Evaporation/condensation boundary conditions for the regularized 13 moment equations

The regularized 13 moment equations (R13) are a macroscopic model for the description of rarefied gas flows in the transition regime. The equations have been shown to give meaningful results for Knudsen numbers up to about 0.5. Here, their range of applicability is extended by boundary conditions for evaporating and condensing interfaces, derived from the microscopic interface conditions of kinetic theory. Simple 1-D problems are used to test the R13 equations with evaporation and condensation

Simulations of condensation flows induced by reflection of weak shocks from liquid surfaces

The condensation of a vapor onto a planar liquid surface, caused by the reflection of a weak shock wave, is studied by three different simulation method. The first one is based on molecular dynamics (MD) simulations of the Lennard-Jones fluid which are supposed to provide reference solutions. The second method is based on a Diffuse Interface Model (DIM), consistent with the thermodynamic properties of the Lennard-Jones fluid as well as with its transport properties. The third method is based on a hybrid model (HM) in which the liquid is described by a purely hydrodynamic approach, whereas the vapor is described by the Boltzmann equation. The two phases are connected by kinetic boundary conditions. The results show that DIM fails to accurately predict the condensation rate when the vapor is dilute but becomes more accurate when the vapor phase gets denser. HM reproduces MD simulations of nearly ideal vapor condensations with good accuracy, assuming unit condensation coefficient

Oxygen transport properties estimation by classical trajectory-direct simulation Monte Carlo

Coupling direct simulation Monte Carlo (DSMC) simulations with classical trajectory calculations is a powerful tool to improve predictive capabilities of computational dilute gas dynamics. The considerable increase in computational effort outlined in early applications of the method can be compensated by running simulations on massively parallel computers. In particular, Graphics Processing Unit acceleration has been found quite effective in reducing computing time of classical trajectory (CT)-DSMC simulations. The aim of the present work is to study dilute molecular oxygen flows by modeling binary collisions, in the rigid rotor approximation, through an accurate Potential Energy Surface (PES), obtained by molecular beams scattering. The PES accuracy is assessed by calculating molecular oxygen transport properties by different equilibrium and non-equilibrium CT-DSMC based simulations that provide close values of the transport properties. Comparisons with available experimental data are presented and discussed in the temperature range 300–900 K, where vibrational degrees of freedom are expected to play a limited (but not always negligible) role

Role of diffusion on molecular tagging velocimetry technique for rarefied gas flow analysis

The molecular tagging velocimetry (MTV) is a well-suited technique for velocity field measurement in gas flows. Typically, a line is tagged by a laser beam within the gas flow seeded with light emitting acetone molecules. Positions of the luminescent molecules are then observed at successive times and the velocity field is deduced from the analysis of the tagged line displacement and deformation. However, the displacement evolution is expected to be affected by molecular diffusion, when the gas is rarefied. Therefore, there is no direct and simple relationship between the velocity field and the measured displacement of the initial tagged line. This paper addresses the study of tracer molecules diffusion through a background gas flowing in a channel delimited by planar walls. Tracer and background species are supposed to be governed by a system of coupled Boltzmann equations, numerically solved by the direct simulation Monte Carlo (DSMC) method. Simulations confirm that the diffusion of tracer species becomes significant as the degree of rarefaction of the gas flow increases. It is shown that a simple advection–diffusion equation provides an accurate description of tracer molecules behavior, in spite of the non-equilibrium state of the background gas. A simple reconstruction algorithm based on the advection–diffusion equation has been developed to obtain the velocity profile from the displacement field. This reconstruction algorithm has been numerically tested on DSMC generated data. Results help estimating an upper bound on the flow rarefaction degree, above which MTV measurements might become problematic

Development of a melting model for meteors

Meteor phenomenon is a frequent event happening on planet Earth. Due to the high entry velocities of these objects the surface of the material undergoes extreme heat loads. Since the material is mainly composed by several oxides, eventually, the surface temperature will overcome the melting point. In this study we propose a melting model, in order to understand the material behavior, coupled with a flow solver. A detailed study of the flow around the stagnation streamline is also presented

Evaporation boundary conditions for the R13 equations of rarefied gas dynamics

The regularized 13 moment (R13) equations are a macroscopic model for the description of rarefied gas flows in the transition regime. The equations have been shown to give meaningful results for Knudsen numbers up to about 0.5. Here, their range of applicability is extended by deriving and testing boundary conditions for evaporating and condensing interfaces. The macroscopic interface conditions are derived from the microscopic interface conditions of kinetic theory. Tests include evaporation into a half-space and evaporation/condensation of a vapor between two liquid surfaces of different temperatures. Comparison indicates that overall the R13 equations agree better with microscopic solutions than classical hydrodynamics

Twenty-six moment equations for the Enskog–Vlasov equation

The Enskog–Vlasov equation is a phenomenological kinetic equation that extends the Enskog equation for the dense (non-ideal) hard-sphere fluid by adding an attractive soft potential tail to the purely repulsive hard-sphere contribution. Simplifying assumptions about pair correlations lead to a Vlasov-like self-consistent force field that adds to the Enskog non-local hard-sphere collision integral. Within the limitations imposed by the underlying assumptions, the extension gives the Enskog–Vlasov equation the ability to give a unified description of ideal and non-ideal fluid flows as well as of those fluid states in which liquid and vapour regions coexist, being separated by a resolved interface. Furthermore, the Enskog–Vlasov fluid can be arbitrarily far from equilibrium. Thus the Enskog–Vlasov model equation provides an excellent, although approximate, tool for modelling processes with liquid–vapour interfaces and adjacent Knudsen layers, and allows us to look at slip, jump and evaporation coefficients from a different perspective. Here, a set of 26 moment equations is derived from the Enskog–Vlasov equation by means of the Grad moment method. The equations provide a meaningful approximation to the underlying kinetic equation, and include the description of Knudsen layers. This work focuses on the – rather involved – derivation of the moment equations, with only a few applications shown

Kinetic theory aspects of non-equilibrium liquid-vapor flows

Kinetic theory of fluids plays an important role in understanding and modeling mass, momentum and energy transfer between the vapor and liquid phase in non-equilibrium two-phase flows, in which evaporation and/or condensation take place. The paper presents a review of the literature which focuses on kinetic modeling of the vapor-liquid interface. Starting from the studies of the Knudsen layer structure in evaporation and condensation, the problem of the formulation of kinetic boundary conditions is described and discussed. The formulation of models based on approximate kinetic descriptions of dense fluids is described and the model capabilities are assessed through the analysis of the results obtained by various author