research article a numerical and experimental study of the aerodynamics and stability … · 2019....

Hindawi Publishing CorporationISRN Aerospace EngineeringVolume 2013 Article ID 320563 8 pageshttpdxdoiorg1011552013320563

Research ArticleA Numerical and Experimental Study ofthe Aerodynamics and Stability of a Horizontal Parachute

Mazyar Dawoodian1 Abdolrahman Dadvand2 and Amir Hassanzadeh3

1 Department of Mechanical Engineering I A University of Takestan Takestan Iran2Department of Mechanical Engineering Urmia University of Technology Urmia Iran3Department of Mechanical Engineering Urmia University Urmia Iran

Correspondence should be addressed to Mazyar Dawoodian mazyar dawoodianyahoocom

Received 24 May 2013 Accepted 26 June 2013

Academic Editors J Lopez-Puente and R K Sharma

Copyright copy 2013 Mazyar Dawoodian et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The flow past a parachute with and without a vent hole at the top is studied both experimentally and numerically The effects ofReynolds number and vent ratio on the flow behaviour as well as on the drag coefficient are examinedThe experiments were carriedout under free-flow conditions In the numerical simulations the flow was considered as unsteady and turbulent and was modelledusing the standard 119896-120576 turbulence model The experimental results reveal good agreement with the numerical ones In both theexperiments and numerical simulations the Reynolds number was varied from 85539 to 357250 and the vent ratio was increasedfrom zero to 20 The results show that the drag coefficient decreases by increasing the Reynolds number for all the cases testedIn addition it was found that at low and high Reynolds numbers the parachutes respectively with 4 vent ratio and withoutvent are deemed more efficient One important result of the present work is related to the effect of vent ratio on the stability of theparachute

1 Introduction

The study of bluff bodies involves the consideration of com-plex aerodynamic phenomena such as semiwake and vortexshedding The analysis of parachute dynamics is one ofthe most interesting problems which would lie within thiscontext One important feature that may distinguish thecomputational fluid dynamics (CFD) modelling from theexperimental analysis of the parachute behaviour is thegeometry flexibility in the latter allowing large variations inthe experiments [1] A parachute is generally equipped witha venthole at the apex to allow some air to flow through theopen canopyThe canopy can be represented by a hemispher-ical shell which has been shown schematically in Figure 1In the numerical simulations carried out in the presentwork the canopy is considered solid and its direction ofmotion is from left to right (ie the flow direction is fromright to left in the positive 119909 direction) The flow structurenear the wake of canopy is responsible for the aerodynamicforces and moments it experiencesThe relationship between

the Reynolds number and flow field structure around spher-ical bodies in incompressible flow regime has been studiedextensively The numerical study carried out by Natarajanand Acrivos [2] indicated that the wake of a sphere becameunstable at a Reynolds number of 105 The experimentalresults of Sakamoto and Haniu [3] showed that the hairpin-shaped vortices begin to be periodically shading when theReynolds number reaches about 350Their research indicatedthat when the Reynolds number exceeds 6000 the vortexsheet separating from the surface of the sphere becomescompletely turbulent

According to the experimental work of Bakic and Peric[4] in wind tunnel and water channel for the Reynoldsnumbers between 22000 and 50000 the near-wake recircu-lation region was observed to be large and the wake wouldperform a progressive wave motion They also found that asthe Reynolds number was increased from 22000 to 350000the boundary layer separation point would move from about82∘ to 132∘

2 ISRN Aerospace Engineering

Velo

city

inle

t

d D

Cano

py

Vent

X

Y

Z

Figure 1 Hemispherical shell with a vent in the Cartesian coordi-nates system

A circular disk can be regarded as a good representativeof round parachutes since the separation line is fixed atthe disk edge Fuchs et al [5] and Berger et al [6] havestudied the flow structure around the disk and identifiedthree instability modes an axisymmetric oscillation of therecirculation bubble at a low Strouhal number (asymp005) alow-frequency mode at a Strouhal number of about 014and a high-frequency mode at a Strouhal number equalsto 16 The main recirculation bubble extends to about 25diameters behind the disk Flow visualization of Higuchi [7]confirmed the primary helical mode at a Reynolds numberof 104 in the disk wake However close-up observationsin a water tunnel revealed that the tilting of vortex ringsresults in asymmetric structures after the first diameter in thedisk wake Peterson et al [8] have studied the characteristicfeatures of parachute canopies during various stages frombreathing to final developing

