Modeling transonic weakly underexpanded turbulent jets

The results of the calculations of model and actual turbulent jet flows with shock waves at low supersonic Mach numbers are presented. The gasdynamic flow features characterizing shock reflection from a mixing layer are analyzed. A possible version of the modified model for the turbulent viscosity is proposed; the model makes it possible to improve the prediction of the shock (rarefaction wave) intensity distribution along jet flows.     

Supersonic Gas Flows in Radial Nozzles

Results of experimental investigations and numerical simulations of supersonic gas flows in radial nozzles with different nozzle widths are presented. It is demonstrated that different types of the flow are formed in the nozzle with a fixed nozzle radius and different nozzle widths: supersonic flows with oblique shock waves inducing boundary layer separation are formed in wide nozzles, and flows with a normal pseudoshock separating the supersonic and subsonic flow domains are formed in narrow nozzles (micronozzles). The pseudoshock structure is studied, and the total pressure loss in the case of the gas flow in a micronozzle is determined.     

The Riemann problem for non-ideal isentropic compressible two phase flows

We consider the Riemann problem for a five-equation, two-pressure (5E2P) model of non-ideal isentropic compressible gas–liquid two-phase flows. This system is more complex due to the extended thermodynamics model for van der Waals gases, that is, typical real gases for gas phase and Tait׳s equation of state for liquid phase. The overall model is strictly hyperbolic and non-conservative form. We investigate the structure of Riemann problem and construct the solution for it. To construct solution of Riemann problem approximately assuming that all waves corresponding to the genuinely non-linear characteristic fields are rarefaction and then we discuss their properties. Lastly, we discuss numerical examples and study the solution influenced by the van der Waals excluded volume.     

A two-parameter model of wave regimes for viscous liquid film flows

Wave regimes of viscous liquid film flows are considered when the viscosity coefficients vary in a wide range. An approximate model system of differential equations with two external governing parameters for the film layer thickness and the local flow rate is derived. The viscous dissipation of a film layer is taken into account in this system more accurately than in the well-known one-parameter Shkadov model. New properties of linear and nonlinear waves caused by the hydrodynamic instability of high-viscous liquid flows under gravity and surface tension are found.     

Drops in annular two-phase flow

Drops, one of the forms in which liquid is present in annular gas—liquid flow, are formed from the wall film, carried by the gas or vapour and redeposited. During this time they exert a strong influence on many important parameters of both flow and heat transfer. The available information on the creation, size and velocity, and removal of drops is identified and reviewed.

This review shows that there is an extensive literature on drops and the associated topic of waves in annular gas—liquid flows. In spite of the large number of papers that have been published, there are still some fundamental questions which remain unanswered and there are large gaps in the parameter ranges to be considered.     

Superposition of two incident shocks in R718 vapor flows

Although the positive values of the fundamental gas-dynamic derivative of R718 near vapor-liquid equilibrium line ensures no occurrence of the non-classical behavior like rarefaction shock waves, the occurrence of the homogenous condensations due to rarefaction waves must be taken into account when using the moving shocks and rarefaction waves in wave devices. In this article, the superposition behaviors such as shockwave refraction and reflection of two moving incident shocks for R718 vapor flows near this the vapor-liquid equilibrium zone, have been intensively studied. And the supercharging characteristic of two superposition moving incident shocks for R718 vapor flows achieves remarkable high boosting pressure ratios of about square of those of one primary equal-intensity shock. This inspiring result could be fully used for vapor recompression in multi-effect distillation technology (MED) for brine water treatment.     

Theoretical and experimental investigation of condensation in a centered rarefaction wave

The analysis of the process of spontaneous condensation in one-dimensional formulation is dealt with adequately in many papers. However, in reality supersonic flows are not one-dimensional. The most striking effect of two-dimensionality is manifested in two-phase flows, for example in nozzles, inclined sections of jet turbine grills and rarefaction waves. The investigation of these flows, both in the experimental and theoretical aspect, is a complex problem for which a solution has been found only recently. The results are given in this paper of a theoretical and experimental investigation of spontaneous condensation of water vapor in a centered rarefaction wave formed by flow around a protuberant angle by a hypersonic stream.Translated from Prikladnaya Mekhanika i Tekhnicheskii Fiziki, No. 5, pp. 117–122, September–October, 1971.     

Interference of oblique shock waves of one family in a hypersonic flow

A study is made of the irregular regime of interaction of two shock waves of the same direction when a hypersonic gas stream flows past bodies of complicated shape. It is shown that the rarefaction waves formed in the flow field significantly weaken the shock wave that approaches the body. This effect is confirmed by the results of an experiment and numerical calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 134–138, September–October, 1982.     

