Prediction of Acoustic Loads on a Launch Vehicle Fairing During Liftoff

Transcription

1 Predcton of Acoustc Loads on a Launch Vehcle Farng Durng Lftoff Mr Md. Maruf Morshed 1 Islamc Unversty of Technology (IUT) Board Bazar Gazpur 1704 Bangladesh Coln H. Hansen 2 The Unversty of Adelade Adelade SA 5005 Australa and Anthony C. Zander 2 The Unversty of Adelade Adelade SA 5005 Australa Durng lftoff of a launch vehcle the acoustc pressure fluctuatons caused by the engne exhaust gases produce hgh nose levels nsde the farng cavty and can damage the payload. Work presented n ths paper nvestgates the nature of the external acoustc pressure dstrbuton n the frequency range from 50Hz to 400Hz on the farng of a launch vehcle durng lftoff. The acoustc pressure actng on a representatve small launch vehcle farng was estmated from the complex acoustc feld generated by the rocket exhaust durng lftoff. The estmaton procedure nvolved the use of a unque source allocaton technque whch consdered acoustc sources along the rocket engne exhaust flow. Numercal and analytcal results for the acoustc loads on the farng agree well. A = coeffcent matrx Nomenclature a = cylnder radus m b = frequency band number C = dagonal matrx C(Q) = sold angle rad c = speed of sound n the exhaust flow m/s 1 Assstant Professor Department of Mechancal and Chemcal Engneerng (MCE) Islamc Unversty of Technology (IUT) Gazpur 1704 Dhaka Bangladesh. 2 Professor School of Mechancal Engneerng The Unversty of Adelade SA 5005 Australa. 2 Assocate Professor School of Mechancal Engneerng The Unversty of Adelade SA 5005 Australa. 1

2 D e = nozzle ext dameter m DI = drectvty ndex db d = projected dstance m E = total number of surface elements E (ξ) = element shape functon F = thrust of rocket engne N f = frequency Hz f b = frequency bandwdth Hz G = Green s functon H = coeffcent matrx H m (z) = Hankel functon or Bessel functon of the thrd knd of m th order and argument z I N = dentty matrx J m (z) = Bessel functon of the frst knd of m th order and argument z k = wavenumber L w = overall acoustc power level db L wb = L Pbϕ = L POAϕ = sound power level for each frequency band db sound pressure level on the crcumference of the vehcle db overall sound pressure level db M = total number of terms M e = Mach number m = term number n = number of nozzles and partcle outward velocty drecton p p = acoustc pressure Pa p = ncdent sound pressure Pa p o = ncdent sound pressure ampltude Pa p s = scattered sound pressure Pa = total sound pressure at the surface of a cylnder db p' = spatally dependent factor 2

3 p = constant nodal pressure on th element Pa P = feld pont or observaton pont Q s = source strength m 3 /s Q = projecton pont and ntegraton pont on the boundary = dstance between the ntegraton pont and observaton pont and resultant oblque dstance m r = radal dstance and dstance of the source from the nozzle ext m r P = dstance of observaton pont m r Q = dstance of ntegraton pont m S = cylnder surface area m 2 U e = exhaust velocty m/s u n = outward normal partcle velocty m/s V = volume of a problem geometry m 3 V e = exteror volume m 3 V = nteror volume m 3 W b = acoustc power for each frequency band Watt W(f) = W OA = sound power per Hz Watt overall acoustc power Watt X = X component of the cylndrcal coordnate axes x 1 = axal dstance of the observaton pont on the vehcle from the nozzle ext m x 2 = vertcal dstance from the nozzle ext of the sources along the flow axs m x 3 = dstance of the source from the vehcle axs along the flow axs m Y = Y component of the cylndrcal coordnate axes Z = Z component of the cylndrcal coordnate axes z = elevaton heght m θ = angle from the horzontal axs of the nose radaton deg = azmuthal angle deg β = nclne angle between the lne jonng the observaton pont to the source locaton and the normal of the vehcle axs deg 3

