1

Prediction of Acoustic Loads on a Launch Vehicle: Non-

Unique Source Allocation Method

Mir Md. Maruf Morshed1

Jubail University College, Jubail Industrial City, Jubail, 31961, Kingdom of Saudi Arabia

Colin H. Hansen2

The University of Adelaide, Adelaide, SA, 5005, Australia

and

Anthony C. Zander3

The University of Adelaide, Adelaide, SA, 5005, Australia

Severe acoustics loading, which occurs during the flight mission of launch vehicles, is

often responsible for damage to the payload inside the fairing compartment. The prediction

of the acoustic loads on the payload fairing generated by large propulsion devices requires

the use of analytical and numerical methods to identify the acoustic sources and the

spectrum of the acoustic loads. Work presented in this manuscript investigates the nature of

the external acoustic pressure excitations on the fairing in the low frequency range from 50

Hz to 400 Hz, during the lift-off of a launch vehicle. The acoustic pressure excitation acting

on a Representative Small Launch Vehicle Fairing (RSLVF) was estimated from the

complex acoustic field generated by the rocket engine exhaust gases. The estimation

procedure involved the use of a non-unique source allocation technique which considered

acoustic sources along the rocket engine exhaust flow. Numerical and analytical results for

the acoustic loads on the fairing agree well.

Nomenclature

� = coefficient matrix

� = cylinder radius, m

�� = speed of sound in the exhaust flow, m/s

1 Assistant Professor, Department of Mechanical Engineering, Jubail University College, Jubail Industrial City

31961, Kingdom of Saudi Arabia. 2 Professor, School of Mechanical Engineering, The University of Adelaide, SA 5005, Australia.

3 Associate Professor, School of Mechanical Engineering, The University of Adelaide, SA 5005, Australia.

2

�� = speed of sound in air, m/s

� = frequency band number

� = diagonal matrix

�(�) = solid angle, rad

� = nozzle exit diameter, m

� = directivity index, dB

� = frequency, Hz

∆�� = frequency bandwidth, Hz

� = coefficient matrix

��(�) = Hankel function or Bessel function of the third kind of mth

order and argument, z

�� = identity matrix

��(�) = Bessel function of the first kind of mth

order and argument, z

� = wavenumber, rad/m

�� = overall acoustic power level, dB

��,���= sound power level for each segment, dB

��,���,� = sound pressure level for each segment in each frequency band, dB

��,���,�,�= sound pressure level on the circumference of the vehicle, dB

� ,!",���,�,� = overall sound pressure level, dB

# = total number of terms

$ = term number

% = total number of point sources

& = source number, and number of nozzles

� = field point or observation point

', ( = acoustic pressure, Pa

') , (* = incident sound pressure, Pa

3

'� = scattered sound pressure, Pa

'+, = total sound pressure at the surface of a cylinder, Pa

- = spatially dependent factor

.� = source strength, m3/s

.� = projection point, and integration point on the boundary

/ = distance between the integration point and observation point, and resultant oblique distance, m

0 = radial distance, and distance of the source from the nozzle to the centre of each segment, m

1� = exhaust velocity, m/s

2���,�= acoustic power of each source for each frequency band, Watt

2(�) = sound power per Hz, Watt

2(0) = sound power as a function of distance between the nozzle exit and the source, Watt

2!" = overall acoustic power, Watt

3 = X component of the cylindrical coordinate axes

4, = core length, m

45 = axial distance of the observation point on the vehicle from the nozzle exit, m

46 = vertical distance from the nozzle exit of the sources along the flow axis, m

47 = distance of the source from the vehicle axis along the flow axis, m

∆4 = length of segment, m

8 = Y component of the cylindrical coordinate axes

9 = Z component of the cylindrical coordinate axes

� = elevation height, m

: = angle from the horizontal axis of the noise radiation, deg

; = azimuthal angle, deg

< = incline angle between the line joining the observation point to the source location and the normal of the

vehicle axis, deg

4

=� = constant

>� = phase angle, rad

? = angular frequency, rad/s

@ = density of air in the exhaust flow, kg/m3

@� = equilibrium density of the fluid, kg/m3

Γ = Surface boundary of the exterior boundarys

I. Introduction

For many years researchers have been trying to develop a suitable analytical methodology for the prediction of

acoustic loads on launch vehicles, based on different sub-scale or full-scale tests of supersonic and subsonic engine

exhaust jet flows. For example, Mayes et al.1 conducted near-field and far-field noise surveys on straight horizontal

solid fuel rocket engines for a range of nozzle exit pressures, although this arrangement excludes the influence of the

launch pad. The measurements were presented for a 1,500-pound-thrust engine and for several 5,000-pound-thrust

engines for which the nozzle exit flow conditions varied widely. From the near-field measurements in the frequency

range from 5 Hz to 2.5 kHz; the apparent source of noise was found to be approximately 20 diameters downstream

of the nozzle exit. The far-field measurements showed that the maximum overall noise levels for all engines occur

between 30° to 45° from the axis of the flow.

