Entropy Fluctuations and Correlations in Compressible Turbulent Plane Channel Flow

Abstract

The thermodynamic turbulence structure of compressible aerodynamic flows is often characterised by the correlation coefficient of entropy with pressure or temperature. We study entropy fluctuations s′ and their correlations with the fluctuations of the other thermodynamic variables in compressible turbulent plane channel flow using dns data. We investigate the influence of the hcb (Huang–Coleman–Bradshaw) friction Reynolds number (100⪅Reτ★⪅1000) and of the centreline Mach number (0.3⪅M¯CLx⪅2.5) on the magnitude and location of the peak of the root-mean-square srms′. The complete series expansions of s′ with respect to the fluctuations of the basic thermodynamic variables (pressure p, density ρ and temperature T) are calculated for the general case of variable heat-capacity cp(T) thermodynamics. The correlation coefficients of s′ with the fluctuations of the basic thermodynamic quantities (cs′p′, cs′ρ′, cs′T′), for varying (Reτ★,M¯CLx), are studied. Insight on these correlations is provided by considering the probability density function (pdf) of s′ and its joint pdfs with the other thermodynamic variables.

Keywords

• turbulent boundary-layers
• compressible boundary-layer
• turbulence theory