高超声速压缩拐角峰值热流位置预测模型研究

旨在通过建立高超声速压缩拐角流动的再附点附近的模型理论来揭示峰值热流的产生机理以及如何可靠预测其位置.首先,分析再附点附近流动特征,提出了基于可压缩斜驻点流动模型来近似该处的局部流动.其次,近似求解了该流动模型,发现边界层厚度存在极小值的特征,从而揭示了再附点后峰值热流的产生机理,并由此得到了再附点和峰值热流点间距离的半解析半数值估算方法.最后,对此结果作了数值验证,并做了讨论.      

A Quasi-Realizable Cubic Low-Reynolds Eddy-Viscosity Turbulence Model with a New Dissipation Rate Equation

A non-linear relationship of the Reynolds stresses in function of the strain rate and vorticity tensors, with terms up to third order, is developed. Anisotropies in the normal stresses, influence from streamline curvature or rotation of the reference frame, and swirl effects are accounted for. The relationship is linked to ak–ε model with a modified transport equation for the dissipation rate. A new low-Reynolds source term is introduced and a model parameter is written in terms of dimensionless rate-of-strain and vorticity. The model is checked on different realizability constraints. It is shown that practically all constraints are fulfilled. The model is numerically tested on a fully developed channel and pipe flow, both stationary and rotating. The plane jet–round jet anomaly is addressed. Finally, the model is applied to the flow over a backward-facing step. Results are compared with a linear low-Reynolds k–ε model and the shear stress transport model. This revised version was published online in July 2006 with corrections to the Cover Date.     

利用修正低雷诺数k—ε模型对管道分离流动的数值研究

采用适合于分离流的修正低雷诺数ｋ－ε模型对突扩园管中的流动进行了数值研究，重点是对近壁流动和再附着点附近流动的研究。从理论上证明了所采用的湍流模型既满足近壁渐进行为，又避免了在通过再附着点截面上μｔ恒为０的困难。和已有的实验数据比较表明，所采用的模型对再附点位置及其附近的流动预测能力优于普通低雷诺数ｋ－ε模型。     

磁流体湍流及数值模拟研究综述

自从20世纪90年代初,AJAX计划的提出掀起了磁流体技术的研究热潮.本文总结了国内外关于磁流体湍流研究的成果,包括两方面:磁流体湍流的特点和数值模型.相比于普通湍流,磁流体湍流表现出电磁诱导的各向异性、线性焦耳耗散、湍流重层流化等特性,本文同时对磁流体湍流的结构和脉动抑制现象进行了描述;数值模型研究从雷诺平均方程和大涡模拟两方面作了介绍.当前研究集中在不可压缩磁流体湍流,距离能够应用于航空航天问题还有很长的路要走.     

Friction and Heat Transfer in a Laminar Separated Flow behind a Rectangular Step with Porous Injection or Suction

Results of a numerical study of a laminar separated flow behind a rectangular step on a porous surface with uniform injection or suction are described. Two cases are considered: an unconfined flow past a step and flow evolution in a confined channel (duct). It is shown that mass transfer on the surface causes strong changes in the flow structure and substantially affects the position of the reattachment point, as well as friction and heat transfer. More intense injection leads first to an increase in the separation-zone length and then to its rapid vanishing due to boundary-layer displacement. Vice versa, suction at high Reynolds numbers Re _s > 100 reduces the separation-zone length. The duct flow has a complicated distribution of friction and heat-transfer coefficients along the porous surface owing to the coupled effect of the transverse flow of the substance and changes in the main flow velocity due to mass transfer. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 18–28, January–February, 2006.     

Modelling of inhomogeneous turbulence in the absence of mean velocity gradients

In this paper we propose a new rational model for turbulent transport of Reynolds stresses and dissipation. For this purpose we first analyse some properties of diffused turbulence i.e. turbulence where dissipation is balanced by turbulent diffusion arising from inhomogeneity. Then we use some of these results to deduce some mathematical requirements that must be satisfied by any rational model and we show that they are not verified by available models. Consequently we derive a more general model taking into account the various properties of diffused turbulence.     

Boundary-layer relaxation after a separated region

With reference particularly to the work of Peter Bradshaw and his associates, some remarks are made about the recovery of previously distorted shear flows. It is emphasized that such recovery is usually extremely slow, and this is further illustrated by new measurements of the velocity field and turbulence structure in the relaxing flow downstream of a separated region. Data have been obtained for downstream distances (x) up to about 20 times the length of the separated region (x_r), or about 75 times the flow thickness at reattachment. This is a significantly more extensive region than has been previously studied, and the data are more comprehensive than any previously available.

It is shown that the recovery is even slower than previously surmized. Furthermore, the measurements demonstrate that the turbulence stresses eventually fall below standard boundary-layer values (at the same Reynolds number), although around reattachment they are very much higher, having values more akin to those in plane mixing layers. This undershoot is apparently a new finding and is argued to be a result of the influence of the outer part of the flow on the growing inner region. The usual log-law only begins to appear beyond x/x_r = 2.5. It effectively “sees” a turbulent outer region that recovers even more slowly than itself, and the response of the inner region therefore has similarities to the response of an ordinary boundary layer to free-stream turbulence.

