On the computation of heat flux in hypersonic flows using residual distribution schemes

The unexpected results identified early in the investigation lead to a thorough analysis to identify the causes of the unphysical hypersonic heating.

The first step taken is the assessment of the quality of flow field and heat transfer predictions obtained with RD methods for subsonic configurations. The result is positive, both for flat plate and cylinder configurations, as RD schemes produce accurate flow solutions and heat flux predictions whenever no shock waves are present, irrespective of the gas model employed.

Subsonic results prove that hypersonic heating anomalies are a consequence of the presence of a shock wave in the domain and/or the way it is handled numerically.

Regarding hypersonic flows, the carbuncle instability is discarded first as the cause of the erroneous stagnation heating. The anomalies are shown next to be insensitive to the kind and level of dissipation introduced via the (quasi-)positive contribution P to blended B schemes. Additionally, insufficient mesh resolution locally over the region where the shock wave is captured numerically is found to be irrelevant.

Capturing the bow shock in a manner that total enthalpy is preserved immediately before and after the numerical shock wave is, on the contrary, important for correct heating prediction.

However, a carefully conceived shock capturing term is, by itself, not sufficient to guarantee correct heating predictions, since the LP scheme employed (be it stand-alone in a shock fitting context or combined into a blended scheme for a shock capturing computation) needs to be immune to spurious recirculations in the stagnation point.

Once the causes inducing the heating anomalies identified, hypersonic shocked flows in TCNEQ conditions are studied.

In order to alleviate the computational effort necessary to handle many species non-equilibrium (NEQ) models, the extension of an entropic (or symmetrizing) variables formulation RD to the nS species, two temperature TCNEQ model is accomplished, and the savings in computational time it allows are demonstrated.

The multi-dimensional generalization of Roe-like linearizations for the TCNEQ model is addressed next: a study on the existence conditions of the linearized state guaranteeing discrete conservation is conducted.

Finally, the new dissipative terms derived for perfect gas are adapted to work under TCNEQ conditions; the resulting numerical schemes are free of the temperature undershoot and Mach number overshoot problem afflicting standard CRD schemes.