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Show Unlike time-averaged models, which only require boundary conditions, LIM simulations are time-dependent and thus begin from a set of initial conditions. The initial conditions correspond to the onset of coal and air inflows into the initially quiescent furnace. For the flow field u(x,r) these are specified via vorticity - surfaces that shed from all inflow edges, as shown by the solid lines emanating from the edges of each of the coal and air inflows in Fig. 4, as well as from all corners in the furnace interior. These surfaces carry information about both the azimuthal vorticity, which is set by the radial inflows to the boiler, and the axial vorticity which is set by the tangential swirl imparted on the inflows by the details of the LNCFS-1 burner design. For the scalar field C,(x,t) the initial conditions are scalar gradient surfaces introduced at the coal nozzles, as shown by the dotted lines emanating from the center of each coal nozzle in Fig. 4. These vorticity and scalar gradient surfaces on which the LIM equations are solved [4, 6] move with the time-varying flow that results in the furnace interior, and thus are rapidly deformed by the underlying flow field, as is evident in Fig. 5. From the local integral moment information at each point on the LIM vorticity surfaces, the flow field u(x,/)and scalar gradient field V£(x,/) are constructed. As these surfaces are deformed by the flow field at each time step, the resulting local strain rate at the typically 80,000 or more points that define the surface enters the LIM equations for the strain-diffusion balance to determine the evolution of the moments at each of these points. 4.2 Coal gas mixture fraction fields In this manner, the flow and mixing processes are advanced forward in time from the initial conditions. After several furnace residence times, each simulation reaches a stage of evolution in which the unsteady flow and mixing processes within the boiler vary with time, but averaged properties have reached a steady state. Examples of the typical instantaneous coal gas mixture fraction fields C,(x,t) at six different instants of time in this nominally steady state condition are shown in Fig. 6. In each panel, the left and right halves show the extent of mixing between the coal and air inflows at separate instants of time. Colors ranging from dark red to bright yellow denote linearly increasing values of the local, instantaneous coal gas mixture fraction, referring here to the mass fraction of fluid that originated in the coal nozzle inflows. From the instantaneous coal gas mixture fraction fields C,(\,t), the corresponding molecular mixing rate fields log V^V^(x,/) are constructed, as shown in Fig. 7. Whereas information of the type in Fig. 6 gives the extent of mixing between the coal and air inflows, fields of the type in Fig. 7 give the local, instantaneous rate of molecular mixing in the flow. In this case, colors ranging from dark blue through red denote logarithmically increasing mixing rates. The combined ^(x,r) and V£-V£(x,r) fields provide the information required to couple nonequilibrium chemistry to these simulations. This can be done in various ways (6), with the choice of coupling method dictated by the degree of nonequilibrium needed to properly account for the chemical system under consideration. Here we use a method based on "well-mixed balloons" that has been previously shown to give accurate results for fuel-lean gas reburn chemistry under conditions typical of large utility boilers. It should be noted in Figs. 5-7 that, as in any axisymmetric simulation, there is no flux across the centerline of the geometry. In the case of averaged simulations the resulting zero net flux is physically correct, and this condition is preserved in the |