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This is my first post and contribution to this community. Hope you all will like the content and also looking forward for valuable suggestions.

There would be no CFD enthusiast who doesn't heard about 

Reynolds Averaged Navier Stokes equation(RANS)

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Today we will try to understand this RANS equation significance in CFD and any fluid flow analysis.

whenever we studied about Navier-Stokes equation, it has certain assumptions while deriving from conservation principles.

so, it is applicable only for some applications like incompressible flow, laminar flow and applications like Couette flow, Poiseuille flow etc...

But, in real life applications we encounter more often with turbulent flow and compressible flows also.

SO, RANS is useful for both laminar and turbulent flows as well as incompressible and compressible flows.

Using Reynolds decomposition which represents instantaneous velocity in terms of mean velocity and fluctuating velocity we derived this RANS equation. 

Mean velocity component is derived by averaging the velocity over a time.so, RANS is also called as Time Averaged RANS equation.

we use this Reynolds decomposition in place of velocity in conservation principles which will reduce to RANS equation by using several mathematical manipulations.

But, if you observe the last term in RANS, it is in the form of fluctuating velocity.

That term we call it as Reynolds stress as the dimensions of it are same as stress.

In fact, the fluctuating velocity is because of the turbulence in the flow. so, we also call that term as Turbulent stress.

Unless we find the turbulent stress, we cannot solve the RANS equation.

but we cannot solve turbulent stress directly in fluctuating velocity.

So, here I would say the heart of RANS equation comes into picture called as Boussinesq approximation.

This approximation converts Reynolds stress into mean velocity gradient and turbulent viscosity.

once we replace Reynolds stress with Boussinesq approximation, whole RANS equation is in the form of mean velocity.

But, this RANS equation is solvable only when we can solve the turbulent viscosity in Boussinesq approximation.

In any RANS based CFD software like FMK we have certain models you might heard about like "K-epsilon model, K-omega model, Spalart Allmaras model" etc...

The purpose of these models is to find out the Turbulent viscosity.

Once we get that turbulent viscosity which leads to find Reynolds stress and then we will be solving RANS equation to find the fluid parameters and flow behavior of fluid.

Hope this post will helped to get some idea about RANS

Comment down your suggestions and any further information can be added to this post.