Tedrick2 conducted acoustical measurements of clustered and single-nozzle rocket engines, and discussed the

characteristics of the near-field and far-field noise fields. Experimental results for various types of rocket engines,

including exhaust flow configurations, and general discussions can be found in a wide range of literature, including

Lassiter and Heitkotter3, Cole et al.

4, Eldred et al.

5 and Morgan et al.

6. Based on several experimental models,

Morgan et al.6, Franken et al.

7 and Potter and Crocker

8 proposed an extensive empirical prediction methodology to

calculate the near-field and far-field noise produced by jet and rocket flows, including the deflected flow from

various types of exhaust deflectors. Mel'nikov et al.9 and Dumnov et al.

10 investigated empirical techniques to define

the maximum acoustic loads on the fairing on the basis of flight and experimental model data. In their work, the

interaction of the jet flow with the launch pad was extensively studied to quantify the noise sources using empirical

techniques. Using experimental and theoretical studies as a basis, Dementjev et al.11

developed a semi-empirical

technique to determine the noise due to the interaction of supersonic high temperature jets with different shaped

5

deflectors. All the aforementioned empirical techniques require a considerable amount of experimental data and this

is one of their major shortcomings. The standard empirical methodologies and recommended implementation

practices are outlined in NASA-SP-807212

, a space vehicle design criteria document, which is used in the current

work to determine the acoustic loading on the launch vehicle fairing.

Two different source allocation techniques have been proposed in NASA-SP-807212

, based on experimental data

for chemical rockets and generalized sound spectrum levels. The first technique (unique source allocation method)

assumes a unique source location along the exhaust flow in each frequency band, whereas the second technique

(non-unique source allocation method) assumes that the noise in each frequency band is generated throughout the

exhaust flow. Although both techniques predict the acoustic loads at a specified point on the launch vehicle, the

effects of the scattering of the sound waves from the launch vehicle surface are completely omitted from the analysis

using either technique. Morshed et al.13

extended the unique source allocation method for scattering effects and

developed analytical and numerical tools to examine the acoustic loads on the surface of a Representative Small

Launch Vehicle Fairing (RSLVF). However, the extended technique considering the scattering effects did not

implement the non-unique source allocation method, and this implementation is the focus of the investigation

reported here which is an extension of the previous work13

. The intention is to provide the inputs needed to evaluate

noise and vibration control treatments for launch vehicles.

The non-unique source allocation method was used here to allocate sources along the engine exhaust flow for

each of three one-third octave bands corresponding to centre frequencies of 50 Hz, 100 Hz and 400 Hz, assuming

that all the power in the one-third octave band is concentrated at a single frequency, and the method was extended,

using the analytical and numerical tools developed by the authors, to examine the acoustic loads at the surface of the

RSLVF. In order to keep the quantity of figures and results for a reasonable amount, only the aforementioned one-

third octave bands were chosen for analysis in this manuscript, however a similar approach can be used for the other

one-third octave bands.

The results reported here and obtained using the non-unique source allocation method are compared with the

results obtained using the unique source allocation method presented in previous work13

. The non-unique source

allocation method was used here as it provides improved accuracy over NASA-SP-807212

and other previous work1-

11. This is a result of the use of the process of combining the new analytical and numerical methods to describe the

sound pressure as a result of the reflecting surface of the launcher, which permits convergence of the external

6

pressure field calculations at the surface of the launcher.

The current work uses the Boundary Element Method (BEM) for numerical calculations to predict the acoustic

load on the RSLVF and to assess the validity of the analytical model. The BEM software used here was written in

MATLAB© and is known as Open BEM, an open source code mainly developed by the Acoustic Laboratory,

Technical University of Denmark14

. The BEM was implemented for the three dimensional geometry of the RSLVF

considering the effects due to the diffraction of sound waves from the ends, and the results are compared with the

results obtained analytically for an infinite cylinder of constant diameter.

