Theoretical Analysis for Residual Thrust of Hybrid Thruster

Recent experimental and numerical studies indicate that post-firing gasification of fuel significantly contributes to residual thrust in hybrid thrusters. This study examines the mechanisms of residual thrust in hybrid thrusters by integrating vacuum chamber firing tests with analytical modeling. Small-scale firing tests were conducted in a vacuum chamber, enabling successful measurement of post-firing chamber pressure attributable to the residual thrust phenomenon. A one-dimensional analytical model was developed, wherein residual thrust is linked to the solid fuel surface temperature, governed by an advection–diffusion equation in a semi-infinite domain with a Neumann boundary condition that accounts for both radiative heating and vaporization effects. Through an appropriate variable transformation, the problem was reduced to a standard diffusion equation, allowing the surface temperature to be represented as the sum of conductive cooling, radiative heating, and vaporization-induced cooling components. Parametric studies, informed by experimental data, revealed that the radiative heat decay coefficient �� primarily controls the decay rate of chamber pressure and residual thrust, whereas the view factor ���� determines their magnitude. These findings highlight the dominant influence of radiative heating from the nozzle on the residual thrust behavior. The proposed model significantly reduces the computational cost while capturing the essential physics of residual thrust. This approach provides a valuable tool for the design and safety assessment of hybrid thrusters for small satellites.