可压缩均匀剪切湍流的二阶矩模拟

基于对可压缩湍流中脉动压力场和脉动速度场特征的理论分析以及ＤＮＳ结果,建立了可均匀剪切湍流中压力－变形率关联的压缩性修正模式,应用这个模式,加上Ｓａｒｋａｒ等建立的脉动体胀率项（ｄｉｌａｔａｔｉｏｎａｌ ｔｅｒｍｓ）的模式,预测可压缩均匀剪切湍流随时间的发展,所得雷诺应力各是性张量的平衡值与Ｂｌａｉｓｄｅｌｌ等的ＤＮＳ数据非常一致。这个模式准确地预测出均匀剪切湍流中压缩性导致的雷诺应力结构的“流向     

Direct numerical simulation of compressible turbulent flows

This paper reviews the authors＇ recent studies on compressible turbulence by using direct numerical simulation （DNS）,including DNS of isotropic（decaying） turbulence, turbulent mixing-layer,turbulent boundary-layer and shock/boundary-layer interaction.Turbulence statistics, compressibility effects,turbulent kinetic energy budget and coherent structures are studied based on the DNS data.The mechanism of sound source in turbulent flows is also analyzed. It shows that DNS is a powerful tool for the mechanistic study of compressible turbulence.     

Direct simulation of compressible turbulence in a shear flow

The purpose of this study is to investigate compressibility effects on the turbulence in homogeneous shear flow. We find that the growth of the turbulent kinetic energy decreases with increasing Mach number—a phenomenon which is similar to the reduction of turbulent velocity intensities observed in experiments on supersonic free shear layers. An examination of the turbulent energy budget shows that both the compressible dissipation and the pressure-dilatation contribute to the decrease in the growth of kinetic energy. The pressure-dilatation is predominantly negative in homogeneous shear flow, in contrast to its predominantly positive behavior in isotropic turbulence. The different signs of the pressure-dilatation are explained by theoretical consideration of the equations for the pressure variance and density variance. We previously obtained the following results for isotropic turbulence: first, the normalized compressible dissipation is of O(M _t ² ), and, second, there is approximate equipartition between the kinetic and potential energies associated with the fluctuating compressible mode. Both these results have now been substantiated in the case of homogeneous shear. The dilatation field is significantly more skewed and intermittent than the vorticity field. Strong compressions seem to be more likely than strong expansions.Dedicated to Professor J.L. Lumley on the occasion of his 60th birthday.This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-18605 while the authors were in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23665, U.S.A.     

无壁面参数低雷诺数非线性涡黏性模式研究

建立了一个低雷诺数的非线性涡黏性湍流模式,该模式的一个显著特性是它不包含壁面参数（如y^ ,n等）,因而特别适用于复杂几何流场的计算,本模式在几种包括回流、分离、激波等典型流动中进行了验证,结果令人满意。     

Explicit algebraic Reynolds stress model (EARSM) for compressible shear flows

We develop an explicit algebraic Reynolds stress model (EARSM) for high-speed compressible shear flows and validate the model with direct numerical simulation (DNS) data of homogeneous shear flow and experimental data of high-speed mixing-layers. Starting from a pressure–strain correlation model that incorporates compressibility effects, the weak-equilibrium assumption is invoked to derive the EARSM closure expression. The resulting closure is fully explicit and physically realizable and is a function of mean flow strain rate, rotation rate, turbulent kinetic energy, dissipation rate, and gradient Mach number. Homogeneous shear flow calculations show that the model captures the asymptotic behavior of DNS quite well. Linear EARSM calculations of a plane supersonic mixing-layer are performed, and comparison with experimental data shows good agreement. Salient results are agreement of streamwise velocity similarity profiles, mixing-layer spreading rates, and capturing the Langley curve trend.     

