Fluid Dynamics & Aerodynamics

Biography

Biography: Maksim V Ustinov

Abstract

Amplification of Tollmien-Schlichting (TS) waves excited by free-stream turbulence (FST) is a dominant mechanism of laminar-turbulent transition in a boundary layer on the airplane wing. Recently FST is usually considered as a superposition of vortices moving with flow velocity. Theory and experiment show that such vortices can generate TS waves by means with interaction with strong boundary layer non-uniformity near the leading edge. Because of strong attenuation of TS wave before the neutral point, this receptivity mechanism is too weak for explanation of experimental dependence of transition Reynolds number from FST level. Alternative approach to description of TS waves generation by FST is considered here. It is based on a treatment of turbulence as a superposition of vortices moving with speed deviated from flow velocity. Part of these vortices has period and frequency equal to these parameters of TS waves. They generate instability waves near the neutral point via resonant interaction or non-localized receptivity mechanism. Amplitude method of laminar-turbulent transition prediction based on this receptivity model and evaluation of TS waves growth from linear stability theory was developed. Dependences of r.m.s. velocity pulsations from the Reynolds number for the flat plate boundary layer computed in this way for different values of turbulence level Tu are plotted in Figure 1: (a). Transition Reynolds number as function of Tu found from these data using amplitude criterion u'=0.03u∞ is presented in Figure 1: (b). Computed dependence of transition Reynolds number from Tu well describes available experimental data. Linear dependence of the critical N factor on the logarithm of Tu known as Mack’s correlation is also validated theoretically. The analytically determined proportionality coefficient of this dependence 17/6 is similar in value to 2.4 obtained from the experimental data.