Abstract
A theoretical approach is developed for solving for the Reynolds stress in turbulent flows, and is validated for canonical flow geometries (flow over a flat plate, rectangular channel flow, and free turbulent jet). The theory is based on the turbulence momentum equation cast in a coordinate frame moving with the mean flow. The formulation leads to an ordinary differential equation for the Reynolds stress, which can either be integrated to provide parameterization in terms of turbulence parameters or can be solved numerically for closure in simple geometries. Results thus far indicate that the good agreement between the current theoretical and experimental/DNS (direct numerical simulation) data is not a fortuitous coincidence, and in the least it works quite well in sensible ways in canonical flow geometries. A closed-form solution for the Reynolds stress is found in terms of the root variables, such as the mean velocity, velocity gradient, turbulence kinetic energy and a viscous term. The form of the solution also provides radically new insight on how the Reynolds stress is generated and distributed.
Highlights
We present a theoretical development and a solution for the Reynolds stress in turbulence
Lee fluctuations) velocity field is quite difficult, or as some argue an overflow of information, here we focus on finding the Reynolds stress as a function of the “root” turbulence parameters, such as the mean velocity and its gradient, turbulence kinetic energy, in particular its longitudinal component, and a viscous term
Data on various turbulence quantities and the Reynolds stress are provided, and various scaling approaches tested with the data, in a well-designed experiment for flows over a flat plate with zero pressure gradient
Summary
Mechanical and Aerospace Engineering, SEMTE Arizona State University, Tempe, USA. (2016) A Theoretical Solution for the Reynolds Stress: Validations in Canonical Flow Geometries. Open Journal of Fluid Dynamics, 6, 272278. Received: September 19, 2016 Accepted: October 18, 2016 Published: October 21, 2016
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