Research Article A Numerical Method for Blast …downloads.hindawi.com/journals/ijae/2015/897213.pdfResearch Article A Numerical Method for Blast Shock Wave Analysis of Missile Launch

Research ArticleA Numerical Method for Blast Shock Wave Analysis of MissileLaunch from Aircraft

Sebastian Heimbs1 Josef Ritzer1 and Johannes Markmiller2

1Department of Structure Engineering Production and Aeromechanics Airbus Group InnovationsWilly-Messerschmitt-Strasse 85521 Ottobrunn Germany2Department of Stress Loads and Crash Airbus Helicopters Industriestrasse 4 86609 Donauworth Germany

Correspondence should be addressed to Sebastian Heimbs sebastianheimbsairbuscom

Received 1 June 2015 Accepted 13 September 2015

Academic Editor Hikmat Asadov

Copyright copy 2015 Sebastian Heimbs 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

An efficient empirical approach was developed to accurately represent the blast shock wave loading resulting from the launch of amissile from amilitary aircraft to be used in numerical analyses Based on experimental test series of missile launches in laboratoryenvironment and from a helicopter equations were derived to predict the time- and position-dependent overpressureThemethodwas finally applied and validated in a structural analysis of a helicopter tail boom under missile launch shock wave loading

1 Introduction

The launch of a space rocket or military missile generatesa shock wave behind the nozzle with high pressure loadingon the surrounding structures If such a missile is launchedfrom a flying military aircraft like a fighter jet or helicopterit has to be assured that the structural loading mainly of therear part of the aircraft does not exceed design limits Inthe past common means of compliance were mainly basedon experimental live fire tests with adequate data acquisitionequipment on the aircraft structure being expensive in bothtime and cost

Aircraft designers seek for more efficient approaches toanalyse the structural loading under missile launch blastshock wave Most attention was recently paid to computa-tional fluid dynamics (CFD) methods to simulate the missilelaunch procedure and missile exhaust plume [1] Such CFDanalyses can be extended to a subsequent structural loadingin a fluid-structure-interaction approach For example Kiddand Cloke [2] and Okamoto et al [3] used CFD modellingto simulate the blast wave development due to the launchof a missile from a helicopter Also the studies by Lee et al[4 5] and Fu et al [6] present CFD models to simulate themissile launch from a canister in general or from a helicopterwith the focus on the missile movement Simulations of the

exhaust plume from launcher rockets using CFD modellingwere performed by Gusman et al [7] Alexeenko et al [8]Ebrahimi et al [9] and Vitkin et al [10] The complex flowfields generated bymissile propulsion systems are challengingfor CFD simulations with Navier-Stokes flow solvers though

Another approach to model the missile exhaust plumebased on molecular gas dynamics is the direct simulationMonte Carlo (DSMC) method which was used for themodelling of the plume flow field of a space orbiter byRault [11] and of a satellite thruster by Park et al [12] Leeand Choi [13] and Chung et al [14] The coupling of thismethod with a CFD analysis is also a common approachthat is often used in space sciences which can be foundfor example in the numerical studies of rocket plumes ofspacecraft thrusters by Feng et al [15] Gatsonis et al [16] andLumpkin et al [17] Markelov et al [18] compute the thermalandmechanical loads froma rocket plume acting on a satelliteusing this combined approach Also Giordano et al [19] usedthis method to optimise a satellite design based on the effectsof the thruster plumes Morris et al [20] used this approachfor the analysis of a lunar lander on a dusty surface Howeverthese methods require numerous details and parameters ofthe specificmissile its solidliquid propellant and chemicallyreacting kinetics which are typically beyond the knowledge

Hindawi Publishing CorporationInternational Journal of Aerospace EngineeringVolume 2015 Article ID 897213 8 pageshttpdxdoiorg1011552015897213

2 International Journal of Aerospace Engineering

Missile launched in canister

Pressure sensorsFragment wall

1

2

3

4

(a)

50 100 150 200 250 300 350 400

Ove

rpre

ssur

e

Time

Sensors 1 2Sensors 3 4

(b)

Figure 1 Illustration (top view) of laboratory test launch of missile with highlighted pressure sensors (a) and qualitative illustration of thepressure-time results (b)

of the structural engineer The computational efforts for suchdetailed analyses are immense too

Therefore it is desired to handle the whole structuralanalysis in the framework of a conventional explicit finiteelement (FE) simulation with a more efficient method forthe complex blast shock wave loading of the aircraft First ofall this paper presents an assessment of potential methodsfor this load case in commercial explicit FE software withan evaluation of the representation of the real physical phe-nomena A new empirical approach is then derived from anexperimental test campaign and finally applied to a helicopterstructure for verification and validation Merits and limitsof this new method are discussed and guidelines for thestructural engineer are given on how to use it for othermissilelaunch load cases It has to be pointed out that due to thesensitivity and confidentiality of this topic no quantitativevalues will be published in this paper

2 Experimental Work

In order to develop a numerical method for the repre-sentation of the shock wave during a missile launch it isnecessary to have detailed data on the time- and position-dependent pressure distribution behind a missile during anactual launch Therefore an experimental campaign of twodifferent test series was conducted