4 ε m = constant terms used n the equatons γ m = phase angle rad ω = angular frequency rad/s ρ = densty of ar n the exhaust flow kg/m 3 ρ o = equlbrum densty of the flud kg/m 3 λ = wavelength m I. Introducton To determne an approprate source model and confguraton that wll accurately represent the sound feld generated by the rocket motor t s necessary to take nto account varous complcatng parameters such as vehcle geometry propulson devce confguraton flow confguraton and launch pad confguraton. The sound felds generated by large propulson devces mx wth the exhaust flow and are also deflected by the deflector below the vehcle and radated back towards the vehcle. The reflectons and dffractons of the sound felds by the vehcle stand and other objects on or near the launch pad may have a sgnfcant effect on the acoustc pressure fluctuatons on the vehcle. However when all of the necessary parameters are known t should be possble to predct the acoustc loads on the vehcle. Nevertheless the predcton of the acoustc loadng on launch vehcles contnues to face tremendous theoretcal and technologcal challenges due to the many complcated parameters and complex geometres nvolved. In the past the predcton of acoustc loads generated by the vehcle propulson system has been undertaken usng sem-emprcal analytcal methods based on expermental data 1-4. The predcton methods for chemcal rockets have been outlned n NASA-SP a space-vehcle desgn crtera document. The recommended methods predct the acoustc loads at a pont on the vehcle usng two dfferent source allocaton methods based on expermental data concernng the sound power spectrum radated by the propulson system the lateral deflecton of the jets exhausted by the rocket engnes and allocaton of the nose generaton sources along the exhaust stream. One of these methods known as the unque source allocaton method assumes that there s a sngle equvalent pont source locaton along the exhaust flow axs for each frequency. The other method the non-unque source allocaton method assumes that there are a number of pont source locatons makng a lne source along the exhaust flow axs for each frequency. The scatterng effects from the vehcle surface are completely omtted n these methods. 4

5 Potter 2 descrbed an analytcal method to mplement scatterng effects from the surface whch nvolved the source allocaton technque and was based on the theoretcal analyses for a smple cylnder presented by Morse 5 Morse & Feshbach 6 and Morse & Ingard 7. Although Potter s technque may be partally sutable for analyzng the total sound pressure ncludng the radaton effects from a cylnder t s not approprate for dealng wth scatterng from a hard cylndrcal wall. Malbequ et al. 8 also consdered the emprcal source allocaton technque to analyse the scatterng of ncdent acoustc waves by the surface of the Arane IV space launcher usng boundary ntegral methods. However ths analyss examned the sound feld n the vcnty of the launcher rather than at the launcher surface and so could not be used to determne the acoustcs loads at the surface whch are necessary for predctons of sound transmsson nto the payload bay. Ths paper s concerned wth the nvestgaton of the acoustc loads ncludng the scatterng effects on an SLVF usng a unque source allocaton method as suggested n NASA-SP Note that the non-unque source allocaton method could be the subject of a future nvestgaton. The unque source allocaton method was used here to allocate unque source locatons for each one-thrd-octave frequency band n the range from 50Hz to 400Hz and the method was extended usng the analytcal and numercal tools developed by the authors to examne the acoustc loads at the surface of the SLVF. The Boundary Element Method (BEM) software used for the numercal predctons was Open BEM an open source code manly developed by the Acoustc Laboratory Techncal Unversty of Denmark 9. The Open BEM codes are able to treat 2D 3D and axsymmetrc problems. In the current work the 3D technque was used to solve the 3D problem geometry. For the purpose of determnng the external acoustc loadng the farng walls were modeled as rgd and thus the blocked loadng was determned. As the acoustc medum s ar ths was consdered to be a good approxmaton of the exact analyss that would nclude the acoustc radaton loadng as well. II. Analytcal Modelng The theoretcal descrptons presented here are for an dealzed long cylnder snce the geometry of a launch vehcle farng s cylndrcal at any gven cross secton. It s assumed that there wll be very lttle effect on the external sound pressure feld due to the dffracton of sound waves from the ends of the cylnder. The dffracton of sound waves from both ends of the cylnder s thus neglected n the followng analyss. Also the cylnder wall s 5

6 consdered to be hard so that all of the scattered waves proceed outward from the surface. Fg. 1 shows the geometry of oblquely ncdent waves mpngng on a cylnder from a source located on the X axs. The cylnder axs s algned wth the Z axs and the Y axs s then perpendcular to these two axes. The angle defnes the poston of the observaton pont at the surface of the cylnder. Snce n the present case the ncdent waves are oblque to the cylnder the resultant crcumferental sound pressure at a pont on the cylnder wll depend not only on ts locaton n the X-Y plane but also ts locaton along the Z axs. Fg. 1: Geometry of oblquely ncdent waves for three-dmensonal cylnder coordnate axes. The approach used here consders a fnte porton of the cylnder of length L and z s the elevaton wthn the regon of the cylnder where the resultant pressure s to be evaluated due to a pont source postoned at a dstance r on the X axs as shown n Fg. 1. Let the projecton of the pont of nterest on the X-Y plane be Q. Then the projected dstance d can be calculated as follows d 2 2 a + r 2ar cosφ =. (1) The resultant oblque dstance can then be calculated as = 2 2 d + z. (2) Now a spatally dependent factor can be consdered whch can gve the soluton for the sound pressure produced by a pont source as a functon of dstance between the pont source and observaton ponts at the surface of the cylnder. Ths spatally dependent factor can be determned as

