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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.

Whether a fire can be initiated in an explosion accident depends on the explosion and deflagration process. In the methane-air explosion in a tunnel, the flame accelerates from the ignition point. However, where it begins to decelerate is not clear. The purpose of this paper is to examine the explosion overpressure, flow and flame propagation beyond the premixed area of methane-air in a tunnel.

The numerical simulation was used to study the explosion processes of methane-air mixtures in a tunnel. Based on the numerical simulation and its analysis, the explosion overpressure, flow and flame propagation rules beyond the premixed area were demonstrated for a methane-air explosion.

The peak overpressure of methane-air mixture explosion was observed to reach its maximum beyond the original premixed area of methane-air. The hazardous effects beyond the premixed area may be stronger than those within the premixed area for a methane-air explosion in a tunnel. Under the conditions of this study, the ratio between the length of combustion area (40 m) and that of original premixed area (28 m) reaches 1.43.

Little attention has been devoted to investigating the explosion overpressure, flow and flam propagations beyond the original premixed area of methane-air in a tunnel. Based on the numerical simulation and the analysis, the propagation rule of overpressure wave and flow inside and outside the space occupied by methane/air mixture at the volume fraction of 9.5 percent in a tunnel were obtained in this work.

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.

In engineering applications, gas-solid two-phase reaction flow with multi-moving boundaries is a common phenomenon. The launch process of multiple projectiles is a typical example. The flow of adjacent powder chambers is coupled by projectile’s motion. The purpose of this paper is to study this flow by numerical simulation.

A one-dimensional two-phase reaction flow model and MacCormack difference scheme are implemented in a computational code, and the code is used to simulate the launch process of a system of multiple projectiles. For different launching rates and loading conditions, the simulated results of the launch process of three projectiles are obtained and discussed.

At low launching rates, projectiles fired earlier in the series have little effect on the launch processes of projectiles fired later. However, at higher launching rates, the projectiles fired first have a great influence on the launch processes of projectiles fired later. As the launching rate increases, the maximum breech pressure for the later projectiles increases. Although the muzzle velocities increase initially, they reach a maximum at some launching rate, and then decrease rapidly. The muzzle velocities and maximum breech pressures of the three projectiles have an approximate linear relationship with the charge weight, propellant web size and chamber volume.

This paper presents a prediction tool to understand the physical phenomenon of the gas-solid two-phase reaction flow with multi-moving boundaries, and can be used as a research tool for future interior ballistics studies of launch system of multiple projectiles.

The numerical simulation of the serial launch process of multiple projectiles is an important engineering problem. However, the projectiles’ motion law is hard to obtain completely only by interior ballistic model. The muzzle flow field affects the projectiles’ velocities when the projectiles pass through it. Also, the propellant gas from previous projectiles may decelerate the later projectiles. Therefore, the aftereffect period should be simulated together with the interior ballistic process of multiple projectiles when researching the serial launch process for accurate motion law of the projectiles.

The computational fluid dynamics (CFD) software is used to simulate the muzzle flow field. A one-dimensional two-phase reaction flow model is implemented in a computational code for the numerical simulation of gas-solid two-phase reaction flow, during the serial launch process. The computational code is coupled with CFD software by a user-defined function.

Compared with the first projectile, the formation process of the shock bottle of the second projectile is different. After the projectile head flies out of the muzzle, the projectile head pressure decreases rapidly, but then, it is not always equal to 0.1 MPa. After the projectiles leave the muzzle, the velocity increments of each projectile are mainly determined by muzzle pressure.

This paper presents a prediction tool to understand the projectiles’ motion law during the serial launch process of the multiple projectiles considering aftereffect period, and can be used as a research tool for future ballistic studies of a serial launch system of multiple projectiles.

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.

The purpose of this work is to present the implementation of weighted essentially non-oscillatory (WENO) wavelet methods for solving multiphase flow problems. The particular interest is gas–liquid two-phase mixture with velocity non-equilibrium. Numerical simulations are carried out on different scenarios of one-dimensional Riemann problems for gas–liquid flows. Results are validated and qualitatively compared with solutions provided by other standard numerical methods.

This paper extends the framework of WENO wavelet adaptive method to a fully hyperbolic two-phase flow model in a conservative form. The grid adaptivity in each time step is provided by the application of a thresholded interpolating wavelet transform. This facilitates the construction of a small yet effective sparse point representation of the solution. The method of Lax–Friedrich flux splitting is used to resolve the spatial operator in which the flux derivatives are approximated by the WENO scheme.

Hyperbolic models of two-phase flow in conservative form are efficiently solved, as shocks and rarefaction waves are precisely captured by the chosen methodology. Substantial computational gains are obtained through the grid reduction feature while maintaining the quality of the solutions. The results indicate that WENO wavelet methods are robust and sufficient to accurately simulate gas–liquid mixtures.

Resolution of two-phase flows is rarely studied using WENO wavelet methods. It is the first time such a study on the relative velocity is reported in two-phase flows using such methods.

A consistent implementation of the general computational framework of unified second-order time accurate integrators via the well-known GSSSS framework in conjunction with the traditional Finite Difference Method is presented to improve the numerical simulations of reactive two-phase flows.

In the present paper, the phase interaction evaluation in the present implementation of the reactive two-phase flows has been derived and implemented to preserve the consistency of the correct time level evaluation during the time integration process for solving the two phase flow dynamics with reactions.

Numerical examples, including the classical Sod shock tube problem and a reactive two-phase flow problem, are exploited to validate the proposed time integration framework and families of algorithms consistently to second order in time accuracy; this is in contrast to the traditional practices which only seem to obtain first-order time accuracy because of the inconsistent time level implementation with respect to the interaction of two phases. The comparisons with the traditional implementation and the advantages of the proposed implementation are given in terms of the improved numerical accuracy in time. The proposed approaches provide a correct numerical simulation implementation to the reactive two-phase flows and can obtain better numerical stability and computational features.

The new algorithmic framework and the consistent time level evaluation extended with the GS4 family encompasses a multitude of past and new schemes and offers a general purpose and unified implementation for fluid dynamics.

In computational fluid dynamics for two-phase reactive flow of interior ballistic, the conventional schemes (MacCormack method, etc.) are known to introduce unphysical oscillations in the region where the gradient is high. This paper aims to improve the ability to capture the complex shock wave during the interior ballistic cycle.

A two-phase flow model is established to describe the complex physical process based on a modified two-fluid theory. The solution of model is obtained including the following key methods: an approximate Riemann solver to construct upwind fluxes, the MUSCL extension to achieve high-order accuracy, a splitting approach to solve source terms, a self-adapting method to expand the computational domain for projectile motion and a control volume conservation method for the moving boundary.

The paper is devoted to applying a high-resolution numerical method to simulate a transient two-phase reactive flow with moving boundary in guns. Several verification tests demonstrate the accuracy and reliability of this approach. Simulation of two-phase reaction flow with a projectile motion in a large-caliber gun shows an excellent agreement between numerical simulation and experimental measurements.

This paper has implications for improving the ability to capture the complex physics phenomena of two-phase flow during interior ballistic cycle and predict the combustion details, such as the flame spreading, the formation of pressure waves and so on.

This approach is reliable as a prediction tool for the understanding of the physical phenomenon and can therefore be used as an assessment tool for future interior ballistics studies.

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.