Instabilities of a gas-liquid flow between two inclined plates analyzed using the Navier–Stokes equations

The paper is devoted to a theoretical analysis of a counter-current gas-liquid flow between two inclined plates. We linearized the Navier–Stokes equations and carried out a stability analysis of the basic steady-state solution over a wide variation of the liquid Reynolds number and the gas superficial velocity. As a result, we found two modes of the unstable disturbances and computed the wavelength and phase velocity of their neutral disturbances varying the liquid and gas Reynolds number. The first mode is a “surface mode” that corresponds to the Kapitza's waves at small values of the gas superficial velocity. We found that the dependence of the neutral disturbance wavelength on the liquid Reynolds number strongly depends on the gas superficial velocity, the distance between the plates and the channel inclination angle for this mode. The second mode of the unstable disturbances corresponds to the transition to a turbulent flow in the gas phase and there is a critical value of the gas Reynolds number for this mode. We obtained that this critical Reynolds number weakly depends on both the channel inclination angle, the distance between the plates and the liquid flow parameters for the conditions considered in the paper. Despite a thorough search, we did not find the unstable modes that may correspond to the instability in frame of the viscous (or inviscid) Kelvin–Helmholtz heuristic analysis.     

Visualization of the gas flow in fuel cell bipolar plates using molecular flow seeding and micro-particle image velocimetry

Main components of proton exchange membrane fuel cells are bipolar plates that electrically connect the electrodes and provide a gas flow to the membrane. We investigate the flow in the channel structures of bipolar plates. Flow seeding is used to visualize the propagating and mixing gas stream. It is shown that a part of the gas is transported perpendicularly to the channel structure. An analysis of the diffusion compared with the convection shows different transport behavior for both flow directions. Additionally, the convective flow field is investigated in detail near the channel wall using Micro-PIV in a Reynolds-number-scaled liquid fluid system. For a more exact comparison of the experimental setups, flow seeding in both gas and liquid systems is performed.     

Discontinuous distribution functions of a gas in an external mass-force field

We examine the velocity distribution function for a gas flowing between parallel plates. It is shown that in a mass-force field acting across the channel the distribution function will be discontinuous in phase space on some hypersurface for any Knudsen numbers. The formula is found for the variation of the discontinuity with increasing distance from one of the boundaries into the volume and an estimate is made of the thickness of the layer within which the discontinuity is significant.     

Laminar bubbly flow in an open capillary channel in microgravity

The study of a bubbly laminar two-phase flow in an open capillary channel under microgravity conditions was conducted aboard the sounding rocket, Texus-45. The channel consists of two parallel plates of width b = 25 mm and distance a = 10 mm. The flow along the length l = 80 mm is confined by a free surface on one side and a plate on the opposite side. The bubbles are injected at the nozzle of the capillary channel via six capillary tubes of 100 μm in inner diameter. Different liquid and gas flow rates were tested leading to different liquid free surface shape and bubble size.     

Unsteady Rarefied Gas Flow with Shock Wave in a Channel

The two-dimensional time-dependent problem of rarefied gas flow in a plane channel, formed by parallel plates of finite length and closed at one end, is solved on the basis of the kinetic S-model. The flow develops as a result of rupture of a diaphragm which separates the gas at rest in the channel and the gas at rest in a reservoir of infinite volume. The effect of gas deceleration at the channel walls under the conditions of diffuse molecular reflection from the channel walls and end face is studied. Decay of a shock wave and disappearance of a homogeneous flow zone behind the shock wave is traced for three variants of conditions at the channel inlet: (1) gas enters the channel from a reservoir of infinite length and width (as the basic variant), the simultaneous motion in the reservoir and channel being studied; (2) the high-pressure reservoir represents a usual channel section; and (3) the motion of the gas in the reservoir is not considered at all, instead of this, the boundary conditions of the evaporation-condensation type under the conditions of gas at rest in the reservoir are imposed in the inlet cross-section.     

