Supersonic flow around the trailing edge of a thin profile

The method of mergeable asymptotic expansions has recently been used effectively in investigations devoted to the study of boundary layer interaction with an external inviscid flow at high subcritical Reynolds numbers Re. The asymptotic analysis permits obtaining a limit pattern of the flow around a solid as Re þ, and determining the similarity and quantitative regularity laws which are in good agreement with experimental results. Thus by using the method of mergeable asymptotic expansions it is shown in [1–4] that near sites with high local curvature of the body contour and flow separation and attachment points, an interaction domain appears that has a small length on the order of Re^-3/8. In this flow domain, which has a three-layer structure, the pressure distribution in a first approximation already depends on the change in boundary-layer displacement thickness, while the induced pressure gradient, in turn, influences the flow in the boundary layer. An analogous situation occurs in the neighborhood of the trailing edge of a flat plate where an interaction domain also appears [5, 6]. The flow in the neighborhood of the trailing edge of a flat plate around which a supersonic viscous gas flows was examined in [7]. Numerical results in this paper show that the friction stress on the plate surface remains positive everywhere in the interaction domain, and grows on approaching the trailing edge. The supersonic flow around the trailing edge of a flat plate at a small angle of attack was investigated in [8, 9], Supersonic flow of a viscous gas in the neighborhood of the trailing edge of a flat plate at zero angle of attack is examined in [10], but with different velocity values in the inviscid part of the flow on the upper and lower sides of the plate. The more general problem of the flow around the trailing edge of a profile with small relative thickness is investigated in this paper.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 36–42, May–June, 1981.     

Mathematical modeling of brush seals

A computational fluid dynamics (CFD)-based model of brush seals has been developed and tested against other workers' experimental data. In the model, the brush is treated as an axisymmetric, anisotropic porous region with nonlinear resistance coefficients. The resistance coefficients are chosen through calibration against measurements. The CFD model gives predictions of flow rate, pressure distribution, velocity field, and bending forces on the bristles. The bristle forces are used in a separate calculation to estimate bristle bending and reaction forces on the shaft and backing plate. Bending in both the axial direction and the orthogonal plane are considered.     

Blowing into a supersonic stream through a permeable surface

Distributed blowing of gas into a supersonic stream from flat surfaces using an inviscid flow model was studied in [1–9]. A characteristic feature of flows of this type is the influence of the conditions specified on the trailing edge of the body on the complete upstream flow field [3–5]. This occurs because the pressure gradient that arises on the flat surface is induced by a blowing layer whose thickness in turn depends on the pressure distribution on the surface. The assumption of a thin blowing layer makes it possible to ignore the transverse pressure gradient in the layer and describe the flow of the blown gas by the approximate thin-layer equations [1–5]. In addition, at moderate Mach numbers of the exterior stream the flow in the blowing layer can be assumed to be incompressible [3]. In [7, 8] a solution was found to the problem of strong blowing of gas into a supersonic stream from the surface of a flat plate when the blowing velocity is constant along the length of the plate. In the present paper, a different blowing law is considered, in accordance with which the flow rate of the blown gas depends on the difference between the pressures on the surface over which the flow occurs and in the reservoir from which the gas is supplied. As in [8, 9], the solution is obtained analytically in the form of universal formulas applicable for any pressure specified on the trailing edge of the plate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 108–114, September–October, 1980.I thank V. A. Levin for suggesting the problem and assistance in the work.     

Numerical and experimental study on parameters distribution inside a two-phase ejector

The two-phase flow process in an ejector was numerically and experimentally studied using R141b as a working fluid. A modified one-dimensional gas–liquid ejector model was proposed to remedy the defect in the traditional one. Gas–liquid boundary layer regions were discussed and used to close the model. Mac Cormack method is used to discrete controlling equations of gas–liquid two-phase flow in the ejector. The radial distribution of velocity and temperature, the variation of void fraction, the axial velocity variation and the influence of primary steam pressure on the mixing process were predicted with the numerical model. An experimental rig was set up to validate the model by comparing the experimental pressure distribution in the ejector with the calculating one.     

An analysis of critical simultaneous gas/liquid flow through a restriction and its application to flowmetering

Summary A theoretical analysis is presented of the mechanism of simultaneous flow of gas and liquid through a restriction at critical speed. The study shows that a relationship exists between the mass flows of gas and liquid, restriction size and upstream pressure. Comparison of this relationship with measurements showed a reasonable agreement. It has therefore been concluded that a restriction can be used as a gas/liquid flowmeter with reasonably high accuracy, provided that the flow is a critical one. Further increase of accuracy seems possible by using a restriction especially designed for the purpose.     