It is concluded that even current second-order (i.e., Reynolds stress) models may not capture the exquisitely slow decay of the strong, large eddy motions in the outer part of the flow and the subtleties of their influence on the inner region.     

Predicting Buoyant Shear Flows Using Anisotropic Dissipation Rate Models

This paper examines the modeling of two-dimensional homogeneous stratified turbulent shear flows using the Reynolds-stress and Reynolds-heat-flux equations. Several closure models have been investigated; the emphasis is placed on assessing the effect of modeling the dissipation rate tensor in the Reynolds-stress equation. Three different approaches are considered; one is an isotropic approach while the other two are anisotropic approaches. The isotropic approach is based on Kolmogorov's hypothesis and a dissipation rate equation modified to account for vortex stretching. One of the anisotropic approaches is based on an algebraic representation of the dissipation rate tensor, while another relies on solving a modeled transport equation for this tensor. In addition, within the former anisotropic approach, two different algebraic representations are examined; one is a function of the Reynolds-stress anisotropy tensor, and the other is a function of the mean velocity gradients. The performance of these closure models is evaluated against experimental and direct numerical simulation data of pure shear flows, pure buoyant flows and buoyant shear flows. Calculations have been carried out over a range of Richardson numbers (Ri) and two different Prandtl numbers (Pr); thus the effect of Pr on the development of counter-gradient heat flux in a stratified shear flow can be assessed. At low Ri, the isotropic model performs well in the predictions of stratified shear flows; however, its performance deteriorates as Ri increases. At high Ri, the transport equation model for the dissipation rate tensor gives the best result. Furthermore, the results also lend credence to the algebraic dissipation rate model based on the Reynolds stress anisotropy tensor. Finally, it is found that Pr has an effect on the development of counter-gradient heat flux. The calculations show that, under the action of shear, counter-gradient heat flux does not occur even at Ri = 1 in an air flow. This revised version was published online in July 2006 with corrections to the Cover Date.     

Constraints on the “rapid” part of the pressure-strain rate correlations derived from the spectral presentation

Based on the exact spectral presentation of the “rapid” part of the pressure-strain rate correlations, semi-empirical approximations used for these correlations within the framework of the second-order closures are analyzed. Simple inequalities relating the values of the model constants, mean velocity parameters, and Reynolds tensor invariants are derived. For certain types of flows, in contrast to conditions of realizability, these inequalities allow verification of the approximations before solving differential equations. It is demonstrated that some models cannot be considered as sufficiently precise ones to describe flows with high degrees of anisotropy. In particular, the condition of non-negative determinacy of the spectral matrix is violated in a considerable region of the physically admissible range of parameters. The boundaries of this region are calculated for an irrotational three-dimensional distortion and for an arbitrary two-dimensional distortion of turbulence in channel flows. Simple constraints on model constants are obtained, which allow these violations to be avoided. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 29–39, March–April, 2008.     

On the Realizability of Nonlinear Stress–Strain Relationships for Reynolds Stress Closures

A class of recently developed explicit algebraic stress models based on tensorially quadratic stress--strain relations [7] is subjected to a systematical realizability analysis. It is found that these models, which are of particular interest for their rigorous derivation from linear second-moment closure models, tend to produce inappropriate unrealizable results like negative turbulence energy components, even in simple shear flows. The cause of the defect is identified in conjunction with a set of realizability-furnishing constraints on the model coefficients. With the exception of the silent normal stress component in accelerated flow, the nature and rationale of the explicit algebraic stress model suggested by Gatski and Speziale [7] can be extended to maintain the realizability principle. Results obtained from the corresponding quasi-realizable quadratic eddy-viscosity model are reported in comparison with other nonlinear modelling practices.     

关于具有剪应力的普通湍流理论发展

本文叙述了周培源1945年发表具有剪应力的普通湍流理论以后,各种湍流模式理论的主要发展概况.     

Spots and turbulent domains in a model of transitional plane Couette flow

A review of the globally subcritical transition to turbulence in shear flows is presented, with an emphasis on the cases of plane and circular Couette flows (pCf and cCf, respectively). A Swift–Hohenberg-like model is next proposed to interpret the behavior of plane Couette flow in the vicinity of its global stability threshold. We present results of numerical simulations supporting this proposal and helping us to raise good questions about the growth and decay of intermittent turbulent domains in this precise context, and more generally about the coexistence of laminar flow and turbulence in other spatio-temporally intermittent flows. PACS 47.27.-i, 47.54.-r, 05.45.-a     

简单剪切流动中转捩的低维模式与数值模拟

回顾了过去10年在壁湍流和自由剪切流转捩问题的数值研究中取得的重要进展, 介绍了数值方法和模式研究方面的进展, 以及由此带来的关于转捩理论认识上的进展. 对于壁面流动, 文中主要介绍了渐进稳定流动中``跨越(bypass)转捩'研究中的各种观点. 本文也简要介绍了对感受性和转捩控制方面的研究.