Experimental investigation of the drag forces on flex-ible rectangular canopies was conducted by Filippone [9]He showed that the drag coefficient decreased weakly byincreasing the Reynolds number to 2000000 and decreasedintensively by increasing the ratio of perforated tape area toplan form area Izadi and Mohammadizadeh [10] and Izadiand Dawoodian [11] have numerically studied the Relation-ship between the drag coefficient and the vent diameterTakizawa et al [12] performed a comprehensive numericalcalculation on the fluid-structure interaction (FSI) modellingof clusters of ringsail parachutes They also presented abrief stability and accuracy analysis for the deforming-spatial-domainstabilized space-time (DSDSST) formula-tion which is the core numerical technology of the SSTFSItechnique Cao and Jiang [13] calculated the drag coefficientfor a parachute using a finite volume method and Spalart-Allmaras turbulencemodelThe separation flowwhich truth-fully reflects the characteristics during the terminal descentaccords with the fluid dynamics rules in their study Caoand Xu [14] analyzed canopy shape and the parameters ofparachute inflation bymeans of establishing parachutersquos flyingphysical model through four methods (ie tiny segmentanalysis method inflating distancemethod momentmethod

and simulating canopy shape method) They concluded thatmoment method and simulating canopy shape method areonly fitted to the main phase of inflating in theory andinflating distance method can be applied to evaluate thedynamic load of parachute inflation

A complete understanding of the flow physics arounda parachute is still one of the most scientific challengingissues fromboth the theoretical and experimental viewpointsRecent efforts that have successfully benefited from usingCFD simulations could explain the basic principles behindthis phenomenonThus far a comprehensive research has notbeen performed to study the variations of drag coefficientof the flexible canopies with the Reynolds number and ventratios In this paper the experimental tests and numericalsimulations are conducted to obtain the drag coefficient on ahemispherical shell for different Reynolds numbers and ventratios The venthole is located at the shell apex The mainpurpose is to find the effects of the Reynolds number and ventdiameter on the drag coefficient as well as on the flow fieldThese findings may be useful in parachute designing and itsapplications

2 Experimental Setup

The experiments were conducted under the free-flow con-ditions (ie at the atmospheric pressure and temperature)The test rig was mounted on a vehicle which moved withthe speed of 83 to 333ms The inflated canopy setupmounted on the vehicle along with the supporting hardwareis shown in Figure 2 schematically The parachute assemblywas positioned in a horizontal orientation The canopy wasattached to a stationary support by six threads The fore-body had a diameter of 14 cm and a length of 2mThe cross-sectional area of the support was less than 2 of the projectedarea of the canopy

By streamlining the support and reducing its diameterthe wakes around the support were kept to a minimumFlow visualization confirmed that the wake of support rodshad a negligible effect on the dynamics of the parachutecanopy The vent ratio of the parachute is varied from 0to 20 (ie 119889119863 = 0ndash02) The Reynolds number for aparachute canopy is commonly based on the diameter 119863In this research the Reynolds number ranges from 85539to 357250 A dynamometer was used to record the force atevery stage of the experiment Figure 3 displays two typicalparachutes with a venthole used in the experiments

3 Numerical Simulation

31 Governing Equations For the external flows aroundspherical obstacles the critical Reynolds number is about800 beyond which the wake flow becomes turbulent [15]Since all the Reynolds numbers considered in the presentwork are much greater than this critical Reynolds the flowaround the parachute is assumed to be turbulent Thereforethe three-dimensional unsteady Reynolds-averaged Navier-Stokes (RANS) equations combined with the standard 119896-120576turbulence model are employed to simulate the flow around

ISRN Aerospace Engineering 3

Dynamometer

Parachute

Support

V

Figure 2 Top view of the experimental setup (not to scale)

Figure 3 Two typical parachutes utilized in the present experi-ments

the parachute It may be noted that the RNG 119896-120576 turbulencemodel and more advanced turbulence models such as theReynolds stress equations were also investigated but thesemodels could not give good numerical results Since theexperiments were performed under the free-flow conditionsthe parachute would not have a significant effect on thetemperature of air so in the simulations the density ofair is assumed constant In addition since the minimumand maximum Mach numbers are equal respectively to0033 and 0137 the flow was considered incompressibleThe governing RANS equations (ie the continuity andmomentum equations) are given as

120597119906119894

120597119909119894

= 0

120588 (120597119906119894

120597119905+ 119906119895

120597119906119894

120597119909119895

) = minus120597119901

120597119909119894

+ 119861119894

+120597

120597119909119895

(120583120597119906119894

120597119909119895

minus 1205881199061015840

119894

1199061015840

119895

)

(1)

119861119894is the body force(s) in the 119894th direction The normal

velocity on all surfaces of the body is considered zero

The turbulence kinetic energy 119896 and its rate of dissipation 120576

are obtained from the following transport equations

120588120597119896

120597119905+ 120588 (119906

119895

120597119896

120597119909119895

) =120597

120597119909119895

[(120583 +120583119905

120590119896

)120597119896

120597119909119895

] + 119866119896

+ 119866119887

minus 120588120576 minus 119884119872

120588120597120576

120597119905+ 120588 (119906

119895

120597120576

120597119909119895

) =120597

120597119909119895

[(120583 +120583119905

120590120576

)120597120576

120597119909119895

]

