Roughness Based Crossflow Transition Control: A Computational Assessment

Abstract

A combination of parabolized stability equations and secondary instability theory has been applied to a low-speed swept airfoil model with a chord Reynolds number of 7.15 million, with the goals of (i) evaluating this methodology in the context of transition prediction for a known configuration for which roughness based crossflow transition control has been demonstrated under flight conditions and (ii) of analyzing the mechanism of transition delay via the introduction of discrete roughness elements (DRE). Roughness based transition control involves controlled seeding of suitable, subdominant crossflow modes, so as to weaken the growth of naturally occurring, linearly more unstable crossflow modes. Therefore, a synthesis of receptivity, linear and nonlinear growth of stationary crossflow disturbances, and the ensuing development of high frequency secondary instabilities is desirable to understand the experimentally observed transition behavior. With further validation, such higher fidelity prediction methodology could be utilized to assess the potential for crossflow transition control at even higher Reynolds numbers, where experimental data is currently unavailable.

Stabilization of a swept-wing boundary layer by distributed roughness elements

“…Also, for this configuration, NPSE solutions confirmed the experimental observations (cf. Li et al 2009). …”

Nonlinear development and secondary instability of traveling crossflow vortices

“…In addition, for monitoring the development of secondary instability using NPSE, 5 Fourier modes are used to resolve the time evolution, i.e., m ranges from −5 to 5. Previous experiences with and tests on similar problems 18,19,31,32 show that the grid resolutions described above are sufficient to resolve all relevant scales up to the transition location for the problems at hand.…”

“…Figure 3(a) shows comparisons of the nonlinear development of stationary and traveling crossflow vortices of the same spanwise wavelength (λ z = 8 mm) and the same initial amplitude (A init = 1 × 10 −5 ). This particular spanwise wave length was chosen because the linear and nonlinear PSE computations by Li et al 31,32 had indicated the crossflow vortex with λ z = 8 mm to be one of the most likely stationary modes to cause transition. The essential results of Ref.…”

“…The main difference between the primary and secondary stability analyses is that the basic state for the secondary modes (i.e., the mean boundary layer flow modified by the primary crossflow mode) varies in both surface normal and spanwise directions and, hence, the instability characteristics of the secondary modes must be analyzed using a planar, partial differential equation based eigenvalue problem, rather than as an ordinary differential equation based eigenvalue problem for the classical analysis. The selection of grid and other aspects of the numerical solution were based on extensive experience with similar class of flows 3,16,19,[29][30][31][32][33] and checks were made to ensure that the impact of variations with respect to those choices was negligible.…”

Excitation of Crossflow Instabilities in a Swept Wing Boundary Layer

“…24 in the context of modeling transition delay via discrete roughness elements (DREs). By applying the same methodology in the absence of any DREs, transition onset location was predicted to shift downstream by approximately 15 percent of the chord length for each orderof-magnitude reduction in the initial amplitude of the dominant 4.5mm stationary crossflow mode.…”