Simulations of two-phase flow distribution in communicating parallel channels for a PEM fuel cell

Numerical simulations utilizing computational fluid dynamics (CFD) with a volume of fluid (VOF) method has been employed to investigate two-phase flow distribution in inter-connected parallel flow channels. The interconnections resemble gas and liquid communications in fuel cell flow fields due to the inherent or artificial structures of gas diffusion layers (GDLs). The simulation results showed that communication between parallel channels could have a great impact on the two-phase flow pattern, gas and water distribution and flow maldistribution. Wide communication channels provide a pathway for gas to short-circuit the liquid, leading to a worsened gas flow distribution. However, when the communication channels are narrow enough, they are helpful for mitigating the flow maldistribution by redistributing the liquid among the parallel flow channels through the communication channels. The simulation results were also verified by comparing the predicted and measured normalized pressure drop and the gas flow ratios at the entrance section of experimental parallel channels.     

Turbulent boundary layer on a catalytic surface in a nonequilibrium dissociating gas

The majority of the studies which consider the flow of a dissociating gas in a turbulent boundary layer are devoted to the investigation of either frozen or equilibrium flows on a flat plate.The frozen turbulent boundary layer has been studied by Dorrance [1], Kutateladze and Leont'ev [2], and Lapin and Sergeev [3]. A study of the effect of catalytic recombination processes at the plate surface on the heat transfer in a frozen turbulent boundary layer was made by Lapin [4].Kosterin and Koshmarov [5], Ginzburg [6], Dorrance [7], and Lapin [8] have studied the turbulent boundary layer on a plate in equilibrium dissociating gas.The calculation of the heat transfer in a turbulent boundary layer on a catalytic plate surface with nonequilibrium dissociation was made by Kulgein [9]. In this study the nonequilibrium nature of the dissociation process was taken into account only in the laminar sublayer, while the flow in the turbulent core was considered frozen. The solution was found numerically using a computer by means of a laborious iteration process.The present paper reports a method for calculating the turbulent boundary layer on a flat catalytic plate with arbitrary dissociation rate. The method, constructed using the assumptions customary for turbulent boundary layer theory, is a successive approximation method. Good convergence of the method is assured by the fact that the effect of the nonequilibrium nature of the dissociation process on the parameter distribution in the boundary layer and, consequently, on the friction and heat transfer may be allowed for merely by finding corrections, usually relatively small, to the distribution of these parameters in the equilibrium or frozen flows. The basis of the study is the two-layer scheme of the turbulent boundary layer. The Prandtl and Schmidt numbers and also their turbulent analogs are taken equal to unity. As the model of the dissociating gas we use the Lighthill model of the ideal dissociating gas [10], extended by Freeman [11] to nonequilibrium flows.     

A fluorescence technique for measurement of slot injected fluid concentration profiles in a turbulent boundary layer

A technique for measuring near instantaneous concentration profiles of a fluid injected through a narrow inclined slot at the wall into a high unit Reynolds number flat plate turbulent boundary layer is discussed. The concentration profiles are determined by measuring the light intensity emitted from a fluorescent dye, premixed into the injectant flow, as the injectant convects through an excitation laser beam. The fluorescence intensity is quantified by an electronically shuttered single stage microchannel plate image intensifier coupled to a linear photodiode array. This instrumentation provided the high spatial and temporal resolution required for these boundary layer concentration profile measurements. The laser induced fluorescence technique is being used to study the diffusion of injected polymer solutions away from the near wall region of the boundary layer where these solutions are effective in reducing drag. The diffusion of slot injected water has also been examined and the present results are in excellent agreement with previous studies.     

Heating enhancement caused by a transverse control jet in hypersonic flow

Experiments are reported in which the heat flux distribution near a single circular, sonic transverse jet on a flat plate exposed to a hypersonic (Mach 6.7) freestream flow was quantitatively measured using thermochromic liquid crystals. The freestream conditions were such that the boundary layer growth on the plate ahead of the jet was laminar. The results indicate that the interaction of the jet with the freestream flow created a complex flowfield with regions of separation and reattachment which caused localised enhancements to the heat flux upstream and to the side of the jet, the magnitudes of which were sensitive to both jet plenum pressure and jet gas composition. Received 28 August 1996 / Accepted 6 June 1997     

Direct numerical simulation of a liquid sheet in a compressible gas stream in axisymmetric and planar configurations

