Graduation Semester and Year




Document Type


Degree Name

Doctor of Philosophy in Aerospace Engineering


Mechanical and Aerospace Engineering

First Advisor

Brian Dennis


A jet in counterflow is a configuration in which a jet is issued into an opposing external stream of fluid. Some of the possible applications of this configuration include study of pollutant discharge into body of water, aerodynamic flame holder in after burner, reduction of drag and cooling of bluff body by ejecting a jet of coolant gas into counterflowing stream, thrust vectoring of supersonic jets, sonic boom mitigation. The instability associated with flow reversal which is observed in this configuration of the jet leads to enhanced mixing. However, a detailed understanding of the dynamics and control is needed to make these applications practical. The goal of this thesis is to perform global stability analysis of a jet in counterflow and understand the characteristics of its stability. Above the critical values of jet Reynolds number and the jet to counterflow velocity ratio, the flowfield becomes unstable and the jet tip oscillates at a low frequency. One of the objectives of this thesis is to find these critical values. Hydrodynamic stability analysis involves the determination of eigenvalues of the perturbation equations, linearized about steady base flow and the corresponding adjoint perturbation equations. When the flow is globally unstable, it is impossible to time-march to steady state. In this research, a feedback control technique known as selective frequency damping (SFD) is implemented. The parameters involved in the SFD method are adapted based on the solution to an optimization problem. However, the SFD method is not suitable for obtaining the base flows in the presence of unstable low frequency and stationary modes. In such a case, base flow solution is obtained using Newtons method. The search for global modes is carried out using the block Krylov-Schur method. The Navier-Stokes equations, the linearized perturbation equations and the adjoint equations are numerically solved using the embedded boundary adaptive refinement strategy. The effect of non-normality of the Navier-Stokes operator on the trasnient energy amplification of perturbations is evaluated. The structural sensitivity of the jet is obtained by computing the adjoint eigenmodes and the regions in the flowfield where the growth rate and frequency of leading eigenmode are most sensitive to forcing are identified.


Global stability, Adjoint analysis, Non-modal stability analysis, Structural sensitivity analysis


Aerospace Engineering | Engineering | Mechanical Engineering


Degree granted by The University of Texas at Arlington