+ 1198621120576

120576

119896(119866119896

+ 1198623120576

119866119887) minus 1198622120576

1205881205762

119896

(2)

In these equations 119866119896 119866119887 and 119884

119872represent the gener-

ation of turbulence kinetic energy due to the mean velocitygradients the generation of turbulence kinetic energy due tobuoyancy and the contribution of the fluctuating dilatationin compressible turbulence to the overall dissipation raterespectively 119862

1120576and 119862

2120576are constants 120590

119896and 120590

120576are the

turbulent Prandtl numbers for 119896 and 120576 respectively Theturbulent (or eddy) viscosity 120583

119905is computed as follows

120583119905

= 120588119862120583

1198962

120576 (3)

where 119862120583is a constant The constants 119862

1120576 1198622120576 119862120583 120590119896 and 120590

120576

take the following values 1198621120576

= 144 1198622120576

= 192 119862120583

= 009120590119896

= 10 and 120590120576

= 13The flow equations described above are solved by FLU-

ENTrsquos pressure-based segregated solver It is worth mention-ing that when Re gt 10

3 the inertial forces dominate and thedrag force is approximately proportional to the square of thevelocity that is 119865

119889= 05120588119862

1198891198601198802

infin

Here 119862

119889is the drag coefficient defined as

119862119889

=119865119889

05120588119860119880 2infin

(4)

where 119860 = (1205871198632

4) is the projected area of the hemi-spherical cup and 119880

infinis the free stream velocity The fluid

properties are considered at standard condition Thereforethe air density 120588 and viscosity 120583 are taken as 125 kgsdotmminus3and 178 times 10

minus5 kgsdotmminus1sdotsminus1 respectivelyThese values are keptconstant during the simulation process

32 Numerical Model Description and Boundary ConditionsFigure 4 depicts the 3D-CFD model of the parachute alongwith the boundary conditions Note that in all of thesimulations carried out in the present work the geometricaldimensions of the parachute are kept constant Howeverthe vent diameter and the Reynolds number are varied inorder to study their effect on the drag coefficient as wellas on the flow structure In addition to linkmatch similarconditions between the simulations and experiments thenumerical Reynolds numbers are chosen the same as thoseof the experiments An unstructured (or irregular) T-Gridmesh with finer mesh points near the parachute body is usedAs shown in Figure 5 the computational domain assumes


Outflow

Parachute

Velocity inlet

XY

Z

Figure 4 CFD mesh points and boundary conditions

16

164

168

172

176

0 5 10 15 20

Dra

g co

effici

ent

Number of grids times105

Figure 5 Grid size-dependence study of drag coefficient at differentmesh densities

a cylindrical shape where A B and C distances are takenas 46 10 and 10 times the parachute diameter 119863 respec-tively

The first order upwind scheme is utilized to discretizethe convective terms and the SIMPLE algorithm is usedfor solving the governing equations It must be noted thatthe calculations are allowed to continue for 8 seconds untilthe parameters like 119862

119889remain constant that is the results

are associated with the steady state condition The outflowboundary condition has been applied at both the lateral andoutlet boundaries and the velocity inlet has been consideredas the inlet boundary condition The no-slip boundarycondition is applied on the body of the hemispherical cupThe main boundaries are shown in Figure 4

33 Grid Dependence Study The numerical simulations havebeen carried out for different grid densities in order to findthe grid independent solutions For this purpose first the gridindependence study has been accomplished for Re = 85539

and 119889119863 = 0 The variations of the drag coefficient as thekey parameter against the number of grid cells have beendepicted in Figure 5 According to this figure a grid system of1344000 tetrahedral cells was found to be sufficient to resolvethe details of the flowfieldTherefore nominally a grid systemof 1344000 tetrahedral cells was used in all the simulationscarried out in the present work

4 Results and Discussions

41 Drag Coefficient In order to investigate the parachuteperformance under different flow conditions six parachuteswith various vent diameter ratios 119889119863 of 0 004 008012 016 and 020 each at different Reynolds numbers of85539 114000 146330 171100 228070 292660 and 357250are studied in both the experimental and numerical casesFigure 6 shows the numerical and experimental drag coeffi-cient 119862

119889variations as a function of the Reynolds number for

different vent ratios of 0ndash20It is clear that for all the vent ratios tested 119862

119889decreases

by increasing the Reynolds number In addition the dragcoefficient seems to experience a (relatively) sharp decreaseat lower Reynolds numbers but it takes a smooth change asthe Reynolds number increases One can also observe that thevalue of 119862

119889reaches a constant value and the diagram finds an

asymptote Although the trend of all the diagrams in Figure 6is roughly the same this tendency is more evident for 119889119863

