Modeling of Combustion Systems

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INVISCID MODEL FOR THE PREDICTION OF THE NEAR FIELD REGION OF SWIRL BURNERS Steven Bortz KVB, Inc. Irvine, California, USA ABSTRACT THE ISOTHERMAL PHASES of the IFRF burner near field aerodynamics project has led to consider­able insight into the relationship between the flow field created by an expanding swirling flow and the initial swirl level and the geometry of the confining surfaces. Analytic inviscid solu­tions to the equations of motion, which indicate that both the initial swirl level and the diame­ter expansion ratio are important in determining the local flow properties, have been shown to be capable of estimating the initial shape and axial position of the IRZ, as well as the mean veloci­ties in the expanding swirling flow. The analytic solutions have also been used to demonstrate that the internally recirculated mass flow strength should be governed by the parameter S(b/a)2, where S is the initial swirl number and (b/a)2 is the area expansion ratio of the flow. The impor­tance of this parameter has been confirmed exper­imentally. The influence of varying the Reynolds number in the range 25,000 to 115,000 on the flow field was shown to be small, and the upstream influences of downstream boundary conditions, such as the fur­nace exit diameter, have been quantified. A b LIST OF NOTATION vortex radius in burner throat outer vortex radius in burner throat for an annular swirling flow inner vortex radius in burner throat for an annular swirling flow burner throat diameter vortex radius at any axial position X (defined by radial position where ~/~0=1) outer vortex radius at any axial position for an annular swirling flow inner vortex radius at any axial position for an annular swirling flow (~/~0=0) 89 B C D De Df E E ECfn E(Q,) Gx H IRZ JO J 1 k L M ~ m mo mr N P, P r S SSBR SRV Uo U U V W a- X YO Y1 Akifusa Hagiwara Nippon Furnace Kogyo Kaisha LTD Yokohama, Japan quarl exit diameter circulation = Wr wave strength in equation (2) furnace exit diameter furnace diameter constant in equation (2) total energy flux axial component of the turbulent kinetic energy tangential component of the turbulent kinetic energy total axial momentum flux Bernoulli function Internal Recirculation Zone zeroth order Bessel function of the first kind first order Bessel function of the first kind 20./Uo=4S/a quarl length constant in equation (4) dynamic axial momentum flux mass flow initial mass flow reverse mass flow constant in equation (4) static pressure radial coordinate swirl number at burner throat Lx/~a solid body rotation swirl profile Rankine vortex swirl profile uniform axial velocity at burner throat axial velocity axial component of the turbulence velocity radial velocity tangential velocity tangential component of the turbulence velocity axial coordinate zeroth order Bessel function of the second kind first order Bessel function of the second kind