Boundary-Layer Receptivity and Integrated Transition Prediction

Abstract

The adjoint p a r a b o l d stability equations (BE) formulation is used to calculate the boundary layer receptivity to localized surface roughness and suction for compressible boundary layers. Receptivity efficiency functions predicted by the adjoint PSE approach agree well with results based on other nonparallel methods including linearized Navier-Stokes equations for both Tollmien-Schlichting waves and crossflow instability in swept wing boundary layers. The receptivity efficiency function can be regarded as the Green's function to the disturbance amplitude evolution in a nonparallel (growing) boundary layer. Given the Fourier transformed geometry factor distribution along the chordwise direction, the linear disturbance amplitude evolution for a finite size, distributed nonuniformity can be computed by evaluating the integral effects of both disturbance generation and linear amplification. The synergistic approach via the linear adjoint PSE for receptivity and nonlinear PSE for disturbance evolution downstream of the leading edge forms the basis for an integrated transition prediction tool. Eventually, such physics-based, high fdelity prediction methods could simulate the transition process from the disturbance generation through the nonlinear breakdown in a holistic manner.

Computational Analysis of the G-III Laminar Flow Glove

“…Saric et al 19 discovered that forcing small wavelength disturbances (i.e., the "control" mode) at relatively high amplitudes changes the boundary-layer mean flow such that the growth of more dominant larger wave length disturbances (i.e., the "target" mode) is pushed downstream, thus delaying transition. This concept has been studied by using nonlinear Parabolized Stability Equations (PSE) 20 and Direct Numerical Simulations (DNS) 21 and both these analyses support the soundness of the fundamental concept. In practice, the control mode is introduced via discrete spanwise periodic roughness elements placed near the neutral point of the instability diagram.…”

Spatially developing secondary instabilities in compressible swept airfoil boundary layers

“…Specifically, the control input must be large enough to provide the desired control action (viz., sufficient modification of the basis state in order to induce the required stabilization of the "dangerous" modes), however, it cannot be excessively large as to precipitate premature transition (and/or reduce the extent of transition delay, as briefly alluded to in section III in the context of the experiments in [27]). As shown below, the secondary instability analysis (in conjunction with receptivity predictions [29]) may provide useful guidance to help select an appropriate range of control input amplitudes.…”

Roughness Based Crossflow Transition Control: A Computational Assessment

“…A number of investigations in existing literature have addressed the former problem (e.g. [9]), but the latter problem does not appear to have been tackled so far. Thus, parametric studies encompassing a range of initial amplitudes of the stationary crossflow vortex as well as the secondary instability modes are used to gauge the resulting variation sin transition characetristics.…”

“…Nonlinear development and breakdown of secondary instability are again computed using LASTRAC. The selection of grid parameters and other aspects of the numerical solution was based on extensive experience with such calculations for similar classes of flows [6,7,9,10], and spot checks were made to ensure that any variations with respect to modifications to those choices were sufficiently small.…”