A thin liquid sheet present in the shear layer of a compressible gas jet is investigated using an Eulerian approach with mixed-fluid treatment for the governing equations describing the gas–liquid two-phase flow system, where the gas is treated as fully compressible and the liquid as incompressible. The effects of different topological configurations, surface tension, gas pressure and liquid sheet thickness on the flow development of the gas–liquid two-phase flow system have been examined by direct solution of the compressible Navier–Stokes equations using highly accurate numerical schemes. The interface dynamics are captured using volume of fluid and continuum surface force models. The simulations show that the dispersion of the liquid sheet is dominated by vortical structures formed at the jet shear layer due to the Kelvin–Helmholtz instability. The axisymmetric case is less vortical than its planar counterpart that exhibits formation of larger vortical structures and larger liquid dispersion. It has been identified that the vorticity development and the liquid dispersion in a planar configuration are increased at the absence of surface tension, which when present, tends to oppose the development of the Kelvin–Helmholtz instability. An opposite trend was observed for an axisymmetric configuration where surface tension tends to promote the development of vorticity. An increase in vorticity development and liquid dispersion was observed for increased liquid sheet thickness, while a decreasing trend was observed for higher gas pressure. Therefore surface tension, liquid sheet thickness and gas pressure factors all affect the flow vorticity which consequently affects the dispersion of the liquid.      

Planar laser-induced fluorescence (PLIF) measurements of liquid film thickness in annular flow. Part I: Methods and data

Most approaches to the modeling of annular flow require information regarding the thin liquid film surrounding the central gas core. This film is hypothesized to present a rough surface to the gas core, enhancing interfacial shear and pressure loss, with the roughness closely linked to the height of the film. This height is typically obtained from conductance probe measurements. The present work used planar laser-induced fluorescence to provide direct visualization of the liquid film in upward vertical air–water annular flow. Images were processed to produce the distribution of film heights. The standard deviation and average film thickness are found to be an increasing function of liquid flow and a decreasing function of gas flow, with the standard deviation approaching 0.4 times the average at sufficient liquid flow.     

Pressure waves in a separated gas-liquid layer in a horizontal duct with a step

Pressure wave propagation into a separated gas-liquid layer in a horizontal duct with a step is investigated analytically. The linear solution is derived assuming a large density ratio of liquid to gas. The solution can be found first for the gas layer and then for the liquid layer. The linear wave in a liquid layer is valid even for fairly large initial pressure ratios, and clearly exhibits the dispersive characteristics of the pressure wave in a liquid layer. As the initial pressure ratio is increased, the pressure wave in the gas layer becomes a shock wave. Thus, its effect on the wave in a liquid layer can be found analytically by modifying the boundary condition in part. The wave in a liquid layer consists of a main wave, which propagates with the shock speed in gas, and a precursor wave, whose front propagates with the speed of sound in liquid. The precursor wave has an oscillatory structure; its amplitude increases with increasing shock strength and also with liquid layer thickness.     

Experimental investigation on the distribution uniformity and pressure drop of perforated plate distributors for the innovative spray-type packed bed thermal storage

As an innovative thermal energy technology, the spray-type packed bed has advantages of high efficiency and low cost. A liquid distributor is the key component for the spray-type packed bed for scattering heat-transfer liquid drops evenly. In this study, the distribution performance and pressure drop of the perforated plate distributors of different orifice diameters were studied experimentally. The experimental results indicate that orifice diameter has a greater effect on the distribution performance compared to flow rate. With an increase in flow rate, the flow pattern through the distributor changes from the uncovered drop to the covered drop and then to the jet flow. The covered drop pattern shows the best performance with a good distribution and a small pressure drop simultaneously, which is the design and optimization principle of the distributor for a spray-type packed bed.     

Analysis and application of solid-gas flow inside a venturi with particle interaction

A two-phase one-dimensional solid—gas flow model which describes the flow inside a variable area duct has been developed. The model includes multiparticle equations and considers particle—particle interaction. Predictions have been compared with experimental data for the pressure drop and pressure recovery through two venturis at different solid to gas loading ratios. Accurate knowledge of the particle-size distribution is extremely important for good comparison. No meaningful single particle-size diameter is found that yields predictions to agree with the measurements. The venturi may be used as a measuring device for solid—gas flow rates for systems if the particle-size distribution is accurately known. However, the venturi-diffuser section loses its effectiveness in recovering the pressure as the solid loading increases.     

Two-phase couette flow

A study is made of plane laminar Couette flow, in which foreign particles are injected through the upper boundary. The effect of the particles on friction and heat transfer is analyzed on the basis of the equations of two-fluid theory. A two-phase boundary layer on a plate has been considered in [1, 2] with the effect of the particles on the gas flow field neglected. A solution has been obtained in [3] for a laminar boundary layer on a plate with allowance for the dynamic and thermal effects of the particles on the gas parameters. There are also solutions for the case of the impulsive motion of a plate in a two-phase medium [4–6], and local rotation of the particles is taken into account in [5, 6]. The simplest model accounting for the effect of the particles on friction and heat transfer for the general case, when the particles are not in equilibrium with the gas at the outer edge of the boundary layer, is Couette flow. This type of flow with particle injection and a fixed surface has been considered in [7] under the assumptions of constant gas viscosity and the simplest drag and heat-transfer law. A solution for an accelerated Couette flow without particle injection and with a wall has been obtained in [6]. In the present paper fairly general assumptions are used to obtain a numerical solution of the problem of two-phase Couette flow with particle injection, and simple formulas useful for estimating the effect of the particles on friction and heat transfer are also obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–46, May–June, 1976.     

