Direct numerical simulation of stable and unstable turbulent thermal boundary layers

This paper presents direct numerical simulations (DNS) of stable and unstable turbulent thermal boundary layers. Since a buoyancy-affected boundary layer is often encountered in an urban environmental space where stable and unstable stratifications exist, exploring a buoyancy-affected boundary layer is very important to know the transport phenomena of the flow in an urban space. Although actual observation may qualitatively provide the characteristics of these flows, the relevant quantitative turbulent quantities are very difficult to measure. Thus, in order to quantitatively investigate a buoyancy-affected boundary layer in detail, we have here carried out for the first time time- and space-developing DNS of slightly stable and unstable turbulent thermal boundary layers. The DNS results show the quantitative turbulent statistics and structures of stable and unstable thermal boundary layers, in which the characteristic transport phenomena of thermally stratified boundary layers are demonstrated by indicating the budgets of turbulent shear stress and turbulent heat flux. Even though the input of buoyant force is not large, the influence of buoyancy is clearly revealed in both stable and unstable turbulent boundary layers. In particular, it is found that both stable and unstable thermal stratifications caused by the weak buoyant force remarkably alter the structure of near-wall turbulence.     

Stratified Atmospheric Boundary Layers and Breakdown of Models

The goal of this study is to assess complications in atmospheric stable boundary layers which are not included in numerical models of the stably stratified boundary layer and to provide a formulation of surface fluxes for use in numerical models. Based on an extensive interpretive literature survey and new eddy correlation data for the stable boundary layer, this study defines two prototype stable boundary layers: the weakly stable case and the very stable case. The weakly stable boundary layer is amenable to existing models. The very stable boundary layer eludes modeling attempts due to breakdown of existing formulations of turbulence and due to features found in the atmosphere which are not normally included in models. The latter includes clear-air radiative cooling, low-level jets, surface heterogeneity, gravity waves, meandering motions, and other mesoscale motions which propagate from outside the local domain. While these mechanisms are not essential to understanding idealized or laboratory versions of the stable boundary layer, they complicate comparisons of numerical models and theories with actual atmospheric boundary layers. Statistics which describe various features of the stable boundary layer are offered for future comparison with modeling results. Received 13 June 1997 and accepted 19 November 1997     

Turbulent Dynamics of a Critically Reflecting Internal Gravity Wave

Results from computational fluid dynamics experiments of internal wave reflection from sloping boundaries are presented. In these experiments the incident wave lies in a plane normal to the slope. When the angle of wave energy propagation is close to the bottom slope the reflection causes wave breakdown into a quasi-periodic, turbulent boundary layer. Boundary layer energetics and vorticity dynamics are examined and indicate the importance of the three-dimensional turbulence. The boundary layer exhibits intermittent turbulence: approximately every 1.2 wave periods the boundary layer mixes energetically for a duration of about one-third of a wave period, and then it restratifies until the next mixing event. Throughout the wave cycle a strong thermal front is observed to move upslope at the phase speed of the incident waves. Simulations demonstrate that the net effects of turbulent mixing are not confined to the boundary layer, but are communicated to the interior stratified fluid by motions induced by buoyancy effects and by the wave field, resulting in progressive weakening of the background density gradient. Transition to turbulence is determined to occur at Reynolds numbers of approximately 1500, based upon the wavelength and maximum current velocity of the oncoming wave train. The boundary layer thickness depends on the Reynolds number for low Richardson numbers, with a characteristic depth of approximately one-half of the vertical wavelength of the oncoming wave. Received 21 May 1997 and accepted 14 October 1997     

Perturbation Structure and Spectra in Turbulent Channel Flow

The strong mean shear in the vicinity of the boundaries in turbulent boundary layer flows preferentially amplifies a particular class of perturbations resulting in the appearance of coherent structures and in characteristic associated spatial and temporal velocity spectra. This enhanced response to certain perturbations can be traced to the nonnormality of the linearized dynamical operator through which transient growth arising in dynamical systems with asymptotically stable operators is expressed. This dynamical amplification process can be comprehensively probed by forcing the linearized operator associated with the boundary layer flow stochastically to obtain the statistically stationary response. In this work the spatial wave-number/temporal frequency spectra obtained by stochastically forcing the linearized model boundary layer operator associated with wall-bounded shear flow at large Reynolds number are compared with observations of boundary layer turbulence. The verisimilitude of the stochastically excited synthetic turbulence supports the identification of the underlying dynamics maintaining the turbulence with nonnormal perturbation growth. Received 30 January 1997 and accepted 27 March 1998     

