Vijay Gopal

Graduation Semester and Year




Document Type


Degree Name

Doctor of Philosophy in Aerospace Engineering


Mechanical and Aerospace Engineering

First Advisor

Luca Maddalena


Mixing enhancement in supersonic flow is an important domain of research for enabling the realization of efficient and scalable high speed air-breathing engines (scramjet). Introducing streamwise vorticies in supersonic flow and tailoring their interactions for mixing enhancement is the primary motivation for the present research study. Leveraging the research performed in the group at the Aerodynamics Research Center (ARC), systematic experimental studies on mixing enhancement is carried out in supersonic flows by tailoring the selected modes of streamwise vortex interactions with the aid of in-house developed reduced order method VorTX. This method utilizes the lifting line-vortex theory in supersonic flow to perform rapid simulations of streamwise vortex-interactions that serves as a guide to design the mixing experiments. One of the difficulties associated with scaling the simulations to higher Mach numbers (M>4) arise from the strong influence of the singularities along the Mach cones emanating from the lifting line-vortex that results in physically inconsistent solution. In this work a fundamental study on vorticity distribution in linearized supersonic flow is carried out. The origin of the aforementioned singularities on the Mach cone is discussed in detail, and the potential candidates for vorticity distribution are proposed to eliminate the singularities and to provide a physically consistent solution of the flow field in supersonic flow. This study presents the successful solution for the elimination of the singularities that has allowed to extend the capability of VorTX to simulate vortex-interactions at higher Mach numbers. Experimental studies on supersonic mixing were carried out using a strut injection platform with vortex generating ramps to introduce streamwise voriticies in supersonic flow. The geometrical configuration of the ramps are chosen using the upgraded VorTX simulations to target the experimental study of two selected modes of vortex interactions. One is the merging of two co-rotating vorticies and the other is the non-merging case where the vorticies interact but do not merge. Mixing measurements in supersonic flow were carried out using the Filtered Rayleigh Scattering (FRS) technique. The measurement yields the mole-fraction of helium (injectant) in a binary mixture of air and helium in supersonic flow. The distributions of helium mole-fraction in the cross flow planes are used to draw conclusions on the level of mixing in the two modes of vortex-interaction. The FRS technique requires two independent experiments. One with helium injection in supersonic air flow and the other with air injection in an identical supersonic air flow. At a given cross-flow plane, to obtain the helium mole-fraction distribution using the FRS signals it is assumed that the total number density is matched in both the experiments. To enhance the reliability of the FRS measurement technique, it is important to minimize and quantify the systematic errors that arise from the assumptions made, particularly, the assumption on matching the total number density. In this work, a method to reduce the systematic errors in FRS experiments is proposed for a canonical case study of a rectangular jet in supersonic flow. To do this, a reduced order model for a rectangular jet in supersonic air flow is successfully developed in order to guide the selection of appropriate injector's plenum conditions to minimize the systematic errors in the future FRS experiments and to retrospectively evaluate and correct the FRS measurements for systematic errors in previously available FRS data on parallel strut injection in supersonic flow.


Supersonic mixing, Vortex dynamics, Filtered Rayleigh scattering


Aerospace Engineering | Engineering | Mechanical Engineering


Degree granted by The University of Texas at Arlington