The first test series was performed under laboratoryconditions with the missile being fixed to a solid test rig andbeing launched under this condition Four pressure sensorswere mounted behind the missilersquos nozzle with differentlateral and axial distances to record the shock wave pressureloading (Figure 1(a)) The illustration in Figure 1(b) depictsthe qualitative results of the different sensors in terms ofoverpressure versus time The curves show a very suddenoverpressure increase up to a peak value followed by adecay even down to negative values and a final convergenceto atmospheric pressure This general behaviour matches

exactly the typical overpressure versus time curves of explo-sive blast shock waves also referred to as the Friedlandercurve [21] suggesting that the theory of explosive blast canalso be applied here Taking a closer look at the results thepressure peak of sensors 1 and 2 occurs earlier compared tosensors 3 and 4 because they are located closer to the missilenozzle However it will be emphasised that the peak value ofsensors 1 and 2 is higher than the value of sensors 3 and 4Thisviolates the general blast theory which expects the pressurepeak to reduce with increasing distance from the detonationpoint [21] In contrast to a singular explosive detonationthe launch of a missile is a continuous more complexprocess resulting from the combustion of the propellantand the resulting hypersonic jet behind the missilersquos nozzleThe physical flow phenomena occurring during a missilelaunch are well described and verified by CFD analysesin [2] After ignition of the missile the compressed air ispushed out of the nozzle and generates a pressure wave withspherical expansion with the speed of sound In addition ahypersonic jet is created by the combustion with a spatialorientation in backward direction This jet interacts with theaforementioned pressure wave in a complex manner andleads to higher overpressure values in the vicinity of the jetflow axis explaining the higher peak value for sensors 3 and4 in Figure 1(b)

The second test series was performed by launching themissile directly from a helicopter both on ground and inflight (Figure 2(a)) For this purpose six pressure sensorswere mounted onto the surface of the helicopter tail boomat various relevant positions In addition four strain gaugeswere used to measure the structural deformation and tocompare it with design limits An Acra Control D120 dataacquisition system was used to link all the measurementequipment A total of eight test repetitions were performedin order to obtain reliable test results The overpressureversus time plots in Figure 2(b) show similar trends as in theprevious test series First of all the general Friedlander-like

International Journal of Aerospace Engineering 3

Missile launched in canisterPressure sensors

x

z

y

1 2 3

45

6

(a)

5 10 15

Ove

rpre

ssur

e

Time

Sensor 1Sensor 2

Sensor 4Sensor 3

Sensor 5

Sensor 6

(b)

Figure 2 Illustration (side view) of missile launch tests from helicopter with highlighted pressure sensors (a) and qualitative illustration ofthe pressure-time results (b)

pressure curve can be observed for each position The orderof peak time corresponds to the distance of the respectivesensors to the missile nozzle The maximum peak valueagain strongly depends on the distance to the jet flow axis(119909-axis) though and not only on the overall distance to thenozzle

3 Assessment of Numerical Methods

Keeping in mind the target of deriving an efficient numericalapproach for the simulation of this shock wave loadingin commercial explicit FE software a short assessment ofpotential numerical strategies will be given

One promising option based on conventional blasttheory and the Friedlander pressure curve is the ConWepmethod which is available in current releases of LS-Dyna[22] and AbaqusExplicit [23] ConWep initially developedby the US Army to calculate the blast effects of conventionalweapons is an empirical approach to calculate blast overpres-sures and their temporal and spatial expansion just based onthe input of an equivalentmass of TNT and the coordinates ofthe detonation point It was applied to air blast simulations ofcomposite panels in [24 25] of composite vessels in [26] andof honeycomb sandwich panels in [27] Although thismethodis very efficient it is only suitable for singular explosions anddoes not represent in a realistic way the observed pressureloading under missile launch with the higher overpressureclose to the jet flow axis

Another popular option to model blast shock wave load-ing with realistic fluid-structure interaction is the coupledEulerian-Lagrangian approach (abbreviated asCELorALE indifferent FE software) With this technique a fixed Eulerianmesh is generated that is initially filled with air normallybeing modelled as an ideal gas The shock wave loadingresults from the detonationmodelling of an explosive chargetypically using a Jones-Wilkins-Lee equation of state [28]Theloaded structure is modelled as a Lagrangian body withinthis Eulerian mesh coupled by a contact formulation [29]This approach was used for example for blast simulationsof composite plates in [30] and for simulations of explosiveblast loads inside metallic aircraft fuselages with LS-Dyna[31 32] or Dytran [33] and inside composite fuselages in [34]Further applications to blast analyses of armoured ground

vehicle are documented in [35] efforts thus making it aninefficient technique However in order to achieve accurateresults with this method the Eulerian mesh needs to be assmall as possible typically leading to millions of elementsand immense computational efforts thusmaking it inefficienttechnique Furthermore it is again only suitable for singularor multiple explosions but not for modelling the combustionjet flow during missile launch