Two-phase flow distributors for fuel cell flow channels

All existing proton exchange membrane （PEM） fuel cell gas flow fields have been designed on the basis of single-phase gas flow distribution. The presence of liquid water in the flow causes non-uniform gas distribution, leading to poor cell performance. This paper demonstrates that a gas flow restrictor/distributor, as is commonly used in two-phase flow to stabilize multiphase transport lines and multiphase reactors, can improve the gas flow distribution by significantly reducing gas real-distribution caused by either non-uniform water formation in parallel flow channels or flow instability associated with negative-slope pressure drop characteristic of two-phase horizontal flow systems.     

Investigation of interaction between a plane transverse gas jet and a supersonic stream

The problem of interaction between a two-dimensional transverse gas jet emerging from a slot on a flat plate and a supersonic stream is considered. Several theoretical methods based on various approaches and physical models have been proposed to determine the characteristics of such a flow. The following fundamental directions can be isolated: a quasi-one-dimensional method [1], use of blast theory [2], and methods based on the equivalence of the effect of the jet and some solid on the external flow [3, 4]. However, the listed computational schemes [1–4] do not permit any clarification of the flow configuration in the jet and in the outer stream (the shock configuration, the jet boundaries, the distribution of the gasdynamic parameters in the flow field, etc.). Extensive experimental investigations of this phenomenon have been carried out simultaneously with the development of the theoretical methods, wherein the flow picture was determined, the pressure distribution was measured in the interaction domain, etc. [5, 6]. A computation method is proposed in this paper which will permit a detailed investigation of the flow structure in the jet and in the outer flow outside the separation region. Underlying the method is a hypothesis verified experimentally: The separating streamline in the mixing layer of the separated boundary layer (the “constant mass∝ line) intersects the jet boundary at the point of maximum jet standoff from the nozzle exit towards the incoming stream.     

An experimental study on the effects of uniform injection through one perforated surface of a square cylinder on some aerodynamic parameters

It is well known that injection/suction (transpiration) through a perforated surface is an efficient way of influencing the characteristics of a turbulent boundary layer. Injection application creates a thicker boundary layer on a flat plate and it thus decreases drag. In aeronautical applications, suction is frequently used to delay boundary layer separation. This paper presents an experimental study on the effects of uniform injection through one perforated surface of a square cylinder on the pressure distribution and drag coefficient in a two-dimensional turbulent flow. For this purpose, surface pressure measurements around a square cylinder have been performed at three different Reynolds numbers in a wind tunnel. The parameters taken into account were injection rate, position of perforated surface (i.e., front, top, and rear), and pressure coefficient and drag coefficient. The results show that variation in pressure coefficient around the square cylinder and drag coefficient were influenced by the position of perforated surface and by injection rate.     

Boundary layer laminarization on a thermally insulated surface with energy supply to the flow

A subsonic stream of gas flowing over a thermally insulated plate and having an elevated temperature in a thin layer adjacent to the surface is considered. This temperature distribution in the flow can be obtained by providing a volume energy supply near the leading edge of the plate. The results of calculating the position of the line of laminar-turbulent transition on the basis of linear stability theory and the e^N method are presented. It is shown that the presence of a heated layer of gas near the surface of the plate leads to an increase in the stability of the laminar flow and an extension of the laminar interval of the boundary layer. A nonmonotonic dependence of the length of the laminar interval on the thickness of the heated layer of gas is detected. Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 58–61, September–October, 1988.     

Dynamics of a liquid film sheared by a co-flowing turbulent gas

Consider the dynamics of a thin laminar liquid film flowing over an inclined wall in the presence of a co-flowing turbulent gas. The solution to the full two-phase flow problem poses substantial technical difficulties. However, by making appropriate assumptions, the solution process can be simplified and can provide valuable insights. The assumptions allow us to solve the gas and liquid problems independently. Solving for the gas flow reduces to finding perturbations to pressure and tangential stresses at the interface, influencing the liquid problem through the boundary conditions. We analyze the effect of gas flow on the liquid problem by developing an integral-boundary-layer model, which is valid up to moderate liquid Reynolds numbers. We seek solitary-wave solutions of this model under the influence of gas flow via a pseudo-arclength continuation method. Our computations demonstrate that as a general trend, the wave speed increases with increasing the gas shear and the liquid flow rate. Further insight into the problem is provided via time-dependent computations of the integral-boundary-layer model.