In this paper,direct numerical simulation(DNS)is presented for spatially evolving turbulent boundary layer over an isothermal flat-plate at Ma∞=2.25,5,6,8.When Ma∞=8,two cases with the ratio of wall-to-reference temperature T_(w)/T_(∞)=1.9 and 10.03 are considered respectively.The wall temperature approaches recovery temperatures for other cases.The characteristics of compressible turbulent boundary layer(CTBL)affected by freestream Mach number and wall temperature are investigated.It focuses on assessing compressibility effects and the validity of Morkovin’s hypothesis through computing and analyzing the mean velocity profile,turbulent intensity,the strong Reynolds analogy(SRA)and possibility density function of dilatation term.The results show that,when the wall temperature approaches recovery temperature,the effects of Mach number on compressibility is insignificant.As a result,the compressibility effect is very weak and the Morkovin’s hypothesis is still valid for Mach number even up to 8.However,when Mach number equal to 8,the wall temperature effect on the compressibility is sensitive.In this case,when T_(w)/T_(∞)=1.9,the Morkovin’s hypothesis is not fully valid.The validity of classical SRA depends on wall temperature directly.A new modified SRA is proposed to eliminate such negative factor in near wall region.Finally the effects of Mach number and wall temperature on streaks are also studied.
In spectral-like resolution-WENO hybrid schemes,if the switch function takes more grid points as discontinuity points,the WENO scheme is often turned on,and the numerical solutions may be too dissipative.Conversely,if the switch function takes less grid points as discontinuity points,the hybrid schemes usually are found to produce oscillatory solutions or just to be unstable.Even if the switch function takes less grid points as discontinuity points,the final hybrid scheme is inclined to be more stable,provided the spectral-like resolution scheme in the hybrid scheme has moderate shock-capturing capability.Following this idea,we propose nonlinear spectral-like schemes named weighted group velocity control(WGVC)schemes.These schemes show not only high-resolution for short waves but also moderate shock capturing capability.Then a new class of hybrid schemes is designed in which the WGVC scheme is used in smooth regions and the WENO scheme is used to capture discontinuities.These hybrid schemes show good resolution for small-scales structures and fine shock-capturing capabilities while the switch function takes less grid points as discontinuity points.The seven-order WGVC-WENO scheme has also been applied successfully to the direct numerical simulation of oblique shock wave-turbulent boundary layer interaction.