Besides this complex fluid-structure-interaction methodthe simplest approach to achieve a time-dependent shockwave pressure loading is to apply the pressure based ontabular input as a function of time either with a simpletriangular pulse or by approximating the Friedlander curveThis method was applied for example in [36] for explosiveblast simulations of stringer-stiffened aluminium plates andin a similar manner for composite plates in [37] Comparableblast simulations of foam core sandwich [38] honeycombsandwich [39] and corrugated aluminium sandwich struc-tures [40] have also been reported A direct application forhelicopter structures is reported by McCarthy [41] who usedthis approach to model the gun blast pressure wave actingon the aircraft structure However it can be stated that auniform loading of the whole aircraft structure would notbe realistic and dividing the structure into several subregionswith different pressure-time functions to approximate the testresults makes the approach inefficient and still not accurateenough

Themethod of choice should be not only time-dependentbut also position-dependent as described in [37 42] Byanalytical equations that were derived from physical con-siderations and experimental test data this approach shouldcalculate and apply the accurate pressure at each time stepfor each element of the structural model The basis for thisapproach is available in AbaqusExplicit as a user-definedsubroutine VDLOAD generating nonuniform distributedloads 119901(119905 119909 119910 119911) as a function of time 119905 and the positioncoordinates 119909 119910 and 119911 Within this subroutine the FEsolver provides for each time step and each integration pointthe input values of the current time (value totalTime) theposition coordinates (value curCoords) and the orientationof the element (value dirCos) Based on this informationthe user is requested to calculate the current pressure whichis then returned to the solver as the output value of thesubroutine


p

pp

p0

tp td

t

Figure 3 Typical Friedlander curve to display blast shock wavepressure versus time

4 Development of Empirical Approach

The major challenge is the development of accurate andphysically meaningful analytical equations to calculate thiscurrent overpressure value 119901(119905 119909 119910 119911) as a function of timeand position coordinates As a starting point it can beobserved from the experimental results in Figures 1(b) and2(b) that the shock wave loading at each spatial position canbe approximated by a Friedlander curve (see Figure 3) whichis expressed as

119901 (119905) = 1199010 for 119905 lt 119905

119901 (1)

119901 (119905) = 119901119901sdot (1 minus

(119905 minus 119905119901)

119905119889

) sdot 119890minus120572sdot((119905minus119905119901)119905119889) for 119905 ge 119905

119901 (2)

In these equations 1199010is the atmospheric pressure 119901

119901is the

peak overpressure 119905119901is the arrival time of the shock front 119905

119889

is the duration of the positive pressure phase after the peakoverpressure and 120572 is a wave form parameter describing thepressure decay

The three fundamental values that are needed for eachspatial position are basically 119905

119901 119901119901 and 119905

119889 Taking into

account the aforementioned experimental test results thesevalues can be derived for all pressure sensor positionsThe empirical approach is then based on the interpolationbetween these known values in order to obtain the wholetime- and position-dependent overpressure Since the testresults of the missile launch from the helicopter appear tobe more realistic compared to the laboratory test launch witha fixed missile those data from one representative test wereused for the following study Another important factor thatneeds to be taken into account is the angular orientationof the pressure sensors to the shock front during the testSince the pressure sensors were directly mounted onto thehelicopter tail boom surface they were not oriented normalto the shock front Under normal orientation theywould haverecorded a higher maximum value which can be comparedto the well-known example of putting a hand out of thewindow of a driving car where the pressure on the hand(=sensor) depends on the angle to the driving directionTherefore the maximum value had to be recalculated usingthe angle between the sensor normal direction (taken from

CADmodel data of the helicopter structure) and the straightline between sensor and missile nozzle

The arrival time of the shock wave 119905119901was then extracted

from the test results and plotted against the distance 119889 of thesensor position to the missile nozzle which is defined as

119889 = radic1199092+ 1199102+ 1199112 (3)

To interpolate between those experimental values inFigure 4(a) a trend line or analytical function wasdetermined From a simplified point of view the arrivaltime 119905

119901is in linear relation to the distance just based on the

speed of sound 119888 for the wave propagation Hence a linearapproach was adopted with the parameter 119888

119905119901 (119889) =

1

119888

sdot 119889 (4)

The experimentally recorded peak overpressure values 119901119901

were not plotted as a function of the spatial distance 119889 butof a weighted distance 1198891015840 which is defined as

1198891015840=

radic1199102+ 1199112

119909

(5)

This approach based on a function similar to a Mach coneallows capturing the experimentally observed effect of highershock wave pressure loads in the vicinity of the jet flow axis(119909-axis) For interpolation a power function was used withthe parameters 119886 and 119899 (Figure 4(b))

119901119901(1198891015840) = 119886 sdot 119889

1015840119899 (6)

It has to be mentioned that this approach is a simplificationand only valid for near field pressure predictionThe effect ofdecreasing peak pressures in large distances on 119909-axis is notcovered in this equation

The duration of the positive pressure phase 119905119889was finally

extracted for all sensors from the experiment and plottedagainst the distance 119889 (Figure 4(c)) An exponential functionwas adopted for interpolation using the twoparameters 119887 and119898

119905119889(119889) = 119887 sdot 119890

119898sdot119889 (7)

With these empirical equations derived from the test data thefinal overpressure 119901(119905 119909 119910 119911) can be calculated for each timestep and for every position For this purpose (3) (4) (5)(6) and (7) are integrated into (2) leading to the combinedequation

119901 (119905 119909 119910 119911) = 119886 sdot (

radic1199102+ 1199112

119909

)

119899

sdot (1 minus

119905 minus ((1119888) sdot radic1199092+ 1199102+ 1199112)

