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AHPCRC Bulletin: Spring 1994 - Volume 4 Number 2

Finite Element Computation of the Dynamics of Large Ram Air Parachutes

Sanjay Mittal, AHPCRC/Aerospace Engineering and Mechanics

Gliding parachutes, which consist of rectangular, ram air inflated wings, have been widely used by the sport parachute community and are finding increasing application in the recovery of large payloads. These parachutes, called parafoils, are largely the result of extensive cut and try design efforts. For personnel applications, parafoils have reached a high degree of reliability and a reasonable level of aerodynamic efficiency. However, large payloads require parafoils which are at least an order of magnitude larger than existing personnel parachutes. The deployment of such large parafoils poses many challenging technical problems, many of which have to do with the unsteady aerodynamics of the parafoil and payload.

Tayfun Tezduyar and William Garrard, both Professors of Aerospace Engineering and Mechanics at the AHPCRC, along with Ph.D. students Vinay Kalro and Shahrouz Aliabadi, M.S. student Joel Luker, Lt. USAF, Keith Stein, Aerospace Engineer at U.S. Army Natick RD&E Center, and this author, are working on understanding the aerodynamics of large ram air parachutes. This investigation is sponsored by the Army Research Office and is monitored by Jagdish Chandra, Director of the Mathematical and Computer Science Division. Earl Steves of the Natick RD&E Center is also involved in this research project which is one of a number of parachute development projects under the overall direction of Maurice Gionfriddo, Director of the Mobility Directorate of the Natick RD&E Center. The aerodynamics of parachutes involves many complex phenomena. The inflation of a parachute is characterized by unsteady turbulent flows, rapidly changing bluff body shapes, and nonlinear interactions between the parachute structure, payload and aerodynamic forces. Most mathematical modeling of parafoils has concentrated on the steady gliding phase of operations in which standard airfoil theory is modified to predict lift to drag ratios and other important aerodynamic parameters. This team of researchers is utilizing the AHPCRC's high performance computing resources in conjunction with the latest CFD tools for simulating 3D flows to understand both the steady and unsteady dynamics of parafoils.
Figure 1. 3D incompressible flow past a parafoil during the very initial stages of its deployment (simulated as an expanding box). Each of the three images show the pressure distribution on the box surface, and the stream tubes color-coded with the pressure.
Figure 1 shows three snapshots from one of the computations to simulate the very initial stages of the parachute deployment. In this stage, the parafoil essentially emerges from a bag and inflates to a fully open configuration. The initial condition for the simulation is the steady- state flow around the packed parafoil that is falling down at a speed of 80 feet/sec and is moving horizontally at 240 feet/sec. The initial dimensions of the parafoil are 44440.6 cubic feet. According to the data from one of the drop tests, the parafoil expands from its initial configuration to a fully open configuration (6042043 cubic feet) in 10 seconds. The Reynolds number, based on the initial chord-length of the parafoil and its speed during the deployment, is 24106. At such high Reynolds numbers, the flow is expected to be turbulent. Therefore, this computation was carried out using a modified Smagorinsky turbulence model. Each of the three frames in Figure 1 shows the pressure distribution on the box surface, and a set of stream tubes color-coded with the pressure.

The computations were carried out by using the Deformable- Spatial-Domain/Stabilized-Space-Time (DSD/SST) procedure developed earlier at the AHPCRC. In this method, the stabilized finite element formulation of a problem is written over the associated space-time domain. This way, the deformation of the spatial domain is taken into account automatically and computations are also protected against numerical oscillations. These numerical methods have been tested over the past three years on various types of problems, including those involving 3D domains, high Mach number and high Reynolds number flows, and moving boundaries and interfaces. The computations were carried out on the AHPCRC's CM-5. To reduce the memory demands, the nonlinear equation systems (with 230,000+ unknowns) resulting from the implicit finite element discretizations were solved using a matrix-free iteration technique. This simulation is based on the data from the Advanced Precision Airborne Delivery System (APADS) and Advanced Recovery System (ARS). In order to have a better understanding of the APADS program, the team of researchers involved in this project are collaborating with William Wailes, Program Manager of the APADS program at Pioneer Aerospace Corporation in Melbourne, Florida.

Figure 2. 3D incompressible flow past a parafoil at Reynolds number 10 million. The image shows the pressure distribution on the parafoil surface, and the stream ribbons color-coded with the pressure.
To establish confidence in the computations, results from numerical simulations were compared with the data sets from ARS test series and the wind tunnel data from parafoil tests performed at the NASA Ames Research Center. Figure 2 shows the flow field from CM-5 simulation of the steady gliding descent of the parafoil at 10o angle of attack. The Reynolds number, based on the mean chord-length of the parafoil, is 107. A modified Prandtl's mixing length turbulence model was employed to model the turbulent flow. The aspect ratio of the parafoil is 3, and its average radius of curvature along the span is 2.5 chord-lengths. The cross section of the parafoil is a 4-digit NACA airfoil with a thickness ratio of 16.7%. The picture shows the pressure distribution on the parafoil surface, and a set of stream ribbons color-coded with the pressure. The aerodynamic coefficients from the computations are in good agreement with the ones from experiments. The computational domain consists of 375,000+ hexahedral elements. At each time step a set of 1,460,000+ coupled nonlinear equations are solved using a matrix-free iteration technique. On a 512 node CM-5, the overall speed of the computation was approximately 6.8 GigaFLOPS.

The class of problems described in this article, i.e., large-scale unsteady 3D simulations, can now be routinely solved as a result of the development of new, efficient algorithms specifically designed for large, distributed memory, scalable parallel systems, such as the AHPCRC's CM-5.