Numerical simulation of stabilization of the boundary layer on a surface with a porous coating in a supersonic separated flow

Stability of a supersonic (M _∞ = 5.373) boundary layer with local separation in a compression corner with a passive porous coating partly absorbing flow perturbations is considered by solving two-dimensional Navier-Stokes equations numerically. The second mode of disturbances of a supersonic boundary layer is demonstrated to be the most important one behind the boundary-layer reattachment point. The possibility of effective stabilization of these disturbances behind the reattachment point with the use of porous coatings is confirmed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 39–47, March–April, 2007.     

Advances in the study of separated flows

This paper consists of three parts. The first deals with the separation conditions for three dimensional steady viscous separated flows, in which the behaviour of separated flow described by Navier-Stokes equations and boundary layer equations is studied. The second part involves an application of differential topology to qualitative analysis of flow fields. Here the distribution rule of singular points on the separation line is studied. The last part discusses the numerical method solving Navier-Stokes equations for separated flows. The obtained computational results are analysed by the above mentioned theories and methods.     

Transient free convection flow of a viscoelastic fluid over vertical surface

In this paper, the viscoelsatic boundary layer flow and the heat transfer near a vertical isothermal impermeable surface and in a quiescent fluid are examined. The gov-erning equations are formulated and solved numerically using MackCormak’s technique. The results show excellent agreement with previously published results by a compari-sion. Representative results for the velocity and temperature profiles, boundary layer thicknesses, Nusselt numbers, and local skin friction coefficients are shown graphically for different values of viscoelsatic parameters. In general, it is found that the velocities increase inside the hydrodynamic boundary layers and the temperatures decrease inside the thermal boundary layers for the viscoelsatic fluid as compared with the Newtonian fluid due to favorable tensile stresses. Consequently, the coefficients of friction and heat transfer enhance for higher viscoelsatic parameters.     

Secondary loss generation by gas turbine support struts

Short cylindrical struts are commonly employed to carry services across the annular flow passages of gas turbines and to provide mechanical support. Velocity variations along the span of the strut will be large and secondary flow becomes important. For bluff bodies, boundary layer separation tends to be fixed close to the maximum thickness of the strut, or any sharp edges, so that secondary flow effects have only a minor influence on wake formation. In the case of more streamlined shapes, the effect of Reynolds number and freestream turbulence level on boundary layer growth are much more significant. Moreover, the secondary flows generated by the interaction between the strut cross-section and the end-wall boundary layers may influence the position of separation, thus changing the distributions of pressure on the strut surface and in the wake. These modifications lead to large variations in the total drag force experienced by the strut. A recent wind tunnel investigation is described in which wake pressure measurements have been used to determine the additional losses produced by the secondary flow generation. Experiments have been performed on isolated struts for both circular and streamlined cross-section over a range of Reynolds number, aspect ratio and thickness-to-chord ratio. A principal finding is that the results for the streamlined struts may be reduced to a correlation which embraces the effects of cross-sectional geometry as well as the end-wall boundary layer thickness, the Reynolds and the Mach numbers.     

An upwind scheme for the three-dimensional boundary layer equations

The development of a calculation method to solve the compressible, three-dimensional, turbulent boundary layer equations is described. An implicit finite difference solution procedure is adopted involving local upwinding of convective transport terms. A consistent approach to discretization and linearization is taken by casting all equations in a similar form. The implementation of algebraic, one-equation and two-equation turbulence models is described. An initial validation of the method is made by comparing prediction with measurements in two quasi-three-dimensional boundary layer flows. Some of the more obvious deficiencies in current turbulence-modelling standards for three-dimensional flows are discussed.     