119887 sdot 119890119898sdotradic119909

2+1199102+1199112

)

sdot 119890minus120572sdot((119905minus((1119888)sdotradic119909

2+1199102+1199112))119887sdot119890119898sdotradic1199092+1199102+1199112

)

(8)


tp

d

(a)

pp

d998400

(b)

td

d

(c)

Figure 4 Illustration of experimental values and trend lines for arrival time of shock wave 119905119901(a) peak overpressure 119901

119901(b) and duration of

positive pressure phase 119905119889(c)

The parameter values 119886 119887 119888 119899 and119898were derived accordingto the trend lines shown in Figure 4 but are not presented heredue to confidentiality The wave form parameter 120572 was set to12 as taken from literature [21]

As a final step the orientation of the loaded elements withrespect to the shock front needs to be taken into accountagain since the current value represents the maximumpressure if the element is oriented perpendicularly to theshock front For this purpose the final pressure value isrecalculated using the angle between the elementrsquos normal(which is provided by the solver) and the connecting line ofelement andmissile nozzle Furthermore the pressure is onlyapplied to an element if this angle is below 90∘ In case ofangles larger than 90∘ the element would be in the shadowand for reasons of simplification would not be loaded

5 Application to HelicopterTail Boom Analysis

Finally this approach was adopted to simulate the missilelaunch shock wave pressure loading on a helicopter structureThe helicopter model is similar to the one of the live firetest campaign and limited to the tail boom which was fullyclamped at the nodes of the forward edge The structureconsistsmainly of lightweight composite and sandwich struc-tures which were modelled using layered shell elements oftype S4 with the Hashin composite damage model and anaverage size of 15mm leading to a total number of 137000elements for the wholemodel Equation (8) was implementedinto the user subroutine VDLOAD in AbaqusExplicit toefficiently simulate the distributed load which was appliedto the whole exterior surface of the helicopter tail boomBased on this equation the subroutine interpolates to applythe correct pressure load at each time step and every positionof the model The average time step size was 00002ms

The only available values to validate the simulation resultsare the pressure recordings and strain gauge data Thenumerically predicted pressure curves in Figure 5 are in good

agreement with the test data and enable a realistic loadingof the aircraft structure Hence the strain values illustratedin Figures 6(b) and 6(c) for two exemplary strain gauges arealso in good agreement and allow for a valuable predictionof the maximum strains to be expected under this loadingImplementation of structural damping in the simulation isrecommended in order to reduce the oscillations from thesudden shock loading of the structure An illustration ofthe maximum deflection of the tail boom during the shockwave loading is presented in Figure 7 using a deformationscale factor of 2 Although the deformation appears to besignificant the structural loading is uncritical as the strainsare far below the design limit

6 Conclusions

The development of an empirical approach to representthe blast shock wave loading resulting from the launch ofa missile from an aircraft based on an experimental testcampaign was presented Similarities to the blast shock waveof a conventional singular detonation of an explosive chargewere highlighted in terms of the possibility to apply the Fried-lander curve to approximate the pressure-time responseHowever large differences to such a conventional explosionalso occur resulting from the physical flow phenomena ofthe continuous jet flow from the missile nozzle makingapproaches like ConWep or coupled Eulerian-Lagrangiansimulations inappropriate Hence an empirical equation wasdeveloped to represent the overpressure at each time andspatial position in a very efficient way Although a testseries of a pressure sensor-instrumented missile launch isrequired to determine the necessary parameters for theequation this loadingmodel can afterwards be applied by theaircraft engineer to various aircraft types or configurationsAn enhancement of the equation or different interpolationfunctions could be assessed if a larger test database comparedto this study was available using more pressure sensors atfurther positions


Ove

rpre

ssur

e

Time

s1 s2 s4

s3

s5

s6

(a) Test

Ove

rpre

ssur

e

Time

s1s2

s4

s3

s5

s6

(b) Simulation

Figure 5 Overpressure versus time curves of pressure sensors in test (a) and simulation (b) with similar axes scale

SG1SG2

(a)

10

Time

Test SG1Simulation

Stra

in (120583

120576)

minus800

minus600

minus400

minus200

0

200

400

600

800

(b)

Time

Test SG2Simulation

Stra

in (120583

120576)

minus800

minus600

minus400

minus200

0

200

400

600

800

(c)

Figure 6 Exemplary contour plot of strain distribution in helicopter tail boom during shock wave loading from missile launch (a) andcomparison with test data for strain gauge SG1 in front of horizontal stabiliser (b) and SG2 behind horizontal stabiliser (c)

Nomenclature119886 Constant in equation for peak

overpressure Pa119887 Constant in equation for positive pressure

duration s119888 Speed of sound msdotsminus1

119889 Distance of sensor to nozzle m1198891015840 Weighted distance119898 Constant in equation for positive pressure

duration ssdotmminus1119899 Constant in equation for peak overpressure119901 Pressure Pa


Undeformed shape

Deformed shape

(a) (b)

Figure 7 Illustration of maximum deflection of tail boom during shock wave loading from missile launch from top view (a) and front view(b) deformation scale factor = 2

