In the present paper we propose a reduced temperature non-equilibrium model for simulating multicomponent flows with inter-phase heat transfer, diffusion processes (including the viscosity and the ...heat conduction) and external energy sources. We derive three equivalent formulations for the proposed model. The first formulation consists of balance equations for partial densities, the mixture momentum, the mixture total energy, and phase volume fractions. The second formulation is symmetric and obtained by replacing the equations for the mixture total energy and volume fractions in the first formulation with balance equations for the phase total energy. Replacing one of the phase total energy equation of the second formulation with the mixture total energy equation gives the third formulation. All the three formulations assume velocity and pressure equilibrium across the material interface. These equivalent forms provide different physical perspectives and numerical conveniences. Temperature equilibration and continuity across the material interfaces are achieved with the instantaneous thermal relaxation. Temperature equilibrium is maintained during the heat conduction process. The proposed models are proved to respect the thermodynamical laws. For numerical solution, the model is split into a hyperbolic partial differential equation (PDE) system and parabolic PDE systems. The former is solved with the high-order Godunov finite volume method that ensures the pressure–velocity–temperature (PVT) equilibrium conduction. The parabolic PDEs are solved with both the implicit and the explicit locally iterative method (LIM) based on Chebyshev parameters. Numerical results are presented for several multicomponent flow problems with diffusion processes. Furthermore, we apply the proposed model to simulate the target ablation problem that is of significance to inertial confinement fusion. Comparisons with one-temperature models in literature demonstrate the ability to maintain the PVT property and superior convergence performance of the proposed model in solving multicomponent problems with diffusions.
•A temperature non-equilibrium model for N-component flows with diffusion•Three equivalent formulations providing new perspectives and numerical conveniences•Models consistent with thermodynamic laws and free of nonphysical oscillations•Explicit locally iterative method for solving the nonlinear diffusion equations•Application for simulating inertial confinement fusion problems
Compressible liquid–vapor flow with phase transitions can be described by systems of Navier–Stokes–Korteweg type. They extend the Navier–Stokes equations by nonlinear higher-grade terms which take ...the form of either differential or nonlocal integral operators. A numerical approximation method on the basis of the Local Discontinuous Galerkin method in multiple space dimensions is suggested for isothermal flows. It relies on a specific discretization of a non-conservative formulation. To enhance the performance of the overall scheme two techniques are used: (i) local spatial adaptivity based on gradient indicators for the density and (ii) parallelism based on domain decomposition.
The paper concludes with numerical experiments in two and three space dimensions. They show the reliability and efficiency of the proposed approach as well as they demonstrate the applicability of the models for several important phase transition phenomena.
•A coupled dual-time stepping and compressive interface capturing scheme is presented.•Interface flows are solved on curvilinear grids.•Accuracy, efficiency, and robustness are assessed for various ...interface flows.
In this paper, a compressive high-resolution interface-capturing scheme is presented for the computation of compressible multi-fluid flows with high-density ratios and strong shocks. The proposed scheme is coupled with a preconditioned dual-time compressible mixture solver for robust and accurate computations over a wide range of Mach numbers. The scheme is simple and relatively easy to implement. It does not require any calculations for the interface curvature and the normal vector. The numerical approximations were implemented on general, structured grids using an implicit MUSCL upwind approach. Validation tests were conducted for a single reversible vortex, advection of an air-water interface, dam-break flow, and air shock-helium bubble interaction. Finally, a three-dimensional gas-lift flow is presented to demonstrate the capability of the present scheme for handling an interface with large jumps in pressure, temperature, and density.
•Graded effects of foam cores of spherical shells are studied in four situations.•The loading conditions of close-in underwater explosions are investigated.•A fluid model which is used in combination ...with Abaqus/Explicit is presented.
