|dc.description.abstract||The law of the wall has been a staple in collapsing the mean velocity profiles of seemingly very different turbulent channel and boundary layer flows into one single, semi-analytical function. Accordingly, it has equipped engineers and scientists with unique predictive capabilities over the randomness of turbulence. Its universality and widespread success for incompressible canonical flows has further encouraged research efforts that seek transformations that scale any type of flow, whether canonical or not, to match with the law of the wall. In this work, the problem of scaling non-adiabatic boundary layer flows is tackled in the high-speed, compressible context.
Starting from a generalization of the two most successful transformations to date, the Van Driest and Trettel and Larsson, the shortcomings of each transformation are highlighted. Following that, and contrary to most classical approaches, an extension is carried out using the conservation of energy, from which a potential velocity transformation is obtained. In turn, by basing the analysis on energy as opposed to momentum, the resulting transformation explicitly accounts for the non-adiabatic condition at the wall.
The transformation is assessed by comparison against the law of the wall in the case of hypersonic, non-adiabatic boundary layer flows. It is found to yield perfect collapse for weakly-to-moderately cooled walls. After factoring in the higher-order fluctuations in the turbulence terms, the transformation is also found to produce excellent agreement for strongly cooled walls.
The findings demonstrate that the physics of non-adiabatic walls cannot be fully captured by solely relying on the conservation of momentum. In addition, in high-speed flows with large heat transfer at the wall, the higher-order turbulence terms cannot be neglected. Ahead of full-scale implementation, the transformation has to be rigorously tested using broader data sets. This is left for future work.||en