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.

RE-EVALUATING MIXING LENGTH IN TURBULENT MIXING LAYER BY MEANS OF HIGH-ORDER STATISTICS OF VELOCITY FIELD

2012 ◽  
Vol 19 ◽  
pp. 154-165 ◽  
Author(s):  
KEH-CHIN CHANG ◽  
KUAN-HUANG LI ◽  
TING-CHENG CHANG
Keyword(s):  
Shear Layer ◽  
Turbulent Mixing ◽  
Near Field ◽  
Mixing Layer ◽  
Sufficient Conditions ◽  
The Self ◽  
Linear Growth Rate ◽  
Mixing Length ◽  
Turbulent Mixing Layer ◽  
Low Speed

A turbulent planar mixing layer is composed of two different flow types in its flow field, namely a shear layer in the central region and two free streams in each outer high- and low-speed side. Shear layer is formed after the trailing edge of the splitting plate and develops stream-wisely through successively distinct regions, namely the near field region and the self-preserving region. Two alternative definitions of the mixing lengths (lS and lF) are proposed in terms of the skewness and flatness factors, respectively, which are of third- and fourth-order of turbulence statistics. It is shown that the linear growth rate of the mixing length (either lS or lF) can be, then, used as one of the necessary and sufficient conditions to identify the achievement of the self-preserving state in turbulent mixing layer. Moreover, lF can be taken as the real length scale of the shear layer, which is of shear turbulence, bounded by the two outer high- and low-speed free streams in a given stream-wise station.

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.

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.

The stability of countercurrent mixing layers in circular jets

1991 ◽  
Vol 227 ◽  
pp. 309-343 ◽  
Author(s):  
P. J. Strykowski ◽  
D. L. Niccum
Keyword(s):  
Shear Layer ◽  
Critical Velocity ◽  
Velocity Ratio ◽  
Mixing Layer ◽  
Mixing Layers ◽  
Mean Velocity ◽  
Axisymmetric Vortex ◽  
Circular Jets ◽  
Axisymmetric Shear ◽  
The Stability

A spatially developing countercurrent mixing layer was established experimentally by applying suction to the periphery of an axisymmetric jet. A laminar mixing region was studied in detail for a velocity ratio R = ΔU/2U between 1 and 1.5, where ΔU describes the intensity of the shear across the layer and U is the average speed of the two streams. Above a critical velocity ratio Rr = 1.32 the shear layer displays energetic oscillations at a discrete frequency which are the result of very organized axisymmetric vortex structures in the mixing layer. The spatial order of the primary vortices inhibits the pairing process and dramatically alters the spatial development of the shear layer downstream. Consequently, the turbulence level in the jet core is significantly reduced, as is the decay rate of the mean velocity on the jet centreline. The response of the shear layer to controlled external forcing indicates that the shear layer oscillations at supercritical velocity ratios are self-excited. The experimentally determined critical velocity ratio of 1.32, established for very thin axisymmetric shear layers, compares favourably with the theoretically predicted value of 1.315 for the transition from convective to absolute instability in plane mixing layers (Huerre & Monkewitz 1985).

On the visual growth of a turbulent mixing layer

1980 ◽  
Vol 96 (3) ◽  
pp. 447-460 ◽  
Author(s):  
J. Jimenez
Keyword(s):  
Turbulent Mixing ◽  
Mixing Layer ◽  
Vortex Sheet ◽  
Spreading Rate ◽  
Layer Growth ◽  
Mixing Layers ◽  
Turbulent Mixing Layer

Two models are discussed to account for the motion of the concentration interface in turbulent mixing layers. In the first one the interface is treated as a vortex sheet and its roll-up is studied. It is argued that this situation represents only the first stages of layer growth and another model is studied in detail in which a row of vortex cores entrains an essentially passive concentration interface with no vorticity. Both models give values of the spreading rate in approximate agreement with observations, and their relation is discussed.

On the turbulent mixing of compressible free shear layers

1990 ◽  
Vol 431 (1882) ◽  
pp. 219-243 ◽  
Keyword(s):  
Stability Analysis ◽  
Shear Layer ◽  
Turbulent Mixing ◽  
Large Scale ◽  
Shear Flows ◽  
Time Dependent ◽  
Turbulent Shear ◽  
Large Scale Structures ◽  
Turbulent Shear Flows ◽  
Scale Structures

