In this paper, first, a theoretical prediction method of regression rates and heat flux to solid fuels of uni-directional vortex injection hybrid rocket engines is developed by introducing a new swirl intensity decline model toward axial direction. Next, a linear propagative relation of heat flux to solid fuels with disturbances of oxidizer mass flux, fuel regression, and initial swirl intensity is derived. The couple of this response model and another unteady response model of solid fuel gasification amplifies oxidizer mass flux disturbance in the form of regression rate oscillation. This is the basic mechanism of low frequency instability unique to hybrid rocket engines. The linear stability analysis for unidirectional vortex types simulating both ILFI amplification source and main stream model is conducted. The result of this analysis shows that uni-directional vortex injection hybrid rocket engines have the same linear unstable mode as axial hybrid rocket engines.
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