II. Theory

A. Analytical Modeling

The theoretical description of the three-dimensional acoustic loading on a cylinder due to a point source has been

extensively discussed previously by Morshed et al.13,15

. This work was used as a basis for the current study and was

extended to apply to a number of point sources along a line as shown in Fig. 3. Following the previous theoretical

work13,15

, the following assumptions were made: (i) the object is an idealized long cylinder, since the geometry of a

launch vehicle fairing is cylindrical, (ii) there will be very little effect on the external sound pressure field due to the

diffraction of sound waves from the ends of the cylinder and thus this effect is neglected in the following analysis,

and (iii) the cylinder wall is considered to be acoustically hard so that all of the scattered waves proceed outward

from the surface.

Consider a point source located on the X axis which produces spherical waves that impinge obliquely on the

surface of the cylinder as shown in Fig. 1. The sound waves travel a distance R from the source and impinge

obliquely on the surface at point P of the cylinder. Without repeating the lengthy mathematical derivations13,15

for

this particular arrangement of acoustic loading on the cylinder, it can be shown that the total external sound pressure

at the surface of the cylinder is the superposition of the incident wave pressure pi and scattered wave pressure p

s as

follows13,15

:

( ) ( )

( )1

1 0

( , , , , , , ) , , , , , , , , , , , ,

, , cos( ) ( ) sin ( ) ,m

t i s

a s s s

MNim

m m m m

n m

p R k a z Q t p R k a z Q t p R k a z Q t

p R z t i m J ka i e H kaγ

φ φ φ

ε φ γ−

−

= =

= +

′= − ∑ ∑ (1)

7

where the first summation on the right hand side is for N point sources along a line and the second summation is for

M terms required in the series calculation. The quantity εm = 1 if m = 0 and 2 if m > 0. The spatially dependent

factor, pʹ (R, z, t), is a function of distance between the point source and observation point at the surface of the

cylinder, and can be determined as15-18

( ) ( ), ,

4

i k R tso

Qp R z t i e

R

ωω ρπ

−′ = − . (2)

Fig. 1: Geometry of obliquely incident waves for three-dimensional cylindrical coordinate axes.

B. Numerical Formulation

The numerical formulation technique using the boundary element method (BEM) for the exterior boundary

problem has been extensively discussed by Morshed et al.13,15

. This technique has been used and extended in the

current work to include a number of point sources along a line.

For the exterior problem where the observation point� is located on the boundary Γ, the Kirchhoff-Helmohltz

(boundary) integral solution for the time harmonic sound pressure p can be determined as19-21

�C�D'C�D = F GHCI�,J�DGKCJ�DL 'C.�DMΓC.�D + 4P')C�D. (3)

Eq. (3) can be reduced to a matrix formulation as13-15

S�TU(V = U(VS�T + 4P(*, (4)

8

where [C] is equal to NIπ2 (IN is an N × N identity matrix of the N calculation points on the N nodes) for the

surface formulation, and [H] is an HH × global matrix of the H calculation points on the H elements. Here both

[C] and [H] are known but the complex vector U(V is unknown. Therefore to find U(V, Eq. (4) reduces to

S�TU(V = −4P(*, (5)

where [A] = [H – C]. The distances between the m integration points Qm (x, y, z), and n source points Pn (X, Y, Z),

need to be determined for the incident sound pressure from each source. Hence, the right side of the Eq. (5) may be

calculated as

( )

1 4

Ni k R ti s

n

Qp i e

R

ωοω ρ

π−

=

= −∑ , (6)

where/ = X.$2 (3,8,9)−&2(4,Z. �) and N is number of point sources.

C. Non-Unique Source Allocation Methodology

The non-unique source allocation method is more complicated than the unique source allocation method

described in the previous study by Morshed et al.13

. The non-unique source allocation method recognizes that the

rocket noise in each frequency band is generated throughout the exhaust flow, and a unique, single equivalent point

source location along the flow axis is not assumed to exist as in the unique source allocation method. The non-

unique source allocation methodology is based on experimentally measured data and normalized results, and is

described in detail in NASA-SP-807212

. Predictions can be made for sources located in the near-field as well as in

the far-field along the exhaust flow. In this section, the acoustic loading on the RSLVF, calculated using the non-

unique source allocation technique, was observed to be dominated by the sources closest to the vehicle, with the

contribution from other sources being negligible.