= 0 012 and 02 There is a good agreement between theexperimental and numerical results for all the cases studiedThe difference between the maximum and minimum valuesof 119862119889is about 02 which corresponds to the case with 119889119863 =

020Figure 7 illustrates the experimental 119862

119889changes versus

vent ratio 119889119863 for different Reynolds numbers The resultsshow that 119862

119889decreases by increasing the Reynolds num-

ber This may be attributed to the fact that the formationof the wakes behind the parachute causes the drag forceto decrease In all the Reynolds numbers tested exceptin the last two ones (ie Re = 292660 and 357250) theparachute with 119889119863 ratio of 004 possesses the highestvalue of the drag coefficient as compared to the other ventratios According to this figure the maximum amount of119862119889achieved during the experiments is 177 which pertains

to Re = 85539 and 119889119863 = 004 For the 119889119863 valuesgreater than 004 119862

119889will be below this value for all the

Reynolds numbers tested Therefore at high Reynolds num-bers it is suggested to use parachutes without vent sincesuch parachutes experience higher 119862

119889in comparison with

the other cases

42 The Flow Field around the Parachute Figure 8 showsthe velocity vectors related to the unsteady turbulent flowaround the parachute obtained from the numerical simula-tions

According to this figure it is evident that for all the ventratios and the Reynolds numbers tested two wakes bothinside and outside the parachute are observed In additionthe outer wakes are responsible for increasing the dragforce

The size of these wakes seems to increase moderatelyas the Reynolds number is increased In general the ventratio is the main cause of the pressure difference decreaseacross the wall of the parachutes (ie between the outerand inner regions of it) In fact by increasing the ventdiameter the outflow flux increases hence decreasing thepressure difference between the inner and outer regions of theparachute


5 15 25 35 45155

16

165

17

175

18Cd

dD = 0

Re (times104)

(a)

5 10 15 20 25 30 35 40155

16

165

17

175

18

Cd

dD = 004

Re (times104)

(b)

15

155

16

165

17

175

Cd

dD = 008

5 10 15 20 25 30 35 40Re (times104)

(c)

dD = 012

15

155

16

165

17

175

Cd

5 10 15 20 25 30 35 40Re (times104)

(d)

ExperimentalNumerical

15

155

16

165

17

175

Cd

5 10 15 20 25 30 35 40

dD = 016

Re (times104)

(e)


5 10 15 20 25 30 35 40145

15

155

16

165

17

dD = 02

Cd

Re (times104)

(f)

Figure 6 Drag coefficient variations as a function of the Reynolds number for different vent ratios

43 Stability Analysis During the experimental tests theparachute was observed to be oscillating when the Reynoldsnumber exceeded some certain values

At low Reynolds numbers the parachute was found tobe stable without any oscillations However as the Reynoldsnumber was increased beyond a certain value the parachute

became unstable So transitions from stable to unstablecondition were observed for all vent ratios Figure 9 showsthe stable and unstable regions observed in the experiments

It is clear that as the vent diameter is increased thetransition from stable to unstable conditions is delayed Forthe parachute without venthole at Re = 85539 no oscillation


Re = 85539Re = 114000Re =146330Re = 171100

Re = 228070Re= 292660Re = 357250

14

145

15

155

16

165

17

175

18

0 004 008 012 016 02

Cd

dD

Figure 7 Experimental drag coefficient variations against vent ratios for different Reynolds numbers

is observed However for Re = 114000 we observed veryintensive oscillations For the parachute with vent of 4 theoscillations were commenced at Re = 114000

It may be noted that by increasing the vent ratio thecritical Reynolds number at which the parachute started tooscillate is increased For parachutes with vent ratios of 8and 12 these critical Reynolds numbers are 171100 and292600 respectively

5 Conclusion

In this paper the dynamic behaviour of a parachute is studiedboth experimentally and numerically Different cases withvarious vent ratios are tested at different Reynolds numbersIn the numerical simulations the flow is considered turbulentand the standard 119896-120576 turbulence model is used to modelthe flow field In addition an unsteady state condition isconsidered for the numerical models but the calculationsare continued until the results remain constant The CFDsimulations have been done by using FLUENT software Theeffects of the vent ratio and the Reynolds number on the dragcoefficient are examined The results show that for all casesas the Reynolds number is increased the drag coefficient isdecreased In addition in all the simulations carried out in thepresent work two wakes are observed behind the parachuteThe maximum value of the drag coefficient measured duringthe experiments is about 177 which is associated with Re =

85539 and 119889119863 = 004 In addition at high Reynoldsnumbers the parachute without vent experiences a higherdrag force as compared with the other cases Comparisonbetween the simulations and experiments evidences goodagreements Finally the experiments show that the parachutebegins oscillating when the Reynolds numbers exceed acertain critical value which is different for different vent

ratios This would imply that every case has a stable andunstable region As the vent ratio increases the oscillationswould occur at higher Reynolds numbers

