Spatial linear global instability analysis of the HIFiRE-5 elliptic cone model flow

Abstract

The linear instability of the three-dimensional boundary-layer over the HIFiRE-5 flight test geometry, i.e. a rounded-tip 2:1 elliptic cone, at Mach 7, has been analyzed through spatial BiGlobal analysis, in a effort to understand transition and accurately predict local heat loads on next-generation flight vehicles. The results at an intermediate axial section of the cone, Rex ≈ 8 × 10 5 , show three different families of spatially amplified linear global modes, the attachment-line and cross-flow modes known from earlier analyses, and a new global mode, peaking in the vicinity of the minor axis of the cone, termed "center-line mode". We discover that a sequence of symmetric and anti-symmetric centerline modes exist and, for the basic flow at hand, are maximally amplified around F * = 130 kHz. The wavenumbers and spatial distribution of amplitude functions of the centerline modes are documented.

Prediction of Transition Locations in Regions of the Minor Axis of Hypersonic Elliptic Cones Using the BiGlobal-$e^N$ Method

“…The eigenfunction shape of sinuous Ymode in Fig. 5 is qualitatively consistent with that of the anti-symmetric mode obtained by Paredes and Theofilis [23][24][25] for a larger vehicle model. Similarly, the eigenfunction shape of varicose Y-mode in Fig.…”

“…Similarly, the eigenfunction shape of varicose Y-mode in Fig. 5 is qualitatively consistent with that of the symmetric mode in references [23][24][25]. The modulus | û| of the varicose mode is the same as that of the sinuous mode.…”

“…More specific parameters were provided by Juliano et al [18]. Although this vehicle model is smaller than that of Paredes and Theofilis [23][24][25], we can still compare our results with those of Paredes and Theofilis [23][24][25] qualitatively. The working conditions here are the same as those for Juliano et al [18], as shown in Table 3.…”

“…Choudhari et al [22] interpreted this as a new kind of unstable mode rather than a second mode perturbation. The approach of Paredes and Theofilis [23] was a milestone on the route to solving this problem. They undertook a BiGlobal stability analysis at a streamwise location of the 2 : 1 elliptic cone at Mach number 7 and found four unstable modes in the region of the minor axis, including two sinuous modes and two varicose modes.…”

Assessment of Linear Methods for Analysis of Boundary Layer Instabilities on a Finned Cone at Mach 6

“…Over the last two decades, a number of methods for predicting the initial growth of boundary-layer instabilities on complex shapes in hypersonic flow have been developed. These methods include spatial BiGlobal analysis [14,15], plane-marching PSE [16,17], One-Way Navier Stokes (OWNS) [18], linearized Direct Numerical Simulation (LDNS) [19], forced DNS coupled with sparsity-promoting Dynamic Mode Decomposition [20], Wavepacket Tracking with Adaptive Mesh Refinement (AMR-WPT) [21], and Input/Output (I/O) analysis [22]. All of these methods are linear and 2 Distribution Statement A: Approved for Public Release; Distribution Unlimited.…”