为了研究径向孔形状对针栓式喷注器液膜下漏率的影响并对其进行准确预估，以径向圆孔液束的相对变形模型为基础，通过类比分析提出了矩形孔的相对变形理论模型，并考虑多喷注单元间相互影响和不同高宽比矩形孔的绕流侧边效应，首次建立了径向矩形孔的下漏率模型。通过试验及数值仿真对模型进行了验证分析，结果表明理论预估结果与数值仿真及试验结果吻合较好，也表明针对矩形孔建立的相对变形模型及下漏率模型具有较好的准确性。另外，研究表明矩形孔的下漏率除了与几何阻塞率、有效动量比及液膜厚度与液束孔宽度之比有关外，还与高宽比有关；3种不同高宽比情况下的下漏率均显著小于几何下漏率；同时下漏率随有效动量比增大而增大的趋势均较平缓。综合分析径向圆孔和3种不同高宽比矩形孔的结果发现，在径向孔横截面积及流量等工况参数完全相同的情况下，径向孔形状对下漏率有显著的影响，矩形孔的下漏率显著低于圆形孔的；矩形孔的高宽比越大，下漏率越大。实际应用中选择矩形孔更有利于控制下漏率，并可通过改变高宽比控制下漏率；同时在变工况过程中，矩形孔的下漏流量也会随着主路推进剂一起调节变化，保持下漏率变化不大，故具有较好的大范围变推力流量匹配特性。
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.
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