7 7 ( ) ( ) t k s o e Q t z p ω π ω ρ = 4. (3) Fnally usng ths spatally dependent factor the total external sound pressure at the surface of the cylnder can be derved as the superposton of the ncdent wave pressure p and scattered wave pressure p s as follows: ( ) ( ) ( ) [ ] = = + = 1 0 ) ( sn ) ( ) cos( ) ( M m m m m m m m s s s s t a ka H e ka J m t z p t Q z a k p t Q z a k p t Q z a k p γ φ ε φ φ φ γ (4) where the summaton s for M number of terms requred n the seres calculaton 1 = m ε f 0 = m and 2 f 0 > m. III. Numercal Modelng Consder an arbtrary shaped structure of volume V surrounded by surface S and placed n an acoustc doman of volume V e as shown n Fg. 2 where Q and P are two ponts at some dstance r Q and r P respectvely from the centre of the body. In other words one s the ntegraton pont on the boundary and the other s the feld pont or source pont whch may be placed n V e V or on S. The Helmholtz ntegral equaton can be wrtten n the form ( ) ( ) ( ) ( ) ( ) ( ) ds n G Q p G Q u P p P C s n o + = ρ ω (5) where p r Q r = and the coeffcent ) (P C s the sold angle measured from V: e S V P S P ds P Q n V P P C = + = =. 4 ; ) ( ; ) ( π π (6) Snce the am of the current work s to nvestgate the scatterng problem from a hard wall only the second term of the ntegraton n Eq. (5) s mportant because the frst term whch represents the normal velocty on the surface of the body can be omtted for a rgd surface. Hence for scatterng from a rgd body Eq. (5) reduces to ( ) ( ) ( ) ( ) ( ) ( ) P p ds P Q e n Q p P p P C P Q k s 4π + = (7) where ( ) ( ) P Q e G Q P k ) ( = s the free feld Green s functon and p represents the ncdent sound

8 pressure on pont P. Eq. (7) can be evaluated numercally by dscretzng the boundary surface nto E surface elements. The dscretzaton of the ntegral Eq. (7) can be approxmated by the sum of ntegrals over the elements as follows C E = 1 s ( P) p( P) p ( Q) E ( ) = k ( Q P e ) ξ ds + 4π p n ( Q P) ( P) (8) where E (ξ) are the element shape functons. For a surface formulaton where r Q = r P solvng E calculatons for all the elements on the surface Eq. (8) can be wrtten n the matrx form where [ ] [ C]{ p} { p}[ H] + 4π p = (9) C s equal to2 πin (I N s an N N dentty matrx of the N calculaton ponts on the N nodes) for the surface formulaton and [ H ] s an H H global matrx of the H calculaton ponts on the H elements. Here both [ C ] and [ H ] are known but the complex vector{ p } s unknown. Therefore to fnd{ p } Eq. (9) reduces to where[ A] [ H C] [ A]{ p} 4π p = (10) =. On each node of the surface the ncdent sound pressure of Eq. (10) can be calculated for a pont source usng Eq. (3). Fg. 2 Geometry of the exteror boundary problem. 8

9 IV. Estmaton of the ocket Engne Exhaust Nose Hgh sound levels produced durng the lft-off of a launch vehcle are related to the varous physcal and operatng condtons of the rocket engne and the ext condtons of the exhaust flow. Therefore for predcton purposes several parameters need to be taken nto account. Operatng and exhaust parameters for varous chemcal rocket engnes are lsted n Table 1 where engne A has multple nozzles (eght nozzles) and the remander have a sngle nozzle. Table 1 ocket engne operatng and exhaust parameters. [Data taken from Mayes et al. 18 ] Engne Average Thrust F x 10 5 (N) Ext Dameter D e (m) Exhaust Velocty U e x 10 3 (m/sec) Mach Number M e A B C D E F The acoustc power generated by the rocket engne s dependent on the mechancal power of the jet stream. Ths can be expressed usng the followng emprcal equaton as suggested n NASA-SP a space-vehcle desgn crtera document: The overall acoustc power level s 4 WOA = nFU e. (11) ( 0.005nFU ) 120 db L w = 10log10 e + (re watts). (12) In Eq. (12) t s assumed that 0.5% of stream power s converted to acoustc power. The overall acoustc power levels for varous engnes are shown n Fg. 3 where t can be seen that engne A generates the hghest and engne F generates the lowest whle the remanng engnes generate almost the same overall acoustc power level. It should be noted that there s a dfference n the magntudes of the results presented here and the prevous results presented by Morshed 19 whch mstakenly neglected to add 120dB as requred n Eq. (12). Therefore the corrected results presented here dffer only n magntude compared to the results presented by Morshed 19. For the current work engne E was chosen for the predcton of acoustc loads on the rocket farng because t has the greatest nozzle ext dameter exhaust velocty and mach number. 9

