Week 8: Literature review - RANS derivation and analysis

Objective:

Apply Reynold's decomposition to the NS equations and come up with the expression for reynold's stress.

• Explain your understanding of the terms reynold's stress
• What is turbulent viscosity? How is it different from molecular viscosity?

Reynolds Stress Derivation:

If we compare to the Navier-Stokes equations it can be seen that besides the viscous part
an additional term has been added to the total shear stress. This term results from the time-average and
is generally the dominant part of the total shear stress. Since the term only appears due to the Reynolds
average, it is called Reynolds stress or apparent turbulent shear stress.

Turbulent Viscosity:

The coefficient that relates the average shear stress and rate of velocity gradient in the turbulent flow is called turbulent viscosity. The viscosity in the turbulent flow is non homogeneous, and it varies in space.

Molecular viscosity is the same as viscosity and it's coefficient is same as the coefficient of dynamic viscosity. Molecular viscosity is the transport of mass motion momentum solely by the random motions of individual molecules not moving together in coherent groups. Molecular viscosity is analogous in laminar flow to eddy viscosity in turbulent flow.