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This paper aims to clarify some aspects of the application of the Godunov method for the Baer–Nunziato equations solution on the example of the problem of shock wave – dense particles cloud interaction.

The statement of the problem corresponds to the natural experiment. Mathematical model is based on the Baer–Nunziato system of equations with algebraic right-hand side source terms that takes into account the interphase friction force. Two numerical approaches are used: Harten-Lax-van Leer method and Godunov method.

For the robust simulation using Godunov method, the application of the pressure relaxation procedure is proposed. The comparative analysis of the simulation results using two methods is carried out. The Godunov method provides significantly smaller numerical diffusion of the solid phase volume fraction in the cloud that leads to the much better agreement of the pressure curves on transducers and the dynamics of the cloud motion with the experimental data.

Godunov method for the Baer–Nunziato equations is applied for the simulation of the natural experiment on the shock wave particles cloud interaction. Up to now, the examples of the application of the Godunov method for the Baer–Nunziato equations to the investigation of the practical problems have been limited by the works of the authors of the method and the field of detonation in the heterogeneous explosives. For the robust simulations in the presence of interphase boundaries, it is proposed to use the Godunov method together with the pressure relaxation procedure.

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 multiphase model shows no jet interaction.

A numerical analysis is given for the prediction of unsteady, two‐dimensional fluid flow induced by a heat and mass source in an initially closed cavity which is vented when the internal overpressure reaches a certain level. A modified ICE technique is used for solving the Navier–Stokes equations governing a compressible flow at a low Mach number and high temperature. Particular attention is focused on the treatment of the boundary conditions on the vent surface. This has been treated by an original procedure using the resolution of a Riemann problem. The configuration investigated may be viewed as a test problem which allows simulation of the ventilation and cooling of such cavities. The injection of hot gases is found to play a key role on the temperature field in the enclosure, whereas the vent seems to produce a distortion of the dynamic flow‐field only. When the injection of hot gases is stopped, the enclosure heat transfer is strongly influenced by the vent. A comparison with the results obtained when the radiative heat transfer between the walls of the enclosure is considered, indicate that radiation dominates the heat transfer in the enclosure and alters the flow patterns significantly.

The purpose of this paper is to quantify the relative importance of the multiphase model for the simulation of a gas bubble impacted by a normal shock wave in water. Both the free-field case and the collapse near a wall are investigated. Simulations are performed on both two- and three-dimensional configurations. The main phenomena involved in the bubble collapse are illustrated. A focus on the maximum pressure reached during the collapse is proposed.

Simulations are performed using an inviscid compressible homogeneous solver based on different systems of equations. It consists in solving different mixture or phasic conservation laws and a transport-equation for the gas volume fraction. Three-dimensional configurations are considered for which an efficient massively parallel strategy was developed. The code is based on a finite volume discretization for which numerical fluxes are computed with a Harten, Lax, Van Leer, Contact (HLLC) scheme.

The comparison of three multiphase models is proposed. It is shown that a simple four-equation model is well-suited to simulate such strong shock-bubble interaction. The three-dimensional collapse near a wall is investigated. It is shown that the intensity of pressure peaks on the wall is drastically increased (more than 200 per cent) in comparison with the cylindrical case.

The study of bubble collapse is a key point to understand the physical mechanism involved in cavitation erosion. The bubble collapse close to the wall has been addressed as the fundamental mechanism producing damage. Its general behavior is characterized by the formation of a water jet that penetrates through the bubble and the generation of a blast wave during the induced collapse. Both the jet and the blast wave are possible damaging mechanisms. However, the high-speed dynamics, the small spatio-temporal scales and the complicated physics involved in these processes make any theoretical and experimental approach a challenge.

Cavitation erosion is a major problem for hydraulic and marine applications. It is a limiting point for the conception and design of such components.

Such a comparison of multiphase models in the case of a strong shock-induced bubble collapse is clearly original. Usually models are tested separately leading to a large dispersion of results. Moreover, simulations of a three-dimensional bubble collapse are scarce in the literature using such fine grids.

The aim of this work is to quantify the relative importance of the turbulence modelling for cavitating flows in thermal regime. A comparison of various transport-equation turbulence models and a study of the influence of the turbulent Prandtl number appearing in the formulation of the turbulent heat flux are proposed. Numerical simulations are performed on a cavitating Venturi flow for which the running fluid is freon R-114 and results are compared with experimental data.

A compressible, two-phase, one-fluid Navier–Stokes solver has been developed to investigate the behaviour of cavitation models including thermodynamic effects. The code is composed by three conservation laws for mixture variables (mass, momentum and total energy) and a supplementary transport equation for the volume fraction of gas. The mass transfer between phases is closed assuming its proportionality to the mixture velocity divergence.

The influence of turbulence model as regard to the cooling effect due to the vaporization is weak. Only the k – ε Jones–Launder model under-estimates the temperature drop. The amplitude of the wall temperature drop near the Venturi throat increases with the augmentation of the turbulent Prandtl number.