Measurement of unsteady boundary layer developed on an oscillating airfoil using multiple hot-film sensors

 The spatial-temporal progressions of the leading-edge stagnation, separation and reattachment points, and the state of the unsteady boundary layer developed on the upper surface of a 6 in. chord NACA 0012 airfoil model, oscillated sinusoidally within and beyond the static-stall angle, were measured using 140 closely-spaced, multiple hot-film sensors (MHFS). The MHFS measurements show that (i) the laminar separation point and transition were delayed with increasing α and the reattachment and relaminarization were promoted with decreasing α, relative to the static case, (ii) the pitchup motion helped to keep the boundary layer attached to higher angles of attack over that could be obtained statically, (iii) the dynamic stall process was initiated by the turbulent flow separation in the leading-edge region as well as by the onset of flow reversal in the trailing-edge region, and (iv) the dynamic stall process was found not to originate with the bursting of a laminar separation bubble, but with a breakdown of the turbulent boundary layer. The MHFS measurements also show that the flow unsteadiness caused by airfoil motion as well as by the flow disturbances can be detected simultaneously and nonintrusively. The MHFS characterizations of the unsteady boundary layers are useful in the study of unsteady separated flowfields generated by rapidly maneuvering aircraft, helicopter rotor blades, and wing energy machines. Received: 17 June 1997 / Accepted: 10 December 1997     

On the behaviour of solid particles in a horizontal boundary layer with turbulence and saltation effects

 A horizontal turbulent boundary layer of air carrying heavy solid particles is investigated experimentally. Mean and r.m.s. velocities of air and particles are measured by LDA, and particle mass flux distributions are obtained by means of a sampling method. The influence of the saltation mechanism is revealed by the large particle r.m.s. velocity in the near-wall region, and by the velocity lag of the particles in the outer region of the boundary layer, which is shown to be closely related to their free fall velocity. The present original results are discussed and compared with available experimental data concerning other kinds of horizontal flows. Received: 17 June 1996/Accepted: 3 April 1997     

LIF measurements of concentration profiles in the aqueous mass boundary layer

 A laser-induced fluorescence (LIF) technique is described to measure vertical concentration profiles of gases in the aqueous mass boundary layer at a free water surface. The technique uses an acid-base reaction of the fluorescence indicator fluorescein at the water surface to visualize the concentration profiles. The technique is capable of measuring two-dimensional vertical concentration profiles at a rate of 200 frames/s and a spatial resolution of 16 μm. The mass boundary layer at a free surface is characterized by significant fluctuations. Direct surface renewal is observed. The mean profiles also support rather surface renewal models than turbulent diffusion models. Received: 21 May 1997/Accepted: 18 December 1997     

Near-wall flow in a three-dimensional boundary layer on the endwall of a 30° bend

 Turbulence measurements are reported on the three-dimensional turbulent boundary layer along the centerline of the flat endwall in a 30° bend. Profiles of mean velocities and Reynolds stresses were obtained down to y ⁺≈2 for the mean flow and y ⁺≈8 for the turbulent stresses. Mean velocity data collapsed well on a simple law-of-the-wall based on the magnitude of the resultant velocity. The turbulence intensity and turbulent shear stress magnitude both increased with increased three-dimensionality. The ratio of these two quantities, the a ₁ structure parameter, decreased in the central regions of the boundary layer and showed profile similarity for y ⁺<50. The shear stress vector angle lagged behind the velocity gradient vector angle in the outer region of the boundary layer, however there was an indication that the shear stress vector tends to lead the velocity gradient vector close to the wall. Received: 16 July 1996/Accepted: 14 July 1997     

Two-component planar Doppler velocimetry in the compressible turbulent boundary layer

