Date of Award

Summer 2003

Document Type


Degree Name

Doctor of Philosophy (PhD)


Aerospace Engineering

Committee Director

Osama A. Kandil

Committee Director

Ponnampalam Balakumar

Committee Member

Robert L. Ash

Committee Member

Chuh Mei


Stability of a hypersonic boundary-layer over a compression corner was investigated numerically. The three-dimensional compressible Navier-Stokes equations were solved using a fifth-order weighted essentially non-oscillating (ArENO) shock capturing scheme to study the shock wave and boundary-layer interactions. The boundary-layer stability was studied in three distinct regions: upstream of the separation region, inside the separation region and downstream of the separation region. After the mean flow field was computed, linear stability theory was employed to predict the unstable disturbance modes in different flow regions and also to find the most amplified disturbance frequency across the compression corner. Gortler instability computations were performed to study the influence of the streamline curvatures on boundary-layer stability, and PSE(parabolized stability equation) method was employed to obtain the initial disturbances for direct numerical simulation.

To study the boundary-layer stability by direct numerical simulation, two- or three-dimensional initial disturbances were introduced at the initial streamwise location of the computational domain. Two-dimensional disturbance evolution simulation shows that two-dimensional high frequency linear disturbances grow exponentially upstream and downstream of the separation region and remain neutral in the separation region, but two-dimensional low frequency linear disturbances only grow in a narrow area inside the separation region and remain neutral upstream and downstream of the separation region. Two-dimensional nonlinear disturbances will saturate downstream of the separation region when their amplitudes reach quit large amplitude.

The three-dimensional disturbance evolution simulations show that three-dimensional linear mono-frequency disturbances are less amplified than its two-dimensional counterpart across the compression corner. The three-dimensional nonlinear mono-frequency disturbance evolution indicates that mode (0,2) is responsible for the oblique breakdown. Three-dimensional disturbances are much more amplified with the presence of two-dimensional primary disturbance due to the secondary instability. Finally, the simulations of three-dimensional random frequency disturbance evolution with the presence of a two-dimensional primary disturbance show that the secondary instability first occurs downstream of the separation region and a fundamental or K-type breakdown will be triggered by this secondary instability.