On the influence of the exit conditions on the entrainment rate in the development region of a free, round, turbulent jet

The development region of a free round turbulent jet was experimentally investigated in order to determine the dependence of the jet development on the exit conditions. In particular the influence of the exit conditions on the entrainment rate in both the axisymmetrix mixing layer region and at a distance of 20D from the nozzle was investigated.The entrainment rate at 20D depends noticeably on the exit boundary layer state, i.e. laminar or turbulent, and on the turbulence intensity of the core. A laminar exit boundary layer showed the highest value of entrainment rate. A turbulent one reduced the entrainment rate at 20D by 15%. A grid placed at the nozzle exit, in order to increase the turbulence intensity of the core, reduced the entrainment rate at 20D by 40%. It must be mentioned that this grid also disturbed the exit boundary layer.An empirical relation for the entrainment rate at the end of the mixing layer region as a function of the mixing layer parameters, is successful in predicting the entrainment rate at 20D within an accuracy of 5%. This result suggests a strong dependence of the jet development region on mixing layer processes, i.e. the development of organized structures and their coalescence. Possibly there is no asymptotic region which is fully independent of the mixing layer processes, and which is not more or less influenced by the exit conditions via the influence on these processes.     

Transverse diffusion and heat conduction in a granular layer

The process of non-steady-state transverse diffusion of a passive additive in a granular layer described by a cellular model is investigated. The general results obtained in [1] are applied to an analysis of concrete transport processes of matter and heat in a granular layer. The following four cell models are treated: (1) ideal mixing cells without stagnation zones; (2) ideal mixing cells with stagnation zones; (3) ideal mixing cells with diffusive stagnation zones; (4) ideal mixing cells with diffusive stagnation zones having a finite exchange rate between the free volume and the stagnation zone. The conditions of applicability for each of the above models are found. The time to establish a normal distribution in the transverse diffusion process is determined for all the models. This quantity is then connected with the physical characteristics of transport processes of matter in a layer of nonporous and porous particles, the transport of heat in a granular layer, and the transport of matter in a layer of particles which adsorb an additive.     

Wavelet analysis of coherent structures in a three-dimensional mixing layer

Wavelet analysis is applied to the results obtained by the direct numerical simulation of a three-dimensional (3D) mixing layer in order to investigate coherent structures in dimension of scale. First, 3D orthonormal wavelet bases are constructed, and the corresponding decomposition algorithm is developed. Then the Navier-Stokes equations are transformed into the wavelet space and the architecture for multi-scale analysis is established. From this architecture, the coarse field images in different scales are obtained and some local statistical quantities are calculated. The results show that, with the development of a mixing layer, the energy spectrum densities for different wavenumbers increase and the energy is transferred from the average flow to vortex structures in different scales. Due to the non-linear interactions between different scales, cascade processes of energy are very complex. Because vortices always roll and pair at special areas, for a definite scale, the energy is obtained from other scales at some areas while it is transferred to other scales at other areas. In addition, energy dissipation and transfer always occur where an intense interaction between vortices exists. The project supported by the Research Fund for the Doctoral Program of Higher Education and the National Natural Science Foundation for Outstanding Youth of China (19925210)     

Modelling of particle layer detachment-Role of transient kinetic effects

Particle layers tend to build up on wails in many filtration and separation processes, calling for periodic removal in order to keep the apparatus running. Important factors are the adhesion of the layer on the substrate and the cohesion of the particles in the layer. Models describing such layer detachment generally assume constant and homogeneous conditions for the forces acting on the layer. But in reality detachment is extremely non-stationary concerning place and time, primarily due to changing conditions of the detaching forces on the one hand and changes in the particle layer morphology on the other. This paper describes a model and a simulation based on this model considering such transient kinetic effects, for which some computing results are presented and discussed.     

Modeling of particle layer detachment-Role of transient kinetic effects

Particle layers tend to build up on walls in many filtration and separation processes, calling for periodic removal in order to keep the apparatus running. Important factors are the adhesion of the layer on the substrate and the cohesion of the particles in the layer. Models describing such layer detachment generally assume constant and homogeneous conditions for the forces acting on the layer. But in reality detachment is extremely non-stationary concerning place and time, primarily due to changing conditions of the detaching forces on the one hand and changes in the particle layer morphology on the other. This paper describes a model and a simulation based on this model considering such transient kinetic effects, for which some computing results are presented and discussed.     

