^{1}

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^{3}

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The flow past a parachute with and without a vent hole at the top is studied both experimentally and numerically. The effects of Reynolds number and vent ratio on the flow behaviour as well as on the drag coefficient are examined. The experiments were carried out under free-flow conditions. In the numerical simulations, the flow was considered as unsteady and turbulent and was modelled using the standard

The study of bluff bodies involves the consideration of complex aerodynamic phenomena such as semiwake and vortex shedding. The analysis of parachute dynamics is one of the most interesting problems, which would lie within this context. One important feature that may distinguish the computational fluid dynamics (CFD) modelling from the experimental analysis of the parachute behaviour is the geometry flexibility in the latter allowing large variations in the experiments [

Hemispherical shell with a vent in the Cartesian coordinates system.

According to the experimental work of Bakic and Peric [

A circular disk can be regarded as a good representative of round parachutes since the separation line is fixed at the disk edge. Fuchs et al. [

Experimental investigation of the drag forces on flexible rectangular canopies was conducted by Filippone [

A complete understanding of the flow physics around a parachute is still one of the most scientific challenging issues from both the theoretical and experimental viewpoints. Recent efforts that have successfully benefited from using CFD simulations could explain the basic principles behind this phenomenon. Thus far, a comprehensive research has not been performed to study the variations of drag coefficient of the flexible canopies with the Reynolds number and vent ratios. In this paper, the experimental tests and numerical simulations are conducted to obtain the drag coefficient on a hemispherical shell for different Reynolds numbers and vent ratios. The venthole is located at the shell apex. The main purpose is to find the effects of the Reynolds number and vent diameter on the drag coefficient as well as on the flow field. These findings may be useful in parachute designing and its applications.

The experiments were conducted under the free-flow conditions (i.e., at the atmospheric pressure and temperature). The test rig was mounted on a vehicle, which moved with the speed of 8.3 to 33.3 m/s. The inflated canopy setup mounted on the vehicle along with the supporting hardware is shown in Figure

Top view of the experimental setup (not to scale).

By streamlining the support and reducing its diameter, the wakes around the support were kept to a minimum. Flow visualization confirmed that the wake of support rods had a negligible effect on the dynamics of the parachute canopy. The vent ratio of the parachute is varied from 0% to 20% (i.e.,

Two typical parachutes utilized in the present experiments.

For the external flows around spherical obstacles, the critical Reynolds number is about 800, beyond which the wake flow becomes turbulent [

In these equations,

The flow equations, described above, are solved by FLUENT’s pressure-based segregated solver. It is worth mentioning that when

Here ^{−3} and ^{−1}·s^{−1}, respectively. These values are kept constant during the simulation process.

Figure

CFD mesh points and boundary conditions.

Grid size-dependence study of drag coefficient at different mesh densities.

The first order upwind scheme is utilized to discretize the convective terms, and the SIMPLE algorithm is used for solving the governing equations. It must be noted that the calculations are allowed to continue for 8 seconds until the parameters like

The numerical simulations have been carried out for different grid densities in order to find the grid independent solutions. For this purpose, first the grid independence study has been accomplished for

In order to investigate the parachute performance under different flow conditions, six parachutes with various vent diameter ratios

Drag coefficient variations as a function of the Reynolds number for different vent ratios.

It is clear that for all the vent ratios tested,

Figure

Experimental drag coefficient variations against vent ratios for different Reynolds numbers.

Figure

Velocity vectors around a hemispherical shell parachute under different conditions.

According to this figure, it is evident that for all the vent ratios and the Reynolds numbers tested, two wakes both inside and outside the parachute are observed. In addition, the outer wakes are responsible for increasing the drag force.

The size of these wakes seems to increase moderately as the Reynolds number is increased. In general, the vent ratio is the main cause of the pressure difference decrease across the wall of the parachutes (i.e., between the outer and inner regions of it). In fact, by increasing the vent diameter the outflow flux increases, hence, decreasing the pressure difference between the inner and outer regions of the parachute.

During the experimental tests, the parachute was observed to be oscillating when the Reynolds number exceeded some certain values.

At low Reynolds numbers, the parachute was found to be stable without any oscillations. However, as the Reynolds number was increased beyond a certain value, the parachute became unstable. So transitions from stable to unstable condition were observed for all vent ratios. Figure

Stable and unstable zones obtained from the experimental analysis.

It is clear that as the vent diameter is increased, the transition from stable to unstable conditions is delayed. For the parachute without venthole, at

It may be noted that by increasing the vent ratio, the critical Reynolds number at which the parachute started to oscillate is increased. For parachutes with vent ratios of 8% and 12%, these critical Reynolds numbers are 171100 and 292600, respectively.

In this paper, the dynamic behaviour of a parachute is studied both experimentally and numerically. Different cases with various vent ratios are tested at different Reynolds numbers. In the numerical simulations, the flow is considered turbulent and the standard

Area (m^{2})

Drag coefficient

Vent diameter (m)

Canopy diameter (m)

Drag force (N)

Turbulence kinetic energy (m^{2}·s^{−2})

Mach number

Pressure (N·m^{−2})

Reynolds number

Free stream velocity (m·s^{−1}).

Turbulence dissipation rate (m^{2} s^{−3})

Density (kg m^{−3})

Dynamic viscosity (kg m^{−1} s^{−1})

Turbulent viscosity (kg m^{−1} s^{−1}).

Direction

Maximum

Minimum.