describes an improved entropy viscosity numerical stabilization method for the nonequilibrium two-phase flow model of RELAP-7. For ease of presentation to the reader, the nonequilibrium two-phase flow model used in RELAP-7 is briefly presented, though for detailed explanation the reader is referred to RELAP-7 Theory Manual [R.A. Berry, J.W. Peterson, H. Zhang, R.C. Martineau, H. Zhao, L. Zou, D. Andrs, “RELAP-7 Theory Manual,” Idaho National Laboratory INL/EXT-14-31366(rev. 1), February 2014].

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS1975

Theoretical study of production of unique glasses in space

The potential of producing the glassy form of selected materials in the weightless, containerless nature of space processing is examined through the development of kinetic relationships describing nucleation and crystallization phenomena. Transformation kinetics are applied to a well-characterized system (SiO2), an excellent glass former (B2O3), and a poor glass former (Al2O3) by conventional earth processing methods. Viscosity and entropy of fusion are shown to be the primary materials parameters controlling the glass forming tendency. For multicomponent systems diffusion-controlled kinetics and heterogeneous nucleation effects are considered. An analytical empirical approach is used to analyze the mullite system. Results are consistent with experimentally observed data and indicate the promise of mullite as a future space processing candidate.

Larsen, D. C.↗
NASA NTRS1989

Shock capturing by the spectral viscosity method

A main disadvantage of using spectral methods for nonlinear conservation laws lies in the formation of Gibbs phenomenon, once spontaneous shock discontinuities appear in the solution. The global nature of spectral methods than pollutes the unstable Gibbs oscillations overall the computational domain, and the lack of entropy dissipation prevents convergences in these cases. The Spectral Viscosity method, which is based on high frequency dependent vanishing viscosity regularization of the classical spectral methods is discussed. It is shown that this method enforces the convergence of nonlinear spectral approximations without sacrificing their overall spectral accuracy.

Tadmor, Eitan↗
DOE OSTI2022

Well-Balanced Second-Order Convex Limiting Technique for Solving the Serre–Green–Naghdi Equations

In this article, we introduce a numerical method for approximating the dispersive Serre–Green–Naghdi equations with topography using continuous finite elements. The method is an extension of the hyperbolic relaxation technique introduced in Guermond et al. (J Comput Phys 450:110809, 2022). It is explicit, second-order accurate in space, third-order accurate in time, and is invariant-domain preserving. It is also well balanced and parameter free. Special attention is given to the convex limiting technique when physical source terms are added in the equations. The method is verified with academic benchmarks and validated by comparison with laboratory experimental data.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2000

On the Coupling of CDISC Design Method with FPX Rotor Code

A rotor section aerodynamics design package is developed by coupling Constrained Direct Iterative Surface Curvature (CDISC) design method with the FPX rotor code. The coupling between the CDISC design and the FPX flow analysis is fully automated. The CDISC design method employs a predictor-corrector procedure iteratively to determine a surface geometry which produces a target pressure distribution, where the target pressure distributions is either pre-defined or automatically generated through flow and geometry constraints. The FPX code is an eXtended Full-Potential rotor Computational Fluid Dynamics (CFD) code, which solves the three-dimensional unsteady full-potential equation in a strong conservative form using an implicit approximate factorization finite-difference scheme with entropy and viscosity corrections. Application of the CDISC design method coupled with the FPX rotor code is made for rotor blades in hovering motions. Several design examples are presented to demonstrate the capability of the new package in rotor section design.

Hu, Hong↗
NASA NTRS1980

An artificial energy method for calculating flows with shocks

The artificial-viscosity method, first proposed by von Neumann and Richtmyer, introduces an artificial viscous pressure term in regions of compression such that an increase in entropy occurs in shock transition zones. The paper describes how dissipative flows can be induced by reducing the total energy available for adiabatic processes in shock zones. A class of inviscid fluid flows, called semiflows, is described in which the flows exhibit thermodynamic differences. Induced dissipative flows modify the pressure in regions of compression in a manner analogous to the artificial-viscosity method and for a gas, the effect is equivalent to suitably modifying the gas constant in the equation of state. By employing MacCormack's method and the usual non-adiabatic equations, numerical solutions of a Riemann problem are compared with the modified artificial energy method, showing that the dissipation effect predicted by the analytical formulation is reflected in the numerical method as well.

Rose, M. E.↗
DOE OSTI2015

Leading-order anisotropic hydrodynamics for central collisions

In this work, we use leading-order anisotropic hydrodynamics to study an azimuthally symmetric boost-invariant quark-gluon plasma. We impose a realistic lattice-based equation of state and perform self-consistent anisotropic freeze-out to hadronic degrees of freedom. We then compare our results for the full spatiotemporal evolution of the quark-gluon plasma and its subsequent freeze-out to results obtained using 1+1D Israel-Stewart second-order viscous hydrodynamics. We find that for small shear viscosities, 4πη/s ~1, the two methods agree well for nucleus-nucleus collisions; however, for large-shear-viscosity-to-entropy-density ratios or proton-nucleus collisions we find important corrections to the Israel-Stewart results for the final particle spectra and the total number of charged particles. Finally, we demonstrate that the total number of charged particles produced is a monotonically increasing function of 4πη/s in Israel-Stewart viscous hydrodynamics, whereas in anisotropic hydrodynamics it has a maximum at 4πη/s ~10. For all 4πη/s > 0, we find that for Pb-Pb collisions Israel-Stewart viscous hydrodynamics predicts more dissipative particle production than anisotropic hydrodynamics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