1199010 Atmospheric pressure Pa119901119901 Peak overpressure Pa119905 Time s119905119889 Duration of positive pressure phase s119905119901 Arrival time of shock front s119909 119910 119911 Position coordinates m120572 Wave form parameter

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] N S Liu ldquoOn the comprehensive modeling and simulation ofcombustion systemsrdquo in Proceedings of the 39th AIAAAerospaceSciences Meeting amp Exhibit Reno Nev USA January 2001

[2] G Kidd and M Cloke ldquoComputational modelling of transientblast wave effectsrdquo in Proceedings of the 42nd AIAA AerospaceSciences Meeting and Exhibit pp 4264ndash4270 Reno Nev USAJanuary 2004

[3] K K Okamoto E P N Duque and J Ahmad ldquoNumeri-cal simulation of an unsteady rocket launch from the AH-64D Apache Longbow helicopterrdquo in Proceedings of the 4thSymposium on Overset Composite Grid amp Solution TechnologyAberdeen Proving Ground Md USA September 1998

[4] H D Lee O J Kwon B S Lee and K H Noh ldquoAerodynamicsimulation of air-launchedmissiles from a complete helicopterrdquoJournal of the Korean Society for Aeronautical amp Space Sciencesvol 39 no 12 pp 1097ndash1106 2011

[5] B S Lee J H Choi and O J Kwon ldquoNumerical simulationof free-flight rockets air-launched from a helicopterrdquo Journal ofAircraft vol 48 no 5 pp 1766ndash1775 2011

[6] D Fu Q Li J Cheng and Y Jiang ldquoNumerical simulation ofmissile launching procedurerdquo Journal of Ballistics vol 16 no 3pp 11ndash16 2004

[7] M Gusman J Housman and C Kiris ldquoBest practices forCFD simulations of launch vehicle ascent with plumesmdashOVERFLOW perspectiverdquo in Proceedings of the 49th AIAAAerospace Meeting Orlando Fla USA January 2011

[8] A A Alexeenko N E Gimelshein D A Levin et al ldquoModelingof flow and radiation in the Atlas plumerdquo Journal of Thermo-physics and Heat Transfer vol 16 no 1 pp 50ndash57 2002

[9] H B Ebrahimi J Levine and A Kawasaki ldquoNumerical inves-tigation of twin-nozzle rocket plume phenomenologyrdquo Journalof Propulsion and Power vol 16 no 2 pp 178ndash186 2000

[10] E I Vitkin V G Karelin A A Kirillov A S Suprun and JV Khadyka ldquoA physico-mathematical model of rocket exhaustplumesrdquo International Journal of Heat and Mass Transfer vol40 no 5 pp 1227ndash1241 1997

[11] D F G Rault ldquoMethodology for thruster plume simulation andimpingement effects characterized usingDSMCrdquo inProceedingsof the 30th AIAA Thermophysics Conference San Diego CalifUSA June 1995

[12] J H Park S W Back and J S Kim ldquoDirect simulationMonte Carlo analysis of thruster plumessatellite base regioninteractionrdquo AIAA Journal vol 42 no 8 pp 1622ndash1632 2004

[13] K H Lee and SW Choi ldquoInteraction effect analysis of thrusterplume on LEO satellite surface using parallel DSMC methodrdquoComputers amp Fluids vol 80 no 1 pp 333ndash341 2013

[14] C-H Chung S C Kim R M Stubbs and K J DeWitt ldquoLow-density nozzle flow by the direct simulation Monte Carlo andcontinuum methodsrdquo Journal of Propulsion and Power vol 11no 1 pp 64ndash70 1995

[15] S Feng W Nie Q Xie and L Duan ldquoNumerical simulationof flow field and radiation of an aluminized solid-propellantrocket multiphase exhaust plumerdquo in Proceedings of the 39thAIAAThermophysics Conference Miami Fla USA June 2007

[16] N A Gatsonis R A Nanson and G J LeBeau ldquoSimulations ofcold-gas nozzle and plume flows and flight data comparisonsrdquoJournal of Spacecraft and Rockets vol 37 no 1 pp 39ndash48 2000

[17] F E Lumpkin III P C Stuart andG J LeBeau ldquoEnhanced anal-ysis of plume impingement during shuttle-Mir docking using


a combinedrdquo in Proceedings of the 31st AIAA ThermophysicsConference New Orleans La USA June 1996

[18] G Markelov R Brand G Ibler and W Supper ldquoNumericalassessment of plume heat and mechanical loads and contami-nation on multi-layer insulation in hard vacuumrdquo Vacuum vol86 no 7 pp 889ndash894 2012

[19] D Giordano M Ivanov A Kashkovsky G Markelov GTumino and G Koppenwallner ldquoApplication of numericalmultizone approach to the study of satellite thruster plumesrdquoJournal of Spacecraft and Rockets vol 35 no 4 pp 502ndash5081998

[20] A B Morris D B Goldstein P L Varghese and L M TraftonldquoPlume impingement on a dusty lunar surfacerdquo in Proceedingsof the 27th International Symposium on Rarefied Gas Dynamicspp 1187ndash1192 Pacific Grove Calif USA July 2010

[21] G F Kinney andK J Graham Explosive Shocks in Air SpringerBerlin Germany 1985