Abbreviations

Nomenclature

119860 Area (m2)119862119889 Drag coefficient

119889 Vent diameter (m)119863 Canopy diameter (m)119865119889 Drag force (N)

119896 Turbulence kinetic energy (m2sdotsminus2)119872 Mach number119901 Pressure (Nsdotmminus2)Re Reynolds number119880infin Free stream velocity (msdotsminus1)

Greek Symbols

120576 Turbulence dissipation rate (m2 sminus3)120588 Density (kgmminus3)120583 Dynamic viscosity (kgmminus1 sminus1)120583119905 Turbulent viscosity (kgmminus1 sminus1)

Subscripts

119894 Directionmax Maximummin Minimum


Re = 85539 Re =146330 Re = 228070 Re = 357250

dD

0

004

008

(a)

Re = 85539 Re =146330 Re = 228070 Re = 357250

dD

012

016

02

(b)

Figure 8 Velocity vectors around a hemispherical shell parachute under different conditions


02

016

012

008

004

0

Vent

ratio

0 5 10 15 20 25 30 35 40 45 50

Stable regionTransition regionUnstable region

Re (times104)

Figure 9 Stable and unstable zones obtained from the experimentalanalysis

References

[1] A Al Musleh and A Frendi ldquoOn the effects of a flexiblestructure on boundary layer stability and transitionrdquo Journal ofFluids Engineering vol 133 no 7 Article ID 071103 6 pages2011

[2] R Natarajan and A Acrivos ldquoThe instability of the steady flowpast spheres and disksrdquo Journal of Fluid Mechanics vol 254 pp323ndash344 1993

[3] H Sakamoto and H Haniu ldquoA study on vortex shedding fromspheres in a uniformflowrdquo Journal of Fluids Engineering vol 112no 4 pp 386ndash392 1990

[4] V Bakic and M Peric ldquoVisualization of flow around spherefor Reynolds numbers between 22000 and 400000rdquo Thermo-physics and Aeromechanics vol 12 no 3 pp 307ndash315 2005

[5] H V Fuchs E Mercker and U Michel ldquoLarge-scale coherentstructures in the wake of axisymmetric bodiesrdquo Journal of FluidMechanics vol 93 no 1 pp 185ndash207 1979

[6] E Berger D Scholz and M Schumm ldquoCoherent vortexstructures in thewake of a sphere and a circular disk at rest andunder forced vibrationsrdquo Journal of Fluids and Structures vol 4no 3 pp 231ndash257 1990

[7] H Higuchi ldquoVisual study on wakes behind solid and slottedaxisymmetric bluff bodiesrdquo Journal of Aircraft vol 28 no 7 pp427ndash430 1991

[8] C W Peterson J H Strickland and H Higuchi ldquoThe fluiddynamics of parachute inflationrdquo Annual Review of FluidMechanics vol 28 pp 361ndash387 1996

[9] A Filippone ldquoOn the flutter and drag forces on flexible rect-angular canopies in normal flowrdquo Journal of Fluids Engineeringvol 130 no 6 Article ID 061203 8 pages 2008

[10] M J Izadi and M Mohammadizadeh ldquoNumerical study of ahemi-spherical cup in steady unsteady laminar and turbulentflow conditions with a vent of air at the toprdquo Fluids AnnualReview of Fluid Mechanics vol 28 pp 361ndash387 2008

[11] M J Izadi andMDawoodian ldquoCFD analysis of drag coefficientof a parachute in steady and turbulent conditions in variousReynolds numbersrdquo in Proceedings of the Fluids EngineeringDivision Summer Conference (FEDSM rsquo09) pp 2285ndash2293ASME Colorado Colo USA August 2009

[12] K Takizawa S Wright C Moorman and T E TezduyarldquoFluid-structure interaction modeling of parachute clustersrdquoInternational Journal for Numerical Methods in Fluids vol 65no 1ndash3 pp 286ndash307 2011

[13] Y Cao and C Jiang ldquoNumerical simulation of the flow fieldaround parachute during terminal descentrdquo Aircraft Engineer-ing and Aerospace Technology vol 79 no 3 pp 268ndash272 2007

[14] Y Cao and H Xu ldquoParachute flying physical model and infla-tion simulation analysisrdquo Aircraft Engineering and AerospaceTechnology vol 76 no 2 pp 215ndash220 2004

[15] D Ormieres andM Provansal ldquoTransition to turbulence in thewake of a sphererdquo Physical Review Letters vol 83 no 1 pp 80ndash83 1999

