Rabindra D. Mehta

Development of a two-stream mixing layer from tripped and untripped boundary layers

A two-stream mixing layer with a velocity ratio of 0.6 was generated with two different initial conditions, one with both initial boundary layers laminar and one where both boundary layers were tripped. Some recent measurements have shown that relatively large spanwise variations can occur in the mean flow and turbulence properties of plane mixing layers, especially in the untripped case. Therefore, for the first time, all the data presented here were averaged over several spanwise locations. The results indicate that both the near- and far-field growth rates for the untripped case are significantly higher than for the tripped case. The maximum Reynolds stresses and higher order products for the two cases behave very differently in the near-field, but asymptotic to approximately the same constant levels far downstream. The mean velocity and turbulence profiles in this region also collapse adequately for the two cases when plotted in similarity coordinates. The distance required to achieve self-similarity was found to be distinctly shorter for the tripped case, in contrast to previous observations. The higher growth rate for the untripped case is attributed to the presence of streamwise vortices, which result in additional entrainment by the mixing layer.

Measurements of the streamwise vortical structures in a plane mixing layer

An experimental study has been conducted to investigate the three-dimensional structure of a plane, two-stream mixing layer through direct measurements. A secondary streamwise vortex structure has been shown to ride among the primary spanwise vortices in past flow visualization investigations. The main objective of the present study was to establish quantitatively the presence and role of the streamwise vortex structure in the development of a plane turbulent mixing layer at relatively high Reynolds numbers ( Re δ ∼ 2.9 × 10 4 ). A two-stream mixing layer with a velocity ratio, U 2 / U 1 = 0.6 was generated with the initial boundary layers laminar and nominally two-dimensional. Mean flow and turbulence measurements were made on fine cross-plane grids across the mixing layer at several streamwise locations with a single rotatable cross-wire probe. The results indicate that the instability, leading to the formation of streamwise vortices, is initially amplified just downstream of the first spanwise roll-up. The streamwise vortices first appear in clusters containing vorticity of both signs. Further downstream, the vortices re-align to form counter-rotating pairs, although there is a relatively large variation in the scale and strengths of the individual vortices. The streamwise vortex spacing increases in a step-wise fashion, at least partially through the amalgamation of like-sign vortices. For the flow conditions investigated, the wavelength associated with the streamwise vortices scales with the mixing-layer vorticity thickness, while their mean strength decays as approximately 1/ X 1.5 . In the near field, the streamwise vortices grossly distort the mean velocity and turbulence distributions within the mixing layer. In particular, the streamwise vorticity is found to be strongly correlated in position, strength and scale with the secondary shear stress (

Measurement of Continuous Pressure and Shear Distributions Using Coating and Imaging Techniques

\overline{u^{\prime}w^{\prime}}

Three-dimensional structure of straight and curved plane wakes

). The secondary shear stress data suggest that the streamwise structures persist through to what would normally be considered the self-similar region, although they are very weak by this point and the mixing layer otherwise appears to be two-dimensional.

Curved two-stream turbulent mixing layers: three-dimensional structure and streamwise evolution

The pressure-sensitive paint (PSP) method and the shear-sensitive liquid crystal coating (SSLCC) method were sequentially applied to measure the areal pressure and shear stress vector distributions on a planar test surface beneath an inclined, axisymmetric, turbulent impinging jet. The combined results provide the first-ever consolidated measurements of the continuous normal and tangential force distributions beneath a fundamental flowfield. Results indicate that the PSP method can be extended to the measurement of small pressure differences (< ∼0.1 psig) encountered in low-speed atmospheric flows. Further, these results provide the first demonstration of the capability of the SSLCC method to measure continuous shear stress vector distributions on planar surfaces beneath flowfields where shear vectors of all possible orientations are present

Effects of imposed spanwise perturbations on plane mixing-layer structure

The formation and evolution of the three-dimensional structure of straight and mildly curved (

Spanwise averaging of plane mixing layer properties

b/\bar{R} ) flat plate wakes at relatively high Reynolds numbers ( Re b = 28 000) have been studied through detailed measurements of the mean and fluctuating velocities. In both cases, the role of initial conditions was examined by generating wakes from untripped (laminar) and tripped (turbulent) initial boundary layers. The curved wake was affected by the angular momentum instability such that the inside half of the wake was unstable, whereas the outside half was stable. In both the straight and curved untripped wakes, large spanwise variations, in the form of ‘pinches’ and ‘crests’, were observed in the contours of mean velocity and Reynolds stresses. Well-organized, ‘spatially stationary’ streamwise vorticity was generated in the near-field region in the form of quadrupoles, to which the spanwise variations in the velocity contours were attributed. The presence of mean streamwise vorticity had a significant effect on the wake growth and defect decay rates, mainly by providing additional entrainment. In the straight wake, the mean streamwise vorticity decayed on both sides of the wake such that it had decayed completely by the far-field region. However, in the curved case, the mean streamwise vorticity on the unstable side decayed at a rate significantly lower than that on the stable side. Despite the decay of mean streamwise vorticity, the spanwise variations persisted into the far wake in both cases. The effects of curvature were also apparent in the Reynolds stress results which showed that the levels on the unstable side were increased significantly compared to those on the stable side, with the effect much stronger in the initially laminar wake. With the initial boundary layers tripped, spatially stationary streamwise vortex structures were not observed in either the straight or curved wakes and the velocity contours appeared nominally two-dimensional. This result further confirms the strong dependency of the three-dimensional structure of plane wakes on initial conditions.

Vortical structure morphology in the initial region of a forced mixing layer: roll-up and pairing

The three-dimensional structure and streamwise evolution of two-stream mixing layers at high Reynolds numbers ( Re δ ∼ 2.7 × 10 4 ) were studied experimentally to determine the effects of mild streamwise curvature (

Three-dimensional structure of a plane mixing layer

\delta/ \overline{R}

Streamwise vortex meander in a plane mixing layer

spatially stationary streamwise vorticity was generated, which produced significant spanwise variations in the mean velocity and Reynolds stress distributions. These vortical structures appear to result from the amplification of small incoming disturbances (as in the straight mixing layer), rather than through the Taylor–Gortler instability. Although the mean streamwise vorticity decayed with downstream distance in both cases, the rate of decay for the unstable case was lower. With the initial boundary layers on the splitter plate turbulent, spatially stationary streamwise vorticity was not generated in either the stable or unstable mixing layer. Linear growth was achieved for both initial conditions, but the rate of growth for the unstable case was higher than that of the stable case. Correspondingly, the far-field spanwise-averaged peak Reynolds stresses were significantly higher for the destabilized cases than for the stabilized cases, which exhibited levels comparable to, or slightly lower than, those for the straight case. A part of the Reynolds stress increase in the unstable layer is attributed to ‘extra’ production through terms in the transport equations which are activated by the angular momentum instability. Velocity spectra also indicated significant differences in the turbulence structure of the two cases, both in the near- and far-field regions.