Near-separating,self-similar turbulent boundary layer

The self-similar flow in a turbulent boundary layer, which is in a state close to separation as a result of the effect of adverse pressure gradient, is investigated. Such a boundary layer has a triple-deck asymptotic structure. Between outer and near-wall regions above the logarithmic sublayer, i. e. the constant-stress layer, an intermediate region — the gradient sublayer — is formed, where the shear stress varies linearly due to adverse longitudinal pressure gradient. In the external part of the gradient sublayer, the velocity profile obeys the square-root law. The velocity profile obtained from the solution for the outer region satisfies a slip condition on the wall. The slip value decreases as the similarity parameter increases and vanishes at the value of Ω = 0.0911, which corresponds to separation, here δ^* is the displacement thickness, and U and U′ are the free-stream velocity and its derivative with respect to the longitudinal coordinate. In this case, the exponent m in the law specifying the free-stream self-similar velocity distribution increases, with separation occurring not at the minimal value of m = −1/3, which corresponds to the strongest adverse pressure gradient, but at the value m = 0.228. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

壁湍流多尺度湍涡结构推广的自相似标度律

在水槽中测量了中等雷诺数下平板湍流边界层中的瞬时流向速度的时间序列,验证了Benzi提出的推广的自相似标度律,用子波变换将壁湍流脉动速度分解为多尺度湍涡结构的速度,研究了每一个尺度的湍涡速度结构函数的推广的自相似标度律。主要结论如下:湍流的统计性质是自相似的,这不仅适用于充分发展湍流,而且适用于中等雷诺数和低雷诺数湍流,而且具有相同的标度指数;推广的自相似标度律的适用的尺度范围远远大于惯性子区的范围,可以一直延伸至耗散区的尺度范围;推广的自相似标度律不仅适用于均匀各向同性湍流,也适用于剪切湍流如边界层湍流。     

Effect of pressure gradient on coherent structures in a turbulent boundary layer

By using the idea of resonant triad of the theory of hydrodynamic stability, the effect of pressure gradient on coherent structures in a turbulent boundary layer is investigated. The favorable pressure gradient suppresses the generation of the coherent structure, while the adverse pressure gradient has the opposite effect. The scale, form, as well as the propagation speed of the coherent structures are different from those with zero pressure gradient. The theoretical results are, in general, in agreement with those found from experiments. From the calculated probability density curve of the circulation differences of the nearly streamwise vortex pairs, it is found that the adverse pressure gradient makes the vortex pair more symmetric. Project supported by the National Natural Science Foundation of China.     

Implementation of near-wall boundary conditions for modeling boundary layers with free-stream turbulence

The paper is devoted to the extension of the near-wall domain decomposition, earlier developed in some previous works by the authors, to modeling flat-plate boundary layers undergoing laminar-to-turbulent bypass transition. The steady-state wall boundary layers at high-intensity free-stream turbulence are studied on the basis of differential turbulence models with the use of non-overlapping domain decomposition. In the approach the near-wall resolution is replaced by the interface boundary conditions of Robin type. In contrast to the previous studies, the main attention is paid to the laminar–turbulent transitional regime. With the use of modified turbulence models we study an effect of free-stream parameters on the development of dynamic processes in the boundary layer including a transitional regime and fully developed turbulent flow. In addition, for the first time a full scale domain decomposition is realized via iterations between the inner and outer subregions until a convergence. The computational profiles of the velocity and intensity of the turbulence kinetic energy are compared with experimental data. A possible range of location of the near-wall interface boundary is found.     

Investigations of shear free turbulent diffusion in a rotating frame

We reconsider the problem of shear free turbulent diffusion in a rotating frame, rotating about x₁. Shear free turbulence is generated at a vibrating grid in the x₂–x₃ plane and diffuses away from the grid in x₁ direction. An important property of this flow case is that there is no mean flow‐velocity. With the help of Lie‐group methods Reynolds‐stress transport models can be analyzed for this kind of flow in a rotating frame. From the analysis it can be found, that the turbulent diffusion only influences a finite domain. Implicating this solution in the model equations shows that even fully nonlinear Reynolds‐stress transport models (non‐linear in the Reynolds‐stresses for the pressure‐strain model) are insensitive to rotation for this type of flow. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

DNS and Lie group analysis of turbulent boundarly layer flow

Lie group approach is used to derive new scaling laws for zero-pressure gradient turbulent boundary layer flow. A direct numerical simulation of the flow at Reynolds number Re_θ = 2240 was performed for the verify theoretical results. Navier-Stokes equations were numerically solved using spectral method with up to 160 million grid points. The numerical simulation shows validity of the theoretical results. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of secondary flow and the related instability on an infinite yawed cylinder with Schubauer’s ellipse as section

