Nonmodal Growth of Traveling Waves on Blunt Cones at Hypersonic Speeds

Paredes, Pedro; Choudhari, Meelan M.; Li, Fēi; Jewell, Joseph S.; Kimmel, Roger L.

doi:10.2514/1.j058290

Cited by 45 publications

(30 citation statements)

References 44 publications

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“…Computational analysis by Cook et al 2018and Paredes et al (2019c,d) has shown significant non-modal growth of both planar and oblique travelling disturbances that peak within the entropy layer and above the boundary-layer edge. The linear, non-modal amplification of the Mack's energy norm associated with the non-stationary disturbances was lower than that for the three-dimensional stationary disturbances, but increased as the nose-tip bluntness was increased (Paredes et al 2019c). Therefore, Paredes et al (2019c) suggested that non-stationary non-modal travelling disturbances that peak within the entropy layer could lead to transition onset in the absence of appreciable modal instability amplification.…”

Section: Introductionmentioning

confidence: 93%

“…The linearly optimal perturbation that results in maximum energy gain at a specified downstream position is used as the inflow condition for the parabolic integration of the nonlinear parabolized stability equations (PSE) and DNS solvers. The inflow profiles used in the present nonlinear study are computed following the linear non-modal analysis of Paredes et al (2019c), who had also established the ability of PSE to adequately capture the linear transient growth over the flow configurations of interest via comparisons with the solutions of linearized Navier-Stokes equations.…”

Section: Theorymentioning

confidence: 99%

“…Density and temperature are denoted by ρ and T. The basic state variables are homogeneous in the azimuthal direction. The linear analysis conducted by Paredes et al (2019c) exploited this characteristic and also introduced the Fourier decomposition of the disturbance variables in the azimuthal direction via the azimuthal wavenumber m. Here, the nonlinear, plane-marching PSE technique is used with Fourier collocation discretization along the azimuthal direction, although a nonlinear, line-marching PSE could also be used for the present flow problem.…”

Section: Parabolized Stability Equationsmentioning

confidence: 99%

“…A detailed modal instability analysis of the present configuration was performed by Jewell et al (2018) and Paredes et al (2019c) at the flow condition of interest and only Mack-mode instabilities had positive growth rates in this case. All entropy-layer modes and first-mode instabilities were found to be damped.…”

Section: Linear Disturbance Evolutionmentioning

confidence: 99%

See 3 more Smart Citations

Mechanism for frustum transition over blunt cones at hypersonic speeds

Paredes

Choudhari

2020

J. Fluid Mech.

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Section: Introductionmentioning

confidence: 93%

Section: Theorymentioning

confidence: 99%

Section: Parabolized Stability Equationsmentioning

confidence: 99%

Section: Linear Disturbance Evolutionmentioning

confidence: 99%

See 2 more Smart Citations

Mechanism for frustum transition over blunt cones at hypersonic speeds

Paredes

Choudhari

2020

J. Fluid Mech.

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“…The second kind of factor influencing hypersonic boundary layer receptivity is wall disturbances, including blow-suction disturbances [ 15 ], wall deformation [ 16 ], local heating/cooling on the wall [ 17 ], and nose-tip bluntness [ 18 , 19 ]. The effect of roughness elements on the hypersonic boundary layer receptivity mechanism has been researched.…”

Section: Introductionmentioning

confidence: 99%

Effect of a Roughness Element on the Hypersonic Boundary Layer Receptivity Due to Different Types of Free-Stream Disturbance with a Single Frequency

Shi

Wang

et al. 2019

Entropy

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The hypersonic flow field around a blunt cone was simulated using a high-order finite difference method. Fast acoustic waves, slow acoustic waves, entropy waves, and vortical waves were introduced into the free-stream to determine the influence of a free-stream with disturbances on the hypersonic flow field and boundary layer. The effect of disturbance type on the evolution of perturbations in the hypersonic boundary layer was analyzed. Fast Fourier Transform was adopted to analyze the effect of the disturbance type on the evolution of different modes in the boundary layer. A roughness element was introduced into the flow field to reveal the impact of the roughness element on hypersonic boundary layer receptivity. The results showed that a free-stream with disturbances affected the hypersonic flow field and boundary layer; acoustic waves had the greatest influence. The impact of slow acoustic waves on the flow field was mainly concentrated in the region between the shock and the boundary layer, whereas the influence of fast acoustic waves was mainly concentrated in the boundary layer. Multi-mode perturbations formed in the boundary layer were caused by the free-stream with disturbances, wherein the fundamental mode was the dominant mode of the perturbations in the boundary layer caused by fast acoustic waves, entropy waves, and vortical waves. The dominant modes of the perturbations in the boundary layer caused by slow acoustic waves were both the fundamental mode and the second harmonic mode. The roughness element changed the propagation process of different modes of perturbations in the boundary layer. In the downstream region of the roughness element, perturbations in the boundary layer caused by the slow acoustic waves had the greatest influence. The second harmonic mode in the boundary layer was significantly suppressed, and the fundamental mode became the dominant mode. The effects of fast acoustic waves and entropy waves on the boundary layer receptivity were similar, except the amplitude of the perturbations in the boundary layer caused by the fast acoustic waves was larger.

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Free-stream receptivity of a hypersonic blunt cone using input–output analysis and a shock-kinematic boundary condition

Cook

Nichols

2022

Theor. Comput. Fluid Dyn.

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Understanding the receptivity of hypersonic flows to free-stream disturbances is crucial for predicting laminar to turbulent boundary layer transition. Input-output analysis as a receptivity tool considers which free-stream disturbances lead to the largest response from the boundary layer using the global linear dynamics. Two technical challenges are addressed. First, we extend recent work by Kamal et al. [1] and restrict the allowable forcing to physically realizable inputs via a free-stream boundary modification to the classic input-output formulation. Second, we develop a hierarchical input-output (H-IO) analysis which allows us to solve the three-dimensional problem at a fraction of the computational cost otherwise associated with directly inverting the fully three-dimensional resolvent operator. Next, we consider Mach 5.8 flows over a sharp cone and blunt cone with a 3.6 mm spherically blunt tip. H-IO correctly predicts that the sharp cone boundary layer is most receptive to slow acoustic waves at an optimal incidence angle of 10 • , validating the method. We then investigate the effect of free-stream disturbances on the blunt cone boundary layer, and identify two distinct vorticity-dominated receptivity mechanisms for the oblique first mode instability at 10 kHz and an entropy layer instability at 75 kHz. Our results reveal these receptivity processes to be highly three-dimensional in nature, involving both the nose-tip and excitation along narrow bands at certain azimuthal angles along the oblique shock downstream. We interpret these processes in terms of critical angles from linear shock/perturbation interaction theory.

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Nonmodal Growth of Traveling Waves on Blunt Cones at Hypersonic Speeds

Cited by 45 publications

References 44 publications

Mechanism for frustum transition over blunt cones at hypersonic speeds

Mechanism for frustum transition over blunt cones at hypersonic speeds

Effect of a Roughness Element on the Hypersonic Boundary Layer Receptivity Due to Different Types of Free-Stream Disturbance with a Single Frequency

Free-stream receptivity of a hypersonic blunt cone using input–output analysis and a shock-kinematic boundary condition

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