For over a quarter of a century it has been recognized that turbulent shear flows are dominated by large-scale structures. Yet the majority of models for turbulent mixing fail to include the properties of the structures either explicitly or implicitly. The results obtained using these models may appear to be satisfactory, when compared with experimental observations, but in general these models require the inclusion of empirical constants, which render the predictions only as good as the empirical database used in the determination of such constants. Existing models of turbulence also fail to provide, apart from its stochastic properties, a description of the time-dependent properties of a turbulent shear flow and its development. In this paper we introduce a model for the large-scale structures in a turbulent shear layer. Although, with certain reservations, the model is applicable to most turbulent shear flows, we restrict ourselves here to the consideration of turbulent mixing in a two-stream compressible shear layer. Two models are developed for this case that describe the influence of the large-scale motions on the turbulent mixing process. The first model simulates the average behaviour by calculating the development of the part of the turbulence spectrum related to the large-scale structures in the flow. The second model simulates the passage of a single train of large-scale structures, thereby modelling a significant part of the time-dependent features of the turbulent flow. In both these treatments the large-scale structures are described by a superposition of instability waves. The local properties of these waves are determined from linear, inviscid, stability analysis. The streamwise development of the mean flow, which includes the amplitude distribution of these instability waves, is determined from an energy integral analysis. The models contain no empirical constants. Predictions are made for the effects of freestream velocity and density ratio as well as freestream Mach number on the growth of the mixing layer. The predictions agree very well with experimental observations. Calculations are also made for the time-dependent motion of the turbulent shear layer in the form of streaklines that agree qualitatively with observation. For some other turbulent shear flows the dominant structure of the large eddies can be obtained similarly using linear stability analysis and a partial justification for this procedure is given in the Appendix. In wall-bounded flows a preliminary analysis indicates that a linear, viscous, stability analysis must be extended to second order to derive the most unstable waves and their subsequent development. The extension of the present model to such cases and the inclusion of the effects of chemical reactions in the models are also discussed.

scholarly journals Near-field Development of a Turbulent Mixing Layer Periodically Forced by a Bimorph PVDF Film Actuator

2010 ◽  
Vol 5 (2) ◽  
pp. 156-168 ◽  
Author(s):  
Yoshitsugu NAKA ◽  
Ken-ichiro TSUBOI ◽  
Yukinori KAMETANI ◽  
Koji FUKAGATA ◽  
Shinnosuke OBI
Keyword(s):  
Turbulent Mixing ◽  
Near Field ◽  
Mixing Layer ◽  
Pvdf Film ◽  
Turbulent Mixing Layer ◽  
Field Development

scholarly journals Large Eddy Simulation and Dynamic Mode Decomposition of Turbulent Mixing Layers

2021 ◽  
Vol 11 (24) ◽  
pp. 12127
Author(s):  
Yuwei Cheng ◽  
Qian Chen
Keyword(s):  
Large Eddy Simulation ◽  
Turbulent Mixing ◽  
Mixing Layer ◽  
Mixing Layers ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Random Disturbance ◽  
Eddy Simulation ◽  
Mode Decomposition ◽  
Large Eddy

Turbulent mixing layers are canonical flow in nature and engineering, and deserve comprehensive studies under various conditions using different methods. In this paper, turbulent mixing layers are investigated using large eddy simulation and dynamic mode decomposition. The accuracy of the computations is verified and validated. Standard dynamic mode decomposition is utilized to flow decomposition, reconstruction and prediction. It was found that the dominant-mode selection criterion based on mode amplitude is more suitable for turbulent mixing layer flow compared with the other three criteria based on singular value, modal energy and integral modal amplitude, respectively. For the mixing layer with random disturbance, the standard dynamic mode decomposition method could accurately reconstruct and predict the region before instability happens, but is not qualified in the regions after that, which implies that improved dynamic mode decomposition methods need to be utilized or developed for the future dynamic mode decomposition of turbulent mixing layers.

Dissipative small-scale actuation of a turbulent shear layer

2010 ◽  
Vol 656 ◽  
pp. 51-81 ◽  
Author(s):  
B. VUKASINOVIC ◽  
Z. RUSAK ◽  
A. GLEZER
Keyword(s):  
Shear Layer ◽  
Large Scale ◽  
Near Field ◽  
Base Flow ◽  
Turbulent Shear ◽  
Small Scale ◽  
Vortical Structures ◽  
Turbulent Shear Layer ◽  
Vorticity Flux ◽  
Inviscid Instability

The effects of small-scale dissipative fluidic actuation on the evolution of large- and small-scale motions in a turbulent shear layer downstream of a backward-facing step are investigated experimentally. Actuation is applied by modulation of the vorticity flux into the shear layer at frequencies that are substantially higher than the frequencies that are typically amplified in the near field, and has a profound effect on the evolution of the vortical structures within the layer. Specifically, there is a strong broadband increase in the energy of the small-scale motions and a nearly uniform decrease in the energy of the large-scale motions which correspond to the most amplified unstable modes of the base flow. The near field of the forced shear layer has three distinct domains. The first domain (x/θ0 < 50) is dominated by significant concomitant increases in the production and dissipation of turbulent kinetic energy and in the shear layer cross-stream width. In the second domain (50 < x/θ0 < 300), the streamwise rates of change of these quantities become similar to the corresponding rates in the unforced flow although their magnitudes are substantially different. Finally, in the third domain (x/θ0 > 350) the inviscid instability of the shear layer re-emerges in what might be described as a ‘new’ baseline flow.

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