 Non-intrusive Planar Doppler Velocimetry (PDV) has been extended to two-component measurements in a Mach 3, flat plate turbulent boundary layer and the distorted boundary layers downstream of 7° and 14° expansions. PDV results were compared to redundant Laser Doppler Velocimetry (LDV) measurements. Mean velocity results obtained with the two techniques agree to within ±5%. PDV measurements were obtained within 0.4 mm of the surface while LDV could be employed only to within approximately 2.0 mm, highlighting a near-wall resolution advantage for PDV. Effects including those associated with separate filtered and reference cameras led to PDV uncertainties of the same order as the encountered moderate turbulence intensities, precluding an investigation of instantaneous turbulence fields. Despite these difficulties, the current multi-component measurements in distorted, compressible boundary layers highlight the potential of PDV and represent progress in its ongoing evolution. Sources of error and improvements required for quantitative turbulence measurements are discussed. Further advances can be expected from ongoing development efforts. Received: 14 February 1997 / Accepted: 26 August 1997     

Transitional intermittency detection by neural network

 A neural network has been used to predict the flow intermittency from velocity signals in the transition zone in a boundary layer. Unlike many of the available intermittency detection methods requiring a proper threshold choice in order to distinguish between the turbulent and non-turbulent parts of a signal, a trained neural network does not involve any threshold decision. The intermittency prediction based on the neural network has been found to be very satisfactory. Received: 15 December 1997/Accepted: 30 December 1998     

Roughness effects in low-<Emphasis Type="Italic"> Re</Emphasis><Subscript><Emphasis Type="Italic"> θ</Emphasis></Subscript> open-channel turbulent boundary layers

This paper reports velocity measurements obtained on a smooth and two geometrically different types of rough surfaces in an open channel. The measurements were obtained using a laser-Doppler anemometer. The recent boundary layer theory proposed by George and Castillo (1997) and conventional scaling laws are used to analyze the data. The present flow shows a strong structural similarity to a canonical turbulent boundary layer in the inner layer. The results demonstrate that surface roughness increases the wake parameter. Surface roughness also enhances the levels of turbulence intensities, Reynolds shear stress and triple correlations over most of the boundary layer, but decreases the stress anisotropy.     

Surface roughness effects in turbulent boundary layers

The effects of surface roughness on a turbulent boundary layer are investigated by comparing measurements over two rough walls with measurements from a smooth wall boundary layer. The two rough surfaces have very different surface geometries although designed to produce the same roughness function, i.e. to have nominally the same effect on the mean velocity profile. Different turbulent transport characteristics are observed for the rough surfaces. Substantial effects on the stresses occur throughout the layer showing that the roughness effects are not confined to the wall region. The turbulent energy production and the turbulent diffusion are significantly different between the two rough surfaces, the diffusion having opposite sign in the region γ/δ < 0.5. Although velocity spectra exhibit differences between the three surfaces, the mean energy dissipation rate does not appear to be significantly affected by the roughness. Received: 19 August 1998/Accepted: 16 February 1999     

Vortex reynolds number in turbulent boundary layers

The effects of vortex Reynolds number on the statistics of turbulence in a turbulent boundary layer have been investigated. Vortex Reynolds number is defined as the ratio of circulation around the vortex structure to the fluid viscosity. The vortex structure of the outer region was modeled and a full numerical simulation was then conducted using a high-order spectral method. A unit domain of the outer region of a turbulent boundary layer was assumed to be composed of essentially three elements: a wall, a Blasius mean shear, and an elliptic vortex inclined at 45° to the flow direction. The laminar base-flow Reynolds number is roughly in the same range as that of a turbulent boundary layer based on eddy viscosity, and the vortex-core diameter based on the boundary-layer thickness is nearly the same as the maximum mixing length in a turbulent boundary layer. The computational box size, namely, 500, 150, and 250 wall units in the streamwise, surface-normal, and spanwise directions, respectively, is approximately the same as the measured quasi-periodic spacings of the near-wall turbulence-producing events in a turbulent boundary layer. The effects of vortex Reynolds number and the signs of the circulation on the moments of turbulence were examined. The signs mimic the ejection and sweep types of organized motions of a turbulent boundary layer. A vortex Reynolds number of 200 describes the turbulence moments in the outer layer reasonably well.     

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).     

