Abstract
Dynamics of low-intensity air shock waves in the shock tube containing an aqueous foam layer is theoretically investigated. Modeling of studied process is carried out using two-phase model ...of aqueous foam developed by the authors in single-pressure, single-speed and two-temperature approximations. The model takes into account the Ranz-Marshall interphase contact heat transfer, effective Herschel-Bulkley viscosity, which describes foam behavior as a non-Newtonian fluid, and elastic properties of aqueous foam under a weak shock impaction without destruction of foam structure. Properties of air and water as the foam components are described by realistic equations of state. Computer implementation of the aqueous foam model is carried out in the solver, developed by the authors in OpenFOAM software. The influence of aqueous foam viscoelastic properties on the intensity and structure of a shock wave has been investigated. When analyzing the obtained solutions, reliability of the proposed model and method of numerical modeling is estimated by comparative analysis of the found solutions and literature experimental data.
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A two-phase model of aqueous foam is proposed. It is based on the laws of conservation of mass, momentum, and energy of the phases in accordance with the single-pressure, two-velocity, and ...two-temperature approximations in the axisymmetric formulation, with account of the interphase drag forces, contact heat transfer, viscoelastic properties, and foam syneresis. The thermodynamic properties of the water and the air are described by the Mie—Grüneisen and Peng—Robinson equations of state, respectively. The model is numerically realized in the OpenFOAM software. The results obtained are in reasonable agreement with the experimental data on the spherical explosion in aqueous foam. The evolution of a spherical shock wave propagating in the aqueous foam is analyzed.
The two-phase model of aqueous foam behavior under strong spherical shock wave (SW) impact, is developed using equations of mixture conservation of momentum, mass and internal energy for each phase ...in Lagrange variables, taking into account bulk viscosity and interphase heat transfer. The numerical implementation of the model was carried out by the counting method, using the Neu-mann-Richtmyer viscosity and the Courant stability condition. The spherical explosion was modeled in the form of a SW, which has the same energy of charge of explosives, as used in experiments. A satisfactory agreement was obtained between the numerical solution, received by the proposed model, the analytical self-similar L.I. Sedov’s solution on a point spherical explosion in a gas and a new experimental data on the spherical explosion in aqueous foam. The causes, which lead to a significant decrease in amplitude and SW velocity in the studied media, are investigated in detail.
The process of interaction of air shock-wave pulse and protective aqueous foam barrier in two-dimensional axisymmetric formulation using two-phase model of gas-liquid mixture including the laws of ...conservation of mass, momentum and energy for each phase is numerically investigated. The numerical implementation of the model is carried out using the twoPhaseEulerFoam solver of the OpenFOAM package. The results are presented in the form of spatial distributions of pressure fields, velocities and streamlines. The causes and dynamics of toroidal vortices formation in gas are investigated.
Numerical study of the features of spherical explosion propagation process in a cylindrical pipe surrounded by an inner layer of aqueous foam with liquid volume fraction α10 = 0.2 has been carried ...out. The solution method is based on a two-phase model of gas-liquid mixture under conditions of single-pressure, two-temperature, two-velocity approximations and is implemented using the twoPhaseEulerFoam solver of the OpenFOAM software. In order to test the proposed model, a comparison was made of the calculations and experimental data on a spherical explosion in aqueous foam with liquid volume fraction α10 = 0.0083. When solving the main task, the efficiency of the considered foam barrier is shown in a comparative analysis with the solution obtained in the absence of a foam layer.
Based on the previously developed simplified method for constructing the equation of state for liquid and vapor phases, the thermodynamically consistent analytical equation of state for liquid and ...gaseous nitrogen in the molecular cryogenic conditions is obtained. While constructing the equation of state, the Mie–Gruneisen form was used as the sum of potential and thermal components for pressure and internal energy. The cold components of pressure and internal energy are described by a potential of the Born–Meyer type. For the thermal components, a simplifying approximation is adopted, which follows from the condition for the constant heat capacity and the dependence of Gruneisen function on the volume. When determining the equation of state for the vapor and liquid phases of nitrogen, the method of minimizing the standard deviation of the experimental and calculated data on isothermal compressibility, including the critical region and the phase equilibrium line, was used. The resulting equation of state for nitrogen makes it possible to study the phenomena associated with the processes of evaporation and condensation of nitrogen when modeling multiphase flows, taking into account interfacial heat and mass transfer under conditions of low pressures and cryogenic temperatures.
The boiling up process of the cryogenic liquid nitrogen jet outflow from a thin nozzle into a vacuum chamber from a high-pressure vessel is studied using the numerical approach that implements the ...developed two-phase model of a vapor-liquid mixture. The proposed model assumes the one-velocity, one-pressure, two-temperature approximations, takes into account contact heat transfer, non-equilibrium mass-transfer processes of evaporation and condensation with conditions control for the transition of bubble flow into vapor-droplet one. Numerical simulation of the process under consideration is performed in a three-dimensional axisymmetric formulation using the OpenFOAM software. Reliability substantiation of the developed model, its numerical implementation and the obtained solutions is given by its comparing with experimental data. Features of the bubble regime formation in the near zone at the nozzle exit with the transition to a vapor-droplet flow as the distance from the jet mouth increases are studied.
Shock-wave (SW) propagation in an aqueous foam layer is investigated using new published experimental data with visualization of the dynamics of the volumetric liquid content of the foam under SW ...impact. A mathematical model has been developed that describes the behavior of the foam as a non-Newtonian fluid taking into account the effective Herschel–Bulkley viscosity, interfacial heat transfer processes according to the Ranz–Marshall model, and realistic equations of state describing the thermodynamic properties of aqueous foam components. The model is numerically implemented in the solver that we developed using the OpenFOAM package. The influence of the behavior of the aqueous foam on the SW evolution is analyzed.
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