Instability Of Mixing Layers Research Articles

Viscous modes in two-phase mixing layers

The temporal instability of parallel viscous two-phase mixing layers is studied by adopting a composite error function flow profile such that boundary layers in each fluid sandwich the interface. Linear spectra and neutral stability curves are calculated numerically and the effects of varying the density ratio, viscosity ratio and Weber number are presented. In addition to the interfacial mode two Tollmien–Schlichting type modes are found and attributed to the presence of the two viscous boundary layers. This is important because it is shown that any of these three modes may be the most unstable, depending on parameter values. Mode multiplicity and competition has not yet been thoroughly explored for this problem even though it is essential to the analysis of experiments and to further stability study of flows relevant to breaking up of interfaces.

Conditional Sampling Of Forest Canopy Gusts

Velocity measurements by a two-component laser-Doppler anemometer have been made in a wind-tunnel flow over a forest of aeroelastically scaled model trees. Mean velocity profiles close above three different model canopies exhibit typical ‘shear-layer’ inflections that are similar, as are the turbulence characteristics, when scaled by characteristic dimensions of the shear layer.A wavelet-based conditional sampling technique is used to generate pseudo-instantaneous flow-field vector maps that are concurrent with significant tree bending events. These diagrams show clear evidence of canopy penetration by coherent gusts.A discussion is offered, of the relationship between the development of coherent gusts and conventional descriptions of mixing layer instability.

Linear instability of dilute particle-laden compressible mixing layers

The effects of fluid–particle interaction on the temporal development of the compressible mixing layer is investigated using a linearization of the set of equations used to describe dilute two-phase flows with an Eulerian approach. The evolution of the characteristics of the most unstable perturbation as a function of the convective Mach number is studied, including the variation of the wave number, the maximum growth rate, and the obliquity of the disturbance. A parametric investigation is conducted on the influence of the particle inertia, mass loading, and specific heat. The results show the important influence of the particles on the three-dimensional perturbation amplification and the growth rate attenuation when compressibility effects increase.

Wave Computation in Compressible Flow Using Space-Time Conservation Element and Solution Element Method

The recently developed space-time conservation element solution element method has several attractive features for aeroacoustic computations. The scheme is robust, possesses almost no dispersion error, and the implementation of nonreflecting boundary conditions is simple and effective. The scheme is tested for several problems ranging from linear acoustic waves to strongly nonlinear phenomena, with special emphasis on mixing-layer instability, and good numerical results are achieved.

Instability of wake-dominated compressible mixing layers

The instability of supersonic mixing layers, with velocity profiles possessing a wake component, is investigated using linear, inviscid, spatial theory. The mean-velocity profile is represented by a hyperbolic-tangent profile plus a wake component. Such profiles are encountered in the initial region of experimental supersonic shear-layer flows, as well as in envisaged hypersonic propulsion systems in which ingested boundary layers generate substantial wake components. Shear-layer and wake instability modes previously found in incompressible mixing layers are also found in compressible mixing layers. The existence of a wake component in the velocity profile renders the mixing layer more unstable at all free-stream Mach numbers. For convective Mach numbers exceeding unity, the shear-layer mode splits into two supersonic modes, and the mixing layer becoming more unstable with increasing wake deficit. The wake mode becomes less unstable and eventually stable with increasing compressibility, i.e., increasing convective Mach numbers.

Nonparallel instabilities of a supersonic mixing layer

Abstract Contrary to the parallel flow approach most often studied, the growth rates of unstable waves of the supersonic mixing layer are analyzed with the consideration of flow nonparallelism by employing the method of multiple scales. Flow parameters including Reynolds number, Mach number, velocity ratios and temperature ratios influencing on the instability‐wave solutions are investigated. The mean flow is determined by solving the compressible boundary layer equations and applying the Sutherland law relating the viscosity to the temperature. In this work, two dimensional compressible stability equations are solved to secure the spatial growth rate of instability waves of the flow.

Parallel calculations on the CM-2: BBS test programs and spectral methods

The implementation of the Because Benchmark Set programs on the Connection Machine CM-2 is presented and discussed. The characteristics of this machine have been taken into account during the BBS implementations, leading to somewhat different formulations, for some of the BBS programs. These situations are detailed to outline the way algorithms work. In a second section, the generation of a Computational Fluid Dynamics software is described; the numerical method used (spectral method) is explained, in order to understand the algorithmic solutions that are proposed. The resulting code has then been run on an example showing mixing layer instability, and then compared with similar codes running on Convex and CRAY II vector supercomputers.