Use of diverging or converging arrangement of plates for the control of chaotic mixing in symmetric sinusoidal plate channels

This paper presents an experimental flow visualization study of the effect that the variation of converging or diverging angles plays in the flow field of a symmetric sinusoidal channel. The experiments were performed in a water tunnel and the visualization technique was laser illumination of seeded particles whose traces were captured using long time exposure photography. Geometrical parameters such as wave amplitude, wavelength and distance between plates were kept constant, while the Reynolds number and divergence or convergence angles were varied. It was found from the experiments that the divergence of the plates is a good way to promote chaotic mixing in channel flows, as the flow becomes more unstable for diverging channels. For the case of converging channels, the flow becomes very stable even for large values of the Reynolds number. These results were compared with those of a channel formed by a pair of sinusoidal parallel plates.     

Random Oscillations of an Antiphase-Excited Aeroelastic System with Synchronization

We examine synchronization of the oscillatory motion of thin elastic cylindrical plates forming the walls of a channel filled by a gas. The gas motion in the channel is described by a system of Navier–Stokes equations solved by the MacCormack method of second-order accuracy. The motion of the channel walls is described by a system of dynamic, geometrically nonlinear equations of the thin-shell theory; this system is solved by the finite difference method. Kinematic and dynamic contact conditions are set at the interface between the media. By means of a numerical experiment, possible scenarios of the transition of the aeroelastic system to in-phase oscillations were identified, and the regime of random oscillations in the system with synchronization under antiphase external excitation was found.     

Sound propagation through a rarefied gas. Influence of the gas–surface interaction

Acoustic waves propagating through a rarefied gas between two plates induced by both oscillation and unsteady heating of one of them are considered on the basis of a model of the linearized Boltzmann equation. The gas flow is considered as fully established so that the dependence of all quantities on time is harmonical. The problem is solved for several values of two main parameters determining its solution, namely, the gas rarefaction defined as the ratio of the distance between the plates to the equivalent free path of gaseous molecules, and the oscillation parameter given as the ratio of the intermolecular collision frequency to the wave frequency. The reciprocal relation for such flows is obtained and verified numerically. An influence of the gas–surface accommodation coefficients on the wave characteristics is analyzed by employing the Cercignani–Lampis scattering kernel to the boundary conditions.     

爆炸焊接基复板间隙中的气体冲击波

通过分析研究爆炸焊接基复板间隙中的气体运动,建立了冲击波传播的理论模型,通过理论分析和计算说明了基复板间存在气体冲击波管道效应。管道效应使复合板尾部在爆炸焊接形成前发生上翘,造成板尾部焊接能量偏大,或使尾部炸药压死,是工程中长大复合板尾部焊接质量降低或失效的主要原因。还通过建立简化模型,分析了复合板宽度、各种保护性气体和粗真空对管道效应的影响,说明了选择爆炸焊接保护气体的原则,进而使用氦气保护进行了钛钢、铝镁爆炸焊接实验验证,为气体保护爆炸焊接、真空爆炸焊接技术的进一步开发研究奠定了理论基础。     

On flow structure, heat transfer and pressure drop in varying aspect ratio two-pass rectangular channel with ribs at 45°

To increase the thermal efficiency of gas turbines, inlet temperature of gas is increased. This results in the requirement of cooling of gas turbine blades and vanes. Internal cooling of gas turbine blades and vanes is one of several options. Two-pass channels are provided with ribs to enhance heat transfer at the expense of an increased pressure drop. The space in the blade is limited and requires channels with small aspect ratios. Numerical simulations have been performed to investigate heat transfer, flow field and pressure loss in a two-pass channel equipped with 45° ribs with aspect ratio (W_in/H) equal to 1:3 in the inlet pass and 1:1 in the outlet pass with both connected together with a 180° bend. The results are compared with a higher aspect ratio channel (W_in/H = 1:2, inlet pass). In the ribbed channel, a decrease in pressure drop was observed with a decrease in the aspect ratio of the channel. The smaller aspect ratio channel not only allows using more cooling channels in the blade, but also results in more heat transfer enhancement. The divider-to-tip wall distance (W_el) has influence on the pressure drop, as well as on the heat transfer enhancement at the bend and outlet pass. Heat transfer decreases with decrease in aspect ratio of the inlet pass of the two-pass channel. With increase in divider-to-tip wall distance, heat transfer tries to attain a constant value.     

