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.     

Application of the Reichardt model in problems of turbulence near the wall

A method is proposed for calculating turbulent boundary layers near the wall, based on the Reichardt semiempirical model of turbulent mixing. The article considers the problem of the turbulent boundary layer of a plate, including the case of supersonic flow around a plate, as well as the problem of the turbulent boundary layer with the nonisothermal flow of turbulent jets around a surface. Here there are introduced several almost self-similar solutions of the differential transfer equations, based on the assumption of the conservative nature of the profiles of the parameters with respect to a change in the sublayer. The results of the calculation are compared with experimental data.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 15–24, March–April, 1972.     

Effect of local heat supply to a turbulent boundary layer on the friction

The results of calculating a supersonic turbulent boundary layer on a flat plate in the presence of thermal energy supply to the boundary layer are presented. Two methods of energy supply are considered: heating a local interval of the surface, which is otherwise thermally insulated and using a local volume heat source. It is shown that for the same amount of heat supplied to the gas volume heating leads, under certain conditions, to greater friction reduction than the surface heating. Localization of the energy supply zone leads to the intensification of the viscous drag reduction effect and to a greater decrease in the local friction coefficient, which extends a considerable distance downstream. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 48–56, January–February, 1997. The work was carried out with financial support from the Russian Foundation for Fundamental Research (project No. 93-013-17600).     

Construction of a method for calculating a plane boundary layer in weak solutions of polymers with laminar,transitional, and turbulent flow zones

The investigation of the effect of small polymer additives on the characteristics of the flow of a viscous liquid is, at the present time, one of the most promising approaches to the lowering of the friction resistance. One interesting question in this connection is the study of the effect of small polymer additives on the characteristics of the transitional region of flow in a boundary layer, as well as on the value of the friction resistance with the presence of laminar, transitional, and turbulent sections in the boundary layer. The article sets forth a possible method for calculation of a plane boundary layer and the friction resistance for the case of the motion of a body in weak polymer solutions with a constant concentration, taking account of the change in the flow conditions in the layer and based on the use of integral relationships. Questions connected with the development of a boundary at a body, with the feeding of a polymer in it, as well as with the effect of degradation or destruction of the polymer in the solution, are not discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–48, May–June, 1977.     

Radiative and convective heat transfer in a plane layer of absorbent curtain

An examination is made of the thermal state of a plane layer of gray gas injected into a turbulent stream of high temperature gas flowing over a permeable flat plate.Similarity-type formulations of problems are encountered both in examination of flow near a stagnation point, and also in analysis of the lifting of the boundary layer by intense injection through a porous plate [1]. The examination described relates to the following idealized formulation of the problem (Fig. la).In a plane layer of gray absorbing medium, formed by plane-parallel diffusely radiating surfaces (1-porous plate; 2-boundary of high temperature turbulent gas stream), heat transfer is accomplished by radiation and convection of the layer normal to the surfaces and by molecular heat conduction. All the physical and optical properties of the medium and of the boundary surfaces are assumed to be constant, independent of temperature.The temperature of the wetted surface of the specimen and also that of the fictitious surface determining the upper bound of the lift-off region, are given.Also assumed given is the velocity of the injected medium, which is constant throughout the entire lift-off layer. This idealization appreciably facilitates our examination without in principle changing its features.A very simplified examination of this problem was given in [2]. The special case of a medium with low optical thickness was examined in [3,4].The problem was examined in [5] under the assumption that molecular heat conduction in the medium is negligibly small.In the formulation considered the generalized energy equation has the form     