For the prediction of the acoustic loading on the vehicle, it is necessary to distribute the sources relative to the

core length along the exhaust flow. The rocket flow can be divided into a number of segments and the overall

acoustic power for each segment can then be calculated using the estimated sound power per unit core length and the

length of each segment using12

9

, 10 10

OA

( )10 log 10logt

w seg W

t

x W r xL L

W x

∆= + +

, (7)

where the term, ( )10 OA10log tx W r W refers to the relative sound power per unit core length at location r and

the subscript ‘seg’ indicates the segments of exhaust flow.

The normalized relative sound power spectrum level with modified Strouhal number, e e of ra U a , is given in

NASA-SP-807212

. This sound power spectrum can then be converted to a conventional one-third octave bandwidth

as follows12

:

, , 10 , 10 10

( , )10log 10log 10log

( )

e o e ow seg b w seg b

e e

U a U aW f rL L f

W r ra ra

= + − + ∆

, (8)

where the term, ( ) ( )1010log , e o eW f r U a W r ra , refers to the relative sound power spectrum level.

The acoustic power of each source corresponding to each segment for a frequency band of interest can be

determined from the acoustic power level, Lw,seg,b presented in Eq. (8), as follows:

, ,

10

, 10w seg bL

seg bW

= , Watts (9)

where the subscript b indicates the frequency band. The strength of each source corresponding to each segment for a

frequency band of interest can be determined as follows22

:

,

, , 2

4 seg b

s seg b

e

WQ

k a

π

ρ= . (10)

The sound pressure level on the circumference of the vehicle, including the effects due to the reflecting surface

of the vehicle, for a band centred on any frequency can be expressed as

( )2

, , , 1010log DI( ) 3 , (dB re 20 Pa), ,, , , , , ,p seg b

tL

a s seg bp R k a z Q tφ θ µφ

= + −

(11)

where the pressure quantity, t

ap , represents the total sound pressure on the vehicle due to incident and scattered

10

waves, and is a function of the distance R from the source to the observation point on the vehicle, wave number k,

radius of the vehicle a, elevation height z, azimuthal angle ϕ and source strength Qs,seg,b, and the term DI (θ) is the

directivity index. The pressure quantity t

ap can be determined using Eqs. (1) and (2) for the analytical calculations

and Eqs. (5) and (6) for the numerical calculations by evaluating {p}. The first summation presented in Eq. (1) and

the summation presented in Eq. (6) need to include all the sources for each frequency band of interest, using

logarithmic summation of Lp,seg,b,ϕ for all the segments. Then the overall sound pressure level calculated by the

logarithmic summation of Lp,seg,b,ϕ over all segments of the exhaust flow for a frequency band of interest

becomes12

, , ,

10,OA , , 10

All

10log 10p seg b

L

p ,seg bseg

Lφ

φ = ∑ , (dB re 20µPa). (12)

In Eqs. (11) and (12), the sound pressure due to scattering from the reflecting surface of the vehicle as well as the

spreading due to distance, are included by the termt

ap . The effect of the scattered sound field on the sound

pressure on the surface of the vehicle was not considered in the previous analysis presented by NASA-SP-807212

.

III Results and Discussions

For the analytical and numerical prediction of acoustic loading on the fairing, a Representative Small Launch

Vehicle Fairing (RSLVF) of overall length 5.33 m and maximum diameter of 1.552 m was used, which has been

used by others in previous work13,23,24

. Figure 2 shows the surface elements and nodes of the RSLVF generated in

ANSYS© using quadratic eight node elements and a ‘mesh-only’ element, which is MESH 200. The ANSYS

© .LIS

files containing the descriptions of all the surface elements (726 elements) and nodes (2120 nodes) were then

imported into MATLAB®

for the numerical BEM analysis using the codes written in MATLAB®. The RSLVF was

considered to be positioned at the top of the rocket during lift-off. The geometry of the launch environment used for

calculating the acoustic loading on the RSLVF is shown in Fig. 3, and is the same as used in previous work13

. The

parameters shown in Fig. 4 are defined in the nomenclature section. It was assumed that all the sources are situated

along the exhaust flow axis, generating spherical waves which impinge obliquely on the fairing.