10 Fg. 3 Overall acoustc power levels for varous rocket engnes A to F. V. Geometry Under Consderaton to Predct the Acoustc Loads For the predcton of external sound pressure loadng on a farng structure a epresentatve Small Launch Vehcle Farng (SLVF) whch has been used n prevous work 2021 was used. The overall dmensons of the SLVF are gven n Table 2. The geometry of the SLVF was represented n ANSYS usng quadratc eght node elements and a mesh-only element MESH200 was used to generate surface elements and nodes as shown n Fg. 4. The model conssted of 726 elements and 2120 nodes at the surface whch was mported nto MATLAB for numercal analyss. For the current work the geometry chosen for the acoustc loadng calculatons s shown n Fg. 5. The parameters shown n Fg. 5 are defned n the nomenclature. The rocket s assumed to be launched vertcally wth a 90 o bucket deflector turnng the exhaust stream horzontally resultng n the flow axs beng perpendcular to the vehcle axs. For ths partcular case t was assumed that all the sources are stuated below the farng along the exhaust flow axs so that all the ncomng waves mpnge oblquely on the farng. The nteracton of the supersonc jet wth the deflector s beyond the scope of the current nvestgaton. Table 2 SLVF physcal dmensons. Property Value Maxmum Dameter 1.552m Overall Length 5.33m 10

11 Fg. 4 SLVF surface elements and nodes. The crcles show the crcumferental nodes at a heght of z = 2.17m on the SLVF. Z Observaton pont P Launch Vehcl Normal to vehcle β x 1 Nozzle x 2 r θ Axs of flow Bucket x 3 Pont source Fg. 5 Geometry of source locatons relatve to the vehcle and exhaust flow axs. 11

12 VI. Predcton of Acoustc Loads Usng the Unque Source Allocaton Method The methodology used here for the predcton of acoustc loads on the vehcle s outlned n NASA-SP Ths technque assumes that the rocket exhaust nose can be modelled as orgnatng from a sngle unque effectve source locaton along the flow axs n each frequency band of nterest. For the current analyss one-thrd-octave band centre frequences from 50Hz to 400Hz are used. A. Predcton Formulatons In the NASA-SP document the normalzed relatve sound power spectrum levels for varous chemcal rockets wth sngle nozzles wthn a thrust range of 1.56 kn to kn are gven n terms of Strouhal number ( f D e U e ). The apparent axal dstance of the source from the nozzle plane s also gven n terms of Strouhal number. Both of these results were used to estmate the sound power level and effectve unque source locaton for each frequency band of nterest. The estmated results for the normalzed relatve sound power level and apparent source locaton for each one-thrd octave band centre frequency of engne E are gven n Fgs. 6 and 7 respectvely as a functon of Strouhal number. Fg. 6 shows that n the low frequency range the sources are located much further downstream than at hgher frequences. However the normalzed relatve sound power spectrum (shown n Fg. 6) can be converted to any acoustc bandwdth as follows 4 The bandwdth ( f ) W Ue Ue Lw b = 10 log10 + Lw 10log log10 fb. (13) WOA De De fb was calculated for each one-thrd octave band centre frequency from 50Hz to 400Hz usng Bes & Hansen 22. Fg. 8 shows the calculated sound power level for each one-thrd octave bandwdth for the current analyss. The drectonal characterstc of the sound radated back to the vehcle depends on Strouhal number exhaust flow drecton effectve source locaton of the rocket exhaust nose and observaton poston on the vehcle. Fg. 9 shows the far-feld drectvty curve for chemcal rockets whch was estmated from NASA-SP In the referenced document there are many drectvty curves presented n terms of Strouhal number( f D e U e ). To smplfy the analyss whle demonstratng the prncples nvolved only one drectvty curve was chosen for engne E for use wth all the frequences and source locatons. To fnd the drectvty ndex from Fg. 9 the drectvty angle θ relatve to the exhaust axs needs to be calculated usng the equvalent source poston for each frequency 12

