The mixing layer between non-parallel streams

Compared to the classical two-dimensional plane mixing layer, the mixing layer between non-parallel streams has an additional degree of freedom: the angle between the streams and the direction perpendicular to the trailing edge. Consequently the mean vorticity vector, which depends on these angles, is no longer by necessity parallel to the trailing edge of the flow. The ensuing coherent structures are generally helices with components normal to the trailing edge. They can be controlled by different mechanisms, depending on the velocity vectors.     

Effect of temperature level on parallel mixing of two gas streams

In the present paper, attention is focused to clarify how temperature level may affect parallel mixing of two gas streams initially separated by a splitter plate. This is achieved by computing distinct cases with different inlet temperatures and comparing the corresponding results. A recently proposed kinetic model is utilized for the simulation of the flow field. The model provides a separate equation set for one component species of the system and an equation set for average quantities of the mixture. Thereby, it can automatically describe diffusion processes without the use of any coefficients for ordinary, pressure, and thermal diffusion which are generally required during Navier-Stokes computations of gas mixtures.     

Certain properties of mixing layers

We are examining the properties of solutions of the Falkner-Skan equation in the limiting case when the parameter in the equation approaches zero. Two types of boundary conditions are formulated. The first type corresponds to flow in a symmetric wake. The second corresponds to flow about a plate. The results of calculations and an asymptotic analysis make it possible to conclude that the transition from one type of boundary conditions to another involves a sharp change in the position of the mixing layer.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 45–54, May–June, 1986.     

High-speed cinematography of compressible mixing layers

Experiments are performed using high-speed film cinematography to temporally resolve compressible planar mixing layer structures using shadowgraphs and planar light sheet visualization. The technique is relatively inexpensive and allows multiple images. The time-dependent shadowgraph and Mie scattering images are documented with a rotating mirror camera operating at approximately 350 kHz. The results show the presence of large scale structures in the mixing layer which flatten as they convect downstream. Both spatial and temporal covariances have been obtained through digital image processing which yield, on average, elliptical structures with convective speeds above the isentropic prediction, and non-isotropic streamwise and transverse scalar transport fluctuations.     

Comparison of three-dimensional and two-dimensional statistical mechanics of shear layers for flow between two parallel plates

It is shown that the averaged velocity profiles predicted by statistical mechanics of point vortices and statistical mechanics of vortex lines are practically indistinguishable for a shear flow between two parallel walls.     

Steady two-dimensional merging flow from two channels into a single channel

Two-dimensional steady symmetric merging flow from two channels into a single one is investigated. The geometry of the configuration has been chosen such that it can be mapped conformally onto a rectangular geometry, thus facilitating the numerical solution procedure for the governing Navier-Stokes equations. Computed velocity profiles and streamline patterns are presented in graphical form. Furthermore, results concerning the inlet length are given.     

Passive mixing control of plane parallel jets

An experimental study on the mixing of two plane, unventilated, parallel jets reveals an instability characterized by sinuous flapping of the jets and enhanced mixing of the jets with the ambient fluid. The frequency and amplitude of the instability is shown to be a function of the jets spacing and momentum flux ratios, with the maximum mixing occurring for cases with matched momentum flux. When the momentum flux of the two jets is mismatched by as much as a factor of three, the flow becomes steady. Schlieren flow visualization and hot-wire anemometry demonstrate and quantify the large-scale mixing. The instability has a strong frequency and amplitude dependence on the momentum ratio of the jets. The Strouhal number is also found to decrease with the spacing between the jets. The instability described provides a means to passively control the jet mixing with the ambient.     

Collision and merging of two equal droplets of propanol

Equally spaced and uniform droplets are produced by a vibrating orifice and move away in a straight line. They intersect with an exactly equal string of droplets and collide one by one. With stroboscopic lighting and multiple exposures, they are photographed. Thus successive stages of the collision process are shown on a single photo. The droplets can be made to collide with or without angular momentum by adjusting the aim of the emitting orifices. The impacting speeds can be varied from 2.8 to 11.7 m/s. Droplet sizes from 70 to 200 m are employed. Motions of the coalesced drop after the merging are bizarre and well-displayed. The results are important for spray modeling. When the streams of droplets merge at higher speeds, they may distort to the extent that the two streams of droplets merge to a single continuous sinuous stream.List of symbols b collision parameter - d diameter - p pressure difference - f frequency - u impact velocity - v droplet velocity - V liquid feed rate - x, y, z rectangular coordinates - angle between droplet stream and symmetry line - G generator - i initial, before the collision - P particle - T droplet - 1, 2 first and second droplet generator     

