Is Re_θ/M_e a Meaningful Transition Criterion?

摘要

So is there any meaning to Re_θ/M_e ? When Re_θ/M_e is written out [Eq. (11)], it is seen that the U_e in the numerator and denominator cancel. Also, a_e and μ_e both depend only on external temperature. Re_θ/M_e = ρ_eU_eθ/μ_e(U_e/a_e) = ρ_ea_eθ/μ_e (11) For entry vehicles, these factors vary slowly with altitude. The density ρ_e, however, depends strongly on pressure and therefore varies very rapidly with altitude. Thus, Re_θ/M_e (or any Reynolds number criterion) might successfully correlate with the altitude at which transition occurs for a given entry vehicle. The bottom line is that Re_θ/M_e does not represent any physical processes. It does not by itself give correct Mach number trends and it neglects pressure-gradient, surface-temperature, and roughness effects. Using Re_θ rather than Re_x tends to reduce data scatter, but the benefit is lost in applying Re_θ to get Re_x. For entry vehicles, Re_θ/M_e might work because density is the dominant factor in Re_θ/M_e and density is very sensitive to altitude. For cruise vehicles, that sensitivity is not relevant because one is interested in the x location of transition at constant altitude. The proper analysis of transition behavior is by physics-based e~N or transient-growth methods. The use of correlations of questionable basis and reliability should be replaced by the physics-based methods.