Free Turbulent Shear Layers on Plug Nozzles

1977 ◽  
Vol 99 (2) ◽  
pp. 301-308
Author(s):  
C. J. Scott ◽  
D. R. Rask
Keyword(s):  
Turbulent Mixing ◽  
Schmidt Number ◽  
Error Function ◽  
Mixing Layer ◽  
Shear Layers ◽  
Turbulent Shear ◽  
Gas Chromatograph ◽  
Plug Nozzle ◽  
Turbulent Schmidt Number ◽  
Plug Nozzles

Two-dimensional, free, turbulent mixing between a uniform stream and a cavity flow is investigated experimentally in a plug nozzle, a geometry that generates idealized mixing layer conditions. Upstream viscous layer effects are minimized through the use of a sharp-expansion plug nozzle. Experimental velocity profiles exhibit close agreement with both similarity analyses and with error function predictions. Refrigerant-12 was injected into the cavity and concentration profiles were obtained using a gas chromatograph. Spreading factors for momentum and mass were determined. Two methods are presented to determine the average turbulent Schmidt number. The relation Sct = Sc is suggested by the data for Sc < 2.0.

scholarly journals Mixing and chemical reactions in a turbulent liquid mixing layer

1986 ◽  
Vol 170 ◽  
pp. 83-112 ◽  
Author(s):  
M. M. Koochesfahani ◽  
P. E. Dimotakis
Keyword(s):  
Reynolds Number ◽  
Gas Phase ◽  
Turbulent Mixing ◽  
High Speed ◽  
High Reynolds Number ◽  
Schmidt Number ◽  
Mixing Layer ◽  
Entrainment Ratio ◽  
High Reynolds ◽  
Mixed Fluid

An experimental investigation of entrainment and mixing in reacting and non-reacting turbulent mixing layers at large Schmidt number is presented. In non-reacting cases, a passive scalar is used to measure the probability density function (p.d.f.) of the composition field. Chemically reacting experiments employ a diffusion-limited acid–base reaction to directly measure the extent of molecular mixing. The measurements make use of laser-induced fluorescence diagnostics and high-speed, real-time digital image-acquisition techniques.Our results show that the vortical structures in the mixing layer initially roll-up with a large excess of fluid from the high-speed stream entrapped in the cores. During the mixing transition, not only does the amount of mixed fluid increase, but its composition also changes. It is found that the range of compositions of the mixed fluid, above the mixing transition and also throughout the transition region, is essentially uniform across the entire transverse extent of the layer. Our measurements indicate that the probability of finding unmixed fluid in the centre of the layer, above the mixing transition, can be as high as 0.45. In addition, the mean concentration of mixed fluid across the layer is found to be approximately constant at a value corresponding to the entrainment ratio. Comparisons with gas-phase data show that the normalized amount of chemical product formed in the liquid layer, at high Reynolds number, is 50% less than the corresponding quantity measured in the gas-phase case. We therefore conclude that Schmidt number plays a role in turbulent mixing of high-Reynolds-number flows.

The potential flow bounded by a mixing layer and a solid surface

1984 ◽  
Vol 395 (1809) ◽  
pp. 265-290 ◽  
Keyword(s):  
Shear Layer ◽  
Solid Surface ◽  
Turbulent Mixing ◽  
Potential Flow ◽  
Near Field ◽  
Mixing Layer ◽  
Detailed Comparison ◽  
Mixing Layers ◽  
Turbulent Shear ◽  
Spatial Correlations

Phillips's ( Proc. Camb. Phil. Soc . 51, 220 (1955)) analysis of the potential 'near field' forced by a turbulent shear layer is extended to include calculation of velocity spectra, spatial correlations and the effect of a solid surface at a finite distance from the shear layer. In the region away from the influence of the wall the theory predicts that correlation scales depend principally on the effective distance from the turbulence. This result suggests that the large correlation scales measured outside turbulent mixing layers do not necessarily demonstrate the essential tow-dimensionality of the large turbulent eddies and shows why mixing layers are more influenced by potential flow effects than are other shear layers. The detailed comparison of the theory to measurements made outside a high Reynolds number single-stream turbulent mixing layer results in an unphysical negative regions are caused by an error in a basic assumption of the theory. However, all the measured correlation scales appear to increase linearly with distance from the turbulence and therefore are consistent with the main result of the analysis. As the potential flow becomes affected by the wind tunnel floor, u 2 — and w 2 — are amplified significantly more than the theory predicts, while v 2 — is not attenuated. These discrepancies are attributed partly to the streamwise inhomogeneity of the flow, which was not incorporated into the analysis.

