Determining the boundary layers in the plane problem for three-layer strips. Part 1

We propose an exact solution of the problem on a boundary layer (a stress-strain state decreasing away from the boundary) for three-layer strips (rods) whose layers are made of different materials. We use the asymptotic integration method to obtain boundary eigenfunctions and a characteristic equation for the parameter describing the boundary layer decay rate. We study how the middle layer material affects the boundary layer extent.     

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。     

对流边界层大涡自组织过程的数值研究

利用简化的边界层日变化干对流模式,结合非线性热力学观点,数值模拟并分析了日间对流边界层中大涡形成、发展及衰亡的动力和热力学特征.结果表明,对流边界层中大涡始终处于不稳定状态,大涡的自组织合并和破碎串级输送过程同时并存,前者与边界层系统的局部减熵相对应,后者与对流边界层的总体增熵效应对应;大涡的演变是对流边界层总体增熵这一稳定因素和局部减熵这一不稳定因素相互竞争的结果.     

Analytical investigation of boundary layer growth and swirl intensity decay rate in a pipe

In this research, the developing turbulent swirling flow in the entrance region of a pipe is investigated analytically by using the boundary layer integral method. The governing equations are integrated through the boundary layer and obtained differential equations are solved with forth-order Adams predictor-corrector method. The general tangential velocity is applied at the inlet region to consider both free and forced vortex velocity profiles. The comparison between present model and available experimental data demonstrates the capability of the model in predicting boundary layer parameters (e.g. boundary layer growth, shear rate and swirl intensity decay rate). Analytical results showed that the free vortex velocity profile can better predict the boundary layer parameters in the entrance region than in the forced one. Also, effects of pressure gradient inside the boundary layer is investigated and showed that if pressure gradient is ignored inside the boundary layer, results deviate greatly from the experimental data.     

Response of skin panels to combined self- and boundary layer-induced fluctuating pressure

Fluctuating pressures are a critical consideration in the life-prediction of thin-gauge hot-structures operating in high-speed flow. Sources include both boundary layer turbulence and self-induced components, where the latter arises from panel vibrations. While a considerable body of research is available for the structural response of thin-gauge panels to self-induced pressure fluctuations, the response to boundary layer turbulence is not well-understood due to the complexity in modeling the loads. Important open issues are the degree of coupling between the boundary layer induced fluctuating loads and the thermo-structural response, and also the potential for interactions between a turbulent boundary layer and structural response to result in structural instabilities. This study seeks to address these issues by incorporating a phenomenological model for turbulent boundary layer loads into an aerothermoelastic framework. The enhanced aerothermoelastic model is then used to study the combined effect of self- and boundary layer-induced fluctuating pressures on responses of simple panels, and to characterize features in the turbulent boundary layer loads that can lead to large amplitude structural vibrations. The developed phenomenological model predicts that the magnitude of the boundary layer induced fluctuating pressure increases with increasing panel inclination, and decreases with increasing temperature. Furthermore, it is found that both RMS magnitude and phase angle of the boundary layer induced pressure loads play key roles in panel response. Certain combinations of these features, coupled with the self-induced pressure fluctuations, are found to cause onset of fluid–structural instabilities earlier than observed when pressure fluctuations from the turbulent boundary layer are either neglected or decoupled from the panel response.     

Turbulent flow in converging nozzles,part one: boundary layer solution

The boundary layer integral method is used to investigate the development of the turbulent swirling flow at the entrance region of a conical nozzle. The governing equations in the spherical coordinate system are simplified with the boundary layer assumptions and integrated through the boundary layer. The resulting sets of differential equations are then solved by the fourth-order Adams predictor-corrector method. The free vortex and uniform velocity profiles are applied for the tangential and axial velocities at the inlet region, respectively. Due to the lack of experimental data for swirling flows in converging nozzles, the developed model is validated against the numerical simulations. The results of numerical simulations demonstrate the capability of the analytical model in predicting boundary layer parameters such as the boundary layer growth, the shear rate, the boundary layer thickness, and the swirl intensity decay rate for different cone angles. The proposed method introduces a simple and robust procedure to investigate the boundary layer parameters inside the converging geometries.     

