Impact Dynamics of Damaged Shells Interacting with a Two-Phase Liquid

The propagation of shock waves in a system consisting of a deformable medium with damage and a two-phase liquid with gas or vapor bubbles are studied. The nonlinear interaction of the media are modeled taking into account phase transformations in the liquid and the damage kinetics of the deformable medium. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 139–152, January–February, 2006.     

Unsteady waves in a liquid containing vapor bubbles

Unsteady wave processes in vapor-liquid media containing bubbles are investigated taking into account the unsteady interphase heat and mass transfer. A single velocity model of the medium with two pressures is used for this, which takes into account the radial inertia of the liquid with a change in volume of the medium and the temperature distribution in it [1]. The system of original differential equations of the model is converted into a form suitable for carrying out numerical integration. The basic principles governing the evolution of unsteady waves are studied. The determining influence of the interphase heat and mass transfer on the wave behavior is demonstrated. It is found that the time and distance at which the waves reach a steady configuration in a vapor-liquid bubble medium are considerably less than the correponding characteristics in a gas-liquid medium. The results of the calculation are compared with experimental data. The propagation of acoustic disturbances in a liquid with vapor bubbles was studied theoretically in [2]. The evolution of waves of small but finite amplitude propagating in one direction in a bubbling vapor-liquid medium is investigated in [3, 4] on the basis of the generalization of the Burgers-Korteweg-de Vries equation obtained by the authors. An experimental investigation of shock waves in such a medium is reported in [5, 6], and the structure of steady shock waves is discussed [7].Translated from Izvestiya Akademii Nauk SSSR, Hekhanika Zhidkosti i Gaza, No. 5, pp. 117–125, September–October, 1984.     

Effect of gas release and condensation on characteristics of two-phase gas-and vapor-liquid slug flow

A model of gas-liquid and vapor-liquid slug flow in vertical channels is suggested. The effect of gas release from a gas-saturated liquid and vapor condensation in a cooling channel on characteristics of two-phase slug flow is investigated. It is shown that gas release and condensation affect significantly the structure of the two-phase gas-liquid and vapor-liquid slug flow.     

Multiphase fluid dynamics and transport processes of low capillary number cavitating flows

To better understand the multiphase fluid dynamics and associated transport processes of cavitating flows at the capillary number of 0.74 and 0.54, and to validate the numerical results, a combined computational and experimental investigation of flows around a hydrofoil is studied based on flow visualizations and time-resolved interface movement. The computational model is based on a modified RNG k-ε model as turbulence closure, along with a vapor-liquid mass transfer model for treating the cavitation process. Overall, favorable agreement between the numerical and experimental results is observed. It is shown that the cavi- tation structure depends on the interaction of the water-vapor mixture and the vapor among the whole cavitation stage, the interface between the vapor and the two-phase mixture exhibits substantial unsteadiness. And, the adverse motion of the interface relates to pressure and velocity fluctuations inside the cavity. In particular, the velocity in the vapor region is lower than that in the two-phase region.     

Dynamics of volumetrically heated matter passing through the liquid–vapor metastable states

Remaining within the pure hydrodynamic approach, we formulate a self-consistent model for simulating the dynamic behavior of matter passing through metastable states in the two-phase liquid–vapor region of the phase diagram. The model is based on the local criterion of explosive boiling, derived by applying the theory of homogeneous bubble nucleation in superheated liquids. Practical application of the proposed model is illustrated with hydrodynamic simulations of a volumetrically uniformly heated planar layer of fused silica SiO₂. Implications for experimentally measurable quantities are briefly discussed. A newly developed equation of state, based on the well known QEOS model and capable of handling homogeneous mixtures of elements, was used in the numerical simulations.     

双相介质P波波动方程小波域多尺度模拟

相比于单相介质理论而言,双相介质理论更接近实际地层的真实情况,因此在地球物理勘探、地震工程和岩土动力学等领域有着广泛的应用。传统的波动方程数值解法由于本身固有的不足不利于求解诸如双相介质波动方程等复杂的非线性和不规则性问题;而小波方法则由于自身良好的特性可以用来构建解决此类问题的自适应性算法。本文详细推导了双相介质P波波动方程的有限差分矩阵表示形式,利用小波变换将其转移到小波域,设置阈值形成更为稀疏的迭代矩阵以构建自适应算法,从而达到减少计算量,增加地震波场数值模拟灵活性和准确性的目的。地球物理勘探的数值模拟实例验证了方法的有效性。     

A New Model and its Application to Investigate Transpiration Cooling with Liquid Coolant Phase Change

This paper presents a new mathematical model, semi-mixing model (SMM), to describe transpiration cooling with coolant phase change from liquid into vapor through two-phase process. The local heat exchange of fluid-solid within pores is considered in this model, and therefore it is closer to real transpiration cooling condition. The differences from the separated phase model and two-phase mixture model are that SMM can overcome the trouble of tracking phase change interface and avoid the inveracious numerical phenomenon, i.e., a thermal insulating layer occurs within the porous matrix. Using SMM, the corresponding numerical method is realized to simulate the processes of coolant moving, absorbing heat and evaporating within porous matrix. To validate SMM and the numerical strategy, an experiment is conducted. Using the validated SMM and numerical strategy, the effects of two-dimensional coolant injection rate and two-dimensional heat flux on transpiration cooling characteristics are simulated and analyzed. The simulations and analysis discover several interesting and valuable phenomena.     