一种新的运动激波--非定常边界层相互干扰现象

本文探讨了一种新的激波－非定常边界层相互干扰现象，这种激波－边界层干扰现象既不同于定常激波－边界层干扰现象，又不同于激波在端面反射后与该激波所诱导的边界层之间的干扰现象，而是运动激波与稀疏波和第一激波所诱导的非这常边界层之间的干扰现象，本文对这种现象用微波动力学理论进行分析，并把这种干扰现象看成激波的绕射现象，同时在稀疏波破膜的双驱动激波管中进行实验观察，最后把理论分析与实验观察进行了比较。     

Nonlinear Stability of Rarefaction Waves for the Boltzmann Equation

It is well known that the Boltzmann equation is related to the Euler and Navier-Stokes equations in the field of gas dynamics. The relation is either for small Knudsen number, or, for dissipative waves in the time-asymptotic sense. In this paper, we show that rarefaction waves for the Boltzmann equation are time-asymptotic stable and tend to the rarefaction waves for the Euler and Navier-Stokes equations. Our main tool is the combination of techniques for viscous conservation laws and the energy method based on micro-macro decomposition of the Boltzmann equation. The expansion nature of the rarefaction waves and the suitable microscopic version of the H-theorem are essential elements of our analysis.     

Some remarks about the resolution of high velocity flows near low densities

High velocity flows which are exposed to strong rarefaction waves and creating low densities regions in it present difficulties and inaccuracies for numerical resolution. In particular, variables related to the internal energy are wrongly evaluated. Use of classical schemes solving the Euler equations in conservative variables introduces significant errors in the determination of temperature. We recommend to employ a non-conservative formulation of the energy equation. Results found to be more accurate in using the present internal energy formulation. In order to have the formulation available for both shock and strong rarefaction waves, we propose a hybrid formulation of conservative and non-conservative ones, depending on a shock indicator. The results are compared with exact solutions and show a significant improvement of the accuracy. The method is then extended to two-dimensional cases. Received 28 March 1997 / Accepted 18 June 1997     

Transformation of the bridge during drop separation

The geometry of flows during separation of pendant drops of liquids with significantly different physical properties (alcohol, water, glycerin, oil) has been studied by high-speed video recording. The dynamics of the processes involving the formation of bridges of two characteristic shapes—slightly nonuniform in thickness and with thinning of the upper and lower ends—has been investigated. It has been shown that the shape change of the separated bridge has a number of stages determined by the properties of the liquid. As a result, the bridge is transformed into a small drop—a satellite drop.     

Experimental study of stability in a layer of a model alloy with a liquid miscibility gap

The stability of Rayleigh-Bénard convection in a transparent model alloy was investigated with holographic interferometry. The dispersed minority phase is the heavier component. The majority component is lighter. A vertical temperature difference was applied to the liquid layer keeping the hot temperature always above phase separation. The upper cold side temperature was kept above or below the phase separation temperature. Fluid separation occurs when the cold temperature drops below consolute temperature. When the liquid is kept at higher than consolute temperature, it is noticed that the stability of the layer is increased when the average temperature approaches the consolute temperature. Received on 13 January 1997     

Specific gasdynamical features of spontaneous condensation in an unsteady rarefaction wave

On the basis of numerical modeling, the formation of an unsteady shock wave induced by a condensation shock in a rarefaction wave moving in the high-pressure channel of a shock tube filled with moist air is demonstrated. It is shown that in a fairly long channel a periodic structure consisting of an alternating sequence of condensation shocks and the shock waves they generate may be formed. This structure is a linear unsteady analog of the self-oscillation regime of type IV in the classification [1] for condensing medium flows in the subsonic section of a Laval nozzle. The specific features detected are important for planning and interpreting experiments aimed at investigating spontaneous condensation using a “condensation shock tube”.     

Experimental study on interfacial waves in stratified horizontal oil–water flow

Interfacial wave characteristics were studied experimentally in horizontal oil–water pipe flows during stratified flow and at the transition to dual continuous flow, where drops of one phase appear into the other (onset of entrainment). The experimental investigations were carried out in a stainless steel test section with 38 mm ID with water and oil (density 828 kg/m³and viscosity 5.5 mPas) as test fluids. Wave characteristics were obtained with a high speed video camera and a parallel wires conductivity probe that measured the instantaneous fluctuations of the interface. Experiments were conducted at 2 m and at 6 m from the inlet. Visual observations revealed that no drops are formed when interfacial waves are absent. It was also found that waves have to reach a certain amplitude before drops can detach from their crests. Wave amplitudes are increased as the superficial velocities of both phases increase. In the stratified region, the mean wave amplitude decreases by increasing the oil–water input ratio while mean wavelength increases as the slip velocity between the two-phase decreases. At the onset of entrainment, the mean amplitude and length are found to be a function of the relative velocity between the oil and water layers and of the turbulence in each layer.     