Receptivity of the Swept Wing Boundary Layer to a Steady Flow Inhomogeneity

The boundary layer on a plate with an inclined blunt leading edge is investigated for a free-stream flow with a small span-periodic velocity inhomogeneity. This flow simulates the penetration of the outer turbulence into the swept wing boundary layer. It is shown that the boundary layer perturbations generated by the inhomogeneity generally have a streamwise velocity component significantly greater than the initial inhomogeneity amplitude. The dependence of the perturbations on the distance from the leading edge and the spanwise inhomogeneity period is found. It is shown that the swept wing boundary layer is less sensitive to the perturbation type in question than the straight wing boundary layer.     

基于网格框架的非结构附面层网格生成技术

附面层网格质量是确保计算流体力学粘性计算精度的关键技术环节.本文针对复杂外形提出了全局一致的高质量附面层网格构造算法,该方法基于针对特征的表面网格区域分解技术,利用表面网格分片后的边界线及其法向量构造最终附面层网格的轮廓框架线,并通过径向基函数及线性插值算法生成完整的附面层网格.通过典型算例分析可以看出,该方法生成的非结构附面层网格精度和全局一致性较高,且能够有效避免复杂外形附面层网格局部及全局交叉现象.     

Experimental observations of the thermal flow around a square obstruction on a vertical wall in a differentially heated cavity

The transient thermal boundary layer flow around a square obstruction placed at the middle of the hot wall in a differentially heated cavity is visualized using a shadowgraph technique. The results show that the thermal boundary layer flow, which is blocked by the obstruction, firstly forms an intrusion head under the obstruction (the lower intrusion head). Subsequently, the lower intrusion head bypasses the obstruction and reattaches to the down-stream boundary. During the reattachment process, a more complicated flow is induced, and eventually both the lower intrusion head and the thermal boundary layer destabilize. After the lower intrusion head is convected away, the thermal boundary layer flow re-stabilizes. At the quasi-steady state, the thermal boundary layer forms a double-layer structure, which is split into two sections by the obstruction. It is demonstrated that both the transient processes and the quasi-steady state flow structures of the thermal boundary layer are significantly altered by the obstruction in comparison with the case without the obstruction.     

Viscous boundary layers in flows through a domain with permeable boundary

The effect of small viscosity on nearly inviscid flows of an incompressible fluid through a given domain with permeable boundary is studied. The Vishik–Lyusternik method is applied to construct a boundary layer asymptotic at the outlet in the limit of vanishing viscosity. Mathematical problems with both consistent and inconsistent initial and boundary conditions at the outlet are considered. It is shown that in the former case, the viscosity leads to a boundary layer only at the outlet. In the latter case, in the leading term of the expansion there is a boundary layer at the outlet and there is no boundary layer at the inlet, but in higher order terms another boundary layer appears at the inlet. To verify the validity of the expansion, a number of simple examples are presented. The examples demonstrate that asymptotic solutions are in quite good agreement with exact or numerical solutions.     

A generalized thermal boundary condition

 A generalized thermal boundary condition is derived to include all thermal effects of a thin layer which is in thermal contact with an adjacent domain. The thin layer may be a stationary or moving solid-skin or fluid-film. The included thermal effects of the thin layer are the thermal capacity of the layer, thermal diffusion, enthalpy flow, viscous dissipation within the layer, convective losses from the layer, and other effects. Six different kinds of thermal boundary conditions can be obtained as special cases of the generalized boundary condition. The generalized boundary condition is given for perfect and imperfect thermal contact between the thin layer and its adjacent domain. The importance of the generalized boundary condition is demonstrated in an example. Received on 23 December 1996     

Laminar boundary layer in an equilibrium dissociated gas for arbitrary external velocity distribution

The development of machine computing technology permits calculating the boundary layer by direct numerical integration of the corresponding system of partial differential equations [1, 2]. In order to derive general conclusions concerning the boundary layer with a pressure gradient we must perform the integration for each concrete form of velocity specification at the outer edge of the boundary layer. The method of calculating the boundary layer used in the present study [3], based on the solution of a universal (independent of the specification of the velocity at the outer edge of the boundary layer) system of equations, permits the clarification of several general relationships.     