Resonant instability of ducted free supersonic mixing layers induced by periodic Mach waves

It is known that the mixing or spreading rate of free mixing layers decreases with an increase in the convective Mach number of the flow. At supersonic convective Mach number the natural rate of mixing of the shear layers is very small. It is believed that the decrease in mixing rate is directly related to the decrease in the rate of growth of the instabilities of these flows. In an earlier study (Tarn & Hu 1989) it was found that inside a rectangular channel supersonic free shear layers can support two families of instability waves and two families of acoustic wave modes. In this paper the possibility of driving these normal acoustic wave modes into resonant instability by using a periodic Mach wave system is investigated. The Mach waves can be generated by wavy walls. By properly choosing the wavelength of the periodic Mach wave system mutual secular excitation of two selected acoustic wave modes can be achieved. In undergoing resonant instability, the acoustic modes are locked into mutual simultaneous forcing. The periodic Mach waves serve as a catalyst without actually being involved in energy transfer. The resonant instability process is analysed by the method of multiple scales. Numerical results indicate that by using wavy walls with an amplitude-to-wavelength ratio of 1½% it is possible to obtain a total spatial growth of e9 folds over a distance of ten channel heights. This offers reasonable promise for mixing enhancement. The results of a parametric study of the effects of flow Mach numbers, temperature ratio, shear-layer thickness, modal numbers as well as three-dimensional effects on the spatial growth rate of the resonant instability are reported and examined so as to provide basic information needed for future feasibility analysis.

Instabilities and large structures in reattaching boundary layers

The underlying premise in this work is that large structures in turbulent shear flows are not universal and similar large structures in different flows owe their origins to basically similar instabilities. The turbulent boundary-layer flow over a backward-facing step and also the reattaching transitional boundary layer behind a large spanwise rod have been studied experimentally in parallel primarily to understand the origin of the curious large structures observed in the far downstream region (after 39 step heights) of the former flowfield. Simultaneous flow visualization and hot-wire anemometry and also plain-flow visualization have been carried out. In the backward-facing step, the three-dimensional mixing layer developing after detachment persists even after reattachment. The flow does not recover fully back to a regular turbulent boundary layer even far downstream of reattachment. The turbulence-producing instability of a turbulent boundary layer continues to compete with the wall-bounded mixing layer instability, giving rise to the curious schismatic arrays of large structures.

Direct Numerical Simulation of Mixing Layer (Effect of Spanwise Disturbance).

The objective of this paper is to clarify the effect of the spanwise wavelength of an initial disturbance on the secondary instability of mixing layers. To achieve this purpose, we have performed a direct numerical simulation of a three-dimensional mixing layer using a spectral method. The results are reported for the case of an initial hyperbolic tangent velocity profile with periodic excitation. From these results, we have obtained the following conclusions : 1) streamwise and transverse velocity fluctuations are slightly affected by the initial spanwise wavelength ; 2) spanwise velocity fluctuation and streamwise vorticity reflect the effect of the initial spanwise wavelength ; and 3) the spanwise perturbation that has the wavelength equal to one-third of the streamwise wavelength has the maximum growth rate.

The instability and acoustic wave modes of supersonic mixing layers inside a rectangular channel

At high supersonic convective Mach numbers the familiar Kelvin-Helmholtz instability of a thin unconfined two-dimensional shear layer becomes neutrally stable. In this paper, it is shown that when the same shear layer is put inside a rectangular channel the coupling between the motion of the shear layer and the acoustic modes of the channel produces new two-dimensional instability waves. The instability mechanism of these waves is examined. Extensive numerical computation of the properties of these new instability waves has been carried out. Based on these results two classes of these waves are identified. Some of the important characteristic features of these waves are reported in this paper. In addition to the unstable waves, a thorough analysis of the normal modes of a supersonic shear layer inside a rectangular channel reveals that there are basically two other families of neutral acoustic waves. Examples of some of the prominent characteristics of these neutral acoustic waves are also provided in this paper. The new instability waves are the dominant instabilities of a confined mixing layer at high supersonic convective Mach number. As such they are very relevant to the supersonic mixing and combustion processes inside a ramjet engine combustion chamber.

Influence of the velocity ratio on the spatial instability of mixing layers

The linear spatial instability of the tanh and Blasius mixing layers is studied for different values of the ratio between the difference and the sum of the velocities of the two co-flowing streams. The growth rate, phase velocity, and perturbation velocity distributions are determined numerically and the results are compared with expansions for small shear or low frequency. It is found that the maximum growth rate is approximately proportional to the velocity ratio. This is shown to be consistent with the observed variation of shear layer spreading rate with velocity ratio and with a recent model of flight effects on jet mixing noise.