[22] G Le Blanc M Adoum and V Lapoujade ldquoExternal blast loadon structuresmdashempirical approachrdquo in Proceedings of the 5thEuropean LS-DYNA User Conference Birmingham UK May2005

[23] S K Lahiri and L Ho ldquoSimulation of rapid structural failuredue to blast loads from conventional weapons (CONWEP)rdquoin Proceedings of the NAFEMS World Congress Boston MassUSA May 2011

[24] G Flanagan S Chatterjee CMeyers andR Steidle ldquoSimplifiedmethods for modeling airblast failure of composite panelsrdquo inProceedings of the SAMPE Baltimore Md USA May 2009

[25] B A Gama V S Chiravuri and J W Gillespie Jr ldquoModelingblast damage of composite structuresrdquo in Proceedings of the11th International LS-DYNA Users Conference Dearborn MichUSA June 2010

[26] B OrsquoToole M B Trabia J Thota T Wilcox and K KNakelswamy ldquoStructural response of blast loaded compositecontainment vesselsrdquo in Proceedings of the SAMPE Long BeachCalif USA April-May 2006

[27] C F Yen R Skaggs and B A Cheeseman ldquoModeling ofshock mitigation sandwich structures for blast protectionrdquo inProceedings of the 3rd International Conference on StructuralStability and Dynamics Kissimmee Fla USA June 2005

[28] M Arrigoni S Kerampran J B Mouillet et al ldquoNumericalsimulation of air blast wavesrdquo in Proceedings of the EuropeanHyperWorks Technology Conference Bonn Germany Novem-ber 2011

[29] M S Chafi G Karami and M Ziejewski ldquoNumerical analysisof blast-induced wave propagation using FSI and ALEmulti-material formulationsrdquo International Journal of Impact Engi-neering vol 36 no 10-11 pp 1269ndash1275 2009

[30] F Dolce M Meo A Wright and M French ldquoStructuralresponse of laminated composite plates to blast loadrdquo inProceedings of the 17th International Conference on CompositeMaterials (ICCM rsquo09) Edinburgh UK July 2009

[31] M J Loikkanen V L Chen M Souli and J Gatto ldquoCom-puter simulation in the design of blast resistant structuresrdquo inProceedings of the 36thAIAAASMEASCEAHSASC StructuresStructural Dynamics and Materials Conference New OrleansLa USA April 1995

[32] A Dacko and J Toczyski ldquoStructural response of a blast loadedfuselagerdquo Journal of KONES Powertrain and Transport vol 17no 1 pp 101ndash109 2010

[33] Y I Moon G Bharatram S A Schimmels and V B VenkayyaldquoA vulnerability map of a commercial aircraftrdquo in Proceedings oftheMSCWorld Usersrsquo Conference Proceedings vol 5 of Paper no44 Newport Beach Calif USA June 1996

[34] T Kotzakolios D E Vlachos and V Kostopoulos ldquoBlastresponse of composite fuselage structures using finite elementanalysisrdquo in Proceedings of the 14th European Conference onCompositeMaterials (ECCM rsquo10) BudapestHungary June 2010

[35] CMougeotte P Carlucci S Recchia andH Ji ldquoNovel approachto conducting blast load analyses using AbaqusExplicit-CELrdquoin Proceedings of the SIMULIA Customer Conference Provi-dence RI USA May 2010

[36] M C Simmons and G K Schleyer ldquoPulse pressure loading ofaircraft structural panelsrdquoThin-Walled Structures vol 44 no 5pp 496ndash506 2006

[37] H S Turkmen and Z Mecitoglu ldquoNonlinear structuralresponse of laminated composite plates subjected to blastloadingrdquo AIAA Journal vol 37 no 12 pp 1639ndash1647 1999

[38] C-F Yen T Cassin J Patterson and M Triplett ldquoProgressivefailure analysis of composite sandwich panels under blastloadingrdquo in Structures Under Extreme Loading Conditions vol361 PVP-Vol 361 ASME 1998

[39] D Karagiozova G N Nurick andG S Langdon ldquoBehaviour ofsandwich panels subject to intense air blasts Part 2 Numericalsimulationrdquo Composite Structures vol 91 no 4 pp 442ndash4502009

[40] I Guven E Celik and E Madenci ldquoTransient response ofcomposite sandwich panels subjected to blast wave pressurerdquo inProceedings of the 47th AIAAASMEASCEAHSASC StructuresStructural Dynamics and Materials Conference pp 5052ndash5061Newport RI USA May 2006

[41] D KMcCarthy ldquoDesign analysis and test of gun blast resistantcomposite structurerdquo in Proceedings of the 54th AmericanHelicopter Society International Annual Forum pp 119ndash127Washington DC USA May 1998

[42] D BalkanOAcarH S Turkmen andZMecitoglu ldquoTransientresponse of a laminated sandwich plate with viscoelastic coresubjected to air blast theory and experimentrdquo in Proceedings ofthe 11th International Conference on Structures Under Shock andImpact pp 113ndash124 Tallinn Estonia July 2010

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Missile launched in canister

Pressure sensorsFragment wall

1

2

3

4

(a)

50 100 150 200 250 300 350 400

Ove

rpre

ssur

e

Time

Sensors 1 2Sensors 3 4

(b)