激波和湍流相互作用的数值模拟

本文综述了关于激波和湍流相互作用数值模拟的近期研究进展, 主要包括激波和均匀各向同性湍流、激波和湍流边界层、激波和射流以及激波和尾迹的相互作用. 激波和湍流相互作用特性受到诸多因素的影响,如激波的强度、位置、形状和流动边界以及来流的湍流状态和可压缩性等. 激波和湍流的相互作用会引起流场结构、激波特性和湍流统计特性的显著变化. 最后简要讨论了激波和湍流相互作用数值研究需要关注的一些问题.      

A method for separating shock wave motion and turbulence in LDV measurements

 Two-component laser Doppler velocimetry (LDV) measurements were made in a planar, two-dimensional flow containing an unsteady oblique shock wave formed by the convergence of two supersonic streams past a thick plate. High-speed wall pressure measurements locate the shock wave and, consequently, allow separation of the effects of shock wave motion from the turbulence fluctuations in the LDV measurements of the shock-separated free shear layer. In the current flow isolating the large-scale changes in the position of the shock from the turbulence primarily reduces the experimental scatter rather than significantly changing the shapes or magnitudes of the turbulent stress profiles. Changes in the direction of shock motion do not significantly affect the mean velocity, but do affect the turbulent stresses. Received: 11 August 1997/Accepted: 30 September 1998     

Direct Numerical Simulation of a Mach 2 shock interacting with isotropic turbulence

Direct Numerical Simulation (DNS) and linear analysis of a shock interacting with incompressible and compressible isotropic turbulence is conducted. A dependence of amplification ratios on the degree of compressibility of the incoming flow is found. It can be shown that the enhancement of rms values of turbulent quantities across the shock varies according to the ratio of compressible to incompressible kinetic energy (exact definition see eq. 8). Inflow conditions with high values of display reduced amplification ratios of TKE and thermodynamic quantities while vorticity fluctuations are enhanced more strongly. The different behaviour of the turbulent kinetic energy (TKE) is due to the reduced pressure diffusion term in the TKE-equation. Experiments show qualitatively a similar behaviour as the simulation with incompressible inflow conditions, but they could so far not confirm our findings of reduced amplification rates in the compressible case, one of the reasons being the lack of knowledge of all flow parameters upstream of the shock front and the inability to generate isotropic turbulence in real life experiments. For the DNS we use a third order in space shock-capturing scheme based on the ENO algorithm of Harten [10] together with an approximate Riemann solver. This non-TVD scheme turned out to have many advantages over other common Godunov-type high resolution schemes for the specific problem of a shock interacting with turbulent fields.     

Compressible Turbulence and Energetic Scales: What Is Known from Experiments in Supersonic Flows?

Some properties of large-scale structures in supersonic turbulent flows are examined through experiments. The large eddies considered here include energetic scales, which contribute predominantly to, say, turbulent energy and coherent structures. Different features are presented, such as the level of energy in supersonic free shear flows, the average size of energetic structures, and their characteristic timescales. It is shown that compressibility affects the level of velocity and the size of the energetic eddies, but in many common supersonic situations, the estimation of the timescales can be made from rules valid for solenoidal turbulence. Some implications for compressible turbulence modeling are suggested. Finally, the properties of coherent structures are considered in the case of mixing layers and in a separated shock/boundary layer interaction. Some features relative to the organization of the large eddies are given and the importance of the shock motion is discussed in relation to the shock/layer interaction. This revised version was published online in August 2006 with corrections to the Cover Date.     

Simulation of sonic boom interaction with shear turbulence

We investigate the interaction of pressure waves with the shear turbulence in a supersonic jet flow obtained from the direct numerical integration of the time-dependent, three-dimensional Euler equations. The resulting self-sustaining turbulent jet flow matches closely the relevant time and length scales of atmospheric turbulence. N-waves, characteristic of sonic booms, are simulated by perturbing the pressure profile and following these perturbations in space and time. The results reproduce most of the wave forms reported in laboratory experiments and in flight test data.     

