基于雷诺应力模型的平衡大气边界层模拟

基于雷诺应力湍流模型（简称RSM模型）,研究了平衡大气边界层风场数值模拟问题．假设流体不可压,且不计雷诺应力输运方程中的对流项、浮力产生项、系统旋转产生项和扩散项,在准各向同性的条件下,推导出RSM模型湍动能k的表达式是标准k-ε模型k常数表达式的0.893倍．考虑k沿高度变化的修正,根据在标准k-ε模型中满足水平均匀性的湍流来流边界条件,提出在RSM模型中产生平衡大气边界层的湍流来流边界条件．基于空风洞的数值模拟结果表明,与工程上常用的湍流来流边界条件相比,基于本文提出的湍流来流边界条件得到的风场水平均匀性更优,且在整个流域内,得到的雷诺应力剖面更合适．从而验证了该湍流来流边界条件的适用性．     

曲率和旋转对离心叶轮叶片上湍流边界层的影响

本文将曲率和旋转项引入二维湍流边界层动量方程中,导出动量损失厚度的积分关系式。分析了曲率和旋转对湍流结构的直接影响,并提出壁面速度分布律的修正表达式。     

Boundary Layer for the Navier-Stokes-alpha Model of Fluid Turbulence

We study boundary-layer turbulence using the Navier-Stokes-alpha model obtaining an extension of the Prandtl equations for the averaged flow in a turbulent boundary layer. In the case of a zero pressure gradient flow along a flat plate, we derive a nonlinear fifth-order ordinary differential equation, which is an extension of the Blasius equation. We study it analytically and prove the existence of a two-parameter family of solutions satisfying physical boundary conditions. Matching these parameters with the skin-friction coefficient and the Reynolds number based on momentum thickness, we get an agreement of the solutions with experimental data in the laminar and transitional boundary layers, as well as in the turbulent boundary layer for moderately large Reynolds numbers.     

Energy-balance equation for turbulent pulsations in the theory of the free turbulent boundary layer

Semiempirical expressions are proposed for the coefficient of turbulent viscosity and for the scale of turbulence in the equations for the free turbulent boundary layer in an incompressible fluid, these equations consisting of the equation of continuity, the equations of motion, and the equation for the average energy balance in the turbulent pulsations. The advantage of the expressions over the existing ones is that the two empirical constants in the equations have nearly the same values for circular and plane turbulent streams and also for a turbulent boundary layer at the edge of a semiinfinite homogeneous flow with a stationary fluid. The mean-energy distribution and the mean energy of the turbulent pulsations computed in this paper agree well with the experimental values.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 75–79, November–December, 1970.     

Turbulent Transport in Stellar Interiors

Differential rotation is probably the major cause of turbulence in stably stratified stellar interiors. The boundary of the superficial solar convection zone plays a critical role for both the large scale circulation and the differential rotation. The turbulence arises from the barotropic instability in a vertically stratified medium and is expected to be anisotropic. It tends to suppress one of its causes, namely differential rotation in latitude. It offers an explanation for the thinness of the solar tachocline, the boundary layer beneath the convection zone where solar seismology shows that rotation varies from differential above to apparently uniform below. The anisotropy of turbulence also strongly reduces the efficiency of vertical particle transport. We show that for an anisotropy A of horizontal to vertical velocities, the vertical diffusivity is a factor A ² less than the horizontal diffusivity. Transport by meridional circulation is also reduced, as well as the efficiency of a composition gradient in suppressing meridional circulation. These effects of anisotropy explain the very small upper limit that observations of the concentration of chemical elements impose to vertical transport in stars. However the recent results of helioseismology, that the solar core rotates at nearly the same rate as the whole radiative zone, cannot currently be explained by anisotropic turbulent transport. It suggests the need for an additional transport process such as a magnetic torquing or gravity waves. Furthermore, near the base of the convection zone, magnetic instabilities could provide an alternate mechanism to mix angular momentum preferentially in latitude compared with radial mixing. The quality of the helioseismology data is improving very rapidly. It holds the promise to determine, within the next few years, the velocity field within the Sun to great accuracy. This should allow us to distinguish between the various hydrodynamical and hydromagnetic models. Received 20 May 1997 and accepted 4 January 1998     

