The Discrete Equation Method (DEM) for Fully Compressible Two-Phase Flows in Ducts of Spatially Varying Cross-Section

Conference · Wed Jul 01 00:00:00 EDT 2009

OSTI ID:950983

Berry, Ray A; Saurel, Richard; Grimmett, Tamara

Typically, multiphase modeling begins with an averaged (or homogenized) system of partial differential equations (traditionally ill-posed) then discretizes this system to form a numerical scheme. Assuming that the ill-posedness problem is avoided by using a well-posed formulation such as the seven-equation model, this presents problems for the numerical approximation of non-conservative terms at discontinuities (interfaces, shocks) as well as unwieldy treatment of fluxes with seven waves. To solve interface problems without conservation errors and to avoid this questionable determination of average variables and the numerical approximation of the non-conservative terms associated with 2 velocity mixture flows we employ a new homogenization method known as the Discrete Equations Method (DEM). Contrary to conventional methods, the averaged equations for the mixture are not used, and this method directly obtains a (well-posed) discrete equation system from the single-phase system to produce a numerical scheme which accurately computes fluxes for arbitrary numbers of phases and solves non-conservative products. The method effectively uses a sequence of single phase Riemann equation solves. Phase interactions are accounted for by Riemann solvers at each interface. Flow topology can change with changing expressions for the fluxes. Non-conservative terms are correctly approximated. Some of the closure relations missing from the traditional approach are automatically obtained. Lastly, we can often times identify the continuous equation system, resulting from taking the continuous limit with weak wave assumptions, of the discrete equations. This can be very useful from a theoretical standpoint. As a first step toward implict integration of the DEM method in multidimensions, in this paper we construct a DEM model for the flow of two compressible phases in 1-D ducts of spatially varying cross-section to test this approach. To relieve time step size restrictions due to stiffness and to achieve tighter coupling of equations, a fully implicit time integration method is employed. For the first time, we demonstrate on a converging-diverging two-phase nozzle that this well-posed, 2 pressure, 2 velocity DEM model can be integrated to a meaningful steady-state with both phases treated as compressible.

• Research Organization: Idaho National Lab. (INL), Idaho Falls, ID (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: DE-AC07-99ID-13727
• OSTI ID: 950983
• Report Number(s): INL/CON-08-15014; TRN: US0902098
• Resource Relation: Conference: 17th International Conference on Nuclear Engineering (ICONE17),Brussels, Belgium,07/12/2009,07/16/2009
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
22 GENERAL STUDIES OF NUCLEAR REACTORS
42 ENGINEERING
APPROXIMATIONS
CLOSURES
DUCTS
FLEXIBILITY
HOMOGENIZATION METHODS
MIXTURES
NOZZLES
NUCLEAR ENGINEERING
PARTIAL DIFFERENTIAL EQUATIONS
SIMULATION
TOPOLOGY
TWO-PHASE FLOW
VELOCITY
compressible flow
DEM
discrete equation method
multiphase flow