13 and observaton pont on the vehcle. Fg. 6 Estmated relatve sound power levels for each one-thrd octave band centre frequency from 50Hz to 400Hz. [Data estmated from Fg. 5 presented n NASA-SP ] Fg. 7 Estmated source locatons for each one-thrd octave band centre frequency from 50Hz to 400Hz. [Data estmated from Fg. 14 presented n NASA-SP ] 13

14 Fg. 8 Calculated sound power levels for each one-thrd octave band from 50Hz to 400Hz. Fg. 9 Smple drectvty curve used n the calculatons for all one-thrd octave bands analysed. [Data estmated from Fg. 10 presented n NASA-SP ] 14

15 The acoustc power of each source for each frequency band can be determned from the acoustc power level L w b presented n Eq. (13) as follows The strength of each source n each frequency band can be determned from 22 Lwb = 10 W 10 b Watts. (14) Qs b 4πWb 2 k ρc = m 3 /s. (15) The sound pressure level on the crcumference around the vehcle ncludng the effects due to the reflectng surface of the vehcle for a band centred on any frequency can be expressed as where the pressure quantty t 2 [ p ( k a z φ Q t) ] + DI( ) 3 L b φ = 10log10 a s b θ p (db re 20 µpa) (16) t p a represents the total sound pressure ampltude on the vehcle due to ncdent and scattered waves and s a functon of the dstance from the source to the observaton pont on the vehcle wave number k radus of the vehcle a elevaton heght z azmuthal angle and source strength Q s b and the term DI(θ ) s the drectvty ndex determned from Fg. 9. Ths pressure quantty can be determned usng Eqs. (4) and (10) for the analytcal and numercal calculatons respectvely. For all the sources Lpb φ must be assumed over all one-thrd octave frequency bands to gve 4 Lp b φ L p OA = 10log φ (db re 20 µpa). (17) Allb In Eqs. (16) and (17) the sound pressure due to scatterng from the reflectng surface of the vehcle as well as the spreadng due to dstance are ncluded. The effect of the scattered sound feld on the sound pressure on the surface of the vehcle was not consdered n the prevous analyss presented by NASA-SP It s also notceable that n the precedng equatons the 4π term has been used because the drectvty ndex DI ( θ) relatve to the exhaust axs ncludes the effect of the sources beng located on a hard surface. of the sound radaton 15

16 B. Acoustc Loadng on the Farng In ths secton the unque source allocaton technque whch approxmates the sound generaton usng an equvalent sngle pont source for each frequency band of nterest along the flow axs was used to predct the acoustc loads on the SLVF both analytcally and numercally. Both calculatons were conducted for each onethrd octave band centre frequency from 50Hz to 400Hz. There are n total 10 equvalent pont sources; one for onethrd octave band. It was assumed that the farng structure and the flow axs are stuated at x = 15D upstream and 1 e x2 = 5D e downstream of the vehcle respectvely. A reference pont was chosen at φ = 0 whch s the front pont on the vehcle facng the exhaust flow. Hence φ =180 s the rear pont on the vehcle. For smplcty t was assumed that the temperature along the flow axs s T = 1000 C. At that temperature the speed of sound and densty n ar s m/s and 0.28 kg/m 3 respectvely. For comparson both the analytcal and numercal calculatons were conducted around the crcumference at a heght of z = 2.17m from the bottom face of the SLVF (see Fg. 4). Ths heght was chosen because at that heght there are sxty crcumferental nodes n the BEM model whch are suffcent to acheve an accurate numercal estmaton of the sound pressure pattern for comparson wth the analytcal results. The estmated and calculated values of all the parameters that were used n the calculatons are gven n Table 3 for each one-thrd octave band centre frequency and the drectvty ndex was assumed to be same for all the crcumferental postons at the observaton heght on the farng. Table 3 Detals of the 10 sources. (All the data gven here for engne E ; overall acoustc power level L w = dB; speed of sound and densty n ar at T = 1000 o C s m/s and 0.28 kg/m 3 respectvely.) Source Number One-Thrd Octave Band Centre Frequency (Hz) Estmated Source Dstance r (m) Source Dstance From the Vehcle Axs x 3(m) Elevaton Angle β (Degrees) Drectvty Angle θ (Degrees) Estmated Drectvty Index DI(θ) (db) Calculated Acoustc Power Level n Each Band L wb (db) Source Strength Q sb 10 7 (m 3 /s)