Approximate dynamic boundary conditions for a thin piezoelectric layer

Approximate dynamic boundary conditions of different orders are derived for the case of a thin piezoelectric coating layer bonded to an elastic material. The approximate boundary conditions are derived using series expansions of the elastic displacements and the electric potential in the thickness coordinate of the layer. All the expansion functions are then eliminated with the aid of the equations of motion and boundary/interface conditions of the layer. This results in boundary conditions on the elastic material that may be truncated to different orders in the thickness of the layer to obtain approximate boundary conditions. The approximate boundary conditions may be used as a replacement for the piezoelectric layer and thus simplify the analysis significantly. Numerical examples show that the approximate boundary conditions give good results for low frequencies and/or thin piezoelectric layers.     

Boundary layer development in a gas flow with stagnation enthalpy varying across the streamlines

We consider a laminar boundary layer for which the stagnation enthalpy specified in the initial section is variable with height. Such problems arise, for example, for bodies located in the wake behind another body, for hypersonic flow past slender blunted bodies (as a result of the large transverse entropy gradients in the highentropy layer), for stepwise variation of the temperature of a surface on which there is an already developed boundary layer, for sudden expansion of the boundary layer as a result of its flow past a corner of the surface, etc.Strictly, we should in such cases solve the boundary layer equations (if the longitudinal gradients are much smaller than the transverse) with the specified initial distribution of the quantities. However, from the physical point of view, the distributed region may be broken down into two regions, the near-wall boundary layer and an outer region which is a gas flow with constant velocity and the specified initial temperature profile, whose calculation yields the edge conditions for the boundary layer. The boundary between the regions is determined from the condition of adequately smooth matching of the solutions. This approach is much preferable to the first, since it permits avoiding (within the framework of boundary layer theory) the difficulties associated with the presence of a possible singularity at the initial point of the surface due to the discontinuity of the boundary conditions at this point, and also permits using conventional boundary layer theory if the effect of the viscosity in the outer region is not significant. However, this partition requires additional justifications of the possibility of independent determination of the solution in the outer region and the determination of the edge of the boundary layer, considered as the region of influence of the wetted surface. The boundary layer in a nonuniform flow has been considered in several works for a linear initial velocity or temperature profile [1–3].It should be noted that the linear initial enthalpy or velocity profiles for constant gas properties do not undergo changes under the influence of viscosity or thermal conductivity. Thus the fundamental characteristic features noted above which are associated with the presence of the two regions and their interaction in essence cannot be investigated using these examples.In this study we obtain and analyze the exact solutions of the equations of the compressible boundary layer for a power-law variation of the initial stagnation enthalpy profile as a function of the stream function for a constant initial velocity. Here it is shown that the influence of the boundary conditions at the wall are actually localized in the near-wall boundary layer, which is similar in dimensions to the conventional velocity or thermal boundary layers. In the region which is external with relation to this layer, in accordance with the physical picture described above, the solution coincides with the solution of the Cauchy problem for the heat conduction equation, which describes the development of the initial temperature profile in an infinite steady-state flow with constant velocity.It is shown that for the sufficiently smooth initial profiles which are of interest in practice the outer flow undergoes practically no changes until we reach the inner boundary layer, and it may be calculated using the perfect gas laws.     

