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Reynolds stress equation model (RSM), also referred to as second moment closures are the most complete classical turbulence model.In these models, the eddy-viscosity hypothesis is avoided and the individual components of the Reynolds stress tensor are directly computed.
In 1978 Patir and Cheng introduced an average flow model, [8] [9] which modifies the Reynolds equation to consider the effects of surface roughness on lubricated contacts. The average flow model spans the regimes of lubrication where the surfaces are close together and/or touching.
The Reynolds-averaged Navier–Stokes equations (RANS equations) are time-averaged [a] equations of motion for fluid flow. The idea behind the equations is Reynolds decomposition , whereby an instantaneous quantity is decomposed into its time-averaged and fluctuating quantities, an idea first proposed by Osborne Reynolds . [ 1 ]
The Reynolds stress equation model (RSM), also referred to as second moment closure model, [12] is the most complete classical turbulence modelling approach. Popular eddy-viscosity based models like the k –ε ( k –epsilon) model and the k –ω ( k –omega) models have significant shortcomings in complex engineering flows.
This has been the subject of intense modeling and interest, for roughly the past century. The problem is recognized as a closure problem, akin to the problem of closure in the BBGKY hierarchy. A transport equation for the Reynolds stress may be found by taking the outer product of the fluid equations for the fluctuating velocity, with itself.
As an example for pipe flows, with the Reynolds number based on the pipe diameter: =. Here l is the turbulence or eddy length scale, given below, and c μ is a k – ε model parameter whose value is typically given as 0.09;
From the equation it is shown that for a flow with a large Reynolds Number there will be a correspondingly small convective boundary layer compared to the vessel’s characteristic length. [5] By knowing the Reynolds and Womersley numbers for a given flow it is possible to calculate both the transient and the convective boundary layer ...
A key tool used to determine the stability of a flow is the Reynolds number (Re), first put forward by George Gabriel Stokes at the start of the 1850s. Associated with Osborne Reynolds who further developed the idea in the early 1880s, this dimensionless number gives the ratio of inertial terms and viscous terms. [4]