A special solution of wave dissipation by finite porous plates

The reflection and transmission of water waves caused by a small amplitude incident wave through finite fine porous plates with equal spacing and permeability in an infinitely long open channel of constant water depth and zero slope are studied. A special solution is obtained when the distance between the two neighbouring plates is an integral multiple of the half-wavelength of the incident wave. It is found, that when the dimensionless porous-effect parameter G_0 is equal to half the total plate number, the wave dissipation reaches a maximum, and only 50% of the incident wave energy remains in the reflected and transmitted waves. Meanwhile, the reflected and transmitted waves have the same amplitude.     

Rarefied flow in a channel and a periodic system of channels

the steady two-dimensional isothermal rarefied flow in a channel formed by two parallel flat plates of finite length is studied on the basis of the numerical solution of a linearized kinetic problem. The channel may either be isolated or constitute a cell of a periodic cascade consisting of zero-thickness plates arranged one above the other. As the channel length increases, the flow in it approaches the asymptotic one-dimensional Poiseuille flow. It is shown that the asymptotic dependence of the gas flow rate on the low Knudsen number corresponding to an infinitely long channel is already attained for a channel of length equal to several channel widths, if the flow rate is referred to the pressure gradient at the middle of the channel rather than to the mean pressure difference at the channel ends. The effect of the boundary conditions imposed on the channel entrance is investigated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 166–175, May–June, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 98-01-00443).     

Simultaneous convection and radiation in flow between two parallel plates

A numerical solution is described for simultaneous forced convection and radiation in flow between two parallel plates forming ahannel. The front plate is transparent to thermal radiation while the back one is thermally insulated. Analyses for both flow and heat are presented for the case of a non-emitting ‘blackened’ fluid. The governing equations of the stream function and the temperature together with their boundary conditions are presented in non-dimensional expressions. The solution is found to depend on eight dimensionless parameters, namely the ratio of the height of the channel to the distance between the plates, the initial dimensionless temperature, the optical thickness, the absorptivities of both plates, the Reynolds number, the Prandtl number and the heat transfer coefficient from the front plate to the surroundings. The numerical solution is obtained using a finite-difference technique. A study has been made of the effect of the initial temperature of the flow at the channel inlet, the dimensionless loss coefficient from the front plate, the absorptivity of the back plate and the optical thickness, on the temperature distribution in the channel, the heat collection efficiency and the average temperature rise in the channel. Results showed that increasing the optical thickness increases the temperature of the front plate and decreases the temperature of the back plate. Also, increasing the optical thickness increases the efficiency of heat collection, which reaches its maximum asymptotic value at an optical thickness of about 1.5. Moreover, the location of the maximum temperature is found to depend on both the optical thickness and the dimensionless heat loss coefficient from the front plate.     

Study of steady viscous flow through a wavy channel: non-orthogonal coordinates

In this paper we consider the steady flow of a viscous fluid through a channel bounded by two sinusoidally varying plates differing in phase by π and separated by a mean distance 2h. For the non-varying channel, the classical parabolic velocity profile for the fully developed flow is well known. An attempt here is made to analyze the flow in a generalized non-orthogonal coordinate system that renders the wavy channels as plane walls. Continuity equation and Navier-Stokes equations are presented in the generalized coordinate system and simplified through use of small perturbation under small Reynolds number approximation. Flow characteristics such as centerline velocity and drag force have been evaluated and discussed.     

Heat transfer analysis of a particle-containing channel flow

This paper describes an analytical model of heat transfer in a two-dimensional, steady, nonreacting particle-containing channel flow. An idealized gas flow of specified uniform velocity between insulated parallel plates is assumed and the nonvaporizing particles are conceptualized as contained within an thin sheet injected at the symmetry plane. Two dimensionless parameters that affect the solution are described. These are the effective gas diffusivityK and the dimensionless particle number densityP. The linear, coupled differential equations governing the energy exchange between the gas and liquid phases are solved by means of the Green's function technique. This procedure yields a Volterra integral-series equation as the solution of the gas-phase energy equation. A series solution of this integral equation is obtained by the method of successive substitutions and terms up to second order are calculated.     