High accuracy non-equidistant method for singular perturbation reaction-diffusion problem

Singular perturbation reaction-diffusion problem with Dirichlet boundary condition is considered. It is a multi-scale problem. Presence of small parameter leads to boundary layer phenomena in both sides of the region. A non-equidistant finite difference method is presented according to the property of boundary layer. The region is divided into an inner boundary layer region and an outer boundary layer region according to transition point of Shishkin. The steps sizes are equidistant in the outer boundary layer region. The step sizes are gradually increased in the inner boundary layer region such that half of the step sizes are different from each other. Truncation error is estimated. The proposed method is stable and uniformly convergent with the order higher than 2. Numerical results are given, which are in agreement with the theoretical result.     

Untersuchungen der Kristallisation an wärmeübertragenden Wänden mit Hilfe der holografischen Interferometrie

The holographic interferometry was used for investigations on temperature and concentration boundary layers during the crystallization of salts from aqueous solutions. Results are discussed for aqueous solutions of sodium sulfate and potassium nitrate. The Nusselt numbers derived from temperature profiles coincide very good with calculated results from heat transfer relations. However, no significant changes of concentration in the vicinity of the surface could be found. Investigations with a dissolving crystallization layer show a distinctive diffusion boundary layer. The measured results led to Sherwood numbers 24% higher than published. On the other hand no diffusion boundary layer could be detected for progressive crystallization. This means that the crystal layer grows is reaction controlled. Microscopical pictures of the crystal layer surface show a strongly rugged surface with steps of about 6o pm height. These coarse structures disturb the formation of a boundary layer and prevent the light beam which passes through the test channel. Therefore an existant diffusion boundary layer maybe covered up by the crystal layer.     

Structures of Density Fluctuations at a Low-Mach-Number Turbulent Boundary Layer by DNS

We performed a direct numerical simulation of a low-Mach-number turbulent boundary layer using fundamental equations of compressible flow to investigate the relation between vortex structures and the density distribution. A fully developed turbulent boundary layer of compressible flow was reproduced in the simulation. From the turbulence statistics and instantaneous structures of the density fluctuation, we identified different features in the three regions of a near-wall field, far field and flow field outside the turbulent boundary layer. Structures of the density fluctuation could correspond to sound sources in a turbulent boundary layer. We then observed fine-scale structures of the density fluctuation that were strongly related to turbulent vortices in the vicinity of the wall. In addition, there were large-scale density structures in the upper boundary layer. The large-scale structures seem to correlate with the fine-scale structures close to the wall, with there being a non-steady larger-scale density fluctuation profile in the outer region of the boundary layer.     

Wall Boundary Layers for Maxwell Liquids

Flows of viscoelastic liquids at high Weissenberg number exhibit stress boundary layers near walls. These boundary layers are caused by the memory of the fluid: while particles at the wall remain in their position, particles at some distance from the wall move a long distance within one relaxation time if the Weissenberg number is high. Since the stresses depend on the flow history, this causes a steep boundary layer to form. A rescaling of the variables exploiting the thinness of this boundary layer can be used to derive a reduced set of boundary layer equations. This paper addresses the question of existence of solutions for these boundary layer equations. Using an implicit function argument, we prove the existence of a large class of solutions which arise from spatially periodic perturbations of uniform shear flow. The solutions we find can be characterized by the shear rate outside the boundary layer, which can be prescribed arbitrarily. Accepted: September 27, 1999     

Effect of a space-time source structure simulating a dielectric barrier discharge on the laminar boundary layer

The time-dependent pulse-periodic action of a surface electric discharge on a flat-plate laminar boundary layer is simulated theoretically. The effect of the discharge is estimated within the framework of the numerical solution of the boundary value problem for the time-dependent two-dimensional compressible boundary layer with additional terms in the momentum and energy conservation equations simulating the force and thermal action of the discharge on the gas flow with allowance for the pressure gradient across the boundary layer induced by the corresponding body force component. The effect of certain parameters of the problem formulated above on the gas velocity induced by the discharge in the boundary layer is also estimated.