Direct numerical simulation of developed compressible flow in square ducts

TL;DR

This study uses direct numerical simulation to analyze compressible flow in square ducts, finding that compressibility effects on secondary motions are minimal and that wall laws for velocity and scalar fields are applicable with certain transformations.

Contribution

It demonstrates that compressibility has negligible effects on secondary motions in square ducts and extends wall law applicability to compressible flows with appropriate transformations.

Findings

Compressibility effects on secondary motions are negligible.

Wall law for mean streamwise velocity applies with transformations.

Temperature does not exhibit inertial layers due to nonuniform heating.

Abstract

We carry out direct numerical simulation of compressible square duct flow in the range of bulk Mach numbers M_b = 0.2-3, and up to friction Reynolds number Re_{\tau} = 500. The effects of flow compressibility on the secondary motions are found to be negligible, as the typical Mach number associated with the cross-stream flow is always less than 0.1. As in the incompressible case, we find that the wall law for the mean streamwise velocity applies with good approximation with respect to the nearest wall, upon suitable compressibility transformation. The same conclusion also applies to a passive scalar field, whereas the mean temperature does not exhibit inertial layers because of nonuniformity of the aerodynamic heating. We further find that the same temperature/velocity relation that holds for planar channels is applicable with good approximation for square ducts, and develop a similar relation between temperature and passive scalars.