| OCR Text |
Show diameter and Ri denotes the Richardson number. In general, a free jet flame may be considered as having a number of distinctive regions (see Figure 3). The region nearest the nozzle exit is momentum dominated, with buoyancy effects playing a negligible role in dictating flame behavior. At a given position downstream, a transition region 'begins where the influence of buoyancy forces becomes increasingly dominant with distance from the fuel nozzle. In a regime farthest from the nozzle, the local momentum flux greatly exceeds the exit momentum flux. In this extreme, the flow behavior will be buoyancy dominated (plume). The position of the flame itself relative to the transition region dictates the influence of buoyancy on combustion and is dependent on the Ri number. Measurements [6] show that the transition from momentum to buoyancy dominated flow begins at £ = 2, where % is defined as g = Rimx/ds This value is fairly consistent over the various propane flames studied in [6] as well as the present H2/N2 flame (see Figure 12). For the flame configuration considered here, this translates to approximately 40 exit diameters downstream. Centerline data are available up to 75 diameters, thus allowing Buoyancy dominated {plume) Transition Momentum dominated for the effects of buoyancy to be considered in the downstream portion of the jet. This is valuable from the perspective of flare flames, where there is an interest in accurate modeling both within and beyond the flame zone. CFD simulations The governing transport equations of mass, momentum, energy and species conservation along with an equation of state and appropriately defined boundary conditions provide a complete and general formulation for reacting flows. However, geometric complexity, detailed reaction mechanisms and widely varying temporal and spatial scales place direct numerical simulations (DNS) of all but the simplest configurations and most modest of turbulent Reynolds numbers far beyond reach. In order to make turbulent flow simulations tractable for practical engineering applications, turbulence and combustion modeling tools are required. Turbulence modeling Traditional approaches to turbulence modeling involve Reynolds averaging of the Navier-Stokes equations, yielding the R A NS equations 14^° |>>A(^-)= dp d -J-+- dx, dx r^8rMr, du , + • ; L ^ dx: dx 1 J J dx \-puy+)p g, Figure 3. Regimes of a buoyant, turbulent jet diffusion flame. Here the overbarred and primed variables represent Favre mean and fluctuating quantities, respectively. The second order moments, commonly referred to as the Reynolds stresses, are unknown and require some form of closure to model all scales of turbulence. Three different R A N S closure models, the standard k-e, realizable k-e, and Reynolds stress model, were employed in this study. A brief review of each is given below. |