Figure 1 Illustration (top view) of laboratory test launch of missile with highlighted pressure sensors (a) and qualitative illustration of thepressure-time results (b)

of the structural engineer The computational efforts for suchdetailed analyses are immense too

Therefore it is desired to handle the whole structuralanalysis in the framework of a conventional explicit finiteelement (FE) simulation with a more efficient method forthe complex blast shock wave loading of the aircraft First ofall this paper presents an assessment of potential methodsfor this load case in commercial explicit FE software withan evaluation of the representation of the real physical phe-nomena A new empirical approach is then derived from anexperimental test campaign and finally applied to a helicopterstructure for verification and validation Merits and limitsof this new method are discussed and guidelines for thestructural engineer are given on how to use it for othermissilelaunch load cases It has to be pointed out that due to thesensitivity and confidentiality of this topic no quantitativevalues will be published in this paper

2 Experimental Work

In order to develop a numerical method for the repre-sentation of the shock wave during a missile launch it isnecessary to have detailed data on the time- and position-dependent pressure distribution behind a missile during anactual launch Therefore an experimental campaign of twodifferent test series was conducted

The first test series was performed under laboratoryconditions with the missile being fixed to a solid test rig andbeing launched under this condition Four pressure sensorswere mounted behind the missilersquos nozzle with differentlateral and axial distances to record the shock wave pressureloading (Figure 1(a)) The illustration in Figure 1(b) depictsthe qualitative results of the different sensors in terms ofoverpressure versus time The curves show a very suddenoverpressure increase up to a peak value followed by adecay even down to negative values and a final convergenceto atmospheric pressure This general behaviour matches

exactly the typical overpressure versus time curves of explo-sive blast shock waves also referred to as the Friedlandercurve [21] suggesting that the theory of explosive blast canalso be applied here Taking a closer look at the results thepressure peak of sensors 1 and 2 occurs earlier compared tosensors 3 and 4 because they are located closer to the missilenozzle However it will be emphasised that the peak value ofsensors 1 and 2 is higher than the value of sensors 3 and 4Thisviolates the general blast theory which expects the pressurepeak to reduce with increasing distance from the detonationpoint [21] In contrast to a singular explosive detonationthe launch of a missile is a continuous more complexprocess resulting from the combustion of the propellantand the resulting hypersonic jet behind the missilersquos nozzleThe physical flow phenomena occurring during a missilelaunch are well described and verified by CFD analysesin [2] After ignition of the missile the compressed air ispushed out of the nozzle and generates a pressure wave withspherical expansion with the speed of sound In addition ahypersonic jet is created by the combustion with a spatialorientation in backward direction This jet interacts with theaforementioned pressure wave in a complex manner andleads to higher overpressure values in the vicinity of the jetflow axis explaining the higher peak value for sensors 3 and4 in Figure 1(b)

The second test series was performed by launching themissile directly from a helicopter both on ground and inflight (Figure 2(a)) For this purpose six pressure sensorswere mounted onto the surface of the helicopter tail boomat various relevant positions In addition four strain gaugeswere used to measure the structural deformation and tocompare it with design limits An Acra Control D120 dataacquisition system was used to link all the measurementequipment A total of eight test repetitions were performedin order to obtain reliable test results The overpressureversus time plots in Figure 2(b) show similar trends as in theprevious test series First of all the general Friedlander-like



x

z

y

1 2 3

45

6

(a)

5 10 15

Ove

rpre

ssur

e

Time

Sensor 1Sensor 2

Sensor 4Sensor 3

Sensor 5

Sensor 6

(b)











p

pp

p0

tp td

t




119901 (119905) = 1199010 for 119905 lt 119905

119901 (1)

119901 (119905) = 119901119901sdot (1 minus

(119905 minus 119905119901)

119905119889


119901 (2)


119901is the


119889



119901 119901119901 and 119905

119889 Taking into





119889 = radic1199092+ 1199102+ 1199112 (3)




119905119901 (119889) =

1

119888

sdot 119889 (4)



1198891015840=

radic1199102+ 1199112

119909

(5)


119901119901(1198891015840) = 119886 sdot 119889

1015840119899 (6)




119905119889(119889) = 119887 sdot 119890

119898sdot119889 (7)


119901 (119905 119909 119910 119911) = 119886 sdot (

radic1199102+ 1199112

119909

)

119899

sdot (1 minus

119905 minus ((1119888) sdot radic1199092+ 1199102+ 1199112)

119887 sdot 119890119898sdotradic119909

2+1199102+1199112

)


2+1199102+1199112))119887sdot119890119898sdotradic1199092+1199102+1199112

)

(8)


tp

d

(a)

pp

d998400

(b)

td

d

(c)










6 Conclusions



Ove

rpre

ssur

e

Time

s1 s2 s4

s3

s5

s6

(a) Test

Ove

rpre

ssur

e

Time

s1s2

s4

s3

s5

s6

(b) Simulation


SG1SG2

(a)

10

Time

Test SG1Simulation

Stra

in (120583

120576)

minus800

minus600

minus400

minus200

0

200

400

600

800

(b)

Time

Test SG2Simulation

Stra

in (120583

120576)

minus800

minus600

minus400

minus200

0

200

400

600

800

(c)








Undeformed shape

Deformed shape

(a) (b)