FLOW STRUCTURE IN THE TURBULENT BOUNDARY LAYER OVER DIRECTIONAL RIBLETS SURFACES

本文采用时间解析的二维粒子图像测速技术,对零压力梯度光滑以及汇聚和发散沟槽表面平板湍流边界层统计特性和流动结构进行了研究.结果表明在垂直于汇聚和发散沟槽表面的对称平面内,相对于光滑壁面,发散沟槽壁面使当地边界层厚度、壁面摩擦阻力、湍流脉动、雷诺应力等明显减小;而汇聚沟槽壁面对湍流边界层特性和流动结构的影响正好相反,汇聚沟槽使壁面流体有远离壁面向上运动的趋势,因而导致边界层厚度增加了约43%;同时,在汇聚沟槽表面情况下流向大尺度相干结构更容易形成,这对减阻是不利的.此外,顺向涡数量在湍流边界层的对数区均存在一个极大值,发散沟槽表面所对应的极大值位置更靠近沟槽壁面,而在汇聚沟槽表面则有远离壁面的趋势,由顺向涡诱导产生的较强的喷射和扫掠运动会在湍流边界层中产生较强的剪切作用,顺向涡数量的减少是发散沟槽壁面当地摩擦阻力降低的主要原因.     

Finite Difference Method for the Acoustic Radiation of an Elastic Plate Excited by a Turbulent Boundary Layer: A Spectral Domain Solution

A finite difference method is developed to study, on a two-dimensional model, the acoustic pressure radiated when a thin elastic plate, clamped at its boundaries, is excited by a turbulent boundary layer. Consider a homogeneous thin elastic plate clamped at its boundaries and extended to infinity by a plane, perfectly rigid, baffle. This plate closes a rectangular cavity. Both the cavity and the outside domain contain a perfect fluid. The fluid in the cavity is at rest. The fluid in the outside domain moves in the direction parallel to the system plate/baffle with a constant speed. A turbulent boundary layer develops at the interface baffle/plate. The wall pressure fluctuations in this boundary layer generates a vibration of the plate and an acoustic radiation in the two fluid domains. Modeling the wall pressure fluctuations spectrum in a turbulent boundary layer developed over a vibrating surface is a very complex and unresolved task. Ducan and Sirkis [1] proposed a model for the two-way interactions between a membrane and a turbulent flow of fluid. The excitation of the membrane is modeled by a potential flow randomly perturbed. This potential flow is modified by the displacement of the membrane. Howe [2] proposed a model for the turbulent wall pressure fluctuations power spectrum over an elastomeric material. The model presented in this article is based on a hypothesis of one-way interaction between the flow and the structure: the flow generates wall pressure fluctuations which are at the origin of the vibration of the plate, but the vibration of the plate does not modify the characteristics of the flow. A finite difference scheme that incorporates the vibration of the plate and the acoustic pressure inside the fluid cavity has been developed and coupled with a boundary element method that ensures the outside domain coupling. In this paper, we focus on the resolution of the coupled vibration/interior acoustic problem. We compare the results obtained with three numerical methods: (a) a finite difference representation for both the plate displacement and the acoustic pressure inside the cavity; (b) a coupled method involving a finite difference representation for the displacement of the plate and a boundary element method for the interior acoustic pressure; (c) a boundary element method for both the vibration of the plate and the interior acoustic pressure. A comparison of the numerical results obtained with two models of turbulent wall pressure fluctuations spectrums - the Corcos model [3] and the Chase model [4] - is proposed. A difference of 20 dB is found in the vibro-acoustic response of the structure. In [3], this difference is explained by calculating a wavenumber transfer function of the plate. In [6], coupled beam-cavity modes for similar geometry are calculated by the finite difference method. This revised version was published online in July 2006 with corrections to the Cover Date.     

Influence of distributed addition of a polymer solution on the characteristics of a turbulent boundary layer

The motion of a plate in the presence of distributed addition of a polymer solution is studied on the basis of a system of partial differential equations. The calculations take into account the influence of the additives on the coefficients of molecular and turbulent viscosity and diffusion. The influence of the concentration and rate of injection of the polymer solution on the profiles of the tangential frictional stress, the averaged velocity, and the local and total frictional drag coefficients is analyzed. The results of calculations are compared with data on the drag of a plate when a polymer solution is injected near its leading edge.     

