Flow Similarity in Strong Swept-Shock/Turbulent-Boundary-Layer Interactions

Abstract

The separation length employed to scale unsteady phenomena in strong (separated) nominally two-dimensional (2-D) shock/turbulent-boundary-layer interactions cannot be directly extended to three-dimensional (3-D) swept interactions, due to the quasi-conical symmetry of 3-D interactions. This paper examines the issue by considering large-eddy simulations of Mach 2 canonical flows arising from plate-mounted swept compression ramps and sharp fins at various interaction strengths, which have been the subject of concurrent experimental campaigns. Several key structural features are discussed that distinguish 3-D interactions from 2-D interactions in the context of free-interaction principles and quasi-conical symmetry, including their relationship to strong crossflow and open separation. The virtual-conical-origin concept is augmented by considering inceptive effects, which motivate the introduction of an inceptive origin. The dependence of the inceptive-origin/virtual-conical-origin relationship with interaction strength yields several insights and provides a more rigorous framework to quantify inception strength than previously available. Finally, examination of the spanwise dependence of the growth of the quasi-conical separated shear layer shows that the outer (main) layer exhibits spanwise-homogeneous symmetry consistent with 2-D free-interaction theory, whereas the inner layer exhibits conical symmetry, consistent with 3-D (conical) free-interaction theory. The ramifications for shear layer and shock unsteadiness, as well as acceleration of the inner layer and secondary separation, are discussed. Recent developments and persisting fundamental challenges are discussed by Clemens and Narayanaswamy [2] and Gaitonde [3]. Significant insight has been gained through recent experimental and high-fidelity numerical efforts for canonical two-dimensional (2-D) configurations, which are spanwise homogeneous apart from side-wall effects. These include the impinging shock [4-7] and compression ramp [8,9] interactions. Comparatively less attention has been focused on the unsteady properties of canonical three-dimensional (3-D) STBLIs. These include configurations for which the mean flow is 3-D; that is, interactions that exhibit spanwise nonhomogeneity caused by the geometry/orientation of the shock generator which cannot be attributed to edge/side-wall effects. Specifically, interactions in which the shock or obstacle is swept with respect to the incoming flow are of interest. These include the sharp-fin (SF), swept-compression-ramp (SCR), and swept-impinging-shock (SIS) configurations, as commonly described [3,10]. Such interactions are of particular concern in application to supersonic/hypersonic inlets with side-wall compression, because side-wall compression may be exploited to increase the total pressure recovery [11,12]. More complex scenarios include flows with multiple interactions (shock trains) in scramjet inlet/ isolator sections, which highlight complexities associated with the dynamic coupling between canonical i...

Dynamics of strong swept-shock/turbulent-boundary-layer interactions

“…Stabilizing dissipation is provided through application of an eighth-order, Padé-type (α f = 0.45), spatial filter (Gaitonde & Visbal 2000). Shock capturing is facilitated through local upwinding of the inviscid fluxes, in regions identified by a Ducros-like shock sensor (Adler & Gaitonde 2019a). Surrounding the shocks, the inviscid fluxes are calculated via Roe flux differencing, from fifth-order, weighted essentially non-oscillatory reconstructions (Mullenix & Gaitonde 2011), without application of the spatial filter.…”

“…Alternatively, the 3-D free-interaction principle (Settles & Kimmel 1986), makes a similar argument for conical symmetry in 3-D STBLIs, in that the separation responds to the 3-D (conical) footprint of the freestream 'pseudo-inviscid' interaction. Recent results (Adler & Gaitonde 2019a) suggest that the mean-flow similarity scaling of the quasi-conical shear layers in 3-D STBLIs exhibit a mix between 2-D and 3-D free-interaction scaling; however, the ramifications of this mean-flow scaling on mid-frequency unsteadiness have not yet been described.…”

“…Consequently, in 3-D STBLIs, there is no recirculation in the strict sense, in which streamlines of the mean-flow feed back onto themselves (Panaras 1996). This observation is linked to the lack of topological separation closure in simple, swept, 3-D interactions; the separation is not closed, in that it is initiated by an attachment-node/separation-saddle pair, but a closing separation-node/saddle pair cannot be realized without breaking the conical symmetry of the interaction (Adler & Gaitonde 2019a). This differs from the separation observed in confined 2-D STBLIs, which are necessarily topologically closed near the sidewalls by additional separationnode/saddle pairs Rabey et al 2019;Xiang & Babinsky 2019) (an example of type-2 separation (Chapman & Yates 1991)); otherwise, for 2-D interactions, a semi-infinite wind tunnel or spanwise-periodic simulation domain effectively closes the separation through 2-D degeneracy (Green 1970a).…”

“…These thrusts have been prompted by several recent advances in massively parallel simulations (Poggie, Bisek & Gosse 2015) as well as time-resolved unsteady measurements of high-speed flows (Beresh et al 2015) and other novel measurement techniques (Fahringer & Thurow 2018). The effort combines experimental measurements of the SCR (Vanstone et al 2016(Vanstone et al , 2018 and SF (Baldwin et al 2016;Jones et al 2017;Arora et al 2018) interactions, along with high-fidelity large-eddy simulations (Adler & Gaitonde 2017, 2018b, 2019a of both configurations. The swept-impinging-shock (SIS) interaction is also of great interest, and is the subject of parallel experimental (Doehrmann et al 2018) and computational (Gross, Little & Fasel 2018) efforts, but is not considered here.…”

“…The primary objective of the current paper is to describe the unsteady properties of the strong, swept interactions of figure 1, using a high-fidelity validated database of 3-D STBLIs, the mean-flow similarity of which was recently described by Adler & Gaitonde (2019a). The simulation database, including flow parameters and the details of the numerical method, is summarized in § 2.…”