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Show The one-dimensional, steady-state model for mixing along the axial direction of a turbulent jet uses two perfectly stirred reactors to represent chemical reactions in two regions of the flow: (1) homogeneous regions, and (2) diffusion flame-sheets. Alternatively, the flame sheets can be modeled more rigorously by a strained diffusion flame, but the added computational expense was not deemed necessary for this study. The homogeneous and flame-sheet reactors are coupled as shown in Fig. 1. Surrounding fluid is entrained into the jet by entering the flame-sheet reactor and mixing with fuel from the homogeneous reactor. The products of the flame-sheet reactor then enter the homogeneous reactor. The turbulent entrainment and mixing rates come from experimental correlations derived by llicou and Spaldingl0 for momentum-driven jets, and by Becker and Yamazaki11 for flames where buoyancy influences the flow. The effect of buoyancy is necessary for laboratory jet flames, because it accelerates the air entrainment rate. The model solves conservation equations for species and energy in the two reactors. The equations for the homogeneous reactor are derived in a fixed (Eulerian) coordinate system, yielding a set of ordinary differential equations with respect to the axial location. The simulation starts with the initial condition near the nozzle, and the integration proceeds downstream as the reactors move (in a Lagrangian sense) with the average velocity of the jet fluid. One may view the reactions as taking place in constant-pressure reactors of increasing volume, that move downstream as the simulation proceeds. The species chemical production rates are evaluated using the Chemkin package.12 A simple "gray-gas" radiation loss term accounts for the energy transferred away from the flame. The emissivity must be adjusted to the measured radiant fraction or observed maximum temperat ure. The flame-sheet reactor approximates the reaction zone in a diffusion layer, so its composition is maintained near stoichiometric. To accomplish this, the model adjusts the flow rate from the homogeneous reactor to the flame-sheet reactor. The conservation equations for the flame-sheet reactor assume quasi-steady state; the residence time is computed for flow through a diffusive layer for the same entrainment rate. MODEL PREDICTIONS OF NOx EMISSIONS FROM METHANE JET FLAMES Computations for a series of piloted methane flames with measurements reported by Turns et al13 are presented in Fig. 2. The emission index is defined as the mass of NOx (using the weight of N O2 for both species) per mass of fuel. An instructive use of the model is to investigate the importance of different physical effects by removing them from the model. The different curves in Fig. 2 examine the influence of the radiation loss and the accelerated entrainment rate caused by buoyancy. Begin by observing that the solution for a constant-momentum, adiabatic flame (dashed curve) overpredicts the NOx emissions, and also predicts the wrong velocity trend. Addition of the influence of buoyancy on the entrainment correlation improves the solution by correcting the trend (dotted curve). Finally, addition of the radiation loss (solid curve), with the emissivity adjusted to the measured radiant fraction, produces a solution for the NOx emission index that is quantitatively correct. The lesson of this series of solutions is that omission of either radiation or buoyancy in the model results in large errors. 2 |