Abstract: To study the effect of the radial orifice shape on the leakage rate of liquid sheet in pintle injectors and to accurately predict the leakage rate, we propose the relative deformation theoretical model of a rectangular orifice jet using analogy analysis based on the relative deformation model of a radial circular liquid jet. Taking the mutual influence of multi-injector units and the side effect of flowing around rectangular orifices with different aspect ratios into consideration, we establish a prediction model of the leakage rate for the radial rectangular orifice for the first time. Comparison of the theoretical data with the experimental and numerical data shows good agreement between the theoretical prediction values and the experimental and numerical values. Moreover, the relative deformation model and the leakage rate model for the rectangular orifice exhibit high accuracy. In addition, the research shows that the leakage rate of the rectangular orifice is related to the geometric blockage rate, the effective momentum ratio and ratio of sheet thickness to jet width, as well as the aspect ratio. The leakage rate at three different aspect ratios is significantly lower than the geometric leakage rate. Meanwhile, the leakage rates of three different rectangular orifices slowly increase with the increase of the effective momentum ratio. Comprehensive analyses of the radial circular orifice and three rectangular orifices with different aspect ratios show that the radial orifice shape has a significant effect on the leakage rate when the radial orifice cross-sectional area and mass flow rate are identical, and the leakage rate of the rectangular orifice is significantly lower than that of the circular orifice. The larger the aspect ratio of the rectangular orifice is, the larger the leakage rate is. In practical applications, the selection of the rectangular orifice is more conducive to the leakage rate control, and the leakage rate can also be controlled by changing the aspect ratio. Simultaneously, in the process of changing working conditions, the leakage mass flow rate of the rectangular orifice is also adjusted and changed along with the main road propellant to prevent the leakage rate from changing much. Therefore, the rectangular orifice has better flow matching characteristics with a wide range of variable thrusts.

Key words: pintle injectors, radial orifice shape, leakage rate, blockage rate, effective impinging momentum ratio