Toward a Turbulence Constitutive Relation for Geophysical Flows

Rapidly rotating turbulent flows are frequently in approximate geostrophic balance. Single-point turbulence closures, in general, are not consistent with a geostrophic balance. This article addresses and resolves the possibility of a constitutive relation for single-point second-order closures for classes of rotating and stratified flows relevant to geophysics. Physical situations in which a geostrophic balance is attained are described. Closely related issues of frame-indifference, horizontal divergence, and the Taylor–Proudman theorem are discussed. It is shown that, in the absence of vortex stretching along the axis of rotation, turbulence is frame-indifferent. Unfortunately, no turbulence closures are consistent with this frame-indifference that is frequently an important feature of rotating or quasi-geostrophic flows. A derivation and discussion of the geostrophic constraint which ensures that the modeled second-moment equations are frame-invariant, in the appropriate limit, is given. It is shown that rotating, stratified, and shallow water flows are situations in which such a constitutive relation procedure is useful. A nonlinear nonconstant coefficient representation for the rapid-pressure strain covariance appearing in the Reynolds stress and heat flux equations, consistent with the geostrophic balance, is described. The rapid-pressure strain closure features coefficients that are not constants determined by numerical optimization but are functions of the state of turbulence as parametrized by the Reynolds stresses and the turbulent heat fluxes as is required by tensor representation theory. These issues are relevant to baroclinic and barotropic atmospheric and oceanic flows. The planetary boundary layers in which there is a transition, with height or depth, from a thermally or shear driven turbulence to a geostrophic turbulence is a classic geophysical example to which the considerations in this article are relevant. Received 14 October 1996 and accepted 9 June 1997     

Numerical computation of an impinging jet with uniform wall suction

The paper presents numerical predictions of a turbulent axisymmetric jet impinging onto a porous plate, based on a finite volume method of solving the Navier-Stokes equations for an incompressible air jet with the K–ε turbulence model. The velocity and pressure terms of the momentum equations are solved by the SIMPLE (semi-implicit method for pressure-linked equation) method. In this study, non-uniform staggered grids are used. The parameters of interest include the nozzle-to-wall distance and the suction velocity. The results of the present calculations are compared with available data reported in the literature. It is found that suction effects reduce the boundary layer thickness and increase the velocity gradient near the wall.     

Evolution of the turbulent wakes of spherical bodies in stably stratified media

A turbulent wake model, based on the Reynolds, energy and turbulence dissipation equations together with the closing relations for the turbulent transport coefficients, is proposed. A comparative investigation of swirled momentumless wakes with zero and nonzero angular momentum is carried out. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 13–22, January–February, 1994.     

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。     

一类平衡大气边界层边界条件研究

基于标准k-ε湍流模型,首先利用湍流粘度方程和剪切应力在整个边界层内恒定的假设,推导出一类耗散率表达式,并根据常用的湍动能入口剖面方程以及平均风速剖面方程,计算获得相应的耗散率方程;然后在输运方程中添加自定义源项,通过已经确定的平均速度方程、湍动能方程、耗散率方程计算得到相应输运方程的自定义源项表达式,并进行空风洞数值模拟,从而得到了一类满足平衡大气边界层的来流边界条件．通过将这种边界条件与由湍流平衡条件得到的边界条件进行比较,表明本方法获得的边界条件更适用．并且,本方法无需考虑修正壁面函数和修正湍流模型常数,因而计算更为简单,可为平衡大气边界层的研究提供一种新的思路．     

An experimental study of turbulent boundary layers approaching separation

The present paper deals with the experimental analysis of a strong decelerated turbulent boundary layer developed on a flat plate. The aim of the study was to examine the effects of pressure gradient on a non-equilibrium boundary layer while indicating local areas of equilibrium flow. The effect of the Reynolds number on a turbulent boundary layer developed with matching the external pressure gradient conditions was also analysed. The emphasis was on the analysis of mean flow statistics i.e. mean velocity profiles, streamwise Reynolds stress and the effect of large- and small-scale interactions by analysing the skewness factor and energy isocontours maps. The comparative analysis of the external data indicated that the structure of the turbulent boundary layer depends not only on local effects of pressure gradient but also on the upstream history of the flow. For the same condition of pressure gradient, the increased momentum is observed near the wall with the increase of the Reynolds number at the Incipient Detachment, where increased turbulence production is also observed, leading to the failure of the outer scaling methods. Surprisingly, the effect of the Reynolds number decays at the intermittent transitory detachment where similar profiles were observed. The upper inflection point in the mean profile corresponded well with the outer maximum of the Reynolds stress and zero crossing of skewness factor. Position of this point occurs at different locations, depending on the flow history effects. The last observation demonstrates that the inflection points results from large- and small-scale interactions, which led to the increased convection velocity of small scales near the wall.     