For the current work, it was assumed that the fairing structure and the flow axis were situated at x1 = 15De

11

upstream and x2 = 5De downstream of the vehicle respectively. A reference point was chosen at °= 0φ , which is the

front point on the vehicle facing the exhaust flow. Hence °=180φ is the rear point on the vehicle. For simplicity, it

was assumed that the temperature along the flow axis was uniform and T = 1000°C. At that temperature the speed of

sound and density in air are 715.49 m/s and 0.28 kg/m3 respectively.

For the analytical and numerical analyses, Engine ‘E’ was used which has the core length of xt = 1.25m and is

the same as used in previous work13

.The flow axis was divided into ten segments along the flow with an assumed

length of 1m for each segment. At the centre of each of the ten segments a point source completely uncorrelated

with the other nine was assumed. The distances from the vehicle axis to the centre of each segment were estimated

and used to determine the necessary parameters for each source. The specifications of each source, and the

calculated and estimated values of all the parameters are reported in Tables A1 and A2 in the Appendix. The

calculated acoustic power level for each band of interest corresponding to each segment is reported in Table A3 in

the Appendix. The calculated source strength of each source corresponding to each segment is provided in Table 1.

The source directivity index was assumed to be the same for radiation to all the circumferential positions on the

vehicle for any specified elevation angle from the source to launch vehicle.

Both the analytical and numerical approaches calculated the acoustic loading around the circumference of the

RSLVF at a height of z = 2.17m from the bottom face of the RSLVF. This height was chosen because at that height

there are sixty circumferential nodes which are sufficient to achieve a good numerical estimation of the sound

pressure pattern for comparison with the analytical result. The descriptions of sixty circumferential nodes and their

respective positions corresponding to azimuthal angles are provided in Table A4.

12

Fig. 2 RSLVF surface elements and nodes. The solid circles show the circumferential nodes at a height of z =

2.17m on the RSLVF.

Fig. 3 Geometry of source locations relative to the vehicle and flow axes.

Axis of flow

Normal to vehicle

Observation

point, P

Bucket

Nozzle

R

Point source

r

Launch

Vehicle

Z

13

Table 1 Calculated source strength for Engine ‘E’ for ten sources corresponding to ten

segments for each 1/3 octave band corresponding to centre frequencies of 50 Hz, 100 Hz

and 400 Hz. Core length, xt = 5.15m; overall acoustic power level, Lw = 176.28dB; length of

each segment, ∆x = 1m; speed of sound and density in air at T = 1000oC are 715.49 m/s

and 0.28 kg/m3 respectively.

Source strength, bsegsQ ,, ×106 (m

3/s)

Source Number

1 2 3 4 5 6 7 8 9 10

50 Hz 0.5005 1.0579 1.7609 2.5246 3.9146 5.0198 5.7968 6.8973 7.7836 7.9373

100 Hz 0.4989 0.8896 1.8308 2.3668 3.3087 4.5724 5.6513 6.7709 8.5339 8.8848

400 Hz 0.4648 0.9787 1.7542 2.3072 3.2553 3.5002 3.6947 4.2864 4.3161 4.3410

For the analytically calculated acoustic loading on the RSLVF, using the non-unique source allocation method,

the maximum diameter of 1.552 m of the RSLVF was used as the infinite cylinder diameter. The surface sound

pressure levels were evaluated as a function of azimuthal angle ;. The calculations were conducted considering the

impacts of the scattered waves using Eqs. (1), (2) and (12), of the acoustic loading on the RSLVF from ten point

sources acting as a line of point sources, as shown in Fig. 3, at each of the 1/3 octave bands corresponding to centre

frequencies of 50 Hz, 100 Hz and 400 Hz. Fig. 4 shows the analytically calculated overall sound pressure levels at

the circumferential surface of the RSLVF at a height of z = 2.17m from the bottom face of the RSLVF. The results

show that for the small chemical rocket Engine ‘E’ the sound pressure level reaches around 134.7 dB at the front of

the RSLVF facing the exhaust flow, for ten point sources located close to the vehicle.