Shock-unsteadiness model applied to oblique shock wave/turbulent boundary-layer interaction

Reynolds-averaged Navier–Stokes prediction of shock wave/turbulent boundary layer interactions can yield significant error in terms of the size of the separation bubble. In many applications, this can alter the shock structure and the resulting surface properties. Shock-unsteadiness modification of Sinha et al. (Physics of Fluids, Vol.15, No.8, 2003) has shown potential in improving separation bubble prediction in compression corner flows. In this article, the modification is applied to oblique shock wave interacting with a turbulent boundary layer. The challenges involved in the implementation of the shock-unsteadiness correction in the presence of multiple shock waves and expansion fans are addressed in detail. The results show that a robust implementation of the model yields appreciable improvement over standard k–ω turbulence model predictions.     

A procedure for the design of nozzles used for the production of turbulent liquid jets

Where turbulent liquid jets are used for cutting and mining purposes the pressure generated by impact must be maximized. Initial jet behaviour has an important influence on subsequent jet impact pressures at medium range. Nozzle wall boundary layer history has a strong influence on the initial jet, and certain boundary layer features can be linked to poor jet performance. The procedure outlined in this paper was developed to eliminate new nozzle designs or changes in operating conditions on the grounds of badly behaved nozzle boundary flow. The design procedure consists of a potential flow analysis and a boundary layer analysis coupled to empirical correlations for boundary layers in accelerated flows. The procedure is exemplified by application to the design of a nozzle to be used for the specific purpose of mining china clay.     

Calculation of the length of the shock-boundary layer interaction zone

An analytic relation for determining the length of the shock-laminar or turbulent boundary layer interaction zone is obtained on the basis of an analysis of the boundary layer separation criterion. It is shown that as the Mach number of the flow increases, the interaction length decreases, and that with increase in the Reynolds number it behaves nonmonotonically: in the laminar region it increases, while on transition to the turbulent regime it falls sharply and then varies along a curve with a maximum. The results of the calculations are in satisfactory agreement with the existing experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 180–183, March–April, 1987.     

Exchange of Chemical Species between the Atmospheric Boundary Layer and the Reservoir Layer: An Analytical Interpretation

The exchange of chemical species between the atmospheric boundary layer and the reservoir layer is investigated by means of an analytical solution of the conservation equation of a decaying chemical species. The exchange mechanism is governed by two parameters: the Damköhler number (the ratio of the turbulence time scale to the chemical time scale) and the ratio of a concentration scale in the atmospheric boundary layer to the concentration in the reservoir layer. Depending on the value of these two parameters, the exchange flux between the two layers can vary in sign and by several orders of magnitude. The study demonstrates to what extent chemical transformation determines the transfer of chemical species between the atmospheric boundary layer and the reservoir layer.     

纳米流体在伸/缩楔体上的MHD流动数值研究

对纳米流体在伸/缩楔体上的磁流体(MHD)流动进行了数值研究。首先,通过相似变换将控制偏微分方程转化为非线性常微分方程组;然后,利用Matlab软件,借助打靶法,结合四阶五常龙格库塔迭代方案进行数值求解;最后,详细讨论了各控制参数对无量纲速度、温度、浓度、表面摩擦系数、局部Nusselt数和局部Sherwood数的影响。结果表明,楔体在拉伸情况下只有唯一解,理论上不会出现边界层分离;而在一定收缩强度范围内存在双解,边界层流动在壁面处可能会出现边界层分离,壁面抽吸会使边界层分离推迟;楔体在拉伸情况下,磁场参数对表面摩擦系数的影响较大,对局部Nusselt数和局部Sherwood数的影响较小。     

