The method of characteristics and computational fluid dynamics applied to the prediction of underexpanded jet flows in annular geometry

Abstract

Natural gas engine efficiency can be improved by enhancing fuel-air mixing through an injection pressure increase. To achieve this mixing benefit, experiments show that a high pressure (3.4 MPa) injection valve needs a shroud to direct the supersonic fuel jet toward the center of the cylinder. Since the fuel jet issuing from the shroud valve has a nearly annular jet flow configuration, it is necessary to analyze the annular jet flow to understand the fuel jet behavior in the mixing process and to improve the shroud design for better mixing. The method of characteristics (MOC) was used as the primary modeling algorithm in this work because the MOC has distinct advantages in computing supersonic flows, notably speed of computation, shock wave capturing and ease of physical interpretation. Computational Fluid Dynamics (CFD) was used primarily to validate the MOC results. A consistent process for dealing with the coalescence of compression characteristic lines into a shock wave during the method of characteristics (MOC) computation was developed. In the MOC results for axisymmetric jet flow, the incident shock wave discontinuity was clearly shown. By the application of shock polar in the pressure-flow angle plane to the incident shock wave for an axisymmetric underexpanded jet, the von Neumann and detachment criteria for the incident shock was compared with the triple point location found in experimental results. It was found that, in the nozzle-exit-to-ambient-static pressure ratios of 2 - 50, a triple point of the axisymmetric jet was located at the point where the flow angle after the incident shock became —5° relative to the axis and this point was situated between the von Neumann and detachment criteria on the incident shock. In addition, the computations showed that the static pressure ahead of the incident shock formed in a sonic jet, when plotted as a function of axial distance, falls on the same curve for pressure ratios of 2 - 50. MOC computations of the jet flow with annular geometry were performed for pressure ratios of 10 and 20 with rannuius = 10-50 units, △r = 2 units. In this pressure ratio range, the MOC results did not predict a Mach disc in the core flow of the annular jet, but did indicate the formation of a Mach disc where the jet meets the axis of symmetry. The MOC results display the annular jet configurations clearly. An outer incident shock much stronger than an inner incident shock in the annular jet flow was seen to occur. Three types of nozzles for application to gas injectors (convergent-divergent nozzle, conical nozzle, and aerospike nozzle) were designed using the MOC and evaluated in on- and off-design conditions using CFD. The average axial momentum per unit mass was improved by 17 to 24 % and the average kinetic energy per unit fuel mass was improved by 30 to 80 % compared with a standard shrouded poppet valve. Of the candidate designs, the convergent-divergent nozzle gave the best performance.