Numerical Study toward Verification of Analogy between Hypersonic Turbulent Transition and Directed Percolation

Abstract

Analogy between the hypersonic turbulent transition and directed percolation (DP), a simple stochastic model, was verified to provide a new insight for predicting the transition which increases the aerodynamic heating. A direct numerical simulation was performed on a Mach number 6 over a flat plate to obtain the values required for the v erification. A blowing and suction disturbance was introduced to the laminar solution to trigger the transition to turbulence. By analyzing the flow behavior in the turbulent transition region, one of the critical exponents of DP was estimated and was compared with the theoretical value. The turbulent fraction at each Reynolds number based on the distance from the leading edge of the flat plate is required to obtain the critical e xponent. The critical exponent depends on the threshold value and the distance from the wall, and some of the critical exponents did not agree with the theoretical value or did not reproduce the turbulent fraction distribution. Conversely, some of the critical exponents obtained from the present numerical simulation results were close to the theoretical value. This suggests that hypersonic turbulent transitions could also belong to DP universality class.