An LES Turbulent Inflow Generator using A Recycling and Rescaling Method

The present paper describes a recycling and rescaling method for generating turbulent inflow conditions for Large Eddy Simulation. The method is first validated by simulating a turbulent boundary layer and a turbulent mixing layer. It is demonstrated that, with input specification of mean velocities and turbulence rms levels (normal stresses) only, it can produce realistic and self-consistent turbulence structures. Comparison of shear stress and integral length scale indicates the success of the method in generating turbulent 1-point and 2-point correlations not specified in the input data. With the turbulent inlet conditions generated by this method, the growth rate of the turbulent boundary/mixing layer is properly predicted. Furthermore, the method can be used for the more complex inlet boundary flow types commonly found in industrial applications, which is demonstrated by generating non-equilibrium turbulent inflow and spanwise inhomogeneous inflow. As a final illustration of the benefits brought by this approach, a droplet-laden mixing layer is simulated. The dispersion of droplets in the near-field immediately downstream of the splitter plate trailing edge where the turbulent mixing layer begins is accurately reproduced due to the realistic turbulent structures captured by the recycling/rescaling method.     

The general form of representation of wall region of a turbulent boundary layer

On the basis of a formal similarity between turbulent momentum, heat/mass flux and probability function a concept of turbulent flux density distribution has been proposed. It has been shown that the characteristic bell shape of this distribution is almost the same, irrespective of the turbulence model from which it was calculated, and can reveal the structure of the turbulent boundary layer, especially the influence of molecularPr orSc number. This concept may also be used to test consistency and to compare differently formulated models of turbulent transport.     

Lower-Dimensional Manifold (Algebraic) Representation of Reynolds Stress Closure Equations

For complex turbulent flows, Reynolds stress closure modeling (RSCM) is the lowest level at which models can be developed with some fidelity to the governing Navier–Stokes equations. Citing computational burden, researchers have long sought to reduce the seven-equation RSCM to the so-called algebraic Reynolds stress model which involves solving only two evolution equations for turbulent kinetic energy and dissipation. In the past, reduction has been accomplished successfully in the weak-equilibrium limit of turbulence. In non-equilibrium turbulence, attempts at reduction have lacked mathematical rigor and have been based on ad hoc hypotheses resulting in less than adequate models.?In this work we undertake a formal (numerical) examination of the dynamical system of equations that constitute the Reynolds stress closure model to investigate the following questions. (i) When does the RSCM equation system formally permit reduced representation? (ii) What is the dimensionality (number of independent variables) of the permitted reduced system? (iii) How can one derive the reduced system (algebraic Reynolds stress model) from the full RSCM equations? Our analysis reveals that a lower-dimensional representation of the RSCM equations is possible not only in the equilibrium limit, but also in the slow-manifold stage of non-equilibrium turbulence. The degree of reduction depends on the type of mean-flow deformation and state of turbulence. We further develop two novel methods for deriving algebraic Reynolds stress models from RSCM equations in non-equilibrium turbulence. The present work is expected to play an important role in bringing much of the sophistication of the RSCM into the realm of two-equation algebraic Reynolds stress models. Another objective of this work is to place the other algebraic stress modeling efforts in the lower-dimensional modeling context. Received 19 November 1999 and accepted 3 August 2000     

The effect of streamwise vortices on the turbulence structure of a separating boundary layer

A high Reynolds number flat plate turbulent boundary layer is investigated in a wind-tunnel experiment. The flow is subjected to an adverse pressure gradient which is strong enough to generate a weak separation bubble. This experimental study attempts to shed some new light on separation control by means of streamwise vortices with emphasize on the change in the boundary layer turbulence structure. In the present case, counter-rotating and initially non-equidistant streamwise vortices become and remain equidistant and confined within the boundary layer, contradictory to the prediction by inviscid theory. The viscous diffusion cause the vortices to grow, the swirling velocity component to decrease and the boundary layer to develop towards a two-dimensional state. At the position of the eliminated separation bubble the following changes in the turbulence structure were observed. The anisotropy state in the near-wall region is unchanged, which indicates that it is determined by the presence of the wall rather than the large scale vortices. However, the turbulence in the outer part of the boundary layer becomes overall more isotropic due to an increased wall-normal mixing and a significantly decreased production of streamwise fluctuations. The turbulent kinetic energy is decreased as a consequence of the latter. Despite the complete change in mean flow, the spatial turbulence structure and the anisotropy state, the process of transfer of turbulent kinetic energy to the spanwise fluctuating component seems to be unchanged. Local regions of anisotropy are strongly connected to maxima in the turbulent production. For example, at spanwise positions in between those of symmetry, the spanwise gradient of the streamwise velocity cause significant production of turbulent fluctuations. Transport of turbulence in the spanwise direction occurs in the same direction as the rotation of the vortices.     