Numerical prediction of turbulent boundary layer noise from a sharp-edged flat plate

An efficient hybrid uncorrelated wall plane waves–boundary element method (UWPW-BEM) technique is proposed to predict the flow-induced noise from a structure in low Mach number turbulent flow. Reynolds-averaged Navier-Stokes equations are used to estimate the turbulent boundary layer parameters such as convective velocity, boundary layer thickness, and wall shear stress over the surface of the structure. The spectrum of the wall pressure fluctuations is evaluated from the turbulent boundary layer parameters and by using semi-empirical models from literature. The wall pressure field underneath the turbulent boundary layer is synthesized by realizations of uncorrelated wall plane waves (UWPW). An acoustic BEM solver is then employed to compute the acoustic pressure scattered by the structure from the synthesized wall pressure field. Finally, the acoustic response of the structure in turbulent flow is obtained as an ensemble average of the acoustic pressures due to all realizations of uncorrelated plane waves. To demonstrate the hybrid UWPW-BEM approach, the self-noise generated by a flat plate in turbulent flow with Reynolds number based on chord Re_c = 4.9 × 10⁵ is predicted. The results are compared with those obtained from a large eddy simulation (LES)-BEM technique as well as with experimental data from literature.     

Friction and heat transfer in laminar and turbulent boundary layers on axisymmetric bodies in nonuniform supersonic flows

Generalized expressions are obtained for calculating the heat fluxes and frictional stresses of the laminar and turbulent flow regimes in a boundary layer in the case of uniform and nonuniform flow past bodies.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 65–72, March–April, 1984.     

Stress response of a rubber block with frictional contact under axial loading

Rubber blocks (or springs) are structural components widely used in many applications. Design characteristics of a rubber block under axial loading are an apparent modulus (or compression modulus) and normal and shear stresses on contact surfaces. These are affected by a contact condition of the rubber block in contact with two rigid plates and the shape of the block. The problem of a rubber block bonded to two rigid plates has been solved using various approaches. In contrast, for a rubber block whose one surface is bonded to a rigid plate and the other surface in contact with a frictional surface, there is little work in spite of practical applications. For this contact condition, approximate solutions for rectangular blocks in plane strain and for axi-symmetric discs are derived under the assumption of Coulomb frictional contact. The problem is treated as an extension of the problem of an incompressible rubber block bonded to two rigid plates with one of the plates having a frictional interaction with the rubber block. In the linear range of deformation, finite element analysis and experimental results for rubber blocks with shape factors ranging from 1 to 6 are compared for the validation of analytic results. It is found that friction coefficients play important roles in the design characteristics of the rubber block.     

Direct numerical simulation of wall turbulent flows with microbubbles

The marker‐density‐function (MDF) method has been developed to conduct direct numerical simulation (DNS) for bubbly flows. The method is applied to turbulent bubbly channel flows to elucidate the interaction between bubbles and wall turbulence. The simulation is designed to clarify the structure of the turbulent boundary layer containing microbubbles and the mechanism of frictional drag reduction. It is deduced from the numerical tests that the interaction between bubbles and wall turbulence depends on the Weber and Froude numbers. The reduction of the frictional resistance on the wall is attained and its mechanism is explained from the modulation of the three‐dimensional structure of the turbulent flow. Copyright © 2001 John Wiley & Sons, Ltd.     

沟槽面湍流边界层结构实验研究

应用激光测速技术和氢气泡流动显示技术对沟槽面湍流边界层特性及近壁区拟序结构特征进行了精细的测量和观察。实验结果表明：与光滑面湍流边界层相比,沟槽面端流边界层的黏性底层厚度、过渡层厚度及流速分布对数公式中的积分常数C均有所增大,说明采用的沟槽面具有减阻特性。此外,无量纲低速带条间距明显减小,最多减小20%,说明无量钢低速带条平均间距的缩短与湍流减阻密切联系。     

