Fluid dynamics numerical modeling of second-mode instability mechanisms at Mach 6
Date
2019
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
University of Delaware
Abstract
This research is a numerical investigation of second-mode stability behavior within hypersonic boundary layers. Two-dimensional, hypersonic boundary layer stability and transition is dominated by second-mode acoustic disturbances at freestream Mach numbers of 4 and higher as shown by Mack. However, the physical mechanisms and amplitude based prediction of the second-mode is not fully understood which are important for sustained and controlled hypersonic flight to become feasible. In this research, the modeled hypersonic flow conditions corresponded to a flared cone tested in the Boeing/AFOSR Mach-6 Quiet Tunnel at Purdue University, and 7 degree half angle straight cones with various nose radii at the new AFOSR-Notre Dame Large Mach 6 Quiet Tunnel. The methodology employed used a computational fluid dynamics (CFD) solver US3D to generate a laminar, steady state solution (basic state). Then, the basic state is fed into stability solvers. Starting with linear stability theory (LST) which is a generalized eigenvalue solver, which also serves as the initial condition for linear and nonlinear parabolized stability equations (PSE) to calculate the disturbance behavior. These stability results are then compared to experimental data and direct numerical simulations (DNS). ☐ Two recent contributions by Kuehl (2017 and 2018) were made regarding second-mode disturbances. The first was the reformulation of the nonlinear parabolized stability equations (NPSE) to quantify the finite bandwidth nature (wavepackets) of the second-mode disturbances. The second was the proposed thermoacoustic interpretation which describes the fundamental physics of second-modes as trapped acoustic waves within an acoustic impedance well. These contributions raised new questions regarding the applications and implications of second-mode behavior. These questions were investigated in this research for improved amplitude based modeling of second-mode physics. Specifically, the following objectives were achieved: wavepacket applications and implications, comparisons of PSE results with experimental data and direct numerical simulation (DNS), applications and implications of the thermoacoustic interpretation, and exploiting this to understand and develop novel second-mode control methods. ☐ Utilizing and improving the wavepacket formulation within NPSE led to second-mode amplitudes between 20% to 40% on the Purdue flared cone. This is in good agreement with Purdue experimental results of ~30%. Another important implication was the onset of spectral broadening which identifies the region where nonlinearities begin to assert themselves. This is where the amplitude ratio of the primary disturbance divided by the first harmonic begin to non-negligibly decrease when moving downstream. As such, the wavepacket NPSE showed the onset of spectral broadening was identified and produced good agreement to experimental results of amplitude ratio. Also, the wavepacket NPSE had good agreement with DNS results for the primary mode and the first harmonic. Therefore, the wavepacket NPSE is capable of improved numerical modeling and amplitude prediction of the second-mode disturbance. ☐ Regarding the thermoacoustic interpretation, it suggests that the second-mode disturbance growth or suppression is tied directly to the strength of the basic state density gradient. The interpretation was applied to identify the physical mechanism for the downstream movement of the transition front caused by increasing the nose radius of a cone. This was an important first step in understanding the blunt body paradox, where once a critical nose radius (bluntness) is reached, transition jumps forward. It was shown that if entropy disrupts the proper formation of the acoustic impedance well by diluting the density gradient, the well becomes weakened, and the second-mode disturbance is no longer able to resonate, thereby suppressing its growth. Conversely, a well-defined density gradient allows acoustic disturbances to resonate within the boundary layer inducing second-mode growth. Subsequently, a criterion was developed based on Lees and Lin generalized inflection point criterion to quantify when the density gradient is strong enough for second-modes to be present. ☐ Finally, the thermoacoustic interpretation aided in describing the behavior of second-mode amplification and damping when cooling and heating the wall of the Purdue flared cone. It was shown that cooling and heating the wall effects the acoustic impedance well length scale, thereby changing the resonant frequency of the second-mode. This led to the concept of upstream cooling and downstream heating which showed potential max N-factor damping of three compared to a non-cooled/heated wall.