An immersed boundary/wall modeling method for RANS simulation of compressible turbulent flows

In this paper, an immersed boundary (IB) method is developed to simulate compressible turbulent flows governed by the Reynolds‐averaged Navier‐Stokes equations. The flow variables at the IB nodes (interior nodes in the immediate vicinity of the solid wall) are evaluated via linear interpolation in the normal direction to close the discrete form of the governing equations. An adaptive wall function and a 2‐layer wall model are introduced to reduce the near‐wall mesh density required by the high resolution of the turbulent boundary layers. The wall shear stress modified by the wall modeling technique and the no‐penetration condition are enforced to evaluate the velocity at an IB node. The pressure and temperature at an IB node are obtained via the local simplified momentum equation and the Crocco‐Busemann relation, respectively. The SST k ? ω and S‐A turbulence models are adopted in the framework of the present IB approach. For the Shear‐Stress Transport (SST) k ? ω model, analytical solutions in near‐wall region are utilized to enforce the boundary conditions of the turbulence equations and evaluate the turbulence variables at an IB node. For the S‐A model, the turbulence variable at an IB node is calculated by using the near‐wall profile of the eddy viscosity. In order to validate the present IB approach, numerical experiments for compressible turbulent flows over stationary and moving bodies have been performed. The predictions show good agreements with the referenced experimental data and numerical results.     

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.     

Large-scale vortex generation driven by nonequilibrium turbulence

The development of large-scale perturbations in a heated layer of rotating fluid is studied within the framework of the nonequilibrium turbulence model with asymmetric Reynolds stress tensor. It is shown that, as in spiral turbulence, when there is no equilibrium on one of the boundaries of the layer large-scale structures develop. Conditions under which both perfect intrinsic matching of turbulence and convection and internal resonance development exist are determined. It is shown that the manifestation in a turbulent medium of properties of the convective vector field such as spirality may be caused by constraints imposed by the angular momentum conservation law.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 47–55, January–February, 1996.     

Application of compressible Reynolds-averaged governing equations to turbulent mixed convection in supercritical fluids in heated vertical tubes

Accurate estimation of thermal-hydraulic characteristics of supercritical flows has long been an attractive but elusive subject to many researchers in spite of tremendous effort devoted to the development of suitable turbulence models. One of the key reasons for the difficulty is a lack of measured turbulence data, which might have been used to formulate adequate turbulence models suitable for highly buoyant fluids. Turbulence models are typically based on the log-law, while the velocity profile in buoyant fluids substantially deviates from the log-law because of significant density variation in a turbulent boundary layer. In this paper, axisymmetric compressible Reynolds-Averaged governing equations were employed together with the property-dependent turbulent Prandtl number to reproduce experimental data representing heat transfer deterioration and consequential sudden temperature increase. The additional turbulence terms associated with turbulent mass flux appeared in the governing equations were modeled using the simple gradient diffusion hypothesis (SGDH). The proposed model successfully reproduced the experimental data. The various turbulence properties are presented and discussed.     

Non-equilibrium turbulent phenomena in the ?ow over a backward-facing ramp

Non-equilibrium turbulence phenomena have raised great interests in recent years. Significant efforts have been devoted to non-equilibrium turbulence properties in canonical flows, e.g., grid turbulence, turbulent wakes, and homogeneous isotropic turbulence(HIT). The non-equilibrium turbulence in non-canonical flows, however, has rarely been studied due to the complexity of the flows. In the present contribution, a directnumerical simulation(DNS) database of a turbulent flow is analyzed over a backwardfacing ramp, the flow near the boundary is demonstrated, and the non-equilibrium turbulent properties of the flow in the wake of the ramp are presented by using the characteristic parameters such as the dissipation coefficient C and the skewness of longitudinal velocity gradient Sk, but with opposite underlying turbulent energy transfer properties. The equation of Lagrangian velocity gradient correlation is examined, and the results show that non-equilibrium turbulence is the result of phase de-coherence phenomena, which is not taken into account in the modeling of non-equilibrium turbulence. These findings are expected to inspire deeper investigation of different non-equilibrium turbulence phenomena in different flow conditions and the improvement of turbulence modeling.