The effect of initial conditions on the development of a free shear layer

1966 ◽  
Vol 26 (2) ◽  
pp. 225-236 ◽  
Author(s):  
P. Bradshaw
Keyword(s):  
Turbulent Mixing ◽  
Initial Conditions ◽  
Mixing Layer ◽  
Initial Boundary ◽  
Shear Layers ◽  
Free Shear Layer ◽  
Turbulent Mixing Layer ◽  
Free Shear Layers ◽  
Final Approach ◽  
Reynolds Number Effects

The distance between the separation point and the final approach to a fully developed turbulent mixing layer is found to be of the order of a thousand times the momentum-deficit thickness of the initial boundary layer, whether the latter be laminar or turbulent. There are correspondingly large shifts in the virtual origin of the mixing layer, resulting in spurious Reynolds-number effects which cause considerable difficulties in tests of model jets or blunt-based bodies, and which are probably responsible for the disagreements over the influence of Mach number on the development of free shear layers. These effects are explained.

Turbulent Hierarchic Structure and Scalar Mixing in a Supersonic Mixing Layer at High Convective Mach Numbers

2007 ◽  
Author(s):  
Hiroshi Maekawa ◽  
Daisuke Watanabe
Keyword(s):  
Mach Number ◽  
Shear Layer ◽  
Turbulent Mixing ◽  
Mixing Layer ◽  
Structure Evolution ◽  
Turbulent Shear ◽  
Scalar Mixing ◽  
Turbulent Structures ◽  
Turbulent Mixing Layer ◽  
Hierarchic Structure

Turbulent structures in a supersonic plane mixing layer at the convective Mach number of Mc=1.2 are studied using spatially developing DNS. High-resolution compact upwind-biased schemes developed by Deng & Maekawa (1996)[1] are employed for spatial derivatives. The numerical results indicate that the turbulent structures are generated after transition in the mixing layer, which are similar to the plane jet turbulent shear layer. The mixing layer Reynolds number based on the vorticity thickness reaches 6500. Unlike low Mach number mixing layers with a roller-like structure, hierarchic structures with hairpin packet-like structure and its cluster vortices are observed in the turbulent mixing layer. The effect of the turbulent hierarchic structure on scalar mixing is investigated using the DNS database. The visualized scalar field associated with vortical structure evolution of the turbulent mixing layer shows that the intermittent hairpin packet-like structure and its cluster govern a large-scale scalar mixing in the shear layer. The turbulent fine structure of pair vortices also plays an important role for scalar mixing. Furthermore, dilatational fields of the mixing layer show intense areoacoustic phenomena associated with the turbulent structure evolution.

A Useful Approximation to the Error Function: Applications to Mass, Momentum, and Energy Transport in Shear Layers

1989 ◽  
Vol 111 (2) ◽  
pp. 224-226 ◽  
Author(s):  
P. R. Greene
Keyword(s):  
Closed Form ◽  
Energy Flux ◽  
Energy Transport ◽  
Error Function ◽  
Gaussian Function ◽  
Inverse Function ◽  
Shear Layers ◽  
Turbulent Shear ◽  
Flux Transport ◽  
Transport Flux

Specific mass, momentum, and energy flux transport integrals are given by the sequence I1 = ∫erfc(x)dx, I2 = ∫erfc2(x)dx, and I3 = ∫erfc3(x)dx for the error function velocity distribution typical of some laminar and turbulent shear layers. In this report, the Gaussian function A exp(−b(x−x0)2) is used to approximate the error function within 0.21 percent, allowing a direct approximate closed-form evaluation of these transport flux integrals. Mass, momentum, and energy flux are accurate to within 0.22, 0.15, and 0.11 percent, respectively, over the entire shear layer. To achieve this same degree of accuracy with a Taylor series requires in excess of 10 terms. Each of the sequence of approximate functions can be inverted to yield the inverse function, i.e., erfc−1(x), etc., also in closed-form. The results presented here are also applicable to the error function as it appears in heat transfer and probability and statistics type problems. A coefficient table is included to allow evaluation of the error function and its various integrals.

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