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Pre-Analysis & Start-Up

Preliminary Analysis

The turbulent equations that we will be solving are the Reynolds equations, where the Navier Stokes equations are transformed by substituting the velocities U(x,t) as the sum of mean velocity <U(x,t)> and the turbulent velocity fluctuations u(x,t). This is known as the Reynolds decomposition. Unfortunately, this substitution into the nonlinear term of the Navier Stokes equations results in additional terms known as the Reynolds stresses. These terms are crucial; they are what separate turbulent flow equations from the well known laminar form. These new Reynolds transport equations cannot be solved without closure models for the Reynolds stresses, because with solving for mean velocity, there will be more unknowns than there are equations.

The k-ε model is one of the most widely used closure models in which two additional equations are solved for variables k and ε. This model is complete, in that these two variables can be manipulated to describe a a turbulent length and time scale.  The assumptions made in using this model are that the two k and ε transport equations are valid, and the turbulent viscosity hypothesis, that the Reynolds stresses are proportional to the mean rate of strain (similar to the Newtonian hypothesis relating stress and strain that is used in the Navier Stokes equations).

Starting Fluent

While the actual jet inflow is much smaller than the mesh, the additional jet area at the inlet allows for entrainment of air near the inlet, and radial dispersal of the fluid into the surroundings as X increases. 

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