17 VII. esults and Dscussons A. Analytcal esults For the analytcally calculated acoustc loadng on the SLVF usng the unque source allocaton technque whch approxmates the sound generaton usng an equvalent sngle pont source for each frequency band of nterest the maxmum dameter of the SLVF (see Table 2) was consdered as a canddate for a representatve evaluaton of the surface sound pressure levels as a functon of azmuthal angle. The scatterng of sound from the surface was consdered n the calculatons as descrbed n Eqs. (4) (16) and (17). The parameters used for the analytcal calculatons are gven n Table 3. Fgs. 10 to 12 show the sound pressure levels at the surface of the SLVF at each one-thrd octave band centre frequency from 50 Hz to 400Hz calculated usng Eqs. (4) and (16) at a heght of z = 2.17m from the bottom face of the SLVF. The overall sound pressure level (OSPL) for the array of ten equvalent pont sources correspondng to one-thrd octave bands from 50Hz to 400Hz calculated usng Eqs. (4) and (17) at a heght of z = 2.17m from the bottom face of the SLVF s shown n Fg. 18. The overall sound pressure levels (OSPL) calculated usng Eqs. (4) and (17) at the forward ( φ = 0 ) and backward ( φ =180 ) pont of the SLVF are db and db respectvely. From these results t can be seen that the sound pressure ampltude vares relatvely smoothly at the front of the SLVF facng the exhaust flow and vares more aggressvely at the back of the SLVF due to postve and/or negatve nterference of the two dffracted waves travellng around the two sdes of the SLVF. The sound pressure fluctuaton ncreases at the back of the SLVF as the frequency ncreases because the level of nterference of the two dffracted waves travellng around the two sdes of the SLVF ncreases. 17

18 Fg. 10 Analytcally calculated sound pressure levels at the SLVF surface for an equvalent sngle pont source for each one-thrd octave band from 50Hz to 100Hz. [z = 2.17m x 1 = 15D e x 2 = 5D e and reference pressure 20µPa] Fg. 11 Analytcally calculated sound pressure levels at the SLVF surface for an equvalent sngle pont source for each one-thrd octave band from 125Hz to 200Hz. [z = 2.17m x 1 = 15D e x 2 = 5D e and reference pressure 20µPa] 18

19 Fg. 12 Analytcally calculated sound pressure levels at the SLVF surface for an equvalent sngle pont source for each one-thrd octave band from 250Hz to 400Hz. [z = 2.17m x 1 = 15D e x 2 = 5D e and reference pressure 20µPa] B. Numercal esults For the numercal analyss the Boundary Element Method (BEM) was used. The parameters used for the numercal calculatons are gven n Table 3 for each equvalent pont source at each one-thrd octave band centre frequency from 50Hz to 400Hz. The numercal results for each one-thrd octave band centre frequency are presented n Fgs. 13 (a-t) calculated usng Eqs. (10) and (16). The results show that for very low frequences (50Hz to 100Hz) the hghest acoustc pressures mostly occur on the surface of the lower portons of the SLVF as shown n Fgs. 13(a-h). The reasons for ths are: (a) the sources are located below the SLVF along the exhaust flow axs; and (b) the SLVF dmenson s relatvely small compared to the wavelength of the very low frequency nose. As the frequency ncreases the wavelength becomes shorter compared to the SLVF length and the sound feld becomes more unformly dstrbuted as shown n Fgs. 13(-t). The numercal results calculated usng Eqs. (10) and (17) for the overall sound pressure dstrbuton for the frequency range from 50Hz to 400Hz are shown n Fgs. 14 (a-b). It appears that the overall sound pressure level reaches around 148dB for ten equvalent sngle pont sources stuated close to the vehcle along the exhaust flow as shown n Fgs. 14(a-b). 19