金属丝壁面加热湍流标度律的实验研究

通过在固壁表面的平板湍流边界层沿流向平行放置若干通电加热的金属细丝,在平板表面形成沿展向周期性分布的温度场,利用该温度场引起的空气热对流,在湍流边界层近壁区域产生一组沿湍流边界层展向周期分布的流向涡结构。对壁湍流小尺度结构标度律统计特性的研究表明,金属丝加热后形成的规则流向涡结构将壁湍流各种尺度湍涡结构不规则的脉动有序地组织起来,增强了湍流小尺度结构的层次结构相似性,减小了壁湍流中小尺度结构的间歇性和奇异性,抑制了壁湍流中奇异的湍涡结构。     

Heat transfer at and near the stagnation point in turbulent flow over bodies

Results are presented of experimental investigations of heat transfer in the neighborhood of the stagnation point in flow of a turbulent gas over bodies. It is assumed that the outer flow is capable of rendering the boundary layer turbulent over the whole body surface, i.e., the hypothesis is invoked that there is a turbulent stagnation point. Using the method of integral relations [1] and the flat plate heat-transfer law, transformed in such a way as to satisfy the heat-transfer conditions at the stagnation point, simple formulas have been obtained for calculating the heat flux.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 177–181, July–August, 1975.     

An experimental-based model for prediction of flow noise with drag reducing polymers

The drag reduction characteristics of certain high molecular weight polymers have been studied by various investigators. Because of the polymer’s ability to reduce turbulent shear stress and dependence of the boundary layer wall pressure spectral amplitude on the shear stress, polymer has the potential to suppress noise and vibration caused by the boundary layer unsteady pressures. Compared to its effect on drag reduction, polymer additive effects on turbulent boundary layer (TBL) wall pressure fluctuations have received little attention. Kadykov and Lyamshev [Sov. Phys. Acoust. 16 (1970) 59], Greshilor et al. [Sov. Phys. Acoust. 21 (1975) 247] showed that drag reducing polymer additives do indeed reduce wall pressure fluctuations, but they have not established any scaling relationship which effectively collapse data. Some effort has been made by Timothy et al. [JASA 108 (1) (2000) 71] at Penn State University to develop a scaling relationship for TBL wall pressure fluctuations that are modified by adding drag reducing polymer to pure water flow. This paper presents a theoretical model based on the work of the Timothy et al. team at ARL, Penn State University. Through this model one can estimate, reduction in TBL flow induced noise and vibration for rigid smooth surfaces due to release of drag reducing polymers in boundary layer region. Using this theoretical model, flow noise as experienced by a typical flush mounted hydrophone has been estimated for a smooth wall plate as a function of polymer additive concentration. Effect of non-dimensionalisation of the wall pressure fluctuations frequency spectra with traditional outer, inner and mixed flow variables will also be addressed in the paper. The paper also covers a model based on molecular relaxation time in polymer additives which not only reduce drag but also flow induced noise up to certain polymer concentration.     

Permissible Height of the Surface Roughness in a Turbulent Boundary Layer with a Streamwise Pressure Gradient

The results of an experimental investigation of the effect of the streamwise pressure gradient in a turbulent boundary layer on the permissible height of the surface roughness of bodies in an incompressible fluid flow are presented. The permissible roughness Reynolds number for which the characteristics of the turbulent boundary layer remain the same as in the case of flow past a smooth surface is determined.     

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.     

壁面湍流发卡涡包空间模态的TRPIV实验研究

运用高时间分辨率粒子图像测速(Time-resolved PIV简称TRPIV),测量得到平板湍流边界层流向/法向平面内瞬时速度矢量空间分布的时间序列;采用空间局部平均速度结构函数的概念,识别和提取湍流边界层中大尺度发卡涡包结构的空间特征。发现在湍流边界层中不同法向位置多个正负发卡涡包结构同时交替存在。这些分布在不同法向高度的发卡涡包结构之间通过倾斜的涡量剪切层相联系,构成了湍流边界层中内、外区紧密相连、相互作用的一种稳态的分布方式。