On the longitudinal heat flux in a Couette flow

The problem of shear motion of a gas (Couette flow) is studied. Two infinite parallel plates with temperatures T₁ and T₂ separated by the distance L each move in their own plane with velocities u₀ and -u₀, respectively. It is assumed that there is a monatomic gas between the plates. In such a formulation, the Couette problem has been considered earlier by many authors. A difference in the present paper is that it investigates the behavior of the heat flux directed along the plates. It has been found that the presence of this heat flux has a strong influence on the direction of energy transfer that is established in a Couette flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 162–166, May–June, 1980.We are grateful to O. S. Ryzhov and A. T. Onufriev for discussions which led to the writing of the present paper.     

Origination of In‐Phase Oscillations of Thin Plates with Aeroelastic Interaction

Synchronization of oscillations of thin elastic plates that are walls of a gasfilled channel is considered. The gas motion is described by a system of Navier–Stokes equations, which is solved using the secondorder MacCormack method with time splitting. The motion of the channel walls is described by a system of geometrically nonlinear dynamic equations of the theory of this plates, which is solved by the finitedifference method. Kinematic and dynamic contact conditions are imposed at the interface between the media. A numerical experiment is performed to determine typical dynamic regimes and study the transition of the aeroelastic system to inphase oscillations.     

Effect of obstacle size and spacing on the initial stage of flame acceleration in a rough tube

Experiments were conducted to study flame acceleration in an orifice plate laden detonation tube. Orifice plate area blockage and spacing were varied to determine their affect on flame acceleration. The tube used in the study was 3.05 m long with an inner diameter of 14.0 cm. Experiments were primarily carried out with stoichiometric propane-air, however the affect of mixture reactivity was also investigated by varying the mixture equivalence ratio. The distance required for the flame to achieve a velocity equal to the speed of sound in the unburned gas mixture was measured. This run-up distance is used to characterize the early stage of the flame acceleration process. It was found that in all cases, the flame run-up distance decreased with increased blockage ratio and with increased mixture reactivity. It was found that for higher blockage ratios plates flame acceleration was greatest for a plate spacing of one tube diameter, but for lower blockage ratio plates the results obtained for one-half, one, and one and one-half tube diameter plate spacing were very similar. The most rapid flame acceleration was observed when the ratio of the orifice plate spacing and the orifice plate height (half of the difference between the tube and orifice plate diameter) is on the order of 5. It is proposed that this optimum acceleration corresponds to the condition where the plate spacing is roughly equal to the length of the unburned gas re-circulation zone downstream from the orifice plate. PACS 47.40.-x; 47.70.Fw This paper was based on work that was presented at the 19th Interna-tional Colloquium on the Dynamics of Explosions and Reactive Sys-tems, Hakone, Japan, July 27 - August 1, 2003     

Flow structure, heat transfer and pressure drop in varying aspect ratio two-pass rectangular smooth channels

Two-pass channels are used for internal cooling in a number of engineering systems e.g., gas turbines. Fluid travelling through the curved path, experiences pressure and centrifugal forces, that result in pressure driven secondary motion. This motion helps in moving the cold high momentum fluid from the channel core to the side walls and plays a significant role in the heat transfer in the channel bend and outlet pass. The present study investigates using Computational Fluid Dynamics (CFD), the flow structure, heat transfer enhancement and pressure drop in a smooth channel with varying aspect ratio channel at different divider-to-tip wall distances. Numerical simulations are performed in two-pass smooth channel with aspect ratio W_in/H = 1:3 at inlet pass and W_out/H = 1:1 at outlet pass for a variety of divider-to-tip wall distances. The results show that with a decrease in aspect ratio of inlet pass of the channel, pressure loss decreases. The divider-to-tip wall distance (W_el) not only influences the pressure drop, but also the heat transfer enhancement at the bend and outlet pass. With an increase in the divider-to-tip wall distance, the areas of enhanced heat transfer shifts from side walls of outlet pass towards the inlet pass. To compromise between heat transfer and pressure drop in the channel, W_el/H = 0.88 is found to be optimum for the channel under study.