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Propagation




Navigation and Observation



DistributedSensor Networks



Velo

city

inle

t

d D

Cano

py

Vent

X

Y

Z

Figure 1 Hemispherical shell with a vent in the Cartesian coordi-nates system

A circular disk can be regarded as a good representativeof round parachutes since the separation line is fixed atthe disk edge Fuchs et al [5] and Berger et al [6] havestudied the flow structure around the disk and identifiedthree instability modes an axisymmetric oscillation of therecirculation bubble at a low Strouhal number (asymp005) alow-frequency mode at a Strouhal number of about 014and a high-frequency mode at a Strouhal number equalsto 16 The main recirculation bubble extends to about 25diameters behind the disk Flow visualization of Higuchi [7]confirmed the primary helical mode at a Reynolds numberof 104 in the disk wake However close-up observationsin a water tunnel revealed that the tilting of vortex ringsresults in asymmetric structures after the first diameter in thedisk wake Peterson et al [8] have studied the characteristicfeatures of parachute canopies during various stages frombreathing to final developing

Experimental investigation of the drag forces on flex-ible rectangular canopies was conducted by Filippone [9]He showed that the drag coefficient decreased weakly byincreasing the Reynolds number to 2000000 and decreasedintensively by increasing the ratio of perforated tape area toplan form area Izadi and Mohammadizadeh [10] and Izadiand Dawoodian [11] have numerically studied the Relation-ship between the drag coefficient and the vent diameterTakizawa et al [12] performed a comprehensive numericalcalculation on the fluid-structure interaction (FSI) modellingof clusters of ringsail parachutes They also presented abrief stability and accuracy analysis for the deforming-spatial-domainstabilized space-time (DSDSST) formula-tion which is the core numerical technology of the SSTFSItechnique Cao and Jiang [13] calculated the drag coefficientfor a parachute using a finite volume method and Spalart-Allmaras turbulencemodelThe separation flowwhich truth-fully reflects the characteristics during the terminal descentaccords with the fluid dynamics rules in their study Caoand Xu [14] analyzed canopy shape and the parameters ofparachute inflation bymeans of establishing parachutersquos flyingphysical model through four methods (ie tiny segmentanalysis method inflating distancemethod momentmethod

and simulating canopy shape method) They concluded thatmoment method and simulating canopy shape method areonly fitted to the main phase of inflating in theory andinflating distance method can be applied to evaluate thedynamic load of parachute inflation

A complete understanding of the flow physics arounda parachute is still one of the most scientific challengingissues fromboth the theoretical and experimental viewpointsRecent efforts that have successfully benefited from usingCFD simulations could explain the basic principles behindthis phenomenonThus far a comprehensive research has notbeen performed to study the variations of drag coefficientof the flexible canopies with the Reynolds number and ventratios In this paper the experimental tests and numericalsimulations are conducted to obtain the drag coefficient on ahemispherical shell for different Reynolds numbers and ventratios The venthole is located at the shell apex The mainpurpose is to find the effects of the Reynolds number and ventdiameter on the drag coefficient as well as on the flow fieldThese findings may be useful in parachute designing and itsapplications

2 Experimental Setup

The experiments were conducted under the free-flow con-ditions (ie at the atmospheric pressure and temperature)The test rig was mounted on a vehicle which moved withthe speed of 83 to 333ms The inflated canopy setupmounted on the vehicle along with the supporting hardwareis shown in Figure 2 schematically The parachute assemblywas positioned in a horizontal orientation The canopy wasattached to a stationary support by six threads The fore-body had a diameter of 14 cm and a length of 2mThe cross-sectional area of the support was less than 2 of the projectedarea of the canopy

By streamlining the support and reducing its diameterthe wakes around the support were kept to a minimumFlow visualization confirmed that the wake of support rodshad a negligible effect on the dynamics of the parachutecanopy The vent ratio of the parachute is varied from 0to 20 (ie 119889119863 = 0ndash02) The Reynolds number for aparachute canopy is commonly based on the diameter 119863In this research the Reynolds number ranges from 85539to 357250 A dynamometer was used to record the force atevery stage of the experiment Figure 3 displays two typicalparachutes with a venthole used in the experiments

3 Numerical Simulation

31 Governing Equations For the external flows aroundspherical obstacles the critical Reynolds number is about800 beyond which the wake flow becomes turbulent [15]Since all the Reynolds numbers considered in the presentwork are much greater than this critical Reynolds the flowaround the parachute is assumed to be turbulent Thereforethe three-dimensional unsteady Reynolds-averaged Navier-Stokes (RANS) equations combined with the standard 119896-120576turbulence model are employed to simulate the flow around


Dynamometer

Parachute

Support

V




120597119906119894

120597119909119894

= 0

120588 (120597119906119894

120597119905+ 119906119895

120597119906119894

120597119909119895

) = minus120597119901

120597119909119894

+ 119861119894

+120597

120597119909119895

(120583120597119906119894

120597119909119895

minus 1205881199061015840

119894

1199061015840

119895

)

