The effect of heat transfer on three-dimensional spatial stability and transition of flat plate boundary layer at mach 3

Abstract

The 3-dim. linear spatial stability of compressible flat plate boundary layers with heat transfer is investigated for the parallel flow assumption. The mean flow is obtained from the standard compressible boundary layer equations assuming perfect gas fluid properties, Sutherland's law of viscosity and constant Prandtl number. Stability characteristics, amplification maps, are obtained for 2-dim. and 3-dim. modes at Mach 3.0 and ratio of wall to adiabatic wall temperature equal to 1.5, 1.25, 1.0, 0.8, 0.7 and 0.3. Results show that the stability of a given boundary layer cannot be concluded simply on the basis of the critical Reynolds number—incorrect conclusions may be made unless the entire instability map, particularly growth factors vs frequency and Reynolds number, is evaluated. Computations for the first 3-dim. mode show that, except for the ‘transition reversal’ the observed variation of the transition Reynolds number with heat transfer at the wall (cooling and heating) is predicted, qualitatively, by linear instability theory. Also, since the dominance of an instability mode can switch as major parameters affecting the disturbance are changed, transition reversal is predicted by the linear theory when with extended surface cooling the first 3-dim. mode, which is monotonically stabilized with cooling, ceases to be important and transition is then determined by the second 2-dim. mode.