High Reynolds number incompressible flow simulation about parachute canopies and similar bluff bodies
A model for the flow around bluff bodies has been developed. It is applied to an investigation of parachute canopy aerodynamic characteristics. Since the model assumes an axisymmetric incompressible high Reynolds number flow, it is only applicable to the calculation of aerodynamic characteristics at zero angle of attack. The flow is assumed to separate from the canopy at its surface discontinuity, i.e. the canopy hemline. The vorticity created in the boundary layer over the canopy upper surface is carried downstream, forming a free shear layer. In the flow field vorticity is confined to the this shear layer, outside it the flow is irrotational. Consequently, in this part of the fluid field a velocity potential can be defined. The wake flow created by bluff canopies is found to consist of a cluster of vortex rings which are shed periodically to the wake. Consequently, the axial aerodynamic force developed on the canopy will exhibit periodic behaviour. The resulting Strouhal number, has been determined to be about 0.13, based on the canopy projected area diameter. For all axisymmetric bluff canopies considered the calculated mean axial force coefficient, based on the canopy projected diameter, was found to be between 1.20 and 1.45. These values, together with the calculated pressure distribution and the wake flow periodicity, are in good agreement with known experiments. For parachute canopies performing an oscillatory axial motion the calculated results compare well with experimental data. However, it is shown that Morison's formula for this axial force is, generally, inadequate. Limited calculations of axial forces developed on the inflating parachute canopies agree with the sparse experimental data available. In the model the real flow field is simulated, basically, by a potential model. The canopy surface is replaced by a vortex ring panel lattice. Each panel contains a circular bound vortex ring which is located at one quarter panel length. For each panel the flow boundary conditions on the canopy surface are fulfilled along a control circle at three quarters of the panel length. A standing eddy which is generated by the high back-flow developed near the canopy hemline, on the canopy under surface is simulated by a standing vortex ring. The simulation of a two-dimensional discrete vortex separated wake is extended to the axisymmetric case by representing the separated wake with axisymmetric discrete vortex rings. The free shear layer emanating from the canopy hemline is represented by discrete free vortex rings which leave the canopy surface tangentially. At each time step in the calculation process a newly-created vortex ring is shed to the wake. In the vortex modelling of the separated wake a number of new elements have been introduced: -improvement of the near wake simulation by accounting for the standing eddy on the canopy under surface; -a simple method of calculating the newly created vortex ring strength & location; -reduction of the free parameters from two, the time step and the number of panels representing the canopy surface to one, i.e. the number of panels. Further model validation & implementation have been suggested. Methods of model development for asymmetric canopy representation have been discussed.