Entropy losses in turbulent boundary layers under non adiabatic wall conditions at different Mach numbers

In the present framework a series of wall-resolved large-eddy simulations are executed in a discrete range of subsonic and mildly supersonic Mach numbers in order to analyse a compressible turbulent boundary layer under wall cooling and heating conditions. The analysis focuses on the mechanisms of entropy generation from a second law thermodynamic perspective, focusing on the viscous and heat conduction as key mechanisms that regulate entropy generation, expanding previous results obtained by Dr. Ing. Francesco De Vanna. The results confirm previous findings, identifying wall cooling as a tool to obtain entropy balanced or cooling dominated regimes, but also producing novel results when analysed from a wall heating perspective which was omitted in previous analysis. Entropy production or destruction is quantified by adopting non-dimensional entropy generation coefficients, which show robust self-similar scalings with the boundary layer momentum Reynolds number. The results show comparable behaviour to previous findings and expand on the characterization of varying thermal conditions in compressible boundary layers. Furthermore, the present research proposes a mono-dimensional numerical model based on novel results from this framework and classical boundary layer correlations, aimed at the generation of non-dimensional entropy maps requiring as inputs only the fluid properties and the flow inlet conditions. The goal of the model is to provide engineering guidance from a first iteration perspective to evaluate the tradeoffs and sizing of an heat exchange system that uses the incoming flow as either the cold or hot side of the exchange. The increased understanding of thermal effects on compressible boundary layers, paired with computationally cheap numerical tools could provide valuable insights for the design of novel engineering systems, with particular attention to those based on turbomachinery and heat exchanger technologies, with the aim of providing a net efficiency increase over the energy expenditure required to cool the flow.