Victor H. Ransom

Hyperbolic two-pressure models for two-phase flow☆

Abstract For some time it has been known that many of the two-phase flow models lead to ill-posed Cauchy problems because they have complex characteristic values. A necessary condition (at least in the linear case) for the Cauchy problem to be well-posed is that it be stable in the sense of von Neumann. For systems of partial differential equations of first order, stability in the sense of von Neumann is essentially equivalent to the condition that the model be hyperbolic (all real characteristic values and complete set of characteristic vectors). Herein models are developed which have real characteristic values for all physically acceptable states (state space) and except for a set of measure zero have a complete set of characteristic vectors in state space. Therefore, these models are hyperbolic a.e. (almost everywhere) in state space. Also, they are stable in the sense of von Neumann a.e. in state space even without inclusion of viscosity terms. The models discussed herein are developed for the case of two-phase separated planar flow and include transverse momentum considerations. These models are referred to as “two-pressure” models because each phase is assumed to exist at an average pressure different from the average pressure in the other phase; the pressure fields are related through momentum considerations. Numerical results on a steady-state problem show good agreement with existing steady-state results. Numerical results on a transient problem agree with a single-pressure model until the onset of numerical instability in the single-pressure model. Compared to the single-pressure (hydrostatic) model, the two-pressure model approximates additional physical features and is shown to be a viable approach for the case of separated flow.

The three-level scaling approach with application to the Purdue University Multi-Dimensional Integral Test assembly (PUMA)

Abstract The three-level scaling approach was developed for the scientific design of an integral test facility and then it was applied to the design of the scaled facility known as the Purdue University Multi-Dimensional Integral Test Assembly (PUMA). The NRC Technical Program Group for severe accident scaling developed the conceptual framework for this scaling methodology. The present scaling method consists of the integral system scaling, whose components comprise the first two levels, and the phenomenological scaling constitutes the third level of scaling. More specifically, the scaling is considered as follows: (1) the integral response function scaling, (2) control volume and boundary flow scaling, and (3) local phenomena scaling. The first two levels are termed the top-down approach while the third level is the bottom-up approach. This scheme provides a scaling methodology that is practical and yields technically justifiable results. It ensures that both the steady state and dynamic conditions are simulated within each component, and also scales the inter-component mass and energy flows as well as the mass and energy inventories within each component.

A CHOKED-FLOW CALCULATION CRITERION FOR NONHOMOGENEOUS, NONEQUILIBRIUM, TWO-PHASE FLOWS

Abstract This study applies the theory of characteristics to a one-dimensional transient model, in order to analyze the conditions for a choked, two-phase flow. The basic hydrodynamic model analyzed is a two-fluid model that includes relative phasic acceleration terms and a nonequilibrium, derivative-dependent exchange of mass. The analytical results provide an algebraic, choked-flow criterion analogous to that for a single-phase flow, except that terms pertaining to relative phase motion and nonequilibrium mass transfer are included. This paper discusses the numerical implementation of the choked-flow criterion in a nonhomogeneous and nonequilibrium finite difference scheme. The use of a mass-transfer model having a derivative dependence is shown to be necessary if self-choking is expected.

Stability, Accuracy, and Convergence of the Numerical Methods in RELAP5/MOD3

Both theoretical and numerical results on the relationships between the magnitude of the interphase drag coefficients, the mesh size, and the stability of the semi-implicit method used in RELAP5 are presented. It is shown that the numerical solutions are both stable and convergent on meshes with a characteristic ratio (ratio of mesh size-to-hydraulic diameter) that is not too small, that the code is capable of simulating physical instabilities on coarse meshes, and that unphysical instabilities will occur only at small mesh size even for problems that admit physical instabilities. Good transition from pre-critical heat flux (CHF) to post-CHF, however, is necessary to improve the accuracy of certain calculations.

Hyperbolic two-pressure models for two-phase flow revisited

This paper presents correction to a previous paper (J. Comput. Phys. 53 (1984). 124) on stability analyses of one-pressure models for two-phase flow. It also presents some extensions and generalization of previous work on two-pressure models. The extensions allow both the slopes to the interfaces and the rates of mass transfer through the interfaces to be non-negligible. These enlargements of the domain of applicability of the two-pressure models introduce extra derivative terms into the models. These extra derivative terms do not change the basic character of the model. The two-pressure models remain stable in the sense of von Neumann a.e. in state space with the more complete modeling of the interface. copyright 1988 Academic Press, Inc.

