Experimental and theoretical investigation on annular injection supersonic ejector equipped with a converging-diverging diffuser was carried out. The effects of the primary nozzle area ratio, the contraction angle of the mixing chamber, and the cross sectional area and L/D ratio of the second-throat...
Experimental and theoretical investigation on annular injection supersonic ejector equipped with a converging-diverging diffuser was carried out. The effects of the primary nozzle area ratio, the contraction angle of the mixing chamber, and the cross sectional area and L/D ratio of the second-throat on the ejector performances were measured with particular emphasis on the starting and unstarting pressures and the secondary flow pressure after the ejector starts. To analyze the dependence of the ejector performances on these parameters, we tested three different sizes for each of the geometric parameter with the rests fixed, resulting in 81 combination of the four parameters listed above. At every configuration, various secondary mass flow rate conditions were tested. Furthermore, at a reference cases, the effects of the secondary flow temperature were investigated. Performance measurements at all the test conditions showed that the starting pressure exhibited dependence on the throat area ratio of the diffuser and primary nozzle when the length of the mixing chamber is less than a certain critical value. For a longer mixing chamber, the starting pressure becomes proportional to the length of the mixing chamber. The unstarting pressure, however, showed no dependence on the length of the mixing chamber but on the throat area ratio of the diffuser to primary nozzle only and could be easily calculated by using the normal shock relation with the throat area ratio. Lastly, the secondary flow pressure was not affected by the second-throat geometry and the back pressure. It means that the secondary flow is aerodynamically choked by the interaction with the primary flow, and the secondary flow is determined by the choking phenomena. Through the experimental understanding, simple theoretical models were developed to predict the secondary flow pressure after the ejector starts, the starting pressure, and the unstarting pressure. For the secondary flow pressure after starting, the assumption that the aerodynamic choking of the secondary flow occurs in the mixing chamber was used. First, for simplicity, a funnel-shaped shock wave generated by the contraction angle at the inlet of the mixing chamber was regarded as a two-dimensional wedge shock wave. In results, the secondary flow pressure predicted by the model agreed reasonably well with measurement for a small contraction angle of the mixing chamber. Using the analysis, the compression ratio, the adiabatic efficiency, Mach number of the secondary flow, and the location of the choking point were calculated and described. Later, a model of the funnel shock wave was developed by using conical and two-dimensional wedge shock wave relations and the secondary flow pressure can be estimated more accurately. For the theoretical analysis of the starting pressure, it was assumed that the ejector starts when a supersonic primary flow reaches the inlet of the second-throat. To determine the distance that the primary supersonic flow travels, the length of the first diamond shock wave pattern of the primary flow was calculated and multiplied by an empirical factor. In result, the complex behavior of the starting pressure according to the mixing chamber length can be explained by the model accurately for a given geometry. Finally, the unstarting pressure obeys the normal shock theory with respect to the throat area ratio of the second-throat to the primary nozzle throat. It means that the unstarting pressure is the minimum pressure to make a normal shock wave maintain at the second-throat.
Experimental and theoretical investigation on annular injection supersonic ejector equipped with a converging-diverging diffuser was carried out. The effects of the primary nozzle area ratio, the contraction angle of the mixing chamber, and the cross sectional area and L/D ratio of the second-throat on the ejector performances were measured with particular emphasis on the starting and unstarting pressures and the secondary flow pressure after the ejector starts. To analyze the dependence of the ejector performances on these parameters, we tested three different sizes for each of the geometric parameter with the rests fixed, resulting in 81 combination of the four parameters listed above. At every configuration, various secondary mass flow rate conditions were tested. Furthermore, at a reference cases, the effects of the secondary flow temperature were investigated. Performance measurements at all the test conditions showed that the starting pressure exhibited dependence on the throat area ratio of the diffuser and primary nozzle when the length of the mixing chamber is less than a certain critical value. For a longer mixing chamber, the starting pressure becomes proportional to the length of the mixing chamber. The unstarting pressure, however, showed no dependence on the length of the mixing chamber but on the throat area ratio of the diffuser to primary nozzle only and could be easily calculated by using the normal shock relation with the throat area ratio. Lastly, the secondary flow pressure was not affected by the second-throat geometry and the back pressure. It means that the secondary flow is aerodynamically choked by the interaction with the primary flow, and the secondary flow is determined by the choking phenomena. Through the experimental understanding, simple theoretical models were developed to predict the secondary flow pressure after the ejector starts, the starting pressure, and the unstarting pressure. For the secondary flow pressure after starting, the assumption that the aerodynamic choking of the secondary flow occurs in the mixing chamber was used. First, for simplicity, a funnel-shaped shock wave generated by the contraction angle at the inlet of the mixing chamber was regarded as a two-dimensional wedge shock wave. In results, the secondary flow pressure predicted by the model agreed reasonably well with measurement for a small contraction angle of the mixing chamber. Using the analysis, the compression ratio, the adiabatic efficiency, Mach number of the secondary flow, and the location of the choking point were calculated and described. Later, a model of the funnel shock wave was developed by using conical and two-dimensional wedge shock wave relations and the secondary flow pressure can be estimated more accurately. For the theoretical analysis of the starting pressure, it was assumed that the ejector starts when a supersonic primary flow reaches the inlet of the second-throat. To determine the distance that the primary supersonic flow travels, the length of the first diamond shock wave pattern of the primary flow was calculated and multiplied by an empirical factor. In result, the complex behavior of the starting pressure according to the mixing chamber length can be explained by the model accurately for a given geometry. Finally, the unstarting pressure obeys the normal shock theory with respect to the throat area ratio of the second-throat to the primary nozzle throat. It means that the unstarting pressure is the minimum pressure to make a normal shock wave maintain at the second-throat.
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