Direct Numerical Simulation on Mach Number and Wall Temperature Effects in the Turbulent Flows of Flat-Plate Boundary Layer (Communications in Computational Physics, 2018)
In this paper, direct numerical simulation (DNS) is presented for spatiallyevolving 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 $T_w/T_∞$=1.9and 10.03 are considered respectively. The wall temperature approaches recovery temperaturesfor other cases. The characteristics of compressible turbulent boundary layer(CTBL) affected by freestream Mach number and wall temperature are investigated. Itfocuses on assessing compressibility effects and the validity of Morkovin's hypothesisthrough computing and analyzing the mean velocity profile, turbulent intensity, thestrong Reynolds analogy (SRA) and possibility density function of dilatation term. Theresults show that, when the wall temperature approaches recovery temperature, theeffects of Mach number on compressibility is insignificant. As a result, the compressibilityeffect is very weak and the Morkovin's hypothesis is still valid for Mach numbereven up to 8. However, when Mach number equal to 8, the wall temperature effect onthe compressibility is sensitive. In this case, when $T_w/T_∞$=1.9, the Morkovin's hypothesisis not fully valid. The validity of classical SRA depends on wall temperaturedirectly. A new modified SRA is proposed to eliminate such negative factor in nearwall region. Finally the effects of Mach number and wall temperature on streaks arealso studied.