Effect of the Large-Scale Structure on Turbulent Prandtl Number in a Turbulent Shear Layer

2019 ◽  
Author(s):  
Kotaro Takamure ◽  
Yasuhiko Sakai ◽  
Yasumasa Ito ◽  
Koji Iwano
Keyword(s):  
Prandtl Number ◽  
Large Scale ◽  
Mixing Layer ◽  
Large Scale Structure ◽  
Scale Structure ◽  
Turbulent Shear ◽  
Turbulent Prandtl Number ◽  
Scalar Flux ◽  
Gradient Direction ◽  
Correlation Term

Abstract We have run a Direct Numerical Simulation of a spatially developing shear mixing layer. The aim of this study is to clarify the influence of the large-scale structure on the turbulent Prandtl number PrT. As a main conclusion, PrT takes a small value (PrT ∼ 0.5) in the dominant region of the large-scale structure. The budget analyses for the Reynolds stress equation and the scalar flux equation revealed that the differences between the momentum and scalar transfer are caused by terms related to pressure (i.e., pressure-strain correlation term, pressure-scalar gradient correlation term, and pressure diffusion terms). Phenomenally, the momentum in the field where a large-scale vortex coexists tends to be transported toward the counter-gradient direction under the influence of pressure, but the scalar is transported toward the gradient direction. As a result, it is thought that the difference in the driving force between the momentum and scalar transport causes the decrease of the PrT.

On the interactions between large-scale structure and finegrained turbulence in a free shear flow II. The development of spatial interactions in the mean

1978 ◽  
Vol 359 (1699) ◽  
pp. 497-523 ◽  
Keyword(s):  
Shear Flow ◽  
Shear Layer ◽  
Large Scale ◽  
Large Scale Structure ◽  
Scale Structure ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Free Shear Layer ◽  
Mean Flow ◽  
The Mean

Organized structures in turbulent shear flow have been observed both in the laboratory and in the atmosphere and ocean. Recent work on modelling such structures in a temporally developing, horizontally homogeneous turbulent free shear layer (Liu & Merkine 19766) has been extended to the spatially developing mixing layer, there being no available rational transformation between the two nonlinear problems. We consider the kinetic energy development of the mean flow, large-scale structure and finegrained turbulence with a conditional average, supplementing the usual time average, to separate the non-random from the random part of the fluctuations. The integrated form of the energy equations and the accompanying shape assumptions are used to derive ‘ amplitude ’ equations for the mean flow, characterized by the shear layer thickness, the non-random and the random components of flow (which are characterized by their respective energy densities). The closure problem was overcome by the shape assumptions which entered into the interaction integrals: the instability-wavelike large-scale structure was taken to be two-dimensional and the local vertical distribution function was obtained by solving the Rayleigh equation for various local frequencies; the vertical shape of the mean stresses of the fine-grained turbulence was estimated by making use of experimental results; the vertical shapes of the wave-induced stresses were calculated locally from their corresponding equations.

Effects of heat release on the large-scale structure in turbulent mixing layers

1989 ◽  
Vol 199 ◽  
pp. 297-332 ◽  
Author(s):  
P. A. Mcmurtry ◽  
J. J. Riley ◽  
R. W. Metcalfe
Keyword(s):  
Heat Release ◽  
Turbulent Mixing ◽  
Large Scale ◽  
Mixing Layer ◽  
Large Scale Structure ◽  
Scale Structure ◽  
Mixing Layers ◽  
Turbulent Mixing Layer ◽  
Large Scale Structures ◽  
Scale Structures

The effects of chemical heat release on the large-scale structure in a chemically reacting, turbulent mixing layer are investigated using direct numerical simulations. Three-dimensional, time-dependent simulations are performed for a binary, single-step chemical reaction occurring across a temporally developing turbulent mixing layer. It is found that moderate heat release slows the development of the large-scale structures and shifts their wavelengths to larger scales. The resulting entrainment of reactants is reduced, decreasing the overall chemical product formation rate. The simulation results are interpreted in terms of turbulence energetics, vorticity dynamics, and stability theory. The baroclinic torque and thermal expansion in the mixing layer produce changes in the flame vortex structure that result in more diffuse vortices than in the constant-density case, resulting in lower rotation rates of the large-scale structures. Previously unexplained anomalies observed in the mean velocity profiles of reacting jets and mixing layers are shown to result from vorticity generation by baroclinic torques.

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