Continuity and Momentum Equations for Turbulent Flows
 

Hello everyone. I am trying to learn CFD by following the book "Computational Fluid Dynamics" by Jiyuan Tu. I know that continuity and momentum equations are sufficient to solve any laminar flow problem. If the problem is simple enough, it is possible to determine analytical solutions. If not, numerical methods are available for solution. In any case, for laminar flows we only need continuity and momentum equations. But for laminar flows, these equations are NOT sufficient to describe flow. Why? The reason given in book is shared below but I am not able to understand it. Can anyone please explain me why is this the case.
"The random nature of flow precludes computations based in the equations that describe fluid motion. Although conservation equations remain applicable, the dependent variable, such as the transient velocity distribution must be interpreted as an instantaneous velocity - a phenomenon that is impossible to predict, as the fluctuating velocity occurs randomly with time."

1) continuity and momentum equations are sufficient for determining solutions not only for laminar flows but for determining all the possible solutions for incompressible homo-thermal (density constant and temperature constant) flows.
2) if the flow is laminar but is governed by the bouyancy, you need to supply also the energy equation.
3) Analytical solutions exist but are limited to specific BC.s and hypothesis.
4) the random nature of the flow is true in the microscopic sense where we consider the "random walk" of a particle. In the continuum we use the PDE equation for averaged regular functions.
5) If you consider turbulence, the random nature of the fluctuations has to be carefully considered: turbulence is not a random phoenomenon.

FMDenaro, Sir point 2,3 and 4 are clear. However, does point 1 mean that all isothermal flows irrespective of their nature (laminar or turbulent) can be described using Continuity and Momentum equations? If this is the case, why do we use turbulence models then?

Using turbulence models is not mandatory, depending on the computational resources You can use the direct nunerical simulation.