Numerical Simulation Of Ram-Air Parachutes With Flap Deflection

Computation of 2-D and 3-D flows past ram-air parachutes was conducted using an unsteady time-derivative preconditioning method for Navier-Stokes equation.First, the state-of-art of preconditioning method was introduced, and the modified preconditioning governing equations and the numerical scheme to solve the steady / unsteady viscous flow fields at all Mach numbers were proposed. Time-derivative preconditioning modifies the time-derivative term in governing equations by pre-multiplying it with a preconditioning matrix. This has the effect of re-scaling the eigenvalue of the system of equations being solved in order to alleviate the numerical stiffness encountered in low Mach number and incompressible flow. To provide for efficient, time-accurate solution of the preconditioned equations, we employed a dual time-stepping, multi-stage scheme. Second, two-dimensional flows past ram-air parafoil at different angles of attack with leading edge cut were simulated using the unsteady preconditioning method. The leading edge cut causes the flow to become unsteady and leads to a significant loss in lift and an increase in drag. The flow inside the parafoil cell remains almost stagnant, resulting in a high value of pressure, which is responsible for giving the parafoil its shape. The value of the lift-to-drag ratio obtained with the present computations was in good agreement with those experiment data reported in the literature. Temporally periodic lift coefficient variation was observed, which is due to the leading edge cut induced periodic vortex shedding on the upper surface of the parafoil. Then, computations of variation of the aerodynamic coefficients with flap deflection, angle of attack and leading edge opening/closing condition were carried out based on the 2-D unsteady preconditioning method. We concluded that (1) augment of the flap deflection angle increases both lift and drag coefficients, (2) both lift and drag coefficients increase with angle of attack in the range from 0° to 15° , and (3) the comparison to the experiments showed good agreement in lift-to-drag ratio, though there were obvious difference in lift and drag coefficients, which is due to the difference between the computational configuration and wind tunnel test models. Finally, 3-D flap deflection simulations were performed for the basic Langley tether model. Compared to the results yielded above, the aerodynamic data from three-dimensional simulations was quite closer to the experiments.