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Time-averaged predictions from unsteady solutions of the two-dimensional Navier-Stokes equations are contrasted with Reynolds-averaged results for a reacting flow problem in a high pressure combustor. The goal is to determine whether the two-dimensional unsteady approximation can be useful as an engineering analysis in problems for which time-averaged quantities are of primary interest. The conditions are taken from an experiment in which non-premixed gaseous oxygen and hydrogen were injected into a combustion chamber through coaxial channels. The resulting flowfield is dominated by a large recirculation zone arising from the back-step created by the injector. The results of steady and time-averaged, unsteady solutions are strikingly different. The unsteady simulation produces strong unsteady structures whose time-averaged results lead to a much wider flame zone, a different recirculation zone structure, and a substantially different wall heat flux. The time-averaged calculations yield the correct combustor chamber pressure and compare considerably more favorably with heat flux measurements than do the RANS results. The two-dimensional approximation, however, overstates the unsteady vortex roll up and precludes large-scale mixing across the axis of symmetry, thereby giving deficient predictions near the centerline. Overall, the present results indicate that capturing large-scale unsteady characteristics can provide more accurate predictions of recirculation dominated reacting flows and suggest that two-dimensional, time-averaged solutions represent a potentially useful engineering tool for problems of this nature while also serving as a precursor for full three-dimensional simulations.

Source terms often appear in various fluid dynamic problems. These source terms not only have an important impact on the physics of the flow but they can also impact the reliability of CFD algorithms. A general recommendation for differencing negative value sources (sinks) is to treat them implicitly, while positive value sources (sources) should be evaluated explicitly. Although this provides improvements compared with evaluating all terms in the same manner, sources with positive values, in particular, often cause convergence difficulties. The present paper addresses the reasons for these difficulties and combines a new source term evaluation method with time step limitation for convection and diffusion terms to give more robust capability. The method is verified by a combination of stability analysis followed by computational experiments to validate the stability findings in meaningful problems. The source Jacobian arising from a twoequation k-� turbulence model is taken as an example to demonstrate our findings.

The initial transient leading to stationary conditions in unsteady combustion simulations is investigated by considering flow establishment in model combustors. Quiescent initial conditions with the chamber initially filled with an inert, hot gas are used to provide physically realistic starting conditions and robust, reliable combustion initiation. Transient processes are visualized by using a distinct initial fluid in the combustor whose concentration is tracked as it is expelled. The duration of the transient is shown to be dependent on the characteristic turn-over time for recirculation zones and the time for the chamber pressure to reach steady conditions. Substantial changes in the initial condition did not materially affect the length of the transient. Different combustor geometries changed the ratio of pressure equilibration time and species replenishment time, but did not have a major effect on the overall duration of the transient. Representative comparisons of the time-averaged, stationary results with experiment are presented to document the computations.