A study on the theoretical model of parachute permeability under supersonic and high-pressure-difference conditions

The supersonic parachute deceleration system (SPDS) plays a critical role in planetary atmospheric entry. During operational phases, the substantial pressure differential across the textile canopy significantly alters fabric permeability, directly impacting deceleration efficiency. Understanding gas transmission characteristics under hypersonic pressure gradients is essential for designing advanced supersonic deceleration systems. This study investigates pore-scale flow mechanisms and permeability evolution in parachute textiles under extreme pressure differentials. We developed three-dimensional woven structural models of representative fabrics and performed computational fluid dynamics (CFD) analyses to resolve the pore-scale flow structures. The results indicate that geometric scaling of woven models preserves both jet structure characteristics and fiber surface pressure distribution. Additionally, windward surface pressure profiles remain independent of canopy pressure differentials. Under high-pressure-difference conditions, fabric pore jets exhibit flow characteristics similar to Laval nozzle, generating supersonic jet structures downstream of textile voids. Furthermore, based on the textile structural parameters and one-dimensional isentropic nozzle flow theory, we developed a parachute permeability model applicable across a wide range of pressure differences. This model, formulated using the second-order Bessel function, demonstrates strong agreement with numerical simulations (coefficient of determination R²=0.978), confirming its effectiveness in predicting supersonic parachute permeability.