Direct numerical simulation of sensitivity coefficients in low Reynolds number turbulent channel flow

Abstract

The sensitivity equation method (SEM) has been implemented in direct numerical simulations (DNS) of smooth-wall turbulent channel flow to quantify Reynolds number effects on the mean flow field. The present approach towards sensitivity analysis represents a departure from conventional parametric studies wherein multiple numerical simulations are performed with discrete increments in the value of the parameter of interest, in this case the Reynolds number. In the present study, sensitivity derivatives (or sensitivity coefficients) represent the rate of change of the primitive variables with respect to the Reynolds number, and are determined directly by numerically solving the discretized continuous sensitivity equations concurrently with the discretized Navier–Stokes equations. Simulations have been performed at Reynolds numbers of 100 and 180, based on the friction velocity and channel half-width, using a finite volume computational scheme. Wall-normal profiles of the mean streamwise velocity and Reynolds stresses compare very well to others in the literature at the same Reynolds numbers [19,20]. The SEM results correctly predict the expected change in both the mean streamwise velocity and Reynolds shear stress profiles with increasing Reynolds number. Furthermore, the mean SEM results correctly predict the local slope of the skin friction coefficient versus Reynolds number curve, which may have potential use in applications such as boundary layer control by surface modification. The present study is novel insofar as it constitutes the first attempt to implement SEM in an unsteady, fully turbulent, three-dimensional flow field. The additional computational expenses incurred in order to run the SEM simulations in this context are also discussed.

Keywords:

• sensitivity analysis
• direct numerical simulation
• sensitivity equation method
• turbulent channel flow

Acknowledgements

This work was supported by a grant from the National Science Foundation (IIS-0428856).