20 The sound pressure levels as a functon of SLVF crcumferental locaton at a heght of z = 2.17m from the bottom face of the SLVF calculated usng BEM are shown n Fgs. 15 to 17. The results show smlar pressure fluctuatons at each band centre frequency to the fluctuatons n the analytcal results shown n Fgs. 10 to 12 whch were obtaned usng the unque source allocaton technque. There are slght dfferences between the overall sound pressure level ampltudes obtaned usng the numercal and analytcal calculatons as shown n Fg. 18 over the frequency range from 50Hz to 400Hz. The reason for the small dfferences s that the dffracton of sound waves around the ends of the SLVF was not consdered n the analytcal source allocaton calculaton but was ncluded n the BEM analyss whch allows determnaton of the sound pressure near the ends of the cylnder by consderng a quarter-pont technque (r 2/3 ) for partcle velocty near the edge of the cylnder where r s dstance from the edge. Ths approach approxmates the condton that the partcle velocty tends to nfnty as r tends to zero as explaned n detal by Juhl 9. It has been observed that the unque source allocaton method s capable of predctng the acoustc loads on the surface of the SLVF n the low frequency range from 50Hz to 400Hz but t approxmates the sound generaton usng an equvalent sngle pont source for each frequency of nterest only. In future work a non-unque source allocaton method wll be of nterest n the low frequency range from 50Hz to 400Hz whch assumes that there are a number of pont source locatons makng an array of pont sources along the exhaust flow axs for each one-thrd octave frequency band of nterest. Ths approach should yeld more accurate results than the unque source allocaton method dscussed n the current work. (a) Front face 50Hz. (b) ear face 50Hz. 20

21 (c) Front face 63Hz. (d) ear face 63Hz. (e) Front face 80Hz. (f) ear face 80Hz. (g) Front face 100Hz. (h) ear face 100Hz. 21

22 () Front face 125Hz. (j) ear face 125Hz. (k) Front face 160Hz. (l) ear face 160Hz. (m) Front face 200Hz. (n) ear face 200Hz. 22

23 (o) Front face 250Hz. (q) Front face 315Hz. (p) ear face 250Hz. (r) ear face 315Hz. (s) Front face 400Hz. (t) ear face 400Hz. Fgs. 13 (a-t) Numercally calculated sound pressure exctaton at the surface of the SLVF for varous onethrd octave band centre frequences from 50Hz to 400Hz. [x1 = 15De x2 = 5De and reference pressure 20µPa] 23

24 (a) Front face 400Hz. (b) ear face 400Hz. Fgs. 14(a-b) Numercally calculated overall sound pressure exctaton at the surface of the SLVF for the entre spectrum of one-thrd octave band centre frequency range from 50Hz to 400Hz. [x 1 = 15D e x 2 = 5D e and reference pressure 20µPa] Fg. 15 Numercally calculated sound pressure levels as a functon of SLVF crcumferental locaton for varous one-thrd octave band centre frequences from 50Hz to 100Hz. [z = 2.17m x 1 = 15D e x 2 = 5D e and reference pressure 20µPa] 24

25 Fg. 16 Numercally calculated sound pressure levels as a functon of SLVF crcumferental locaton for varous one-thrd octave band centre frequences from 125Hz to 200Hz. [z = 2.17m x 1 = 15D e x 2 = 5D e and reference pressure 20µPa] Fg. 17 Numercally calculated sound pressure levels as a functon of SLVF crcumferental locaton for varous one-thrd octave band centre frequences from 250Hz to 400Hz. [z = 2.17m x 1 = 15D e x 2 = 5D e and reference pressure 20µPa] 25

26 Fg. 18 Comparson of the overall sound pressure level between the numercal and analytcal results for the entre spectrum of one-thrd octave band centre frequency range from 50Hz to 400Hz. [z = 2.17m x 1 = 15D e x 2 = 5D e and reference pressure 20µPa] VIII. Conclusons The acoustc feld generated on a launch vehcle farng durng launch has been estmated for a chemcal rocket engne E. The engne exhaust nose has been assumed to be orgnatng along the exhaust flow perpendcular to the vehcle axs and has been modelled usng the unque source allocaton method to determne the acoustc pressure loadng at the surface of the epresentatve Small Launch Vehcle Farng (SLVF) n the frequency range from 50Hz to 400Hz. The unque source allocaton method assumes that the rocket nose can be modelled usng a sngle unque source locaton along the flow axs for each one-thrd octave frequency band. The analytcal and numercal results obtaned usng ths method showed that the overall sound pressure level (OSPL) reaches an OSPL of around 148 db for ten equvalent sngle pont sources n an array along the exhaust flow over the frequency range from 50Hz to 400Hz. The method descrbed here allows analyss of the acoustc feld at the surface of a launch vehcle farng for ncdent oblque waves and the theoretcal analyss showed good agreement wth the numercal results. However the dffracton of sound waves around the ends of the farng was not taken nto account n the analytcal calculatons n contrast to the results calculated usng the Boundary Element Method (BEM) resultng n a small varaton 26