A miniature triple hot-wire probe for wall bounded flows

 Four orthogonal and one non-orthogonal miniature triple hot-wire probes have been developed and tested in a two-dimensional turbulent boundary layer. The influence of the different wire configurations on measurements of the Reynolds stresses has been studied. A directional calibration with an analytical solution for the wire response equations was used for the measurements of the non-orthogonal probe and was tested for the orthogonal probes in order to correct their possible geometrical imperfections. It is shown that a directional calibration does not significantly improve the quality of the measurements for precisely manufactured orthogonal probes and that measuring errors are related rather to the measuring volume, the size of the domain of unique solutions for the instantaneous velocity vector and interference effects, i.e. the wire configuration itself. Received: 7 February 1997/Accepted: 18 November 1997     

高超声速激波湍流边界层干扰直接数值模拟研究

高超声速激波与湍流边界层干扰会导致飞行器表面出现局部热流峰值,严重影响飞行器气动性能和飞行安全. 针对高马赫数激波干扰问题,以往数值研究多采用雷诺平均方法,而在直接数值模拟方面的相关工作较为少见. 开展高超声速激波与湍流边界层干扰的直接数值模拟研究,有助于进一步提升对其复杂流动机理认识和理解,同时也将为现有湍流模型和亚格子应力模型的改进提供理论依据. 采用直接数值模拟方法对来流马赫数6.0,34°压缩拐角内激波与湍流边界层的干扰问题进行了研究. 基于雷诺应力各向异性张量,分析了高超声速湍流边界层在压缩拐角内的演化特性. 通过对湍动能输运方程的逐项分析,系统地研究了可压缩效应对湍动能及其输运的影响机制. 采用动态模态分解方法,探讨了干扰流场的非定常运动历程. 研究结果表明,随着湍流边界层往下游发展,近壁湍流的雷诺应力状态由两组元轴对称状态逐渐演化为两组元状态,外层区域则由轴对称膨胀趋近于各向同性. 干扰流场内存在强内在压缩性效应(声效应),其对湍动能输运的影响主要体现在压力--膨胀项,而对膨胀--耗散项影响较小. 高超声速下压缩拐角内的非定常运动仍存在以分离泡膨胀/收缩为特征的低频振荡特性,其物理机制与分离泡剪切层密切相关.      

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.     

强吸气旋转圆筒壁面湍流边界层建模及计算

提出了湍流边界层的一种简单、快速计算方法, 用以求解强吸气作用下旋转圆筒表面边界层流动. 首先, 理论分析了同心圆筒间的旋转流体运动, 外筒静止、内筒旋转且为多孔吸气条件. 强吸气情况下旋转流动主要表现为内筒壁面附近的边界层流动, 基于这一事实得到了周向速度分布的解析表达式. 其次, 通过引入新参数扩展Cebeci-Smith代数湍流模型, 使其能考虑流线曲率、壁面吸气、低Reynolds数效应等因素. 针对这些因素的综合影响, 采用解析修正和经验参数对模型进行调整. 同时, 基于Reynolds应力湍流模型的仿真结果, 校准代数湍流模型中的经验参数. 最后, 给出基于广义Cebeci-Smith湍流模型的旋转壁面边界层流动的迭代算法, 该算法适用于需要特殊迭代过程的轴向及周向流动均匀情况. 计算了不同旋转速度和吸气强度组合工况下的边界层流动, 其周向速度和湍流强度分布与基于Reynolds应力湍流模型的计算结果非常接近. 并且表明, 当Reynolds应力湍流模型数值模拟预测内筒边界层为稳定层流时, 该方法也再现了相同初始条件下的层流边界层.      

壁面加热湍流相干结构的子波分析实验研究

通过在平板湍流边界层沿流向固壁表面平行放置若干条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大尺度流向涡结构,改变了平板湍流边界层中不同尺度结构及其能量分布。采用对壁湍流多尺度结构的子波分析表明,在湍流边界层近壁区域产生规则的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,抑制了壁湍流各种尺度湍涡结构脉动,特别抑制了能量最大尺度湍涡结构的脉动,减小由于湍流脉动引起的在湍流边界层法向和展向的动量和能量损耗,从而减小了湍流的阻力。