Unsteady Separation Processes at High Reynolds Number and Their Control

Physical situations where a viscous boundary layer breaks down and interacts strongly with an effectively inviscid external flow are common place. For large Reynolds numbers, viscous effects are normally confined to thin boundary layers on all solid surfaces for the majority of any observation time. In most practical situations, exposure of such layers to an adverse pressure gradient is inevitable and in this circumstance, a sequence of events commences near the wall that culminates in an eruption and a strong viscous-inviscid interaction with the external flow. The events leading up to eruption are known as the Van Dommelen–Shen process and the eruption itself is referred to as boundary-layer separation; here the term ‘separation’ denotes the first process of interaction between a hitherto thin boundary layer and the external flow. The event is sufficiently complicated that extraordinary measures are needed to compute its evolution. In most situations, the onset of separation is subtle and hard to detect and thus development of rational control procedures is a challenging task. Here recent calculations of unsteady separation events are discussed for two- and three-dimensional flows. The phenomena involved are generic but leading-edge separation on airfoils and rotorcraft blades is emphasized. Recent studies on various control mechanisms are described, which are found to have the effect of slowing down and/or weakening the separation process. For some control processes, it has proved possible to eliminate separation entirely.     

Disturbed boundary layer flow with local time-dependent surface heating

Local flows in a laminar boundary layer flowing over surface heating elements are investigated. Mathematical models of disturbed flows are constructed on the basis of an asymptotic analysis and the similarity parameters are determined. The time-dependent local heating regimes ensuring control of separation and flow stability in the boundary layer are studied. The results of a numerical and analytic analysis are obtained.     

Numerical boundary conditions for unsteady transonic flow calculations

In calculations of transonic flows it is necessary to limit the domain of computation to a size that is manageable by computers. At the boundary of the computational domain, boundary conditions are required to ensure a unique solution. Since wave solutions exist in the unsteady transonic flow field, incorrect boundary conditions may result in spurious reflections from the computational boundary. This may introduce errors into the solution. To prevent the spurious reflections, absorbing boundary conditions are often used on the computational boundary. In this paper we describe a method to derive absorbing boudary conditions for transonic calculations. We demonstrate both theoretically and numerically that the use of the absorbing boundary conditions will reduce the spurious reflections in the calculation.     

Effect of the turbulent viscosity relaxation time on the modeling of nozzle and jet flows

Certain modifications of three-equation turbulence models are proposed. They are intended for increasing the accuracy of the calculations of turbulent flows in nozzles with boundary layer separation and in supersonic jets with complicated shock wave structures. Basing on the idea of the inclusion of flow prehistory in terms of an additional relaxation equation for nonequilibrium turbulent viscosity we propose three modifications of the k-ω-µ _t model based on the k-ω model and a version of the k- ?-µ _t turbulence model. In these modifications we introduce an additional dependence of the nonequilibrium turbulent viscosity relaxation time on different physical parameters which can be important near the point of boundary layer separation from the nozzle wall, such as viscous effects and effects of large gradients of the mean velocity and the kinetic energy of turbulence (turbulent pressure). The comparison of the results of the calculations with the experimental data shows that all the proposed versions of the three-equation models make it possible to improve the accuracy of the calculations of turbulent flows in nozzles and jets.     

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.     

Influence of viscosity on the flow over the sharp edge of bodies consisting of a spherical segment joined to an inverted cone

The results are given of an experimental investigation of the supersonic axisymmetric flow over a body consisting of a spherical segment joined to an inverted cone in the neighborhood of the point of inflection of the profile (Fig. 1a). For the limiting case of a cylinder with a flat end and M = 3, a study was made of the influence of the Reynolds number and the state of the boundary layer on the parameters of the local separation region formed near the inflection (Fig. 1b). It was found that there is an appreciable decrease in the length of the separation region and the pressure in it when the Reynolds number increases in the range Re = 10⁵– 10⁷ in the case of a laminar boundary layer on the flat end near the inflection point. A low level of the pressure on the surface of the body was achieved — of the order of thousandths of the pressure behind a normal shock. There was found to be a sharp increase in the pressure in the separation region when the boundary layer on the end becomes turbulent with transition to a flow regime that is self-similar with respect to the Reynolds number. Under conditions of a turbulent boundary layer, systematic experimental data on the pressure on the inverted cone near the point of inflection of such bodies were obtained and generalized.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 154–157, January–February, 1981.     