Modeling plane turbulent Couette flow

Among the salient features of shear-driven plane Couette flow is the constancy of the total shear stress (viscous and turbulent) across the flow. This constancy gives rise to a quasi-homogenous core region, which makes the bulk of the flow substantially different from pressure-driven Poiseuille flow. The present second-moment closure study addresses the conflicting hypotheses relating to turbulent Couette flow. The inclusion of a new wall-proximity function in the wall-reflection part of the pressure-strain model seems mandatory, and the greement with recent experimental and direct numerical simulation (DNS) results is encouraging. Analysis of model computations in the range 750 ≤ Re ≤ 35,000 and comparisons with low-Re DNS data suggest that plane Couette flow exhibits a local-equilibrium core region, in which anisotropic, homogeneous turbulence prevails. However, the associated variation of the mean velocity in the core, as obtained by the model, conflicts with the intuitively appealing assumption of homogeneous mean shear. The constancy of the velocity gradient exhibited by the DNS therefore signals a deficiency in the modeled transport equation for the energy dissipation rate.     

可压缩各向同性衰减湍流直接数值模拟研究

采用五阶有限差分WENO格式直接模拟了高初始湍流Mach数的可压缩均匀各向同性湍流,主要分析了湍流的统计特性 和压缩性的影响,包括能谱特征、激波串、耗散率、标度律等. 研究表明,湍动能主要来自于速度场螺旋分量的贡献;各向同性湍流的小尺度脉动对压缩性更为敏感,并且压缩性的增强加快了湍流大 尺度脉动向小尺度脉动的湍动能输运;随着湍流Mach数的升高,胀量(压缩)耗散率所占比率也显著增长. 标度律分析表明,强可压缩湍流的横向速度结构函数仍然具有扩展自相似性;当阶数较高(p ≥ 5)时,纵向速度结构函数的扩展自相似性则不再成立. 对于压缩性较弱的湍流,与不可压缩湍流一致,横向湍流脉动的间歇性要强于纵向湍流脉动;而对于强可压缩湍流,纵向湍流脉动的 间歇性要强于横向湍流脉动.     

A calculating method of shock wave oscillating frequency due to turbulent shear layer fluctuations in supersonic flow

One of the more severe fluctuating pressure environments encountered in supersonic orhypersonic flows is the shock wave oscillation driven by interaction of a shock wave withboundary layer.The high intensity oscillating shock wave may induce structure resonanceof a high speed vehicle.The research for the shock oscillation used to adopt empirical orsemiempirical methods because the phenomenon is very complex.In this paper atheoretical solution on shock oscillating frequency due to turbulent shear layer fluctuationshas been obtained from basic conservation equations.Moreover,we have attained theregularity of the frequency of oscillating shock varying with incoming flow Mach numbersM_∞and turning angleθ.The calculating results indicate excellent agreement withmeasurements.This paper has supplied a valuable analytical method to study aeroelasticproblems produced by shock wave oscillation.     

Explicit algebraic Reynolds stress model for shock-dominated flows

Shock waves drastically alter the nature of Reynolds stresses in a turbulent flow, and conventional turbulence models cannot reproduce this effect. In the present study, we employ explicit algebraic Reynolds stress model (EARSM) to predict the Reynolds stress anisotropy generated by a shockwave. The model by Wallin and Johansson (2000) is used as the baseline model. It is found to over-predict the post-shock Reynolds stresses in canonical shock turbulence interaction. The budget of the transport equation of Reynolds stresses computed using linear interaction analysis shows that the unsteady shock distortion mechanism and the pressure–velocity correlations are important. We propose improvement to the baseline model using linear interaction analysis results and redistribute the turbulent kinetic energy between the principle Reynolds stresses. The new model matches DNS data for the amplification of Reynolds stresses across the shock and their post-shock evolution, for a range of Mach numbers. It is applied to oblique shock/boundary-layer interaction at Mach 5. Significant improvements are observed in predicting surface pressure and skin friction coefficient, with respect to experimental measurements.     

