Question

How many additional terms are present in the x-momentum equation Reynolds-Averaged Navier-Stokes equations?

(a) No additional terms

(b) Six additional terms

(c) Three additional terms

(d) Two additional terms

The question was posed to me during an online interview.

The doubt is from Turbulence Modelling in portion Turbulence Modelling of Computational Fluid Dynamics

Answer 1

Correct option is (c) Three additional terms

For explanation: The non-reduced x-momentum equation is

\(\frac{\partial(\rho u)}{\partial t}+div(\rho u \vec{V})=-\frac{\partial p}{\partial x}+div(\mu\,grad(u))+S\)

The Reynolds-Averaged x-momentum equation is

\(\frac{\partial(\overline{\rho}\tilde{u})}{\partial t} + div(\overline{\rho}\tilde{u}\widetilde{(\vec{V})}) =

 -\frac{\partial\tilde{p}}{\partial x} + div(\mu grad\widetilde{(\vec{V})}) + (-\frac{\partial\overline{(\overline{\rho} u{‘}^2)}}{\partial x} – \frac{\partial\overline{(\overline{\rho}u{‘}v{‘})}}{\partial y} – \frac{\partial\overline{(\overline{\rho}u{‘}w{‘})}}{\partial z})+S\)

Here, the terms (ρu’^2), (ρu’v’) and (ρu’v’) are the three extra terms.