We use the front tracking method on a spring-mass system to model the dynamic evolution of parachute canopy and risers. Our spring-mass model is echanced to include both tencil-stiffness and angular-stiffness, which has the capability of duplicating the realistic strain and stress of the elastic membrane and conforms with both Young's modulus and Poisson ratio. This mechanical structure is coupled with the incompressible turbulence fluid solver through the "impulse method". The on-going work focus on the effects due to porosity and the wake of parachuist body or payload. In addition, GPU-based parallel computing techniques are applied to accelerate the computational speed and increase the resolution of numerical results.
The Spring-Mass Model for Fabric Surface
In our parachute project, a mesoscale spring-mass model is used to mimic fabric surface motion. Through coupling with an incompressible fluid solver, the spring-mass model is applied to the simulation of the dynamic phenomenon of parachute inflation. Both the tensile stiffness and the angular stiffness of the spring conform with the material's Young modulus and Poisson ratio.
The geometrical deformation of a fabric surface is the major source of stress on the material. The stress causes surface tension in parachute canopy and exerts a normal component of force which the parachute canopy interacts with the surrounding fluid to produce drag of the deceleration. The stress is also an important engineering variable in the parachute safety design. Therefore accurate computation of stress will not only help to understand the fluid dynamics of the parachute, but also to ensure that the material will not be ripped apart during the deceleration.
|Figure: the left plot shows spring-mass model on a triangulated surface mesh and the right plot shows the Von-Mises stress on the canopy surface. The figure demonstrates that the areas near the canopy–string connection points are the most stressful part of the parachute during inflation.|
The breathing motion is an oscillatory motion. The canopy appeared to expel the excess air by means of the breathing. In the experiment, the breathing motion was also caused by the constraint on the parachute, imposed by the guide wire. The breathing motion in the simulation is smaller because there is no vertical motion restriction such as guide wire.
|Fig: The left plot shows the parachute breathing motion. The right plot compares the drag force measured in simulation and experiments|
Turbulence flow and rigid body
The dimensions of parachutist or cargo are usually smaller than the parachute canopy. However, when air flows around the parachutist or cargo, the vorticity and turbulence of the flow will have different patterns that with different Reynolds numbers. These perturbed flow will reach the parachute canopy and contribute to the instability of the canopy motion. Therefore the inclusion of parachutists will make numerical simulation of parachuts closer to reality.
|Figure: A closer look at the parachutists|
The parachutist or cargo is added as a rigid body interacting with the surrounding fluid flow, and it is connected to the parachute canopy through string chords.
|Figure: vorticity near parachute with cargo considered as a mass point and a rigid body|
A numerical scheme aiming to model the permeability of the fabric surface in incompressible fluid was proposed by coupling the projection method with Ghost Fluid Method in the front tracking framework. The pressure jump condition is considered by adding a source term to the pressure Poisson equation without modification on its coefficients.
|Figure: comparison of flow pattern between fabric with low porosity and high porosity. The left plot is a canopy with high porosity and right one with low porosity. The parachute system is more stable with high porosity canopy but will have smaller drag force.|
Resolution of collision between different parts of fabric surface or between fabric surface and rigid body is a very delicate problem in mathematical algorithm and computational geometry. In order to resolve fabric collision during parachute inflation process, we have implemented a collision handling function to detect and unwrap the surface in each time step. This method can guarantee no dynamic self-interference of cloth after a successful call of the function. Our algorithm can efficiently and robustly handle the fabric-fabric and fabric-rigid body collision. We are still in the process of implementing and testing the fabric-string and string-string collision.
|Figure: fabric collision with different objects.|
Parallelization and Multi-parachute system
The parachute code is parallelized on both CPU and GPU system. It adopts a hybrid parallel algorithm which solves the fluid equation through domain decomposition using MPI and the spring-mass system (an ODE system) through using GPU processors. The software is also capable of simulating multi-parachute system.
|Figure: parallelization in 16 processors and simulation of multi-parachute inflation|
This work is sponsored by the Department of Defense through the Army Research Office under the award "Robust and High Order Computational Methods for Parachute Air Delivery and MAV Systems" W911NF-14-1-0428, and the DURIP (Defense University Research Instrumentation Program) award "A Transitional Computational Platform to Migrate Parachute Simulation from Workstation to HPC" W911NF-15-1-0403, with Xiaolin Li as the principal investigator.