Boundary layer on the moving surface of a cylinder

A study is made of the problem of the boundary layer on a cylinder with a moving surface when the cylinder moves with constant velocity in an incompressible fluid. Expressions are obtained for the distributions of the frictional stress on the surface of the cylinder and the coordinate of the singular point in the solution of the boundary layer equations that indicates the appearance of a region of reverse flow for different values of the relative velocity of the motion of the surface of the cylinder. Numerical calculations have been made of the work of the force of friction associated with displacement of the cylinder, the work expended on the motion of its surface, and, in the case of flow separation, the work of the pressure forces (it being assumed here that the pressure and friction on the wall behind the singular point are constant and equal to the pressure and friction at the singular point).     

Excitation of controllable perturbations in the three-dimensional boundary layer using plasma actuators

Two versions of the structure of a multi-discharge plasma actuator intended to excite boundary layer perturbations in the neighborhood of the leading swept-wing edge are suggested. The actuator must prevent from appearance and development of the crossflow instability modes leading to laminarturbulent transition under the normal conditions. In the case of flow past a swept wing, excitation of controllable perturbations by the plasma actuator is simulated numerically in the steady-state approximation under the typical conditions of cruising flight of a subsonic aircraft. The local body force and thermal impact on the boundary layer flow which is periodic along the leading wing edge is considered. The calculations are carried out for the physical impact parameters realizable in the near-surface dielectric barrier discharge.     

Extension of the local domain-free discretization method to large eddy simulation of turbulent flows

In this work, an immersed boundary method, called the local domain-free discretization (DFD) method, is extended to large eddy simulation (LES) of turbulent flows. The discrete form of partial differential equations at an interior node may involve some nodes outside the solution domain. The flow variables at these exterior dependent nodes are evaluated via linear extrapolation along the direction normal to the wall. To alleviate the requirement of mesh resolution in the near-wall region, a wall model based on the turbulence boundary layer equations is introduced. The wall shear stress yielded by the wall model and the no-penetration condition are enforced at the immersed boundary to evaluate the velocity components at an exterior dependent node. For turbulence closure, a dynamic subgrid scale (SGS) model is adopted and the Lagrangian averaging procedure is used to compute the model coefficient. The SGS eddy viscosity at an exterior dependent node is set to be equal to that at the outer layer. To maintain the mass conservation near the immersed boundary, a mass source/sink term is added into the continuity equation. Numerical experiments on relatively coarse meshes with stationary or moving solid boundaries have been conducted to verify the ability of the present LES-DFD method. The predicted results agree well with the published experimental or numerical data.     

PIV study on a shock-induced separation in a transonic flow

A transonic interaction between a steady shock wave and a turbulent boundary layer in a Mach 1.4 channel flow is experimentally investigated by means of particle image velocimetry (PIV). In the test section, the lower wall is equipped with a contour profile shaped as a bump allowing flow separation. The transonic interaction, characterized by the existence in the outer flow of a lambda shock pattern, causes the separation of the boundary layer, and a low-speed recirculating bubble is observed downstream of the shock foot. Two-component PIV velocity measurements have been performed using an iterative gradient-based cross-correlation algorithm, providing high-speed and flexible calculations, instead of the classic multi-pass processing with FFT-based cross-correlation. The experiments are performed discussing all the hypotheses linked to the experimental set-up and the technique of investigation such as the two-dimensionality assumption of the flow, the particle response assessment, the seeding system, and the PIV correlation uncertainty. Mean velocity fields are presented for the whole interaction with particular attention for the recirculating bubble downstream of the detachment, especially in the mixing layer zone where the effects of the shear stress are most relevant. Turbulence is discussed in details, the results are compared to previous study, and new results are given for the turbulent production term and the return to isotropy mechanism. Finally, using different camera lens, a zoom in the vicinity of the wall presents mean and turbulent velocity fields for the incoming boundary layer.