Confined Shear Layer Research Articles

Transition to chaos in a reduced-order model of a shear layer

The present work studies the nonlinear dynamics of a shear layer, driven by a body force and confined between parallel walls, a simplified setting to study transitional and turbulent shear layers. It was introduced by Nogueira & Cavalieri (J. Fluid Mech., vol. 907, 2021, A32), and is here studied using a reduced-order model based on a Galerkin projection of the Navier–Stokes system. By considering a confined shear layer with free-slip boundary conditions on the walls, periodic boundary conditions in streamwise and spanwise directions may be used, simplifying the system and enabling the use of methods of dynamical systems theory. A basis of eight modes is used in the Galerkin projection, representing the mean flow, Kelvin–Helmholtz vortices, rolls, streaks and oblique waves, structures observed in the cited work, and also present in shear layers and jets. A dynamical system is obtained, and its transition to chaos is studied. Increasing Reynolds number $Re$ leads to pitchfork and Hopf bifurcations, and the latter leads to a limit cycle with amplitude modulation of vortices, as in the direct numerical simulations by Nogueira & Cavalieri. Further increase of $Re$ leads to the appearance of a chaotic saddle, followed by the emergence of quasi-periodic and chaotic attractors. The chaotic attractors suffer a merging crisis for higher $Re$ , leading to a chaotic dynamics with amplitude modulation and phase jumps of vortices. This is reminiscent of observations of coherent structures in turbulent jets, suggesting that the model represents a dynamics consistent with features of shear layers and jets.

Effect of confinement in high-speed reacting mixing layer

High Mach number mixing layers play an important role in the development of supersonic combustor ramjet (scramjet) engines. The mixing of air and fuel is hindered by both shorter combustor residence time and by stability of supersonic shear layer relative to subsonic counterpart. Although many experimental and computational investigations were carried out for supersonic free shear layer [1, 2, 3, 4 and 5] and confined shear layer [6, 7, 8 and 9], the effect of lateral confinement on supersonic mixing layer is not clearly brought out. The fundamental difference in the development of turbulence in the mixing layer and wall boundary layer can affect the structure of the flow and the growth rate of mixing layer significantly. Chakraborty et al. [9] have performed two-dimensional direct numerical simulation (DNS) for high-speed confined reacting shear layer with finite rate chemical kinetics with seven species and seven reactions. Arguments have been provided for treating two-dimensional calculation using the work of Lu and Wu [8], Zhuang et al. [10], Farouk et al. [7], and others who have conducted computational study of the compressibility of high-speed mixing layer and shown that two-dimensional simulation is satisfactory for confined mixing layer. Good comparison of experimental wall pressure distribution with DNS results obtained was considered the basis of further investigations.

Measurements of Turbulence Statistics and Energy Budgets in a Model Combustor

Simultaneous two-component laser-Doppler-velocimeter measurements were made in an axisymmetric sudden expansion to measure the flow properties of a confined, isothermal flow-field of a research dump combustor. Measurements of mean velocities, Reynolds stresses, and triple products were carried out at axial distances ranging from 0.38 H ( H=step height) to 18 H downstream of the dump plane. Detailed experimental data are provided to help in understanding the behavior of turbulent transport characteristics of the confined shear layer. Data from this study could be used to upgrade or evaluate advanced numerical codes used to predict complex turbulent flows. The turbulent kinetic energy terms (i.e. convection, diffusion, and production terms) were computed directly from the experimental data using central differences, while the viscous dissipation term was obtained from the energy balance equation. Detailed comparison of the present data with similar work shows that the general behavior of the flow-field and energy budget results are in excellent agreement. The shear-layer flow created by sudden expansion enhances combustor performance by serving as a turbulence generator mechanism.

Effect of density gradients in confined supersonic shear layers. II. Three-dimensional modes

The effect of density gradients on three-dimensional (3-D) supersonic acoustic modes and 3-D subsonic modes in a compressible confined shear layer were investigated using linear analysis. The compressible Rayleigh equation with the solution of the steady compressible boundary layer equations as its basic profiles was solved for two different density ratios, 1.398 and 3.0, and several spanwise wave numbers. For a density ratio of 1.398, the 2-D C01 mode had the highest growth rate for a fixed aspect ratio B/H=2. At the higher-density ratio, the 3-D mode had a slightly higher maximum growth rate than the two-dimensional (2-D) mode, and the maximum growth rate was at a location where the phase speed was supersonic with respect to the fast stream.

