Jung J. Choi

Effect of combustion on near-critical swirling flow

This paper examines the manner in which heat release resulting from premixed combustion alters the nature of near-critical, axisymmetric, swirling flow in a straight circular pipe. Attention is confined to dilute premixtures so that exothermicity is weak and a small-disturbance approach applicable. The weak exothermicity is found to have a considerably larger effect on the flow. In the absence of combustion, the columnar solution loses stability via a transcritical bifurcation as the level of swirl rises beyond a critical value. Exothermicity splits the bifurcation portrait into two branches separated by a gap in the level of swirl; within this gap steady, near-columnar solutions cease to exist. As a result the critical value of swirl for a combusting flow is smaller than that for the cold flow. For a certain range of swirl below this critical value and for small enough heat release, the solution branch is double-valued and yields two equilibria, one corresponding to a near-columnar state and the other pointing to the appearance of a large-amplitude structure. For larger heat release the double-valued branch loses its fold, suggesting the gradual appearance of large-amplitude disturbances with increasing levels of swirl. The mechanism that governs the behaviour of the reactive flow with swirl, and the relevance of the results to combustion states with vortex breakdown, are also discussed.

Bifurcation and stability of near-critical compressible swirling flows

The bifurcation and global nonlinear stability of near-critical states of a compressible and axisymmetric swirling flow of a perfect gas in a finite-length straight, circular pipe is studied. This work extends the bifurcation and stability analyses of Wang and Rusak [Phys. Fluids 8, 1007 (1996); Wang and Rusak Phys. Fluids8, 1017 (1996)] to include the influence of Mach number on the flow dynamics. The first- and second-order equations of motion for the evolution of small axially symmetric perturbations on a base columnar state are developed. These equations are reduced to an eigenvalue problem for the perturbation shape function and critical swirl ratio and a model ordinary differential equation for the nonlinear evolution of the perturbations’ amplitude as function of swirl level and Mach number. It is found that noncolumnar equilibrium states bifurcate from the branch of the base columnar equilibrium states at the critical swirl ratio of a compressible vortex flow in the form of a transcritical bifurca...

Numerical simulation of premixed chemical reactions with swirl

Direct numerical simulation is used to study the development of exothermic chemical reactions in a dilute, premixed, low speed, inviscid, axisymmetric, swirling flow in a straight, open, cylindrical pipe. Attention is focused on the complex interplay between the swirl and heat release of the chemical reaction and the objective is to determine, as a function of exothermicity, the critical swirl level corresponding to the first appearance of vortex breakdown in the reactive flow. It is found that for a given exothermicity, a large-amplitude structure develops around the pipe axis as the swirl level increases, and a near-stagnant breakdown zone appears when the swirl exceeds a critical level. These features are accompanied by significant changes in the temperature and reactant fields and the appearance of a hot core close to the inlet. As exothermicity is raised from low levels to higher, the critical swirl exhibits a nonlinear change; it first decreases and then, above a certain level of exothemicity, increases. An analysis of the governing equations attributes this behaviour to the nonlinear interaction between the advection of azimuthal vorticity and the baroclinic effects resulting from the coupling between the velocity and temperature gradients.

A small-disturbance model of transonic combustion

A new small-disturbance model for a steady, lean, premixed combustion at transonic speeds in a channel of slightly varying area is presented. Attention is confined to dilute premixtures so that exothermicity is weak. The study uses a distinguished limit type of analysis where the nonlinear interactions between (i) the near-sonic speed of the flow, (ii) the small changes in geometry from a straight channel, and (iii) the small heat release due to the one-step first-order Arrhenius chemical reaction, are explored. The asymptotic analysis results in the similarity parameters that govern the reacting flow field. Also, the flow can be described by a nonhomogeneous (extended) transonic small-disturbance (TSD) equation which is coupled with an ordinary differential equation for the calculation of the reactant mass fraction in the combustible gas. An iterative numerical scheme which combines the Murman and Cole method for the solution of the TSD equation with Simpsons integration rule for the estimation of the reactant mass fraction is developed. It is demonstrated that steady-state solutions of the compressible reacting flow problem with detonations behind shock waves can be found. The model is used to study transonic combustion at various inlet Mach numbers, amounts of incoming reactant mass, reaction rates, and channel geometries.