Question

The Reynolds stress term arises in the turbulent equation only when ____________

(a) two quantities are correlated

(b) two quantities are uncorrelated

(c) the flow is steady

(d) the flow is unsteady

The question was posed to me in an interview for internship.

My enquiry is from Turbulence Modelling in portion Turbulence Modelling of Computational Fluid Dynamics

Answer 1

The correct answer is:

(a) two quantities are correlated

Explanation:

The Reynolds stress term arises in the context of turbulent flow because of the correlation between fluctuating velocity components. Specifically, these stresses result from the turbulent velocity fluctuations interacting with each other. In the Reynolds-averaged Navier-Stokes (RANS) equations, the Reynolds stress tensor represents the transport of momentum due to turbulence and is typically expressed as:

uiuj‾=ρui′uj′‾\overline{u_i u_j} = \rho \overline{u'_i u'_j}ui​uj​​=ρui′​uj′​​

Where:

• ui′u'_iui′​ and uj′u'_juj′​ are the velocity fluctuations from the mean flow.
• uiuj‾\overline{u_i u_j}ui​uj​​ represents the Reynolds stress tensor.

This term appears because of the correlation between the fluctuating velocity components in different directions. These correlations represent the turbulent momentum transport that is not accounted for in the laminar flow model.

Thus, the Reynolds stress term arises specifically when two quantities (velocity fluctuations) are correlated.