References















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











x

z

y

1 2 3

45

6

(a)

5 10 15

Ove

rpre

ssur

e

Time

Sensor 1Sensor 2

Sensor 4Sensor 3

Sensor 5

Sensor 6

(b)











p

pp

p0

tp td

t




119901 (119905) = 1199010 for 119905 lt 119905

119901 (1)

119901 (119905) = 119901119901sdot (1 minus

(119905 minus 119905119901)

119905119889


119901 (2)


119901is the


119889



119901 119901119901 and 119905

119889 Taking into





119889 = radic1199092+ 1199102+ 1199112 (3)




119905119901 (119889) =

1

119888

sdot 119889 (4)



1198891015840=

radic1199102+ 1199112

119909

(5)


119901119901(1198891015840) = 119886 sdot 119889

1015840119899 (6)




119905119889(119889) = 119887 sdot 119890

119898sdot119889 (7)


119901 (119905 119909 119910 119911) = 119886 sdot (

radic1199102+ 1199112

119909

)

119899

sdot (1 minus

119905 minus ((1119888) sdot radic1199092+ 1199102+ 1199112)

119887 sdot 119890119898sdotradic119909

2+1199102+1199112

)


2+1199102+1199112))119887sdot119890119898sdotradic1199092+1199102+1199112

)

(8)


tp

d

(a)

pp

d998400

(b)

td

d

(c)










6 Conclusions



Ove

rpre

ssur

e

Time

s1 s2 s4

s3

s5

s6

(a) Test

Ove

rpre

ssur

e

Time

s1s2

s4

s3

s5

s6

(b) Simulation


SG1SG2

(a)

10

Time

Test SG1Simulation

Stra

in (120583

120576)

minus800

minus600

minus400

minus200

0

200

400

600

800

(b)

Time

Test SG2Simulation

Stra

in (120583

120576)

minus800

minus600

minus400

minus200

0

200

400

600

800

(c)








Undeformed shape

Deformed shape

(a) (b)





References















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










p

pp

p0

tp td

t




119901 (119905) = 1199010 for 119905 lt 119905

119901 (1)

119901 (119905) = 119901119901sdot (1 minus

(119905 minus 119905119901)

119905119889


119901 (2)


119901is the


119889



119901 119901119901 and 119905

119889 Taking into





119889 = radic1199092+ 1199102+ 1199112 (3)




119905119901 (119889) =

1

119888

sdot 119889 (4)



1198891015840=

radic1199102+ 1199112

119909

(5)


119901119901(1198891015840) = 119886 sdot 119889

1015840119899 (6)




119905119889(119889) = 119887 sdot 119890

119898sdot119889 (7)


119901 (119905 119909 119910 119911) = 119886 sdot (

radic1199102+ 1199112

119909

)

119899

sdot (1 minus

119905 minus ((1119888) sdot radic1199092+ 1199102+ 1199112)

119887 sdot 119890119898sdotradic119909

2+1199102+1199112

)


2+1199102+1199112))119887sdot119890119898sdotradic1199092+1199102+1199112

)

(8)


tp

d

(a)

pp

d998400

(b)

td

d

(c)










6 Conclusions



Ove

rpre

ssur

e

Time

s1 s2 s4

s3

s5

s6

(a) Test

Ove

rpre

ssur

e

Time

s1s2

s4

s3

s5

s6

(b) Simulation


SG1SG2

(a)

10

Time

Test SG1Simulation

Stra

in (120583

120576)

minus800

minus600

minus400

minus200

0

200

400

600

800

(b)

Time

Test SG2Simulation

Stra

in (120583

120576)

minus800

minus600

minus400

minus200

0

200

400

600

800

(c)








Undeformed shape

Deformed shape

(a) (b)





References















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










tp

d

(a)

pp

d998400

(b)

td

d

(c)










6 Conclusions



Ove

rpre

ssur

e

Time

s1 s2 s4

s3

s5

s6

(a) Test

Ove

rpre

ssur

e

Time

s1s2

s4

s3

s5

s6

(b) Simulation


SG1SG2

(a)

10

Time

Test SG1Simulation

Stra

in (120583

120576)

minus800

minus600

minus400

minus200

0

200

400

600

800

(b)

Time

Test SG2Simulation

Stra

in (120583

120576)

minus800

minus600

minus400

minus200

0

200

400

600

800

(c)








Undeformed shape

Deformed shape

(a) (b)





References















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Ove

rpre

ssur

e

Time

s1 s2 s4

s3

s5

s6

(a) Test

Ove

rpre

ssur

e

Time

s1s2

s4

s3

s5

s6

(b) Simulation


SG1SG2

(a)

10

Time

Test SG1Simulation

Stra

in (120583

120576)

minus800

minus600

minus400

minus200

0

200

400

600

800

(b)

Time

Test SG2Simulation

Stra

in (120583

120576)

minus800

minus600

minus400

minus200

0

200

400

600

800

(c)








Undeformed shape

Deformed shape

(a) (b)





References















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Undeformed shape

Deformed shape

(a) (b)





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











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article A Numerical Method for Blast …downloads.hindawi.com/journals/ijae/2015/897213.pdfResearch Article A Numerical Method for Blast Shock Wave Analysis of Missile Launch