Kana Yoshida 1,2 , Reha Avsar 3 , Aaron Hartmann 3 , Taro Kanai 4 , Takafumi Sasaki 4 , Kenji Takizawa 4 and Tayfun E. Tezduyar 3 1 Department of Mechanical Engineering, Tottori University, Tottori, Japan. 2 TOMODACHI STEM Program @ Rice University, Houston, Texas, USA. 3 Mechanical Engineering, Rice University, Houston, Texas, USA. 4 Department of Modern Mechanical Engineering, Waseda University, Tokyo, Japan. [email protected] Structural Mechanics Computation of the Orion Spacecraft Drogue Parachute in Compressible-Flow Regime Methods and Conditions Base Computation (Case 0) Pressure Dependence Time Resolution Effect Orion spacecraft parachute sequence From NASA site Drogue parachutes Compressible flow Main parachutes Incompressible flow Background - Orion Drogue Parachute Drop test From NASA site Cost is about a million dollar for each test. Wind-tunnel test From NASA site Scaling challenge due to coupling between the canopy deformation and the airflow. - Field Tests Computational analysis can serve as a practical alternative. • How the solution and the solution process vary → Pressure : Parachute diameter and vertical position change. → Dt : Computing time can be reduced by increasing Dt. → η : The settled shapes are close, but η =140 s -1 leaves out movement details, which are actually not needed. • Larger time-step size? → With larger Dt, we can reach the settled shape sooner, with almost the same shape as in Case 0, but with less computing time. References [1] K. Takizawa, T.E. Tezduyar, and R. Kolesar, “FSI modeling of the Orion spacecraft drogue parachutes, Computational Mechanics, Vol. 55, pp.1167-1179, 2015. [2] K. Takizawa, T.E. Tezduyar, and T. Kanai, “Porosity models and computational methods for compressible-flow aerodynamics of parachutes with geometric porosity”, Mathematical Models and Methods in Applied Sciences, DOI: 10.1142/S0218202517500166, 2017. This research was conducted as part of the 2017 TOMODACHI STEM @ Rice University Program which is funded by a grant from the TOMODACHI Initiative, a program of the US–Japan Council. For more information on TOMODACHI program, see http://tomodachistem.rice.edu/. We are grateful to Tatsuya Tanaka for using some of the background material from his poster. - Governing Equations Structural mechanics equations - Spatial Discretization Finite element method Parachute configuration [1] Mach number 0.5 Altitude (ft) 35,000 Base conditions • Case 3 parachute shape settles sooner than Case 0. • Case 3 parachute shape is almost the same as it was in Case 0. • Case 4 parachute shape settles even sooner than Case 3. • Case 4 parachute shape is almost the same as it was in Case 0. • Larger time-step sizes save computing time. • Parachute canopy in Case 1 is positioned lower than it was in Case 0. • Parachute diameter in Case 1 is smaller than it was in Case 0. Case 1 Case 2 Case 3 Case 4 Case 0 results look reasonable. We test • different pressures • different time-step sizes (Dt) • different structural damping coefficients (η) to see how the settled parachute shape changes. • Obtain deformed parachute shape for fluid computations of the Orion drogue parachute [1] in compressible-flow regime [2] • Study the pressure dependence and effect of time-step size, and damping coefficient • Mesh resolution effect • Fluid computations with the deformed shape Pressure (Pa) Dt (s) η (s -1 ) 1,000 0.001 0 Pressure (Pa) Dt (s) η (s -1 ) 1,500 0.002 0 Pressure (Pa) Dt (s) η (s -1 ) 1,500 0.003 0 • Parachute canopy in Case 2 is positioned higher than it was in Case 0. • Parachute diameter in Case 2 is larger than it was in Case 0. Pressure (Pa) Dt (s) η (s -1 ) 1,500 0.001 0 Pressure (Pa) Dt (s) η (s -1 ) 3,000 0.001 0 Case 0 (76.0% D 0 ) Case 4 (76.8% D 0 ) Case 3 (76.4% D 0 ) Initial shape (D 0 = 23 ft) Settled shape (76.0% D 0 ) Objective Case 0 (76.0% D 0 ) Case 1 (75.6% D 0 ) Case 2 (76.8% D 0 ) Acknowledgement Conclusions Damping Effect Case 5 Case 6 • Parachute movement in Case 5 is close to what it was in Case 0. • Movement details in Case 6 are not captured, but not needed. • Settled parachute diameter in both cases is close to what it was in Case 0. • Initial movement in both cases is different from what it was in Case 0. • The settled shape is almost the same. Pressure (Pa) Dt (s) η (s -1 ) 1,500 0.001 14 Pressure (Pa) Dt (s) η (s -1 ) 1,500 0.001 140 Future Directions Case 5 (76.2% D 0 ) Case 6 (76.3% D 0 ) Case 0 (76.0% D 0 )