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The equation can either be used with consistent units or nondimensionalized. The Reynolds Equation assumes: The fluid is Newtonian. Fluid viscous forces dominate over fluid inertia forces. This is the principle of the Reynolds number. Fluid body forces are negligible.
A common solution is to model these terms by simple ad hoc prescriptions. The theory of the Reynolds stress is quite analogous to the kinetic theory of gases, and indeed the stress tensor in a fluid at a point may be seen to be the ensemble average of the stress due to the thermal velocities of molecules at a given point in a fluid. Thus, by ...
In these models, the eddy-viscosity hypothesis is avoided and the individual components of the Reynolds stress tensor are directly computed. These models use the exact Reynolds stress transport equation for their formulation. They account for the directional effects of the Reynolds stresses and the complex interactions in turbulent flows.
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 arises due to the ...
In the frame work of single-point closures (Reynolds-stress transport models = RSTM) still provide the best representation of flow physics. Due to numeric requirements an explicit formulation based on a low number of tensors is desirable and was already introduced originally most explicit algebraic stress models are formulated using a 10-term basis:
The Reynolds number has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing. It is used to predict the transition from laminar to turbulent flow and is used in the scaling of similar but different-sized flow situations, such as between an aircraft model in a wind tunnel and the full-size version ...
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 and Womersley Numbers are also used to calculate the thicknesses of the boundary layers that can form from the fluid flow’s viscous effects. The Reynolds number is used to calculate the convective inertial boundary layer thickness that can form, and the Womersley number is used to calculate the transient inertial boundary thickness that can form.