The interaction between Reynolds-averaged Navier–Stokes turbulence closure and non-isothermal phase transition is rarely studied. It is the first time such a study on the turbulent Prandtl number effect is reported in cavitating flows.

This study aims to evaluate blast loads on and the response of submerged structures.

An arbitrary Lagrangian–Eulerian method is developed to model fluid–structure interaction (FSI) problems of close-in underwater explosions (UNDEX). The “fluid” part provides the loads for the structure considers air, water and high explosive materials. The spatial discretization for the fluid domain is performed with a second-order vertex-based finite volume scheme with a tangent of hyperbola interface capturing technique. The temporal discretization is based on explicit Runge–Kutta methods. The structure is described by a large-deformation Lagrangian formulation and discretized via finite elements. First, one-dimensional test cases are given to show that the numerical method is free of mesh movement effects. Thereafter, three-dimensional FSI problems of close-in UNDEX are studied. Finally, the computation of UNDEX near a ship compartment is performed.

The difference in the flow mechanisms between rigid targets and deforming targets is quantified and evaluated.

Cavitation is modeled only approximately and may require further refinement/modeling.

The results demonstrate that the proposed numerical method is accurate, robust and versatile for practical use.

Better design of naval infrastructure [such as bridges, ports, etc.].

To the best of the authors’ knowledge, this study has been conducted for the first time.

Ultrahigh-speed projectile running in water with the velocity close to the speed of sound usually causes large supercavity. The computation of such transonic cavitating flows is usually difficult, thus high-speed model reflecting the compressibility of both the liquid and the vapor phases should be introduced to model such flow. The purpose of this paper is to achieve a model within an in-house developed solver to simulate the ultrahigh-speed subsonic supercavitating flows.

An improved TAIT equation adjusted by local temperature is adopted as the equation of state (EOS) for the liquid phase, and the Peng-Robinson EOS is used for the vapor phase. An all-speed variable coupling algorithm is used to unify the computations and regulate the convergence at arbitrary Mach number. The ultrahigh-speed (Ma=0.7) supercavitating flows around circular disk are investigated in contrast with the case of low subsonic (Ma=0.007) flow.

The characteristic physical variables are reasonably predicted, and the cavity profiles are compared to be close to the experimental empirical formula. An important conclusion in the compressible cavitating flow theory is verified by the numerical result that, at any specific cavitation number the cavity’s size and the drag coefficient both increase along with the rise of Mach number. On the contrary, it is found as well that the cavity’s slenderness ratio decreases when Mach number goes up. It indicates that the compressibility has different influences on the length and the radius of the supercavity.

A high-speed model reflecting the compressibility of both the liquid and the vapor phases was suggested to model the ultrahigh-speed supercavitating flows around underwater projectiles.

The aim of the study is to present a piecewise parabolic method (PPM) for numerical simulation of barotropic and nonbarotropic two‐fluid flows in more than one space dimension.

In transition layers of two components, a fluid mixture model system is introduced. Besides, conserving the mass, momentum and energy for the mixture, the model is supplemented with an advection equation for the volume fraction of one of the two fluid components to recover the pressure and track interfaces. The Tait and stiffened gas equations of state are used to describe thermodynamic properties of the barotropic and nonbarotropic components, respectively. To close the model system, a mixture equation of state is derived. The classical third‐order PPM is extended to the two‐fluid case and used to solve the model system.

The feasibility of this method has been demonstrated by good results of sample applications. Each of the material interfaces is resolved with two grid cells and there is no any pressure oscillation on the interfaces.

With the mixture model system, there may be energy gain or loss for the nonbarotropic component on the material interfaces.

The method can be applied to a wide range of practical problems.

The method is simple. It not only has the advantage of Lagrangian‐type schemes but also keeps the robustness of Eulerian schemes.

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.

The purpose of this study is to investigate the combustion of the n-Heptane droplets in the supersonic combustor with a cavity-based fuel injection configuration. The focus is on the impacts of the droplet size on combustion efficiency.

The finite volume solver is developed to simulate the two-phase reacting turbulent compressible flow using a single step reaction mechanism as finite rate chemistry. Three different fuel injection settings are studied for the considered physical geometry and flow conditions: the gas fuel injection, small droplet liquid fuel injection and big droplet fuel. The fuel is injected as a slot wall jet from the bottom of the cavity.

The results show that using the small droplet size, the complete fuel consumption and combustion efficiency can be achieved but using the big droplet sizes, most fuel exit the combustor in the liquid phase and gasified unburned fuel. It is also demonstrated that the cavity's temperature distribution of the liquid fuel case is different from the gas fuel, and two flame branches are observed there due to the droplet evaporation and combustion in the cavity.

To the best of the authors’ knowledge, this study is performed for the first time on the combustion of the n-Heptane fuel droplets in scramjet configuration, which is promising propulsion system for the future economic flights.