An improved Baldwin-Lomax algebraic wall model for high-speed canonical turbulent boundary layers using established scalings

In this work, well-established relations for compressible turbulent mean flows, including the velocity transformation and algebraic temperature–velocity relation, are utilized for an improved algebraic Baldwin–Lomax (BL) wall model for high-speed zero-pressure-gradient boundary layers. Any new functions or coefficients fitted by ourselves are avoided. Twelve published direct numerical simulation (DNS) datasets are employed for a priori inspiration and a posteriori examination, with edge Mach numbers up to 14 under adiabatic, cold and heated walls. The baseline BL model is the widely used one with semi-local scaling. Three targeted modifications are made. First, the GFM transformation (Griffin et al., Proc. Natl. Acad. Sci., vol.118, 2021, p.34) is applied to the inner-layer eddy viscosity for improved scaling up to the logarithmic region. Second, the van Driest transformation is utilized in the outer layer based on compressible defect velocity scaling. Third, considering the difficulty in modelling the rapidly varying and singular turbulent Prandtl number near the temperature peak in cold-wall cases, the quadratic temperature–velocity relation is used to formulate the inner-layer temperature. Numerical results prove that the modifications take effect as designed. The prediction accuracy for mean streamwise velocity is notably improved for diabatic cases, especially in the logarithmic region. Moreover, a significant improvement in mean temperature is realized for both adiabatic and diabatic cases. The mean relative errors of temperature to DNS for all cases are down to 0.4% in logarithmic wall-normal coordinate and 3.4% in the normal coordinate, around one-third of those in the baseline model.

Multi-scale analysis of the space-time properties in incompressible wall-bounded turbulence

It is believed that the space-time correlation is a fundamental statistical theory for analyzing the dynamic coupling between spatial and temporal scales of the motions in turbulent flows. In this paper, by coupling the inner-outer interaction model (IOIM) with attached-eddy hypothesis, the space-time correlations of both wall-shear fluctuations and the streamwise velocity fluctuations carried by wall-attached eddies at a given length-scale are investigated. The present results demonstrate that the space-time correlations for the wall-shear stress fluctuation are mainly dominated by near-wall small-scale motions, and the superposition effects generated by wall-attached eddies are only reflected in the weakly correlated regions with large space separations and/or time delays. Furthermore, the findings in the present study demonstrate that, for the first time, wall-attached eddies at a given length scale feature distinctly different space-time properties as compared to that of ensembled eddies with multiple length scales, which provides a new perspective for analyzing the decorrelation mechanisms in turbulence theory and developing an advanced space-time correlation model.