UC San Diego

Theoretical and numerical techniques are used to investigate three different problems involving non-isothermal fluid flow.

The first part of the dissertation investigates flame dynamics in a strained mixing layer established between two-dimensional counterflowing streams of fuel and oxidizer. When a one-step Arrhenius chemistry model is employed for the chemistry description, the numerical computations for small values of the stoichiometric mixture fraction yield a C-shaped premixed front with a trailing diffusion flame attached to one of its ends, a structure that is markedly different to the tri-brachial structure found in previous studies. Analytic predictions from the G equation are found to agree well with the numerical results. An explanation for these unexpected shapes is obtained by analyzing the variation with dilution of the burning velocity of planar premixed flames. Detailed-chemistry results are presented next for H$_2$-O$_2$-N$_2$ systems with high degrees of N$_2$ dilution, such that the resulting flame temperature lies close to the crossover value. Under these near-critical conditions, the flame dynamics is found to be strongly dependent on the initial conditions. A bifurcation diagram is presented in the stoichiometric mixture-fraction vs. strain-rate plane that identifies six different combustion regimes involving four different flame types, namely, one-dimensional diffusion flames, propagating/retreating edge flames, broken flame tubes, and isolated flame tubes.

A spherically symmetric heterogeneous fuel-oxidizer system is investigated next as an ignition model for hypergolic gelled propellants. Depending on the conditions, the fuel-oxidizer system may approach an explosive mode or it may settle into a steady-state mode. The critical condition defining the transition between these two states is determined analytically and the ignition time for the explosive mode is approximated by solving an integral equation for the interface temperature, employing activation-energy asymptotics.

A non-Boussinesq stability analysis of natural-convection boundary-layer flows over hot inclined surfaces is presented in the last part of the dissertation. Depending on the inclination angle, the disturbances are seen to evolve into either streamwise vortices or spanwise traveling waves. The critical inclination angle at which transition between the two instability modes occurs is calculated as a function of wall-to-ambient temperature ratio. For sufficiently large values of this ratio, wave modes are found to be always predominant, regardless of the inclination angle.