A fluid model is developed and used in combination with Abaqus/Explicit to investigate the effects of graded foam cores on the loading of a sandwich spherical shell subject to underwater explosion from the inner side, after having validated the modeling technique by reproducing results by other authors. Based on the relation between the core strength and the stiffness of the outer face sheet (OFS), four different situations are considered to discuss the graded effects. It is demonstrated that for the case of relatively strong cores and the OFS with low stiffness or soft cores and the OFS with high stiffness, the core arrangement of low/medium/high (relative density from the inside to the outside) has the best performance to shock loadings which is a consequence of the effects of the fluid–structure interaction and the energy absorption capability; on the other hand, for the case of intermediate core strengths and stiffness of the OFS where the pulling-back force due to the stretching of the OFS is close to the core strength, the configuration of high/medium/low has the best performance due to its higher energy absorption efficiency of the foam and lower transmitted stress.
This work describes particle-resolved simulations of a single aluminum particle within a larger layer of particles that is interacting with a strong nitromethane shock. The objective is to observe ...how varying the particle’s volume fraction within a planar particle curtain changes the deformation of the particles as well as the fluid dynamics around them. First the isolated particle limit, when the distance between the neighbors is very large, is simulated; this is followed by simulating a single-layer of particles subjected to a planar shock propagating normal to the layer. Several initial particle volume fractions of the curtain are considered, and the results are compared and discussed. The results show that the presence and proximity of neighboring particles influence the shape and magnitude of the particle’s plastic deformation. The presence of neighboring particles also increases the initial average pressure within the particle during shock interaction as well as the average velocity of the particle afterwards. The strength of the reflected shock from the curtain of particles increases in magnitude and becomes more planar as the volume fraction increases due to neighboring particles’ individual reflections that coalesce to form a singular planar shock. The results obtained provide valuable insight into the microscale physics of shock interaction with an array of deformable particles.
•Fully compressible three-phase flow model with mass transfers is presented.•Interfaces are captured with a compressive interface solution of two interface advection equations.•Numerical scheme is ...examined for bubble condensation of pure steam and steam–air mixture.•The effects of air void fraction on steam condensation are investigated.
A coupled compressive interface capturing scheme and dual-time preconditioned approach was developed for the two-dimensional axisymmetric computation of compressible interface flows with mass transfers. The fully-compressible three-phase homogeneous mixture flow model was implicitly solved using the dual-time preconditioned technique on generalized curvilinear grids. The interfaces between the three phases were captured by the solution of two interface advection equations using a compressive high resolution interface capturing method. The predictive capabilities of the numerical scheme were examined for a series of bubble condensations of pure steam and steam–air mixtures in different thermal and hydrodynamic subcooled boiling flows. Reasonably good agreement with the experimental data was obtained. Subsequently, several test cases on the condensation of single steam–air mixture bubbles were performed to investigate the effects of non-condensable gases on the characteristics of a condensing bubble. The numerical results revealed a nearly linear decrease of the condensation rate with an increase of the non-condensable gas void fraction in the mixture bubble.
We present the development of an experimentally validated computational fluid dynamics model for liquid micro jets. Such jets are produced by focusing hydrodynamic momentum from a co-flowing sheath ...of gas on a liquid stream in a nozzle. The numerical model based on laminar two-phase, Newtonian, compressible Navier–Stokes equations is solved with finite volume method, where the phase interface is treated by the volume of fluid approach. A mixture model of the two-phase system is solved in axisymmetry using ~ 300,000 finite volumes, while ensuring mesh independence with the finite volumes of the size 0.25 µm in the vicinity of the jet and drops. The numerical model is evaluated by comparing jet diameters and jet lengths obtained experimentally and from scaling analysis. They are not affected by the strong temperature and viscosity changes in the focusing gas while expanding at nozzle outlet. A range of gas and liquid-operating parameters is investigated numerically to understand their influence on the jet performance. The study is performed for gas and liquid Reynolds numbers in the range 17–1222 and 110–215, and Weber numbers in the range 3–320, respectively. A reasonably good agreement between experimental and scaling results is found for the range of operating parameters never tackled before. This study provides a basis for further computational designs as well as adjustments of the operating conditions for specific liquids and gases.
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