Harten-Lax-van Leer-contact (HLLC) approximation Riemann solver with elastic waves for one-dimensional elastic-plastic problems

A Harten-Lax-van Leer-contact (HLLC) approximate Riemann solver is built with elastic waves (HLLCE) for one-dimensional elastic-plastic flows with a hypoelastic constitutive model and the von Mises’ yielding criterion. Based on the HLLCE, a third-order cell-centered Lagrangian scheme is built for one-dimensional elastic-plastic problems. A number of numerical experiments are carried out. The numerical results show that the proposed third-order scheme achieves the desired order of accuracy. The third-order scheme is used to the numerical solution of the problems with elastic shock waves and elastic rarefaction waves. The numerical results are compared with a reference solution and the results obtained by other authors. The comparison shows that the presented high-order scheme is convergent, stable, and essentially non-oscillatory. Moreover, the HLLCE is more efficient than the two-rarefaction Riemann solver with elastic waves (TRRSE).     

A continuum traffic flow model with the consideration of coupling effect for two-lane freeways

A new higher-order continuum model is proposed by considering the coupling and lane changing effects of the vehicles on two adjacent lanes. A stability analysis of the proposed model provides the conditions that ensure its linear stability. Issues related to lane changing, shock waves and rarefaction waves, local clustering and phase transition are also investigated with numerical experiments. The simulation results show that the proposed model is capable of providing explanations to some particular traffic phenomena commonly observable in real traffic flows.     

Numerical simulation of compressible two-phase flow using a diffuse interface method

In this article, a high-resolution diffuse interface method is investigated for simulation of compressible two-phase gas–gas and gas–liquid flows, both in the presence of shock wave and in flows with strong rarefaction waves similar to cavitations. A Godunov method and HLLC Riemann solver is used for discretization of the Kapila five-equation model and a modified Schmidt equation of state (EOS) is used to simulate the cavitation regions. This method is applied successfully to some one- and two-dimensional compressible two-phase flows with interface conditions that contain shock wave and cavitations. The numerical results obtained in this attempt exhibit very good agreement with experimental results, as well as previous numerical results presented by other researchers based on other numerical methods. In particular, the algorithm can capture the complex flow features of transient shocks, such as the material discontinuities and interfacial instabilities, without any oscillation and additional diffusion. Numerical examples show that the results of the method presented here compare well with other sophisticated modeling methods like adaptive mesh refinement (AMR) and local mesh refinement (LMR) for one- and two-dimensional problems.     

Nonlinearwaves in a liquid film-gas flow system

The instability and regular nonlinear waves in the film of a heavy viscous liquid flowing along the wall of a round tube and interacting with a gas flow are investigated. The solutions for the wave film flows are numerically obtained in the regimes from free flow-down in a counter-current gas stream to cocurrent upward flow of the film and the gas at fairly large gas velocities. Continuous transition from the counter-current to the cocurrent flow via the state with a maximum amplitude of nonlinear waves and zero values of the liquid flow rate and the phase velocity is investigated. The Kapitsa-Shkadov method is used to reduce a boundary value problem to a system of evolutionary equations for the local values of the layer thickness and the liquid flow rate.     

Investigation on onset of shock-induced separation

A great number of experimental data indicating shock wave/boundary layer interactions in internal or external supersonic flows were reviewed to make clear the mechanism of the interaction and to decide the onset of shock-induced separation. The interesting conclusions were obtained for the considerably wide range of flow geometries that the onset of separation is independent of the flow geometries and the boundary layer Reynolds number. It is found that the pressure rise necessary to separate the boundary layer in supersonic external flows could be applied to such internal flows as overexpanded nozzles or diffusers. This is due to the fact that the separation phenomenon caused by shock wave/boundary layer interactions is processed through a supersonic deceleration. The shock-induced separation in almost all of interacting flow fields is governed by the concept of free interaction, and the onset of shock-induced separation is only a function of the Mach number just upstream of shock wave. However, physical scales of the produced separation are not independent of the downstream flow fields.