The Riemann problem for fluid flow of real materials

Menikoff, Ralph; Plohr, Bradley J.

doi:10.1103/revmodphys.61.75

Cited by 652 publications

(569 citation statements)

References 79 publications

Supporting

Mentioning

560

Contrasting

Unclassified

Order By: Relevance

“…In the NASG formulation, the parameters b and p ∞ are considered constant, yielding simplicity while ensuring presence of the main molecular forces present in a fluid. In addition, as the formulation is close to the ideal gas expression, it facilitates the resolution of the Riemann problem (Plohr [24], Menikoff and Plohr [25], Cocchi and Saurel [26]). The Riemann problem is indeed the cornerstone of numerical methods used to solve hydrodynamic problem (see Toro [27] for example).…”

Section: Extended Nasg Eosmentioning

confidence: 99%

See 1 more Smart Citation

Extended Noble–Abel Stiffened-Gas Equation of State for Sub-and-Supercritical Liquid-Gas Systems Far from the Critical Point

Chiapolino

Saurel

2018

Fluids

View full text Add to dashboard Cite

Abstract:The Noble-Abel Stiffened-Gas (NASG) equation of state (Le Métayer, O. and Saurel, R. proposed in 2016) is extended to variable attractive and repulsive effects to improve the liquid phase accuracy when large temperature and pressure variation ranges are under consideration. The transition from pure phase to supercritical state is of interest as well. The gas phase is considered through the ideal gas assumption with variable specific heat rendering the formulation valid for high temperatures. The liquid equation-of-state constants are determined through the saturation curves making the formulation suitable for two-phase mixtures at thermodynamic equilibrium. The overall formulation is compared to experimental characteristic curves of the phase diagram showing good agreement for various fluids (water, oxygen). Compared to existing cubic equations of state, the present one is convex, a key feature for computations with hyperbolic flow models.

show abstract

Section: Extended Nasg Eosmentioning

confidence: 99%

“…Convexity of the equation of state requires fulfillment of five different conditions (Godunov et al [33], Menikoff and Plohr [25] that are analyzed hereafter,…”

Section: Appendix a Convexity Of The Enasg Formulationmentioning

confidence: 99%

Extended Noble–Abel Stiffened-Gas Equation of State for Sub-and-Supercritical Liquid-Gas Systems Far from the Critical Point

Chiapolino

Saurel

2018

Fluids

View full text Add to dashboard Cite

show abstract

“…The Rankine-Hugoniot relations must be supplemented with suitable admissibility criteria in order to rule out unphysical solutions. One sufficient condition is that shock waves arise as limits of travelling-wave profiles including viscosity and heat conduction (see Menikoff & Plohr 1989;Kluwick 2001). This admissibility criterion has a direct and convenient graphical interpretation: the straight segment connecting the pre-shock and post-shock states in the P-v plane (commonly referred to as the Rayleigh line) must be located either completely above or completely below the shock adiabat centred on the pre-shock state.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Isentropes in figure 1(a) intersect the liquid-vapour phase boundary along curve labelled M sat . A wide portion of the saturated vapour boundary of the fluid considered is retrograde (see Thompson, Carofano & Kim 1986;Menikoff & Plohr 1989), meaning that isentropes cross the phase boundary from the mixed towards the pure phase, in the direction of decreasing density. However, all isentropes eventually enter the two-phase region crossing a non-retrograde saturated phase boundary.…”

Section: Isentropic Flowmentioning

confidence: 99%

Exact solutions to non-classical steady nozzle flows of Bethe–Zel’dovich–Thompson fluids

Guardone

Vimercati

2016

J. Fluid Mech.

View full text Add to dashboard Cite

Steady nozzle flows of Bethe-Zel'dovich-Thompson fluids -substances exhibiting non-classical gasdynamic behaviour in a finite vapour-phase thermodynamic region in close proximity to the liquid-vapour saturation curve -are examined. Non-classical flow features include rarefaction shock waves, shock waves with either upstream or downstream sonic states and split shocks. Exact solutions for a mono-component single-phase fluid expanding from a reservoir into a stationary atmosphere through a conventional converging-diverging nozzle are determined within the quasi-onedimensional inviscid flow approximation. The novel analytical approach makes it possible to elucidate the connection between the adiabatic, possibly non-isentropic flow field and the underlying local isentropic-flow features, including the possible qualitative alterations in passing through shock waves. Contrary to previous predictions based on isentropic-flow inspection, shock disintegration is found to occur also from reservoir states corresponding to a single sonic point. The global layout of the flow configurations produced by a monotonic decrease in the ambient pressure, namely the functioning regime, is examined for reservoir conditions resulting in single-phase flows. Accordingly, a classification of steady nozzle flows into 10 different functioning regimes is proposed. Flow conditions determining the transition between the different classes of flow are investigated and each functioning regime is associated with the corresponding thermodynamic region of reservoir states.

show abstract

“…On the other hand, there are several successful methods that account for the flow wave structure through a superposition of Riemann solutions. These are local solutions of the hyperbolic equations which are composed of elementary waves (Menikoff and Plhor, 1989). These methods are based on characteristic upwind differencing and have been applied from nuclear and oil industries to solid combustion.…”

Section: Introductionmentioning

confidence: 99%

A comparison of hyperbolic solvers II: ausm-type and Hybrid Lax-Wendroff-Lax-Friedrichs methods for two-phase flows

Coelho

Lage

Telles

2010

Braz. J. Chem. Eng.

View full text Add to dashboard Cite

-Riemann-solver based schemes are difficult and sometimes impossible to be applied for complex flows due to the required average state. Other methods that do not use Riemann-solvers are best suited for such cases. Among them, AUSM+, AUSMDV and the recently proposed Hybrid Lax-Friedrichs-Lax-Wendroff (HLFW) have been extended to two-phase flows. The eigenstructure of the two-fluid model is complex due to the phase interactions, leading to numerous numerical difficulties. One of them is the well-posedness of the equation system because it may lose hyperbolicity. Therefore, the methods that are not based on the wave structure and that are not TVNI could lead to strong oscillations. The common strategy to handle this problem is the adoption of a pressure correction due to interfacial effects. In this work, this procedure was applied to HLFW and AUSM-type methods and their results analyzed. The AUSM+ and AUSMDV were extended to achieve second-order using the MUSCL strategy for which a conservative and a non-conservative formulation were tested. Additionally, several AUSMDV weighting functions were compared. The first and second-order AUSM-type and HLFW methods were compared for the solution of the water faucet and the shock tube benchmark problems. The pressure correction strategy was efficient to ensure hyperbolicity, but numerical diffusion increased. The MUSCL AUSMDV and HLFW methods with pressure correction strategy were, on average, the best of the analyzed methods for these test problems. The HLFW was more stable than the other methods when the pressure correction was considered.

show abstract

The Riemann problem for fluid flow of real materials

Cited by 652 publications

References 79 publications

Extended Noble–Abel Stiffened-Gas Equation of State for Sub-and-Supercritical Liquid-Gas Systems Far from the Critical Point

Extended Noble–Abel Stiffened-Gas Equation of State for Sub-and-Supercritical Liquid-Gas Systems Far from the Critical Point

Exact solutions to non-classical steady nozzle flows of Bethe–Zel’dovich–Thompson fluids

A comparison of hyperbolic solvers II: ausm-type and Hybrid Lax-Wendroff-Lax-Friedrichs methods for two-phase flows

Contact Info

Product

Resources

About