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.     

Transient behavior of an axisymmetric turbulent jet

The prediction of the response of unsteady flows submitted to external excitation is a real challenge for the optimization of industrial processes. As the jet flow is a very basic turbulent flow related to mixing and entrainment phenomena via turbulent structure dynamic, we investigate the transient behavior of an axisymmetric jet submitted to a large and sudden decrease of its ejection velocity. The non stationary flow evolution is studied experimentally. Measurements along the jet axis based on pure ensemble averaging show clearly the convective motion of the perturbation and the adaptation of the local interaction to the local jet time scale. A transverse investigation in the non stationary region show that the mean flow and its turbulence is deeply affected during the local velocity decrease.     

可压缩燃烧反应转捩混合层直接数值模拟

针对三维时间发展可压缩氢/氧非预混燃烧反应平面自由剪切混合层,采用5阶迎风/6阶对称紧致混合差分格式以及3阶显式Runge-Kutta时间推进方法,直接数值模拟了伴随燃烧产物生成和反应能量释放, 流动受扰动激发失稳并转捩的演化过程. 在转捩初期, 获得了${\it\Lambda}$涡、马蹄涡等典型的大尺度拟序结构,观察到了流动失稳后发生双马蹄涡三维对并的现象, 大尺度结构呈较好的对称性.在流动演化后期, 大尺度结构逐次破碎形成小尺度结构, 混合层进入转捩末期,呈明显的不对称性.      

高亚临界雷诺数圆柱绕流的尺度自适应模拟

借助γ-Re_θ转捩模型,实现了高亚临界雷诺数（Re=1.4×105）下圆柱层流分离流动的尺度自适应模拟.统计平均结果表明数值计算和实验测量较为接近,尤其在圆柱后半段的分离区中,压力系数和实验符合得很好,误差主要源于分离点预测的不准确. 瞬态流动则显示,层流分离的剪切层中出现了展向不稳定,且在向下游的输运过程中不断增强,最后转捩为完全湍流. 在湍流分离模拟中,由于缺乏剪切层失稳的非定常性,SST-SAS 模型的尺度分辨能力变弱,因此在分离区以及下游尾迹中求解出的湍流尺度要明显较层流分离时大.      

SCALE ADAPTIVE SIMULATION OF FLOWS AROUND A CIRCULAR CYLINDER AT HIGH SUB-CRITICAL REYNOLDS NUMBER

借助γ-Re_θ转捩模型,实现了高亚临界雷诺数（Re=1.4×10⁵）下圆柱层流分离流动的尺度自适应模拟.统计平均结果表明数值计算和实验测量较为接近,尤其在圆柱后半段的分离区中,压力系数和实验符合得很好,误差主要源于分离点预测的不准确. 瞬态流动则显示,层流分离的剪切层中出现了展向不稳定,且在向下游的输运过程中不断增强,最后转捩为完全湍流. 在湍流分离模拟中,由于缺乏剪切层失稳的非定常性,SST-SAS 模型的尺度分辨能力变弱,因此在分离区以及下游尾迹中求解出的湍流尺度要明显较层流分离时大.     

The structure and dynamics of reacting plane mixing layers

The reacting two-dimensional plane mixing layer has been studied in two configurations: a rearward facing step and a two-stream mixing layer. Observations have been made of the steady state behavior, and the unsteady behavior when the flow was forced by a specific acoustic frequency. The steady behavior of the mean properties of the reacting flows is similar to that of non-reacting free shear flows except for the global effects of thermodynamic property changes. The structure of these flows is qualitatively similar to that of non-reacting flows. Vortices form by the two-dimensional Kelvin-Helmholtz instability and grow by subharmonic combination until the mixing layer interacts with the walls. Entrainment is dominated by the two-dimensional vortex motion. Three-dimensional instabilities give rise to secondary vortices which are coherent over several Kelvin-Helmholtz structures and dominate the fine scale mixing process. The mixing transition corresponds to a loss of coherence in the layer. Unsteady behavior occurs when there are resonant interactions with the Kelvin-Helmholtz instability or the instability associated with the recirculation vortex in the rearward facing step flow. Modeling efforts are reported which show promise of simulating the essential features of plane mixing layers.A version of this paper was presented at the ASME Winter Annual Meeting of 1984 and printed in AMD-Vol. 66     

