Compressibility effect in hypersonic boundary layer with isothermal wall condition

The compressibility effect in isothermal hypersonic boundary layer is studied with direct numerical simulation (DNS) using Helmholtz decomposition. The dilatational components of the diagonal Reynolds stress are enhanced by the cold wall condition in the near-wall region. The outward (Q1) and ejection (Q2) events are mainly located in the expansion region, while the inward (Q3) and sweep (Q4) events are primarily situated in the compression region near the wall. It is found that the cold wall condition can enhance the inward (Q3) event mainly in the compression region and enhance the ejection (Q2) event mainly in the expansion region near the wall. In particular, the cold wall can significantly enhance the positive streamwise solenoidal fluctuating velocity and negative wall-normal dilatational fluctuating velocity events. Moreover, the cold wall condition enhances the positive correlation of streamwise velocity fluctuation and fluctuating temperature, and suppresses the negative correlation of wall-normal velocity fluctuation and fluctuating temperature in the near-wall region, while it slightly weakens the negative correlation of streamwise velocity fluctuation and fluctuating temperature and the positive correlation of wall-normal velocity fluctuation and fluctuating temperature far from the wall. It is also found that the dilatational components of correlations are dominated in the near-wall region, while the solenoidal components govern the correlations far from the wall. Most of the interactions among mean and fluctuating fields of kinetic and internal energy are governed by the solenoidal components, except for the terms associated with the pressure, which are governed by the dilatational components.