Physics and Modelling of Compressible Turbulent Boundary Layer

Abstract

Key findings from a research study that focuses on understanding the effect of Mach number, Reynolds number and wall temperature on compressible turbulent boundary layers (CTBL) in the hypersonic regime are presented in this dissertation. The study utilizes a comprehensive CTBL database developed using an in-house direct numerical simulation (DNS) code at the CRoCCo laboratory. The database encompasses a range of semi-local Reynolds numbers (800 to 34,000) and Mach numbers up to 12, incorporating wall-cooling.

The effects of density and viscosity fluctuations on the total stress balance are identified and used to create a new mean velocity transformation for compressible boundary layers. The role, significance and physical mechanisms connecting density and viscosity fluctuations to the momentum balance and to the viscous, turbulent and total stresses are presented, allowing the creation of generalized formulations. We identify the significant properties that thus-far have been neglected in the derivation of velocity transformations: (1) the Mach-invariance of the near-wall momentum balance for the generalized total stress, and (2) the Mach-invariance of the relative contributions from the generalized viscous and Reynolds stresses to the total stress. The proposed velocity transformation integrates both properties into a single transformation equation and successfully demonstrates a collapsing of all currently considered compressible cases onto the incompressible law of the wall, within the bounds of reported slope and intercept for incompressible data. Based on the physics embedded in the two scaling properties, the success of the newly proposed transformation is attributed to considering the effects of the viscous stress and turbulent stresses as well as mean and fluctuating density viscosity in a single transformation form.

The Reynolds number trends of large turbulent structures in compressible turbulent boundary layers are investigated using the pre-multiplied energy spectra based on the density corrected fluctuating streamwise velocity signal. Results demonstrate the existence of friction as well as semi-local Reynolds number trend associated with large-scale structures, similar to trends observable in incompressible turbulent boundary layers (ITBL). In particular, the behavior of turbulence in the inner layer is seen to exhibit dependence based on both definitions of Reynolds numbers. On the contrary, the strength of large turbulent structures is seen to be only dependent on friction Reynolds number. This result directly contrasts with the observation of the near-wall turbulent intensity peak increasing with semi-local Reynolds number. The discrepancy is mended with a suggestion that the large turbulent scales in the log layer of which the strength increases with friction Reynolds number, are modified through the changes in local fluid properties such that the scale interaction near the wall increases as semi-local Reynolds number. In another words, closer to the wall, the CTBL flow behaves like a semi-local Reynolds number flow, while closer to the freestream, it behaves like a friction Reynolds number flow. Furthermore, the present study examines the Reynolds number dependence of the length scale between small and large turbulent scales. The analysis highlights the inadequacy of using a univariable wavelength based on viscous, semi-local or outer length scales to differentiate small and large scales. Based on this, the use of Reynolds number-dependent length scales is recommended. Overall, the study provides valuable insights into the Reynolds number trends of large turbulent structures in CTBL, emphasizing the influence of both semi-local Reynolds number and friction Reynolds number on turbulence characteristics.