This paper presents the principal results of a theoretical investigation of the secondary flow and the related instability performed in the laminar incompressible boundary layer on an infinite uniform yawed solid cylinder with Schubauer’s ellipse of axial ratio 2·96:1 as the section normal to the leading edge. The secondary flow profiles and the value of the instability criterion are obtained at different points of the wing section and for various angles of sweepback. It is found that in favourable pressure gradients and at pressure minimum, the secondary flow profiles have negative values. In regions of adverse pressure gradients after the pressure minimum the secondary flow changes sign from negative to positive values and have points of inflexion. The change of sign starts from the surface and extends to the edge of the boundary layer downstream. At some points in adverse pressure gradients the secondary flow profiles have double points of inflexion and values of both signs simultaneously. It is found that an adverse pressure gradient produces more powerful secondary flow than a favourable pressure gradient of the same strength. It is also found that the values of the instability criterion increase with the increasing sweepback whether the pressure gradient is favourable or adverse. At every point of the wing section, there are two values of the criterion for a given sweepback. The effect of adverse pressure gradient on the variation of the criterion is much more pronounced than that of a favourable pressure gradient. It is also seen that the flow is intermittently laminar and turbulent for low values of the chordwise free stream Reynolds number and for low values of sweepback and consists of an irregular sequence of laminar and turbulent regions.     

Hartmann duct flow at moderate magnetic Reynolds numbers

The application of a uniform external magnetic field on the turbulent duct flow of an electrically conducting fluid leads to several interesting changes in the structure and the mean charateristics of the flow. This is fairly well understood from the existing studies of duct flows in the low magnetic Reynolds number (R_m) limit. In this paper, we present the results for magnetohydrodynamic duct flow at moderate R_m obtained from direct numerical simulations (DNS). Several differences are observed to occur in this case as compared to low R_m flows, such as increased Hartmann layer thickness and enhanced large scale turbulence in the core region of the duct cross-section due to partial expulsion of magnetic flux. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of secondary flow instability on an infinite yawed cylinder with 15 per cent. Thick joukowski profile as section

This paper contains a theoretical investigation of the secondary flow instability in the incompressible boundary layer on an infinite yawed cylinder with chordwise section as Joukowski profile of 15 per cent. thickness at zero incidence and with homogeneous suction, the suction mass flow coefficient being equal to 0·2085. Values of the instability criterion are obtained at different points of the wing section and for various angles of sweepback. It is found that the values of the criterion increase with the increasing sweepback whether the pressure gradient is favourable or adverse. The effect of adverse pressure gradient on the variation of the criterion is more pronounced than that of a favourable pressure gradient. At some points in adverse pressure gradients, there are two values of the criterion for a given sweepback. It is also found that the flow is intermittently laminar and turbulent for low values of the chordwise free stream Reynolds number and consists of an irregular sequence of laminar and turbulent regions.     

壁面加热湍流耗散率标度指数测量的实验研究

对中等雷诺数下壁面常温和壁面加热的平板湍流边界层中速度和温度粗粒化的耗散率结构函数标度指数进行了实验测量.用热线风速仪测量了风洞中壁面常温和加热的平板湍流边界层中不同法向位置的流向速度分量和温度的时间序列信号,研究了由于湍流边界层近壁区域相干结构的存在而导致的非各向同性、非均匀性对湍流耗散率结构函数标度指数的影响,研究发现,中等雷诺数下壁面加热的边界条件和剪切湍流的平均速度梯度对速度和温度耗散率结构函数的标度指数没有影响,均匀各向同性湍流的耗散率结构函数标度指数的层次结构模型对壁面加热平板湍流边界层的速度和温度耗散率结构函数的标度指数也是适用的.     

Variation of friction drag via spanwise transversal surface waves

Introducing spanwise velocity components into the near-wall flow field of a turbulent boundary layer has shown to be an effective mean of influencing the wall shear stress. The underlying physical mechanisms leading to the drag reduction have however not been fully understood. The presented investigation uses sinusoidal transversal travelling surface waves to influence the near-wall turbulence to achieve drag reduction. Two distinct wave configurations are analysed in detail and compared to an unactuated turbulent flat plate boundary layer flow to gain inside into the drag reducing mechanisms. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Asymptotic and numerical solutions of three‐dimensional boundary‐layer flow past a moving wedge

We consider a laminar boundary‐layer flow of a viscous and incompressible fluid past a moving wedge in which the wedge is moving either in the direction of the mainstream flow or opposite to it. The mainstream flows outside the boundary layer are approximated by a power of the distance from the leading boundary layer. The variable pressure gradient is imposed on the boundary layer so that the system admits similarity solutions. The model is described using 3‐dimensional boundary‐layer equations that contains 2 physical parameters: pressure gradient (β) and shear‐to‐strain‐rate ratio parameter (α). Two methods are used: a linear asymptotic analysis in the neighborhood of the edge of the boundary layer and the Keller‐box numerical method for the full nonlinear system. The results show that the flow field is divided into near‐field region (mainly dominated by viscous forces) and far‐field region (mainstream flows); the velocity profiles form through an interaction between 2 regions. Also, all simulations show that the subsequent dynamics involving overshoot and undershoot of the solutions for varying parameter characterizing 3‐dimensional flows. The pressure gradient (favorable) has a tendency of decreasing the boundary‐layer thickness in which the velocity profiles are benign. The wall shear stresses increase unboundedly for increasing α when the wedge is moving in the x‐direction, while the case is different when it is moving in the y‐direction. Further, both analysis show that 3‐dimensional boundary‐layer solutions exist in the range −1<α<∞. These are some interesting results linked to an important class of boundary‐layer flows.     