27 between the analytcal and numercal results. It s ntended to extend the present work n the future by consderaton of the followng: 1) the effects due to the dffracton around the ends of the cylnder whch have been avoded n the analytcal modelng work could be ncluded n a future nvestgaton to develop a full analytcal model of acoustc loadng on fnte length cylnders such as cylndrcal launch vehcles; and 2) a non-unque source allocaton method can be nvestgated n the low frequency range from 50Hz to 400Hz whch assumes that there are a number of pont source locatons makng an array of pont sources along the exhaust flow for each frequency of nterest. eferences 1 Franken P. A. and Kerwn E. M. Methods of Space Vehcle Nose Predcton WADC T Wrght Paterson AFB Oho Potter. C. Correlaton Patterns of the Acoustc Pressure Fluctuatons on the S-IC Vehcle Due to the Exhaust Nose of the Test and Launch Stand Wyle Labs ept. W Contract NAS Potter. C. and Crocker M. J. Acoustc Predcton Methods for ocket Engnes Includng the Effects of Clustered Engnes and Deflected Exhaust Flow NASA C Acoustcs Loads Generated by the Propulson System NASA SP-8072 NASA Space Vehcle Desgn Crtera (Structures) Morse P. M. Vbraton and Sound 1 st ed. McGraw-Hll Book Company New York Chap Morse P. M. and Feshbach H. Methods of Theoretcal Physcs Part-II Internatonal student ed. McGraw-Hll New York 1953 Chap Morse P. M. and Ingard K. U. Theoretcal Acoustcs McGraw-Hll New York 1986 Chap Malbequ P. Candel S. M. and gnot E. Boundary Integral Calculatons of Scattered Feld: Applcaton to a Spacecraft Launcher Journal of the Acoustcal Socety of Amerca Vol. 82 No pp do: / Juhl P. M. The Boundary Element Method for Sound Feld Calculatons Acoustc Lab Techncal Unversty of Denmark ept. 9 Aug Morshed M. M. M. Zander A. C. and Hansen C. H. Two-Dmensonal and Three-Dmensonal Acoustc Loadngs on Cylnders Due to a Pont Source AIAA Journal Vol 49 No. 11 Nov pp do: /1.j Morse P. M. Vbraton and Sound 1 st ed. McGraw-Hll New York Chap Fahy F. Sound and Structural Vbraton : radaton transmsson and response 1 st ed. Academc London Seybert A. F. Soenarko B. zzo F. J. and Shppy D. J. An Advanced Computatonal Method for adaton and Scatterng of Acoustc Waves n Three Dmensons Journal of the Acoustcal Socety of Amerca Vol. 77 No pp do: /

28 14 Seybert A. F. Soenarko B. zzo F. J. and Shppy D. J. A Specal Integral Equaton Formulaton for Acoustc adaton and Scatterng for Axsymmetrc Bodes and Boundary Condtons Journal of the Acoustcal Socety of Amerca Vol. 80 No pp do: / Seybert A. F. and Casey D. K. An Integral Equaton Method for Coupled Flud/Flud Scatterng n Three Dmensons Journal of the Acoustcal Socety of Amerca Vol. 84 No pp do: / Seybert A. F. Cheng C. Y.. and Wu T. W. The Soluton of Coupled Interor/Exteror Acoustc Problems Usng the Boundary Element Method Journal of the Acoustcal Socety of Amerca Vol. 88 No pp do: / Wu T. W. Boundary Element Acoustcs: Fundamentals and Computer Codes WIT Boston 2000 Chap Mayes W. H. Lanford W. E. and Hubbard H. H. Near Feld and Far Feld Nose Surveys of Sold Fuel ocket Engnes for a ange of Nozzle Ext Pressures NASA TN D Morshed M. M. M. Investgaton of External Acoustc Loadngs on a Launch Vehcle Farng Durng Lft-off Ph.D. Dssertaton School of Mechancal Engneerng Unv. of Adelade SA Australa Howard C. Q.Hansen C. H. and Zander A. C. Vbro-acoustc Nose Control Treatments for Payload Bays of Launch Vehcles: Dscrete to Fuzzy Solutons Appled Acoustcs Vol. 66 No. 11 Nov pp do: /j.apacoust Howard C. Q.Hansen C. H. and Zander A. C. Nose educton of a ocket Payload Farng Usng Tuned Vbraton Absorbers wth Translatonal and otatonal DOFs Proceedngs of Acoustcs Busselton Western Australa Australa 9-11 Nov pp Bes D. A. and Hansen C. H. Engneerng Nose Control 3 rd ed. Spon London Chaps