Jean-Claude Loraud

A multiphase formulation for two phase flows

This paper investigates the multi‐phase behaviour of droplets injected into a nozzle at two separate wall locations. The physical features of the droplets (rate of mass, density and radius) at each injector location are identical. This system can be described by a two‐phase Eulerian—Eulerian approach that yields classical systems of equations: three for the gaseous phase and three for the dispersed droplet phase. An underlying assumption in the two phase model is that no interaction occurs between droplets. The numerical solution of the model (using the MacCormack scheme) indicates however that the opposite jets do interact to form one jet. This inconsistency is overcome in the current paper by associating the droplets from a given injection location with a separate phase and subsequently solving equations describing a multiphase system (here, three‐phase system). Comparison of numerical predications between the two‐phase and the multiphase model shows significantly different results. In particular the mu...

Droplet break-up through an oblique shock wave

The interaction of a two-phase flow with a wedge where a stationary shock wave is initially settled is studied in a two-dimensional configuration. Before the introduction of the dispersed phase, the flow around the wedge is a supersonic one phase flow such as an attached stationary shock wave is present. Then, the dispersed phase is introduced upstream the initial position of the stationary shock wave. The purpose of this study is to point out two-phase and droplets break-up effects on the oblique shock wave. The two-dimensional equations are solved by a TVD scheme where fluxes are computed by using Riemann solver for the gas phase equations and also for the dispersed phase equations wich is an original approach due to the authors (Saurel et al. 1994). In addition to drag forces and heat and mass transfers, the process of droplets fragmentation based on the particle oscillation is considered.

Effets de l'injection de gouttes sur une onde de choc stationnaire dans une tuyère

Resume Une simulation numerique de lecoulement de gaz dans une tuyere convergente-divergente, lorsque des gouttes sont injectees dans une section du divergent, est presentee. Les equations bidimensionnelles sont resolues par un schema TVD ou les flux sont calcules en utilisant la resolution des problemes de Riemann pour les equations des phases dispersee et gazeuse. Le comportement de londe de choc initiale depend de la position de linjection des particules.

An exact Riemann solver for detonation products

Numerical methods based upon the Riemann Problem are considered for solving the general initial-value problem for the Euler equations applied to real gases. Most of such methods use an approximate solution of the Riemann problem when real gases are involved. These approximate Riemann solvers do not yield always a good resolution of the flow field, especially for contact surfaces and expansion waves. Moreover, approximate Riemann solvers cannot produce exact solutions for the boundary points. In order to overcome these shortcomings, an exact solution of the Riemann problem is developed, valid for real gases. The method is applied to detonation products obeying a 5th order virial equation of state, in the shock-tube test case. Comparisons between our solver, as implemented in Random Choice Method, and finite difference methods, which do not employ a Riemann solver, are given.

Influence de l'injection de gouttes d'eau dans de la vapeur d'eau en écoulement dans une tuyère

Resume Une simulation numerique de lecoulement de gaz chauds dans une tuyere convergente-divergente, lorsque des gouttes sont injectees dans une section du divergent est presentee. La methode est basee sur le schema explicite aux differences finies de MacCormack. Lexistence et le maintien au cours du temps dun regime decoulement sonique au col sont analyses en fonction des differents phenomenes, tels que les effets geometriques, les effets dus aux forces de frottement et au transfert de masse entre phases, qui resultent du passage de lecoulement monophasique en ecoulement diphasique.

Numerical simulation of a two‐phase dilute flow in a diffuser pipe

A numerical simulation of a two‐phase dilute flow (droplet‐gas mixture) is carried out by using a finite volume method based on Riemann solvers. The computational domain represents a one‐ended pipe with holes at its upper wall which lead into an enclosure. The aim of this study is to determine the parameters of such a flow. More specially, an analytical solution is compared with numerical results to assess the mass flow rates through the vents in the pipe. Inertia effects dominate the dynamic behaviour of droplets, which causes a non‐homogeneous flow in the cavity. The unsteady effects are also important, which makes isentropical calculation irrelevant and shows the necessity of the use of CFD tools to predict such flows. No relation can be extracted from the numerical results between the gas and the dispersed mass flow rates across the holes. But a linear variation law for the droplet mass flow versus the position of the holes is pointed out, which is independent of the incoming flow when the evaporating effects are quite low.

Analytical and numerical results on the attenuation and dispersion of an acoustic wave through a two‐phase flow

Presents validation of the Eulerian approach for unsteady two‐phase flows, whose behaviour depends on the coupling between the two phases, on the basis of the study of attentuation and dispersion of an acoustic wave propagating into a one dimensional two‐phase flow. This approach and the corresponding numerical aspects are accurate enough for later applications in more complex geometries, where “vortex shedding” phenomena take place. Attenuation and dispersion of a pressure wave in a two‐phase medium of rest was previously studied by Temkin and Dobbins. Present work is an extension of this theory to the case of a two‐phase flow. This theoretical approach leads to a numerical solution of the problem. Compares the derived results with those obtained from a direct numerical simulation based on MacCormack scheme in a finite volume formulation. Verifies that analytical and numerical approaches are in good agreement.

Unsteady convection in a cavity due to pyrolysis

Abstract Unsteady convection in a square enclosure produced by pyrolysis of combustible wall is numerically studied. Gas phase processes including mass, momentum and heat transfers are coupled with solid phase processes, heat conduction and thermal degradation (pyrolysis) through conditions at the solid interface. For the gas phase, the unsteady two dimensional Navier-Stokes equations are written in stream-function vorticity formulation under the Boussinesq approximation. Solid phase processes are described by a conduction equation. This study examines the results obtained in the case of a right combustible wall, and compares them with the case of a floor combustible wall.

Effects of the Injection of Droplets on a Stationary Shock Wave in a Nozzle

A numerical simulation of the flow of gases through a converging-diverging nozzle, where droplets are injected in a given section of the divergent, is presented. The two-dimensional equations are solved by a TVD scheme where fluxes are computed by using a new Riemann solver for the dispersed phase, and an exact Riemann solver for the gas phase equations. The behaviour of the initial shock wave as a function of the particles injection location is examined in this paper.

Solid-propellant fire in an enclosure fitted with a ceiling safety-vent

Abstract The response of an enclosure having a ceiling safety-vent to a fire of solid propellant located on the floor is investigated numerically. The full Navier—Stokes equations are solved along with the species continuity equations. A recent method is used to compute chemical equilibria and the coupling between chemistry and thermodynamics is treated according to a new strategy. The particular boundaries, which are the combustion zone of the propellant and the outflow section, require an original treatment by solving a set of ‘full’ or ‘half’ Riemann problems taking into account the transport of chemical species. The SOLAICE algorithm is successfully developed for the reactive-diffusive case dealing with particular boundaries. A fire of a standard hot homogeneous propellant in a rectangular cavity initially filled with air is simulated for two opening conditions of the safety-vent. They predict the increase in the rates of energy release and CO2/H2O production in the reaction zone caused by afterburning processes involving the air of the enclosure. The course of the compartment fire is described in terms of time evolution of the average gas temperature and pressure, and oxygen depletion for both opening configurations.