Self-similar turbulent boundary layer in pressure gradient

Self-similar flows in a turbulent boundary layer when the free-stream velocity is specified as a power function of longitudinal coordinate are investigated. The self-similar formulation not only simplifies solving of the problem by reducing the equations of motion to ordinary differential equations but also provides a mean for formulating closure conditions. It is shown that for the class of flows under consideration that depend on three governing parameters the dimensionless mixing length is a function of the normalised distance from the wall and the exponent in the law specifying the free-stream velocity distribution in the outer region and a universal function of local Reynolds number in the wall region, the latter corollary being true even when the skin friction vanishes. In calculations this function is set to be independent of pressure gradient, which gives the results very close to experimental data. There exist four different self-similar flow regimes. Each regime is related to its similarity parameter, one of which is the well-known Clauser equilibrium parameter and the other three are established for the first time. In case of adverse pressure gradient when the exponent lies within certain limits, which depend on Reynolds number, the problem has two solutions with different values of the boundary layer thickness and skin friction, which points out the possibility of hysteresis in near-separating flow. Separation occurs not at the minimum value of the exponent that corresponds to the strongest adverse pressure gradient but at a higher one whose dependence on Reynolds number is calculated in the paper. The results of the theory are in good agreement with experimental data. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effects of plane strain on inhomogeneous turbulence

The influence of the mean plane strain on the turbulence transportation is investigated by large eddy simulation (LES) in the shearless turbulence mixing layer. It is found that the mean strains enhance the turbulent fluctuations in the mixing region. Compression in the inhomogeneous direction can greatly increase the transport of turbulent kinetic energy by triple correlation terms, while stretching in the inhomogeneous direction decreases the turbulence transportation. The gradient diffusion models for turbulent transportation are evaluated and it is found that the intermittency consideration can improve the prediction ability of the gradient-type models for the triple correlation terms. Project supported by the Sino-French Laboratory in Beijing and the National Natural Science Foundation of China (Grant No. 19572041).     

Longitudinal and transversal two-point correlations in a turbulent flow

Based on measurements with hot-wire anemometers in a fully developed turbulent flow in the wake of a cylinder we investigate different aspects of longitudinal and transversal two-point correlations. In particular we use Taylor's hypothesis as well as simultaneous measurements with two X-hot-wire probes, and investigate how these correlations change with the relative orientation of their separation vector with respect to the mean flow direction. For the wake at a distance of eighty cylinder diameters at a Reynolds number Re = 28 000 (Taylor-based Reynolds number Re_λ = 290), we find evidence of strong anisotropy. We analyze the data using increment statistics, in particular increment distributions and structure functions. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigating Asymptotic Suction Boundary Layers using a One-Dimensional Stochastic Turbulence Model

The one-dimensional turbulence model (ODT) is applied to study turbulent asymptotic suction boundary layers for a Reynolds number of Re = u_∞/v₀ = 333, where u_∞ and v₀ are the free stream and suction velocity, respectively. In here we will demonstrate that a large eddy suppression mechanism may reduce the influence of ODT model parameters, such as the viscous cut-off parameter Z. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamical structure of the turbulent boundary layer on rough surface

The experiments on structure of turbulent boundary layer on the plane rough wall without pressure gradient are presented. Sand roughness of the wall is considered. Measurements are carried out using Time-Resolved PIV technique in planes parallel and perpendicular to the wall. The results on rough wall are compared with the base case of boundary layer on smooth wall. Hairpin vortices have been detected. Topology and typical size of those structures substantially differ in the cases in question. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analytic Study of Magnetohydrodynamic Flow and Boundary Layer Control Over a Wedge

A genuine variational principle developed by Gyarmati, in the field of thermodynamics of irreversible processes unifying the theoretical requirements of technical, environmental and biological sciences is employed to study the effects of uniform suction and injection on MHD flow adjacent to an isothermal wedge with pressure gradient in the presence of a transverse magnetic field. The velocity distribution inside the boundary layer has been considered as a simple polynomial function and the variational principle is formulated. The Euler-Lagrange equation is reduced to a simple polynomial equation in terms of momentum boundary layer thickness. The velocity profiles, displacement thickness and the coefficient of skin friction are calculated for various values of wedge angle parameter m, magnetic parameter ξ and suction/injection parameter H. The present results are compared with known available results and the comparison is found to be satisfactory. The present study establishes high accuracy of results obtained by this variational technique.