Modelling of pressure–strain correlation in compressible turbulent flow

Previous studies carried out in the early 1990s conjectured that the main compressible effects could be associated with the dilatational effects of velocity fluctuation. Later, it was shown that the main compressibility effect came from the reduced pressure-strain term due to reduced pressure fluctuations. Although better understanding of the compressible turbulence is generally achieved with the increased DNS and experimental research effort, there are still some discrepancies among these recent findings. Analysis of the DNS and experimental data suggests that some of the discrepancies are apparent if the compressible effect is related to the turbulent Mach number, Mt. From the comparison of two classes of compressible flow, homogenous shear flow and inhomogeneous shear flow （mixing layer）, we found that the effect of compressibility on both classes of shear flow can be characterized in three categories corresponding to three regions of turbulent Mach numbers： the low-Mr, the moderate-Mr and high-Mr regions. In these three regions the effect of compressibility on the growth rate of the turbulent mixing layer thickness is rather different. A simple approach to the reduced pressure-strain effect may not necessarily reduce the mixing-layer growth rate, and may even cause an increase in the growth rate. The present work develops a new second-moment model for the compressible turbulence through the introduction of some blending functions of Mt to account for the compressibility effects on the flow. The model has been successfully applied to the compressible mixing layers.     

Numerical simulation of expansion/compression effect on shock induced turbulent flow

The interaction of homogeneous and isotropic turbulence with a shock wave is observed by solving the Reynolds-averaged Navier–Stokes equations with the k–? turbulence model. All turbulent fluctuations are measured at the period of expansion in the turbulent field and during compression by the reflected shock on turbulent field, and it is observed that the longitudinal turbulent velocity fluctuation is enhanced more at the period of expansion due to incident shock wave movement far from the turbulent field. The amplification of the turbulent kinetic energy (TKE) level in the shock/turbulence interaction depends on the shock wave strength and the longitudinal velocity difference across the shock wave. On decreasing the longitudinal velocity difference across the shock, the turbulent kinetic energy (TKE) level is less amplified. The TKE level is amplified by the factor of 1.5–1.8 in the shock/turbulence interaction where the dissipation rate of TKE decreases in all cases of shock/turbulence interaction. After the shock/turbulence interaction, the turbulent dissipative-length scale is amplified slightly and the amplification of the length scales decreases when increasing the shock strength. To cite this article: M.A. Jinnah, K. Takayama, C. R. Mecanique 333 (2005).     

LES-based filter-matrix lattice Boltzmann model for simulating fully developed turbulent channel flow

In this paper, a three-dimensional filter-matrix lattice Boltzmann (FMLB) model based on large eddy simulation (LES) was verified for simulating wall-bounded turbulent flows. The Vreman subgrid-scale model was employed in the present FMLB–LES framework, which had been proved to be capable of predicting turbulent near-wall region accurately. The fully developed turbulent channel flows were performed at a friction Reynolds number Re_τ of 180. The turbulence statistics computed from the present FMLB–LES simulations, including mean stream velocity profile, Reynolds stress profile and root-mean-square velocity fluctuations greed well with the LES results of multiple-relaxation-time (MRT) LB model, and some discrepancies in comparison with those direct numerical simulation (DNS) data of Kim et al. was also observed due to the relatively low grid resolution. Moreover, to investigate the influence of grid resolution on the present LES simulation, a DNS simulation on a finer gird was also implemented by present FMLB–D3Q19 model. Comparisons of detailed computed various turbulence statistics with available benchmark data of DNS showed quite well agreement.     