(1)





120588120597119896

120597119905+ 120588 (119906

119895

120597119896

120597119909119895

) =120597

120597119909119895

[(120583 +120583119905

120590119896

)120597119896

120597119909119895

] + 119866119896

+ 119866119887

minus 120588120576 minus 119884119872

120588120597120576

120597119905+ 120588 (119906

119895

120597120576

120597119909119895

) =120597

120597119909119895

[(120583 +120583119905

120590120576

)120597120576

120597119909119895

]

+ 1198621120576

120576

119896(119866119896

+ 1198623120576

119866119887) minus 1198622120576

1205881205762

119896

(2)




1120576and 119862


119896and 120590

120576are the



120583119905

= 120588119862120583

1198962

120576 (3)


1120576 1198622120576 119862120583 120590119896 and 120590

120576


= 144 1198622120576

= 192 119862120583

= 009120590119896

= 10 and 120590120576




119889= 05120588119862

1198891198601198802

infin

Here 119862


119862119889

=119865119889

05120588119860119880 2infin

(4)

where 119860 = (1205871198632







Outflow

Parachute

Velocity inlet

XY

Z


16

164

168

172

176

0 5 10 15 20

Dra

g co

effici

ent













119889decreases














the other cases





5 15 25 35 45155

16

165

17

175

18Cd

dD = 0

Re (times104)

(a)

5 10 15 20 25 30 35 40155

16

165

17

175

18

Cd

dD = 004

Re (times104)

(b)

15

155

16

165

17

175

Cd

dD = 008

5 10 15 20 25 30 35 40Re (times104)

(c)

dD = 012

15

155

16

165

17

175

Cd

5 10 15 20 25 30 35 40Re (times104)

(d)


15

155

16

165

17

175

Cd

5 10 15 20 25 30 35 40

dD = 016

Re (times104)

(e)


5 10 15 20 25 30 35 40145

15

155

16

165

17

dD = 02

Cd

Re (times104)

(f)







Re = 85539Re = 114000Re =146330Re = 171100

Re = 228070Re= 292660Re = 357250

14

145

15

155

16

165

17

175

18

0 004 008 012 016 02

Cd

dD




5 Conclusion




Abbreviations

Nomenclature




Greek Symbols


Subscripts



Re = 85539 Re =146330 Re = 228070 Re = 357250

dD

0

004

008

(a)

Re = 85539 Re =146330 Re = 228070 Re = 357250

dD

012

016

02

(b)



02

016

012

008

004

0

Vent

ratio

0 5 10 15 20 25 30 35 40 45 50


Re (times104)


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Dynamometer

Parachute

Support

V




120597119906119894

120597119909119894

= 0

120588 (120597119906119894

120597119905+ 119906119895

120597119906119894

120597119909119895

) = minus120597119901

120597119909119894

+ 119861119894

+120597

120597119909119895

(120583120597119906119894

120597119909119895

minus 1205881199061015840

119894

1199061015840

119895

)

(1)





120588120597119896

120597119905+ 120588 (119906

119895

120597119896

120597119909119895

) =120597

120597119909119895

[(120583 +120583119905

120590119896

)120597119896

120597119909119895

] + 119866119896

+ 119866119887

minus 120588120576 minus 119884119872

120588120597120576

120597119905+ 120588 (119906

119895

120597120576

120597119909119895

) =120597

120597119909119895

[(120583 +120583119905

120590120576

)120597120576

120597119909119895

]

+ 1198621120576

120576

119896(119866119896

+ 1198623120576

119866119887) minus 1198622120576

1205881205762

119896

(2)




1120576and 119862


119896and 120590

120576are the



120583119905

= 120588119862120583

1198962

120576 (3)


1120576 1198622120576 119862120583 120590119896 and 120590

120576


= 144 1198622120576

= 192 119862120583

= 009120590119896

= 10 and 120590120576




119889= 05120588119862

1198891198601198802

infin

Here 119862


119862119889

=119865119889

05120588119860119880 2infin

(4)

where 119860 = (1205871198632







Outflow

Parachute

Velocity inlet

XY

Z


16

164

168

172

176

0 5 10 15 20

Dra

g co

effici

ent













119889decreases














the other cases





5 15 25 35 45155

16

165

17

175

18Cd

dD = 0

Re (times104)

(a)

5 10 15 20 25 30 35 40155

16

165

17

175

18

Cd

dD = 004

Re (times104)

(b)

15

155

16

165

17

175

Cd

dD = 008

5 10 15 20 25 30 35 40Re (times104)

(c)

dD = 012

15

155

16

165

17

175

Cd

5 10 15 20 25 30 35 40Re (times104)

(d)