Mean and turbulent velocity measurements of supersonic mixing layers

The behavior of supersonic mixing layers under three conditions has been examined by schlieren photography and laser Doppler velocimetry. In the schlieren photographs, some large-scale, repetitive patterns were observed within the mixing layer; however, these structures do not appear to dominate the mixing layer character under the present flow conditions. It was found that higher levels of secondary freestream turbulence did not increase the peak turbulence intensity observed within the mixing layer, but slightly increased the growth rate. Higher levels of freestream turbulence also reduced the axial distance required for development of the mean velocity. At higher convective Mach numbers, the mixing layer growth rate was found to be smaller than that of an incompressible mixing layer at the same velocity and freestream density ratio. The increase in convective Mach number also caused a decrease in the turbulence intensity ( _u/U).List of symbols a speed of sound - b total mixing layer thickness between U ₁ – 0.1 U and U ₂ + 0.1 U - f normalized third moment of u-velocity, f u³/(U)³ - g normalized triple product of u² , g u²/(U)³ - h normalized triple product of u ², h u ²/(U)³ - l _u axial distance for similarity in the mean velocity - l _u axial distance for similarity in the turbulence intensity - M Mach number - M _c convective Mach number (for ₁ = ₂), M _c (U ₁ – U ₂)/(a ₁ + a ₂) - P static pressure - r freestream velocity ratio, r U ₂/U ₁ - Re unit Reynolds number, Re U/ - s freestream density ratio, s ₂/₁ - T _t total temperature - u instantaneous streamwise velocity - u deviation of u-velocity, uu – U - U local mean streamwise velocity - U ₁ primary freestream velocity - U ₂ secondary freestream velocity - average of freestream velocities, (U ₁ + U ₂)/2 - U freestream velocity difference, U U ₁ – U ₂ - instantaneous transverse velocity - v deviation of -velocity, – V - V local mean transverse velocity - x streamwise coordinate - y transverse coordinate - y ₀ transverse location of the mixing layer centerline - ensemble average - ratio of specific heats - boundary layer thickness (y-location at 99.5% of free-stream velocity) - similarity coordinate, (y – y ₀)/b - compressible boundary layer momentum thickness - viscosity - density - standard deviation - dimensionless velocity, (U – U ₂)/U - 1 primary stream - 2 secondary stream A version of this paper was presented at the 11th Symposium on Turbulence, October 17–19, 1988, University of Missouri-Rolla     

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     

用格子Boltzmann方法数值模拟混合层中旋涡的合并过程

用格子Boltzmann方法计算混合层中的流动问题。在流场的入口处加不同频率、振幅和相位的小扰动,观察混合层中旋涡的演进机理,模拟二维混合层中旋涡合并现象。在基本扰动波的基础上,又加入频率为基本波频率一半的亚谐波,得到了两个涡合并的计算结果,当加入的亚谐波频率为基本波频率的三分之一时,得到了三个涡合并的计算结果。这些计算结果与已有文献的结果基本一致,显示用格子Boltzmann方法模拟混合层问题是可行的。     

Instantaneous velocity and pressure measurements in turbulent mixing layers

This paper presents a comprehensive comparison of the mean velocity and turbulence measurements from a four-hole pressure probe, also known as the Cobra probe, and an X-probe in plane mixing layers. The objective is to validate the measurement accuracy of the Cobra probe in a flow where the turbulence reaches high levels, but whose properties are well known. The comparison is made for the mean velocities, Reynolds stresses, triple products, and spectra, and demonstrates that the Cobra probe has reasonable accuracy for some of these quantities, such as the mean streamwise velocity and primary shear stress, but not for others, such as the mean normal velocity. The correlation of the pressure and the streamwise velocity, measured by the Cobra probe, behaves correctly in the potential flow. However, the correlation of the pressure and the cross-stream velocity, which appears in the transport equation for the turbulent kinetic energy, and the pressure redistribution term in the corresponding equation for the streamwise normal stress, are poorly measured.     

Numerical simulations of vortices in mixing layers and plane jets

Direct numerical simulations of two-dimensional mixing layers and jets are presented first within the temporal approximation, and then with spatial calculations. The evolution of a temperature field as a passive scalar is investigated simultaneously. Besides usual statistical quantities, the results are presented through visualisations of coloured vorticity- and temperature-contours in order to describe the evolutions of the fields with time. Concentrated vortices develop and the evolution of the layer is dominated by the interactions between these eddies which can be viewed as the coherent structures observed in laboratory experiments.     

