Receptivity of the compressible boundary layer to entropy waves
File(s)
Author(s)
Keshari, Sharad
Type
Thesis
Abstract
A high Reynolds number compressible gas flow over a flat plate with a roughness element is considered. It is known that small amplitude perturbations in the free-stream can be decomposed in three modes, namely acoustic, vorticity and entropy waves. Boundary layer receptivity due to the first two have been studied extensively in the literature before but entropy waves were not given attention. In this research, the interaction of entropy waves in free stream with the compressible boundary layer is studied. The focus is only on linear receptivity and thus the roughness considered is assumed shallow. The research has been conducted for the cases of two-dimensional and three-dimensional roughness.
The analysis of flow in subsonic regime for the flow around a two-dimensional roughness is performed in the context of triple-deck theory. An expression for pressure in the near-wall viscous sublayer downstream of roughness has been derived. It is found that this pressure is directly proportional to the height of roughness and amplitude of oncoming entropy waves. It also depends on the Fourier transform of roughness shape function and the so-called receptivity coefficient which measures the efficiency of receptivity process. It is shown that the receptivity process becomes stronger both with increasing angular frequency of entropy waves and free-stream Mach number. The corresponding behaviors are shown by suitable plots of receptivity coefficient. It is found that the strength of receptivity to entropy waves is comparable to that to vorticity waves but weaker than to acoustic waves. The methodology employed for transonic receptivity is same as in the case of subsonic receptivity despite that the triple-deck region assumes different asymptotic scales. A mathematical expression for transonic receptivity coefficient is deduced.
The three-dimensional roughness problem in subsonic regime has been studied using a three-dimensional version of triple-deck theory and the pressure is computed by evaluating the inverse-Fourier transforms computed numerically. Two examples of roughness shapes namely Gaussian and skewed roughness are considered. For Gaussian roughness, it is found that the pressure amplitude dampens upto a finite distance in streamwise direction. The limiting case of transonic regime has also been studied for both types of roughness and again it is observed that the pressure amplitude dampens in streamwise direction.
The thesis concludes with a receptivity analysis when entropy waves appear as a initial condition in the free-stream flow. The corresponding initial boundary value problem has been formulated and solved numerically. It is found that a pressure wave packet forms downstream of roughness. With increasing free-stream Mach numbers and angular frequency of entropy waves, the amplitude of pressure perturbations increases but the overall shape of wavepacket remains the same. The amplification rate of pressure perturbations and the group velocity of the wave packet are calculated using the method of steepest descent. It is observed that the amplification rate achieves a maxima for certain group velocity and a numerical value of maximum amplification rate is calculated.
The analysis of flow in subsonic regime for the flow around a two-dimensional roughness is performed in the context of triple-deck theory. An expression for pressure in the near-wall viscous sublayer downstream of roughness has been derived. It is found that this pressure is directly proportional to the height of roughness and amplitude of oncoming entropy waves. It also depends on the Fourier transform of roughness shape function and the so-called receptivity coefficient which measures the efficiency of receptivity process. It is shown that the receptivity process becomes stronger both with increasing angular frequency of entropy waves and free-stream Mach number. The corresponding behaviors are shown by suitable plots of receptivity coefficient. It is found that the strength of receptivity to entropy waves is comparable to that to vorticity waves but weaker than to acoustic waves. The methodology employed for transonic receptivity is same as in the case of subsonic receptivity despite that the triple-deck region assumes different asymptotic scales. A mathematical expression for transonic receptivity coefficient is deduced.
The three-dimensional roughness problem in subsonic regime has been studied using a three-dimensional version of triple-deck theory and the pressure is computed by evaluating the inverse-Fourier transforms computed numerically. Two examples of roughness shapes namely Gaussian and skewed roughness are considered. For Gaussian roughness, it is found that the pressure amplitude dampens upto a finite distance in streamwise direction. The limiting case of transonic regime has also been studied for both types of roughness and again it is observed that the pressure amplitude dampens in streamwise direction.
The thesis concludes with a receptivity analysis when entropy waves appear as a initial condition in the free-stream flow. The corresponding initial boundary value problem has been formulated and solved numerically. It is found that a pressure wave packet forms downstream of roughness. With increasing free-stream Mach numbers and angular frequency of entropy waves, the amplitude of pressure perturbations increases but the overall shape of wavepacket remains the same. The amplification rate of pressure perturbations and the group velocity of the wave packet are calculated using the method of steepest descent. It is observed that the amplification rate achieves a maxima for certain group velocity and a numerical value of maximum amplification rate is calculated.
Version
Open Access
Date Issued
2022-09
Date Awarded
2023-11
Copyright Statement
Creative Commons Attribution NonCommercial NoDerivatives Licence
Advisor
Ruban, Anatoly
Mughal, Mohammed
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)