Direct numerical simulation of a freely decaying turbulent interfacial flow

Whereas Large Eddy Simulation (LES) of single-phase flows is already widely used in the CFD world, even for industrial applications, LES of two-phase interfacial flows, i.e. two-phase flows where an interface separates liquid and gas phases, still remains a challenging task. The main issue is the development of subgrid scale models well suited for two-phase interfacial flows. The aim of this work is to generate a detailed data base from direct numerical simulation (DNS) of two-phase interfacial flows in order to clearly understand interactions between small turbulent scales and the interface separating the two phases. This work is a first contribution in the study of the interface/turbulence interaction in the configuration where the interface is widely deformed and where both phases are resolved by DNS. To do this, the interaction between an initially plane interface and a freely decaying homogeneous isotropic turbulence (HIT) is studied. The densities and viscosities are the same for both phases in order to focus on the effect of the surface tension coefficient. Comparisons with existing theories built on wall-bounded or free-surface turbulence are carried out. To understand energy transfers between the interfacial energy and the turbulent one, PDFs of the droplet sizes distribution are calculated. An energy budget is carried out and turbulent statistics are performed including the distance to the interface as a parameter. A spectral analysis is achieved to highlight the energy transfer between turbulent scales of different sizes. The originality of this work is the study of the interface/turbulence interactions in the case of a widely deformed interface evolving in a turbulent flow.     

Thermodynamic fluctuations in canonical shock–turbulence interaction: effect of shock strength

In this work, we use numerical simulation and linear inviscid theory to study the thermodynamic field generated by the interaction of a shock wave with homogeneous isotropic turbulence. Fluctuations in density, pressure, temperature and entropy can play an important role in shock-induced mixing, combustion and energy transfer processes. Data from shock-captured direct numerical simulations (scDNS) are used to investigate the variation of thermodynamic fluctuations for varying shock strengths, and the results are compared with linear interaction analysis (LIA). The density, pressure and temperature variances attain large values at the shock, followed by, in general, a rapid decay in the downstream flow. The rapid variation behind the shock makes it difficult to compare numerical results with theoretical predictions. A threshold method based on instantaneous shock dilatation is used to overcome this problem, and it gives excellent match between scDNS and LIA. We find cases with non-monotonic variation with Mach number as well as local peaks in density fluctuations behind the shock. These are explained in terms of the contribution of the post-shock acoustic and entropy modes in the LIA solution and their cross-correlation. Budget of the transport equations reveals interesting insight into the physics governing the thermodynamic field behind the shock wave. It is found that the variances are primarily determined by the competing effects of dilatational and dissipation mechanisms. The dominant mechanisms are identified for a range of conditions, and their implication for developing predictive models is highlighted.     

Effects of Compressibility and Shock-Wave Interactions on Turbulent Shear Flows

Compressibility effects are present in many practical turbulent flows, ranging from shock-wave/boundary-layer interactions on the wings of aircraft operating in the transonic flight regime to supersonic and hypersonic engine intake flows. Besides shock wave interactions, compressible flows have additional dilatational effects and, due to the finite sound speed, pressure fluctuations are localized and modified relative to incompressible turbulent flows. Such changes can be highly significant, for example the growth rates of mixing layers and turbulent spots are reduced by factors of more than three at high Mach number. The present contribution contains a combination of review and original material. We first review some of the basic effects of compressibility on canonical turbulent flows and attempt to rationalise the differing effects of Mach number in different flows using a flow instability concept. We then turn our attention to shock-wave/boundary-layer interactions, reviewing recent progress for cases where strong interactions lead to separated flow zones and where a simplified spanwise-homogeneous problem is amenable to numerical simulation. This has led to improved understanding, in particular of the origin of low-frequency behaviour of the shock wave and shown how this is coupled to the separation bubble. Finally, we consider a class of problems including side walls that is becoming amenable to simulation. Direct effects of shock waves, due to their penetration into the outer part of the boundary layer, are observed, as well as indirect effects due to the high convective Mach number of the shock-induced separation zone. It is noted in particular how shock-induced turning of the detached shear layer results in strong localized damping of turbulence kinetic energy.