A Second-Order Bicharacteristics Method for Three-Dimensional, Steady, Supersonic Flow

A numerical method based on a bicharacteristics scheme for the solution of three-dimensi onal, steady, supersonic flows has been developed which has second-order accuracy. The method has been tested for order of accuracy using the exact solutions for source flow and Prandtl-Meyer flow. Comparisons with existing methods for the solution of axisymmetric flows have shown that the scheme produces accuracies comparable to that of the twodimensional method of characteristi cs. Flowfields for several three-dimensional nozzle contours were obtained. These results revealed the complex nature of the three-dimensional flows and verified the general inadequacy of quasi three-dimensional analyses which neglect cross flow. Experimental comparisons were made for a threedimensional, super-elliptic contour, and a reasonable correlation between predicted and measured pressures was obtained.

Use of an ideal scaled model for scaling evaluation

In this paper a method is described for using RELAP5 models to corroborate the scaling methodology that has been used for design of the Purdue University multidimensional Test Apparatus. This facility was built for the U.S. NRC to obtain data on the performance of the passive safety systems of the General Electric Company simplified boiling water reactor. Similarity between the prototype system and the scaled test facility is investigated for a main steam line break accident.

The particle fluid model and using Lagrangian representation in two-phase flow modeling

Abstract Particle Fluid Model (PFM) is an intermediate method between the numerically intractable local instant model and the fully averaged two-fluid model for simulating transient two-phase flows. PFM uses a Lagrangian description for the dispersed phase and an Eulerian description for the continuous phase. In this paper we report a new way to model bubble lateral transport and the resulting void–fraction profile in bubbly flows simulated by the PFM. This model is based on eddy–bubble interactions. Eddies are generated by two mechanisms namely the wall-shear induced turbulence and the bubble–wake induced turbulence. Fluctuating components of velocity due to both of these effects are obtained separately. A linear superposition of turbulent kinetic energies is performed to obtain the resultant velocity fluctuations. An empirical model is used to determine the eddy size distribution in the pipe. The bubble momentum equation is solved through a succession of eddies to establish the lateral position of that bubble. This paper presents details of our bubble dispersion model and its assessment using experimental data of Serizawa.

RELAP5 Analysis of Two-Phase Decompression and Rarefaction Wave Propagation Under a Temperature Gradient

Abstract The capability of RELAP5 to model single- and two-phase acoustic wave propagation is demonstrated with the use of fine temporal and spatial discretizations. Two cases were considered: a single-phase air shock tube problem that was simulated, resulting in a shock wave and a rarefaction wave that lie within 1% error of the analytic solution, and pressure oscillations observed by Takeda and Toda in a two-phase decompression experiment in a pipe under a temperature gradient. Whereas the agreement for the single-phase case is excellent, some discrepancies were observed in the two-phase case: 1. Thermal nonequilibrium and the associated delay in the bubble growth were identified as the cause for the dispersion of the rarefaction wave as it becomes trapped inside a two-phase fluid region. The short timescale of the experiment justifies the use of a bubble diameter that is one order of magnitude smaller than the standard RELAP5 predicted bubble diameter, which is calibrated for longer transients. 2. The initial depressurization undershoots seen in the Takeda and Toda experiment were overpredicted by the RELAP5 model. Improved agreement with the experiment was obtained by altering the discharge coefficient in the choked flow model to account for uncertainties in the discharge geometry and/or the choked flow model at low pressure. By adjusting these parameters RELAP5 produced markedly better comparisons with the experimental data. These results illustrate two generic shortcomings of nuclear reactor system codes, i.e., the absence of a dynamic model for the interfacial area concentration and uncertainty in two-phase choked flow modeling. However, it is remarkable that RELAP5 could predict the complex dynamics of the two-phase acoustic phenomena in the Takeda and Toda experiment in spite of these shortcomings.

Athena Aide - An Expert System for Athena Code Input Model Preparation

An expert system called the ATHENA AIDE that assists in the preparation of input models for the ATHENA thermal-hydraulics code has been developed by researchers at the Idaho National Engineering Laboratory. The ATHENA AIDE uses a menu driven graphics interface and rule-based and object-oriented programming techniques to assist users of the ATHENA code in performing the tasks involved in preparing the card image input files required to run ATHENA calculations. The ATHENA AIDE was developed and currently runs on single-user Xerox artificial intelligence workstations. Experience has shown that the intelligent modeling environment provided by the ATHENA AIDE expert system helps ease the modeling task by relieving the analyst of many mundane, repetitive, and error prone procedures involved in the construction of an input model. This reduces errors in the resulting models, helps promote standardized modeling practices, and allows models to be constructed more quickly than was previously possible.