Near-field turbulence properties of single- and two-stream plane mixing layers

Detailed mean flow and turbulence measurements have been made in the near-field of two plane mixing layers in air with a maximum velocity of 21 m/s. The experimental rig enabled mixing layers of velocity ratios 0 and 0.46 to be generated simultaneously. Cases with both tripped and untripped initial boundary layers were studied. In all cases, it was found that the two-stream layer developed to the self-preserving state in a distance much shorter than the single-stream layer, which followed accepted criteria for the development distance. The asymptotic levels of the turbulence quantities in the two-stream layer and the development of the single-stream layer showed agreement with existing data. The results suggest that the two-stream mixing layer should provide a better test case for the development of turbulence models and calculation methods than the single-stream mixing layer.     

Formation and evolution of the streamwise vortices in mixing layers

The evolution of the three-dimensional time-developing mixing layer is simulated numerically using the pseudo-spectral method. The initial perturbations used in this study consisted of the two-dimensional fundamental wave and the streamwise-invariant three-dimensional disturbance. A comparison of the formations of the streamwise vortices with different amplitude functions for three-dimensional disturbances is made. In one case the results are similar to that of Rogers & Moser^[1], whereas a different way in which the quadrupole forms and sudden expansion of the rib are observed in another case. The simulation also confirms that the stretching by the forming roller rather than Rayleigh centrifugal instability is responsible for the formation of the rib. Finally, numerical flow visualization results are presented. The project supported by the Zhejiang Province Natural Science Special Fund for Youth Scientistis' Cultivation.     

Load transfer from a web to two parallel sheets

This paper deals with the elastostatic transfer of a tensile load from an infinite strip-shaped web of uniform rectangular cross section to two identical parallel sheets of infinite extent. The web is perpendicular to the sheets and is continuously bonded to the latter along finite portions of its “top” and “bottom” edges. The sheets are treated within the two-dimensional theory of generalized planes stress. On the other hand, two alternative models for the web are considered: (a) the web likewise is regarded as a two-dimensional continuum within the conventional theory of generalized plane stress and (b) the web is idealized as a one-dimensional elastic continuum. In either case, an integral equation with a Cauchy-type singular kernel is obtained for the density of the bond force between the web and the sheets. This equation, in turn, is reduced to a Fredholm integral equation of the second kind. Numerical results for the axial force in the web and the bond force are presented for several combinations of the governing material and geometrical parameters.     

The nonlinear evolution of two-dimensional and three-dimensional waves in mixing layers

The authors consider problems connected with stability [1–3] and the nonlinear development of perturbations in a plane mixing layer [4–7]. Attention is principally given to the problem of the nonlinear interaction of two-dimensional and three-dimensional perturbations [6, 7], and also to developing the corresponding method of numerical analysis based on the application to problems in the theory of hydrodynamic stability of the Bubnov—Galerkin method [8–14].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhldkosti i Gaza, No. 1, pp. 10–18, January–February, 1985.     

Calculation of base pressure and enthalpy behind a blunt trailing edge separating two supersonic streams with allowance for boundary layers and heat fluxes

A relatively simple method of calculating the parameters of the flow behind a blunt trailing edge separating two supersonic streams is developed. The method is based on the use of the boundary layer approximation and integral laws of mass and energy conservation (viscous-inviscid interaction model). It makes it possible to determine the base pressure and base enthalpy with allowance for the effect of Mach numbers, Reynolds numbers, initial boundary layer thicknesses, specific heat ratios and wall enthalpies for various ratios of the total pressures and enthalpies of the two streams.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 167–176, September–October, 1991.     

The merging of two co-rotating vortices: a numerical study

The merging of two-dimensional co-rotating vortices is analysed through direct numerical simulations at large Reynolds numbers. It is shown how the Reynolds number affects each of the three phases that characterise this phenomenon. In the first phase, we examine the merging onset and focus on its definition. During the second rapid phase, the contributions of various flow regions upon the dynamics of a vortex are quantitatively studied. These regions are respectively the companion vortex, the filaments and an intermediate zone between vortices and filaments. The third phase is interpreted in terms of an advection diffusion process. Finally the final profile and circulation of the merged vortex is determined: the two thirds of the total circulation of the two initial vortices is contained in the newly formed vortex.