Numerical simulations of three-dimensional natural transition in the compressible confined shear layer

The spatial supersonic shear layer in a rectangular channel is investigated by numerical simulation with the piecewise parabolic method, a high-order Godunov-type scheme. Both streams are supersonic with Mach number 4.5 and 1.6, respectively. A weak broadbanded noise is introduced at the inflow boundary and the growth of multiple unstable modes is observed. In order to extract detailed information from the computed data, the time-dependent flow field is Fourier transformed in time and in the spanwise direction. For a given frequency and a given spanwise wave number the complex eigenfunction and streamwise wave number can be compared to results from linear stability theory. This work aims at investigating in detail the limit of the linear development of the flow and to describe the transition to turbulence. In particular, this technique enables one to distinguish between oblique subsonic instabilities of the Kelvin–Helmholtz (KH) type and supersonic wall modes. A good agreement with linear stability theory is obtained in two and three dimensions until a characteristic streamwise distance is reached, where the flow becomes nonlinear. It is shown that it is mainly the oblique KH modes which are responsible for an increase in the spreading rate during transition and that the nonlinear regime in three dimensions is therefore essentially different from that in two dimensions. The most unstable mode in our configuration is a wall mode and the frequency spectra are largely dominated by the wall modes. However, it turns out that the transition is not governed by the wall modes, but by the oblique KH modes, which evolve into longitudinal streaks.

Model for entropy production and pressure variation in confined turbulent mixing

A quasi-one-dimensional model for the planar, confined shear layer is constructed with the purpose of obtaining estimates of entropy production and pressure variation due to turbulent mixing. The turbulent Prandtl and Lewis numbers are assumed to be unity. It is found that entropy production is strongly coupled to the intrinsic compressibility, with total pressure losses becoming significant as the convective Mach number increases

The nonlinear development of supersonic instability waves in a mixing layer

The nonlinear development of two-dimensional supersonic instability waves in a mixing layer is investigated by solving the full unsteady Navier–Stokes equations. A finite-difference predictor–corrector explicit method is used. The method is second-order accurate in time and fourth-order accurate in space. The results have also been checked using a fourth-order central-difference scheme with a Runge–Kutta time marching. Both confined and unconfined shear layers are simulated. For a fast or a slow mode of instability, in which the flow relative to the wave is subsonic on one side of the shear layer and supersonic on the other side, rolled up vortical structures are observed on the subsonic side only. The development of these structures is enhanced by confining the layer between parallel walls. Contours of a passive scalar show that the core of the rolled up vortex contains fluid predominantly from the subsonic side. Oblique shock waves develop in the side where the relative flow is supersonic. In the unconfined case, shock waves form in the far field as a result of the coalescence of compression waves initiated at the deforming shear layer. In the confined shear layer case, they appear as reflections of compression waves off the side wall. In the case of supersonic relative Mach numbers on both sides of the layer, no vortical roll-up is observed; only a staggered pattern of oblique shock waves is found.

Turbulent mixing and atomization in a confined shear layer

The influence of mean air velocity and shear-layer strength on turbulent mixing times and airblast atomization is investigated. Experiments carried out in a two-dimensional, two-stream wind tunnel have been developed to simulate the mixing region (i.e., shear layer with liquid injection) found in the primary zone of a gas turbine combustor. A turbulent mixing time defined as the ratio of length scale and fluctuating component of velocity (l/u^) is found to be an appropriate parameter to describe the mixing process. For a given value of shearlayer strength, these mixing times are found to be inversely proportional to the inlet mass average velocity. These mixing times are also shown to decrease with increasing shear-layer strength. Thus both shear-layer strength and inlet velocity have a strong influence on mixing time and, in relation to an actual combustor, on flame stabilization and combustion efficiency. Both of these parameters are also found to influence atomization quality, with Sauter mean diameter increasing with increasing shear-layer strength and decreasing with increasing velocity.

Influence of the system response on the coherent structures in a confined shear layer

The existence of coherent structures in mixing layers is now well-known but some aspects of their dynamics are not clarified. In particular, the influence of the eigenfrequency of the experimental apparatus on the layer development is generally not studied. The present experimental evidence indicates that the frequency response of an apparently unexcited plane mixing layer is, in fact, a characteristic of the setup.