New receptivity mechanisms of supersonic boundary layers
File(s)
Author(s)
Gonzalez Hernandez, Carlos
Type
Thesis
Abstract
In this thesis we investigate, using high-Reynolds-number asymptotic techniques,
three problems related to the receptivity of supersonic boundary layers. The first
problem concerns two new receptivity mechanism to impinging acoustic waves,
whose phase velocity (O(R−1/8 U)) is much slower than the free-stream velocity
U, where R is the Reynolds number based on L, the distance to the leading edge,
and U. A sound wave on this scale has the special property that it induces in the
boundary layer a viscous response that is greater by a factor of O(R^1/8) than the
disturbance in the free-stream. The sound-sound, or sound-roughness, interactions
generate a forcing in resonance with a neutral T-S wave. The triple-deck formalism
is adopted to describe impingement and reflection of the acoustic waves, and
ensuing receptivity, allowing the coupling coefficient to be calculated. The two
receptivity processes are much more effective compared with those involving usual sound waves, with the coupling coefficient being greater by a factor of O(R^1/4) and O(R^1/8) in the S-S (sound-sound) and S-R (sound-roughness) interactions, respectively. A parametric study is conducted for representative T-S waves, to
assess the influence of the streamwise and spanwise wavenumbers, and the phase
speed of the sound wave. The second problem deals with the connection of the inviscid and viscous branches of instability modes in supersonic boundary layers, following the previous investigation
of Goldstein and Ricco (2018). The upper and lower branches of the neutral curve are connected, as indicated by finite-Reynolds-number calculations. A new intermediate regime, identified in a previous preliminary study (Yang, 2017), is discussed further in the present work. This regime is described by triple-deck theory, although its scaling is not standard. The instability is studied and the
dispersion relation is calculated for different Mach numbers. It is shown that this regime was missed by the previous work of Goldstein and Ricco (2018). The third problem concerns the study of a new mechanism for the generation of T-S waves, which involves an incident sound wave with its frequency and wavelength on the triple-deck scale and free-stream vortical disturbances with spanwise wavelength on the triple-deck scale too but long streamwise wavelength. The longwavelength vortical disturbances with O(\epsilon_v) intensity in the free-stream induce in the boundary layer much larger O(\epsilon_v R^3/8) streamwise velocity in response to them, which manifests as streaks. With the appropriate choice of the spanwise wavelength on the triple deck scale, the acoustic signature and streaks interact in the main boundary layer as well as in the lower deck, to generate a forcing in resonance with a neutral T-S wave. The receptivity of this mechanism is found to
be greater than those in Hernández and Wu (2019) and Wu (1999) by a factor of O(R^1/8) and O(R^3/8), respectively.
three problems related to the receptivity of supersonic boundary layers. The first
problem concerns two new receptivity mechanism to impinging acoustic waves,
whose phase velocity (O(R−1/8 U)) is much slower than the free-stream velocity
U, where R is the Reynolds number based on L, the distance to the leading edge,
and U. A sound wave on this scale has the special property that it induces in the
boundary layer a viscous response that is greater by a factor of O(R^1/8) than the
disturbance in the free-stream. The sound-sound, or sound-roughness, interactions
generate a forcing in resonance with a neutral T-S wave. The triple-deck formalism
is adopted to describe impingement and reflection of the acoustic waves, and
ensuing receptivity, allowing the coupling coefficient to be calculated. The two
receptivity processes are much more effective compared with those involving usual sound waves, with the coupling coefficient being greater by a factor of O(R^1/4) and O(R^1/8) in the S-S (sound-sound) and S-R (sound-roughness) interactions, respectively. A parametric study is conducted for representative T-S waves, to
assess the influence of the streamwise and spanwise wavenumbers, and the phase
speed of the sound wave. The second problem deals with the connection of the inviscid and viscous branches of instability modes in supersonic boundary layers, following the previous investigation
of Goldstein and Ricco (2018). The upper and lower branches of the neutral curve are connected, as indicated by finite-Reynolds-number calculations. A new intermediate regime, identified in a previous preliminary study (Yang, 2017), is discussed further in the present work. This regime is described by triple-deck theory, although its scaling is not standard. The instability is studied and the
dispersion relation is calculated for different Mach numbers. It is shown that this regime was missed by the previous work of Goldstein and Ricco (2018). The third problem concerns the study of a new mechanism for the generation of T-S waves, which involves an incident sound wave with its frequency and wavelength on the triple-deck scale and free-stream vortical disturbances with spanwise wavelength on the triple-deck scale too but long streamwise wavelength. The longwavelength vortical disturbances with O(\epsilon_v) intensity in the free-stream induce in the boundary layer much larger O(\epsilon_v R^3/8) streamwise velocity in response to them, which manifests as streaks. With the appropriate choice of the spanwise wavelength on the triple deck scale, the acoustic signature and streaks interact in the main boundary layer as well as in the lower deck, to generate a forcing in resonance with a neutral T-S wave. The receptivity of this mechanism is found to
be greater than those in Hernández and Wu (2019) and Wu (1999) by a factor of O(R^1/8) and O(R^3/8), respectively.
Version
Open Access
Date Issued
2020-09
Date Awarded
2021-09
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Wu, Xuesong
Sponsor
Engineering and Physical Sciences Research Council
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)