15

155

16

165

17

175

Cd

5 10 15 20 25 30 35 40

dD = 016

Re (times104)

(e)


5 10 15 20 25 30 35 40145

15

155

16

165

17

dD = 02

Cd

Re (times104)

(f)







Re = 85539Re = 114000Re =146330Re = 171100

Re = 228070Re= 292660Re = 357250

14

145

15

155

16

165

17

175

18

0 004 008 012 016 02

Cd

dD




5 Conclusion




Abbreviations

Nomenclature




Greek Symbols


Subscripts



Re = 85539 Re =146330 Re = 228070 Re = 357250

dD

0

004

008

(a)

Re = 85539 Re =146330 Re = 228070 Re = 357250

dD

012

016

02

(b)



02

016

012

008

004

0

Vent

ratio

0 5 10 15 20 25 30 35 40 45 50


Re (times104)


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Outflow

Parachute

Velocity inlet

XY

Z


16

164

168

172

176

0 5 10 15 20

Dra

g co

effici

ent













119889decreases














the other cases





5 15 25 35 45155

16

165

17

175

18Cd

dD = 0

Re (times104)

(a)

5 10 15 20 25 30 35 40155

16

165

17

175

18

Cd

dD = 004

Re (times104)

(b)

15

155

16

165

17

175

Cd

dD = 008

5 10 15 20 25 30 35 40Re (times104)

(c)

dD = 012

15

155

16

165

17

175

Cd

5 10 15 20 25 30 35 40Re (times104)

(d)


15

155

16

165

17

175

Cd

5 10 15 20 25 30 35 40

dD = 016

Re (times104)

(e)


5 10 15 20 25 30 35 40145

15

155

16

165

17

dD = 02

Cd

Re (times104)

(f)







Re = 85539Re = 114000Re =146330Re = 171100

Re = 228070Re= 292660Re = 357250

14

145

15

155

16

165

17

175

18

0 004 008 012 016 02

Cd

dD




5 Conclusion




Abbreviations

Nomenclature




Greek Symbols


Subscripts



Re = 85539 Re =146330 Re = 228070 Re = 357250

dD

0

004

008

(a)

Re = 85539 Re =146330 Re = 228070 Re = 357250

dD

012

016

02

(b)



02

016

012

008

004

0

Vent

ratio

0 5 10 15 20 25 30 35 40 45 50


Re (times104)


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










5 15 25 35 45155

16

165

17

175

18Cd

dD = 0

Re (times104)

(a)

5 10 15 20 25 30 35 40155

16

165

17

175

18

Cd

dD = 004

Re (times104)

(b)

15

155

16

165

17

175

Cd

dD = 008

5 10 15 20 25 30 35 40Re (times104)

(c)

dD = 012

15

155

16

165

17

175

Cd

5 10 15 20 25 30 35 40Re (times104)

(d)


15

155

16

165

17

175

Cd

5 10 15 20 25 30 35 40

dD = 016

Re (times104)

(e)


5 10 15 20 25 30 35 40145

15

155

16

165

17

dD = 02

Cd

Re (times104)

(f)







Re = 85539Re = 114000Re =146330Re = 171100

Re = 228070Re= 292660Re = 357250

14

145

15

155

16

165

17

175

18

0 004 008 012 016 02

Cd

dD




5 Conclusion




Abbreviations

Nomenclature




Greek Symbols


Subscripts



Re = 85539 Re =146330 Re = 228070 Re = 357250

dD

0

004

008

(a)

Re = 85539 Re =146330 Re = 228070 Re = 357250

dD

012

016

02

(b)



02

016

012

008

004

0

Vent

ratio

0 5 10 15 20 25 30 35 40 45 50


Re (times104)


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Re = 85539Re = 114000Re =146330Re = 171100

Re = 228070Re= 292660Re = 357250

14

145

15

155

16

165

17

175

18

0 004 008 012 016 02

Cd

dD




5 Conclusion




Abbreviations

Nomenclature




Greek Symbols


Subscripts



Re = 85539 Re =146330 Re = 228070 Re = 357250

dD

0

004

008

(a)

Re = 85539 Re =146330 Re = 228070 Re = 357250

dD

012

016

02

(b)



02

016

012

008

004

0

Vent

ratio

0 5 10 15 20 25 30 35 40 45 50


Re (times104)


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Re = 85539 Re =146330 Re = 228070 Re = 357250

dD

0

004

008

(a)

Re = 85539 Re =146330 Re = 228070 Re = 357250

dD

012

016

02

(b)



02

016

012

008

004

0

Vent

ratio

0 5 10 15 20 25 30 35 40 45 50


Re (times104)


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










02

016

012

008

004

0

Vent

ratio

0 5 10 15 20 25 30 35 40 45 50


Re (times104)


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article a numerical and experimental study of the aerodynamics and stability … · 2019....

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