Numerical investigation of unsteady shock waves in vapor-gas-droplet mixtures

The results of mathematical modeling of the evolution of unsteady shock waves in two-phase mixtures of inert gas, vapor and suspended liquid droplets with allowance for dynamic, thermal and mass phase interaction processes are presented. The influence of interphase mass transfer effects (droplet breakdown and evaporation, vapor condensation) on the structure of unsteady shock waves in vapor-gas-droplet mixtures is analyzed. The important influence of phase mass transfer and, in particular, droplet breakdown as a result of surface layer stripping by the gas flow on the distribution of the parameters of the carrier and dispersed components of the mixture behind the shock front is demonstrated. The effect of the principal governing parameters of the two-phase mixture on the unsteady shock wave propagation process is analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 67–75, July–August, 1992.     

Experimental and Numerical Investigation on Cavitating Flows in Diesel Injection Systems

The present study is concerned with the phase change during rapid depressurization of fluids: the role of vapor bubbles nucleation and growth and the effect on the system fluid dynamics were modeled and experimental measurements were made. Following a control-volume approach, averaged equations governing the motion of a one-dimensional, homogeneous, no-slip two-phase flow were used considering both thermal equilibrium (equal temperature) and non-equilibrium (non-equal temperature) between the liquid and vapor phases. In the non-equilibrium model, the heat transfer from the liquid to the vapor and the corresponding mass transfer velocity were modeled. Model results were compared with experimental data for a loss-of-coolant accident in nuclear power plants: the comparison of numerical vs. experimental data showed the role of nucleation velocity during the earliest phase of rapid depressurization. The experimental study of two-phase flow in a diesel engine injection system has been carried out using a rotative pump which is operated by using a purpose-developed test-bench; pressure measurements inside the system pipes were performed using pressure transducers; moreover, an ultrasonic technique was employed to study phase change phenomena. Several measurements were performed comparing the results obtained by different experimental techniques with the model outputs.Sommario.presente studio riguarda il fenomeno della cavitazione durante la depressurizzazione di fluidi. E'stata considerata la velocità di formazione e nucleazione delle bolle di vapore e le equazioni di conservazione sono state integrate con solutori al 1°e 2°ordine di tipo ENO. Sono stati utilizzati dati sperimentali ottenuti durante incidenti per perdita di refrigerante in centrali nucleari; per quanto riguarda gli apparati di iniezione, gli autori hanno sviluppato due differenti tecniche sperimentali, basate rispettivamente sulla pressione e sulla riflessione degli ultrasuoni. Il confronto dei risultati numerici con quelli sperimentali è stato soddisfacente.     

Speed of sound in two-phase vapor-liquid systems

The principal theorems of thermodynamics of irreversible processes are applied to the process of propagation of acoustic waves in a two-phase medium. Expressions are derived which determine the dependence of the sound speed in a vapor-liquid medium on the degree of dryness and the degree of nonequilibrium of different relaxation processes accompanying the propagation of acoustic waves. In the limiting case of equilibrium these expressions reduce to the well-known formulas obtained in equilibrium thermodynamics.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 78–85, September–October, 1970.     

Effect of fluids properties on non-equilibrium capillarity effects: Dynamic pore-network modeling

We have developed a Dynamic Pore-network model for Simulating Two-phase flow in porous media (DYPOSIT). The model is applicable to both drainage and imbibition processes. Employing improved numerical and geometrical features in the model facilitate a physically-based pore-scale simulator. This computational tool is employed to perform several numerical experiments (primary and main drainage, main imbibition) to investigate the current capillarity theory. Traditional two-phase flow formulations state that the pressure difference between the two phase is equal to the capillary pressure, which is assumed to be a function of saturation only. Many theoretical and experimental studies have shown that this assumption is invalid and the pressure difference between the two fluids is not only equal to the capillary pressure but is also related to the variation of saturation with time in the domain; this is referred to as the non-equilibrium capillarity effect. To date, non-equilibrium capillarity effect has been investigated mainly under drainage. In this study, we analyze the non-equilibrium capillarity theory under drainage and imbibition as a function of saturation, viscosity ratio, and effective viscosity. Other aspects of the dynamics of two-phase flow such as trapping and saturation profile are also studied.     

Dynamics of vapor bubbles

The nonlinear problem of the thermal, mass, and dynamic interaction of a single vapor bubble with the surrounding liquid is discussed. This problem has ramifications in research on flows of vapor-liquid mixtures with a bubble-matrix structure, in particular, the propagation of shock waves in such media. Results are given from a numerical solution of the problem of the radial motion imparted to a bubble by a sudden change of pressure in the liquid; this problem corresponds, in particular, to the behavior of bubbles behind a shock front when the latter enters a bubble curtain.     

