Twenty-Third Symposium (International) on Combustion/The Combustion Institute, 1990/pp. 1461-1467 THE DESIGN OF PRESSURE SWIRL ATOMIZERS C. DUMOUCHEL AND M. LEDOUX URA 230/CORIA-B.P. 118 76134 Mont Saint Aignan, France AND M. I. G. BLOOR, N. DOMBROWSKI, AND D. B. INGHAM University of Leeds West Yorkshire, Leeds LS2 9JT, U.K. Introduction D2d~ = - i l (1.a) The swirl atomizer is widely used in domestic and industrial combustion systems. In this nozzle liquid is caused to emerge from an orifice with a swirl velocity component resulting from its path through tangential or helical passages upstream of the off- flee. A thinning conical sheet is produced which in- tereacts with the surrounding atmosphere and sub- sequently disintegrates into a cloud of drops. The flow characteristics both within and beyond the nozzle have been the subject of a large number of theoretical and experimental studies. However, as yet, nozzles can be designed only on an empircal basis particularly when dealing with highly viscous liquids In this paper an attempt is made to extend our knowledge of the whole process by carrying out a more rigorous analysis of the overall flow system. The first part of the paper deals with the fluid me- chanics of the viscous flow within the nozzle and this provides a means of determining the sheet an- gle. In the second part, an analysis is made of the break down of an inviseid liquid cone from which the relationship between the operating variables and the mean drop size may be deduced. Viscous Flow in a Pressure Swirl Atomizer Analysis: Cylindrical coordinates (r, O, z) are used to ana- lyse the flow system shown in Fig. 1. The flow which has three components of velocity i.e. radial, axial and spin (or azimuthal) is assumed to be steady and axisymmetric and is goverened by the Navier Stokes and continutity equations. This analysis uses the stream function--vorticity formulation and hence, taking the curl of the equation of motion, it may be rewritten as the system of partial differential equations: 1 Ot~ OV 1 Ot~ OV] (1.b) = Re Lr o-7 oz r oz OrJ [lOOOf~ 10r D2il = Re Lr-~r az r Oz Or 2n0, 2 v vl +r ~ Oz-~ ~zJ (Lc) where all quantifies have been normalised using the length Lg and the velocity Ue. In practice an air core develops along the axis of symmetry. However, in this apppoach the volume taken up by the core is considered to be filled by liquid since it is reasonable to assume that the cor- responding momentum is negligible compared with the bulk flow. The system of Eqs. (1) is of an elliptic nature and therefore conditions need to be specified over the boundary of the solution domain. At solid bound- aries the no slip condition is imposed and the ve- locity normal to the boundary is zero. Along the axis of symmetry the radial and spin velocities must be equal to zero. The flow conditions at the entry are characterised by Re and K = Ve/Ue and both the radial and azimuthal velocity profiles are taken to be fiat apart the region within one mesh width of the wall where the velocity diminishes rapidly in order to satisfy the no slip condition. In terms of the solution variables, ~, V and II, the boundary conditions present no mathematical problems. The system of Eq. (1) is solved using a finite dif- ference scheme with a Gauss Seidel relaxation pro- cedure. To ensure the diagonal dominance and therefore the convergence, backward or forward differencing is used for oV/az, aV/Or, all/az, and all~Or on the right hand sides of (1.b) and (1.c) according the sign of ate~Or and aO/Oz. 1461