PIV measurements in a weakly separating and reattaching turbulent boundary layer

A high Reynolds number flat plate turbulent boundary layer was studied in a wind-tunnel experiment using particle image velocimetry (PIV). The flow is subjected to an adverse pressure gradient (APG) which is designed such that the boundary layer separates and reattaches, forming a weak separation bubble. With PIV we are able to get a more complete picture of this complex flow phenomenon. The view of a separation bubble being composed of large scale coherent regions of instantaneous backflow occurring randomly in a three-dimensional manner in space and time is verified by the present PIV measurements. The PIV database was used to test the applicability of various velocity scalings around the separation bubble. We found that the mean velocity profiles in the outer part of the boundary layer, and to some extent also the Reynolds shear-stress, are self-similar when using a velocity scale based on the local pressure gradient. The same can be said for the so called Perry–Schofield scaling, which suggests that the two velocity scales are connected. This can also be interpreted as an experimental evidence of the claimed relation between the latter velocity scale and the maximum Reynolds shear-stress.     

On the evolution of large scale structures in three-dimensional mixing layers

In this paper, several mathematical models for the large scale structures in some special kinds of mixing layers, which might be practically useful for enhancing the mixing, are proposed. First, the linear growth rate of the large scale structures in the mixing layers was calculated. Then, using the much improved weakly non-linear theory, combined with the energy method, the non-linear evolution of large scale structures in two special mixing layer configurations is calculated. One of the mixing layers has equal magnitudes of the upstream velocity vectors, while the angles between the velocity vectors and the trailing edge were π/2-φ and π/2+φ, respectively. The other mixing layer was generated by a splitter-plate with a 45-degree-sweep trailing edge. The project supported by the National Natural Science Foundation of China (19642001) and Deutsche Forschungsgemeinschaft (DFG)     

Detached Eddy Simulation of Flow around A-Airfoil

In this study the flow around the Aérospatiale A-airfoil at maximum lift (α = 13.3°) and Re = 2 × 10⁶ is investigated by RANS and DES to quantify the influence of transient flow patterns on the quality of the flow prediction. This flow features a highly unsteady pressure-induced trailing-edge separation. The fairly high Reynolds number makes LES rather unattractive from a practical point of view as the numerical costs scale with ≈ Re^1.95 [9] and lead to an unreasonable effort to carry out these simulations. Like LES, DES is designed to capture the unsteady flow features and consequently is supposed to give results superior to RANS. The RANS solution captures the separation, but is notable to predict transient vortex shedding. The application of DES to a 2D domain leads to results comparable to those obtained by 2D-RANS. Only the 3D-DES is capable of predicting both the unsteady flow features and the development of the boundary layer on the airfoil. As expected, the spanwise resolution has a strong impact on the vortex shedding and on the size of the separation bubble. Attention must be paid to both accommodating the full extent of the flow structures and providing the adequate spatial resolution in order to accomplish satisfactory results – that compare favourably with LES – at only a fraction of computational cost.     

Study of the shock motion in a hypersonic shock system/turbulent boundary layer interaction

Wall pressure fluctuations and surface heat transfer signals have been measured in the hypersonic turbulent boundary layer over a number of compression-corner models. The distributions of the separation shock oscillation frequencies and periods have been calculated using a conditional sampling algorithm. In all cases the oscillation frequency distributions are of broad band, but the most probable frequencies are low. The VITA method is used for deducing large scale disturbances at the wall in the incoming boundary layer and the separated flow region. The results at present showed the existence of coherent structures in the two regions. The zero-cross frequencies of the large scale structures in the two regions are of the same order as that of the separation shock oscillation. The average amplitude of the large scale structures in the separated region is much higher than that in the incoming boundary layer. The length scale of the separation shock motion region is found to increase with the disturbance strength. The results show that the shock oscillation is of inherent nature in the shock wave/turbulent boundary layer interaction with separation. The shock oscillation is considered to be the consequence of the coherent structures in the separated region.This work was supported by the Chinese National Science Foundation. Thanks for Prof. Z. B. Lin and Miss X. Y. Feng for their helps. The authors wish to express thanks to Professor W. Merzkirch who has helped us to check the paper again and again.     

