The first step in performing the FSI simulation was to perform a structural dynamics (SD) simulation of the parachute given a static uniform pressure field. The results from the SD simulation were later used to determine a static geometry for the standalone CFD simulation.
The SD simulation was conducted using both Tension7 (developed at U. Conn) and fluid-structure interaction software developed by the T*AFSM .
Nine-noded membrane elements (320) and two- and three-noded cable elements (800) were used to describe the geometry of a flat cross parachute. The flat geometry was then inflated to a near-steady-state via the SD simulation, with final geometry as shown below. A comparison of the assumed geometry as given by the SD simulation with the final geometry as given by the FSI simulation was also made.
Final geometry of cross parachute with cables, after a standalone SD simulation.
Next, the SD final geometry was used in a computational fluid dynamics (CFD) simulation.
The CFD mesh, composed of 4-noded tetrahedral elements, was created with several different levels of refinement. The entire mesh generation process takes between one and five hours of computer time on an SGI workstation, depending on refinement, and requires between fifteen and forty-five minutes of user time. The resulting mesh is unstructured and includes several different refinement regions according to the expected flow field.
The boundary conditions of the CFD mesh were defined to correlate with the actual conditions of the wind tunnel: inlet flow was set at a constant dimensional velocity of 60 ft/s (resulting in a fully developed flow field in approximately five seconds of simulation time), outlet flow was free, and flow velocity normal to the sides of the domain was fixed at zero. In additon, a no-slip condition was imposed upon the surface of the cross parachute.
Average drag for the parachute calculated from the results of the CFD simulations showed convergence to a value of 91.0 lbs as mesh refinement increased.
An animation showing the developing flow field from time zero is available. It is interesting because it depicts several intervals of time where the drag on the parachute is "negative"--in other words, where pressure waves caused by the sudden start of the inlet velocity at time zero in the simulation actually threaten to implode the top of the parachute. The CFD simulation does not take structural dynamics into account, so the implosion does not occur, but this type of effect can often be seen in studies of real parachutes upon opening.
|Developing CFD Flow Field, Velocity Magnitude and Pressure (376 kB)|
Shown below are depictions of the fully-developed flow field after the CFD simulation, colored with velocity magnitude and with pressure, along a plane cutting directly through the middle of the cross parachute. Red is high velocity and high pressure, blue is low velocity and low pressure.
An animation showing the flow field along a plane moving dynamically through the parachute is also available:
|Dynamic CFD Results, Velocity Magnitude and Pressure (486 kB)|
In order to couple both the fluid and structural solvers into a single fluid structure interaction (FSI) simulation, an interface must be created to transfer information back and forth at each time step. This interface is a surface map, allowing information transfer across the surface of the cross parachute, where both fluid and structural information is required. In this simulation it was assumed that the cables of the parachute have no effect on the fluid flow; if this assumption had not been made, an additional interface would have been created for the cables.
Definition of the surface interface, as well as of several other required data files, was accomplished using a series of FORTRAN routines written by Tim Bretl. These routines can be executed in sequence by a master UNIX shell; total computational time is between five minutes and one hour, depending on mesh refinement.
Average drag for the parachute calculated from the results of the FSI simulations exhibited indications of likely convergence to a value of 90.0 lbs as mesh refinement increased.
The geometry of the FSI simulation, already discussed in relation to the standalone SD simulation above, quickly reached a steady-state final position. The fact that a steady-state condition was rapidly obtained is due in part to the small size of the domain; high-velocity fluid jets between the cross parachute and the walls of the wind tunnel allow little positional overshoot, and the extremely high-pressure area underneath the cross parachute allows little rebound. However, the domain could not have been the only reason, since when a simulation was conducted with a wide domain--outer tunnel dimensions were doubled--steady state was reached almost as quickly. The geometry of the cross parachute itself probably makes aids the most in achieving steady state: the cut-out corners of the parachute greatly increase its stability.
For a picture of the geometry of the FSI simulation, either look at the comparison of the initial (assumed) and final geometries, or look at one of the following animations:
|Cross Section View, Velocity Magnitude (692 kB)|
|Structural View, Stress (176 kB)|
One interesting effect of the changing geometry of the cross parachute is the creation of a pressure wave at the beginning of the FSI simulation. As stated above, the geometry changes from the initial assumed position to the final position fairly rapidly, causing changes in the flow field. An animation displays this effect dynamically, tracking a moving pressure isosurface for the first ten seconds of the simulation:
|Pressure Wave as Geometry Changes in FSI Simulation (1.4 MB)|
As mentioned above, it was noticed that the flow during both the CFD and FSI simulations experienced a high degree of blockage between the sides of the parachute and the sides of the wind tunnel, since the wind tunnel dimensions are barely larger than those of the cross parachute. To determine exactly what effect such a small domain had on the flow, another simulation was conducted using a wider domain, where the x- and y- dimensions of the wind tunnel were doubled.
|Normal Domain, Velocity Magnitude|
|Wide Domain, Velocity Magnitude|
Indeed, the flow conditions are substantially different, as shown in the cross-sectional views above, colored with velocity magnitude. The jets between the cross parachute and the walls of the wind tunnel are stronger and the wake closes much faster in the normal domain as opposed to the wide domain.
The following animation shows dynamically the difference in flow conditions between the normal and wide domains:
|Dynamic FSI Results, Normal and Wide Domains, Velocity Magnitude (487 kB)|