Study of two-phase bubbly flow dynamics in binary mixtures

The results of an investigation of the bubble dynamics and wave phenomena in two-component vapor-liquid mixtures are presented. These mixtures are widely used in industrial systems as heat transfer media. The effects of various additives on the wave dynamics of vapor-liquid mixtures are of particular interest. A single-velocity two-pressure model was used which takes into account both the liquid radial inertia due to medium volume changes, and the temperature distribution around the bubbles. The claim that mixture composition may have a peculiar effect on the bubble dynamics of a boiling non-ideal solution is substantiated. It is noted that the small free radial oscillation damping ratio for some binary systems lies outside the domain defined by the damping ratio of the constituents as a result of phase change diffusion effects. A criterion is proposed to identify cases of diffusion resistance responsible for the anomalous effect of component concentration on bubble behavior. The phase change delay due to diffusion results in observably higher mixture wave velocities and a smaller damping ratio than for respective single-component systems.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1992 and the AMS fonts, developed by the American Mathematical Society.     

汽液两相流机械密封的研究进展

液体润滑端面机械密封是流程工业用机泵轴端密封的主要形式，且大量应用于航空航天、海洋工程装备和高端制造装备中，实际运行过程中其端面间液体膜常常发生相变，由此产生端面变形、干磨和密封失稳等现象，甚至完全失效，严重影响了有关设备或整个装置的安全可靠与稳定运行，因此开展汽液两相流端面机械密封研究具有重要意义. 本文中综述了近50年来汽液两相端面机械密封的研究现状，归纳出了机械密封的典型热源及其热传播途径，阐述了机械密封的相变原理，总结了端面流体膜参数的测量技术与方法；在试验研究方面，提出机械密封的端面液膜汽化主要与操作工况、几何尺寸和表面形貌或表面织构有关，其中端面液体入口和出口工况、平衡比和端面变形程度等受到关注，但缺少关于端面形貌或织构的深度研究，也缺少端面摩擦副合理配对的系统研究；在理论研究方面，提出了机械密封相变稳定性判据，以及间断沸腾模型、连续沸腾模型和薄膜均相沸腾模型等3种理论模型，比较了3种模型的优缺点并指出其适用范围. 指出建立合理的相变理论模型，实现相变密封的稳定运行，突破相变密封监控关键技术，构建智能型液体润滑机械密封是未来两相流机械密封的研究重点.      

Contributions to numerical developments in shock waves attenuation in porous filters

The paper deals with the numerical method of the compressible gas flow through a porous filter emphasizing the treatment of the interface between a pure gaseous phase and a solid phase. An incident shock wave is initiated in the gaseous phase interacting with a porous filter inducing a transmitted and a reflected wave. To take into account the discontinuity jump in the porosity between the gaseous phase and the porous filter, an approximate Riemann solver is used to compute homogeneous non-conservative Euler equations in porous media using ideal gas state law. The discretization of this problem is based on a finite volume method where the fluxes are evaluated by a “volumes finis Roe” (VFRoe) scheme. A stationary solution is determined with a continuous variable porosity in order to test the numerical scheme. Numerical results are compared with the two-phase shock tube experiments and simulations of a shock wave attenuation and gas filtration in porous filters are presented.      

流体饱和两相多孔介质拟静态问题的有限元解法

给出基于混合物理论的流体饱和两相多孔介质模型,该模型由一可变形固体 一流体相组成。采用Ｇａｌｅｒｋｉｎ加权残值法导出求解拟静态问题的有限元公式,并编制了二维有限元程序。用程序分析了一维和二维问题,得到合理的结果。     

Chemical potential tensor for a two-phase continuous medium model

Relations for jumps of thermodynamic variables with allowance for inertial terms are derived under conditions of thermal equilibrium and in the absence of dissipation on the interphase surface. The notion of the chemical potential tensor is generalized for this case within the framework of the elastic continuous medium model. A thermodynamically well-posed definition of the chemical potential tensor is proposed for a class of two-phase models of deformable solids. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 12–22, May–June, 2005.     

Film boiling on a hot body moving in a fluid

We investigate the transient film boiling in the vicinity of a stagnation point on the frontal surface of a very hot blunt body which moves with a constant velocity in an incompressible viscous fluid in the presence of a vapor layer near the body surface. Within the unsteady two-phase boundary layer approximation, the equations of motion of the liquid and vapor phases are formulatedwith account of the conservation of mass, momentum, and energy on the a priori unknown phase interface. In the vicinity of the stagnation point on the body surface, the solution of the boundary layer equations is sought in the form of series in the longitudinal coordinate. For the leading terms of the series, a parabolic system of partial differential equations is obtained, which is solved numerically. The similarity parameters controlling the film boiling process are determined. On the basis of parametric numerical calculations, the dynamics of the vapor layer are investigated for the case of a plane hot body moving in water with the room pressure and temperature. In the space of governing parameters, the limits of the existence of steady and unsteady film boiling regimes are found.