基于电容法的温度对舰船汽轮机油分水性影响研究

依据汽轮机油与水的介电常数差值大,其混合相作为电介质,会发生电容值变化显著的原理,采用同轴圆柱形电容作为测试传感器,选取符合世界主流海军舰船汽轮机油产品规范的8个油样,利用电容法对比研究室温(18~24 ℃)和54 ℃对油样的分水性影响规律,选取了分水性变化明显的油样进行分水后油层微观形貌分析. 试验结果表明:在54 ℃条件下,从油水混合到分离结束,电容值-时间曲线重合度更高,油水均匀混合重复性好,表现出了优于室温的重复性和稳定性;分水速率曲线具有良好的重复性,验证了电容法评定汽轮机油分水性的可靠性,在相同温度下分水速率和破乳化时间受水相分布与运动态势影响小;确定用电容法评定汽轮机油分水性时,环境温度选择54 ℃为最佳;作用机理分析说明,温度是影响舰船汽轮机油分水性的关键指标.      

Investigation of scalar measurement error in diffusion and mixing processes

In variable density, multi-fluid and reacting flows, the degree of molecular mixing is a critical component of turbulent transfer and mixing models. Also, in many microflows and low Reynolds number flows, scalar diffusion length- and time-scales play a significant role in the mixing dynamics. Characterization of such molecular mixing processes requires scalar measurement devices with a small probe volume size. Spatial averaging, which occurs due to finite probe volume size, can lead to errors in resolving the density or scalar gradients between pockets of unmixed fluids. Given a probe volume size and a priori knowledge of the functional profile of the diffusion layer being measured, we obtain an estimate for the measurement error due to spatial averaging and make the corrections accordingly. An analytical model for the measure of scalar mixing is developed as a predictor for the growth of scalar gradients in a variable scalar flow. The model is applied to a buoyancy-driven mixing layer with a Prandtl number of 7. Measurements within the mixing layer have shown that initial entrainment of unmixed fluid causes a decrease in the measured amount of molecular mixing at the centerplane. Following this period of initial entrainment, the fluids within the mixing layer exhibit an increase in the degree of molecular mixing.     

Application of unsteady mixing equations to some aerodynamic problems

Tangential discontinuities [1] are introduced in solving several transient and steady-state problems of gas dynamics. These discontinuities are unstable [2] as a result of the effects of viscosity and thermal conductivity. Therefore it is advisable to replace the tangential discontinuity by a mixing region and account for its interaction with the inviscid flows, establishing on the boundaries of this region the conditions of vanishing friction stress and equality of the velocity and temperature components to the corresponding velocity and temperature components of the inviscid flows. This formulation improves the accuracy of the solution of such problems by posing them as problems with irregular reflection and intersection of shock waves [1].The consideration of the interaction of unsteady turbulent mixing regions with the inviscid flow also permits the formulation of several problems in which the effects of viscosity lead to complete rearrangement of the flow pattern (the lambda-configuration) with the interaction of the reflected shock wave with the boundary layer in the shock tube [3,4], the formation of zones of developed separation ahead of obstacles, etc.).In this connection, §1 presents an analysis of the self-similar solutions of the unsteady turbulent mixing equations (a corresponding analysis of the laminar mixing equations which coincide with the boundary layer equations is presented in [1]). It is shown that these self-similar solutions describe, along with the several problems noted above, the problems of the formation of steady jets and mixing zones in the base wake.As an example, §2 presents, within the framework of the proposed schematization, an approximate solution of the problem of the interaction of a shock wave reflected from a semi-infinite wall with the boundary layer on a horizontal plate behind the incident shock wave. The results obtained are applied to the analysis of reflection in a shock tube. Computational results are presented which are in qualitative agreement with experiment [3, 4].