For the numerical calculations, Eqs, (5) (6) and (12) were used and the results for each band centered on

respective center frequencies are shown in Figs. 5a-5f. The results show that for very low frequencies (50 Hz and

100 Hz), the highest acoustic pressures mostly occur on the surface of lower portions of the RSLVF, as shown in

Figs. 5a-5d. The reasons for this are: (a) the sources are located below the RSLVF, along the exhaust flow axis; and

(b) the RSLVF dimension is relatively small compared to the wavelength of the low frequency noise. As the

frequency increases much of the acoustic pressure incident on the vehicle becomes scattered over the entire RSLVF

since the RSLVF dimension is no longer smaller than the acoustic wavelength, as shown in Figs. 5e-5f. It appears that

the overall sound pressure level reaches around 135.62 dB for ten individual point sources situated close to the vehicle

acting as a line of point sources, along the exhaust flow, as shown in Figs. 5e-5f for the frequency of 400 Hz. The

sound pressure levels on the circumferential nodes at a height of z = 2.17m of the RSLVF were calculated for each one-

third octave band corresponding to centre frequencies of 50 Hz, 100 Hz and 400 Hz and are shown in Fig. 6. The

results show similar pressure fluctuations to the analytical results shown in Fig. 4, which were calculated using the non-

14

unique source allocation method. The small differences in pressure magnitude are a result of diffraction around the

ends of the cylinder which is taken into account in the BEM analysis but not in the analytical model. The BEM analysis

allows determination of the sound pressure near the ends of the cylinder by considering a quarter-point technique

(r2/3

) for particle velocity near the edge of the cylinder, where r is the distance from the edge. This approach

approximates the condition that the particle velocity tends to infinity as r tends to zero, as explained in detail by

Juhl14

.

The analytical and numerical results also indicate that for each frequency band of interest, the sound pressure

amplitude varies relatively smoothly at the front face of the RSLVF facing the exhaust flow and varies aggressively

at the back of the RSLVF, due to the reinforcement and cancellation that occurs between the diffracted waves

passing around each side of the RSLVF. The sound pressure fluctuation increases as the frequency band of interest

increases because the amount of interference of the two diffracted waves passing around the two sides of the RSLVF

increases.

It is noticeable that the non-unique source allocation method results in a smaller acoustic pressure magnitude

compared with the results presented in Figs. 7 and 8 (Morshed et al.13

) , using the unique source allocation method.

The reason for this is that for each frequency band of interest, the source strength of each source calculated using the

non-unique source allocation method was less than the source strength of a single equivalent point source calculated

using the unique source allocation method (see Table 2 for source strengths calculated using unique source

allocation method, in Morshed et al.13

).

15

Fig. 4 Analytically calculated overall sound pressure level at the RSLVF surface, using the non-unique

source allocation method, for ten individual point sources along the exhaust flow, for each one-third octave

band corresponding to centre frequencies of 50 Hz, 100 Hz and 400 Hz. [x1 = 15De, x2 = 5De and reference

pressure 20µPa]

(a) Front face, 50 Hz. (b) Rear face, 50 Hz.

16

(c) Front face, 100 Hz. (d) Rear face, 100 Hz.

(e) Front face, 400 Hz. (f) Rear face, 400 Hz.

Fig. 5 Numerically calculated sound pressure excitation at the surface of the RSLVF at each one-third octave

band corresponding to centre frequencies of 50 Hz, 100 Hz and 400 Hz, using the non-unique source

allocation method. [x1 = 15De, x2 = 5De and reference pressure 20µPa]

17

Fig. 6 Numerically calculated sound pressure levels as a function of RSLVF circumferential location for

each one-third octave band corresponding to centre frequencies of 50 Hz, 100 Hz and 400 Hz, using the non-

unique source allocation method. [ z = 2.17m, x1 = 15De, x2 = 5De and reference pressure 20µPa]

Fig. 7 Analytically calculated sound pressure levels at the RSLVF surface, for an equivalent single point

source for each one-third octave band corresponding to centre frequencies of 50 Hz, 100 Hz and 400 Hz,

using the unique source allocation method. Results taken from Morshed et al.13

.[z = 2.17m, x1 = 15De, x2 = 5De

and reference pressure 20µPa]

18

Fig. 8 Numerically calculated sound pressure levels as a function of RSLVF circumferential location, for

each one-third octave band corresponding to centre frequencies of 50 Hz, 100 Hz and 400 Hz, using the

unique source allocation method. Results taken from Morshed et al.13

. [z = 2.17m, x1 = 15De, x2 = 5De and

reference pressure 20µPa]

Table 2 Calculated source strength for Engine ‘E’ for each 1/3 octave band corresponding

to centre frequencies of 50 Hz, 100 Hz and 400 Hz, using the unique source allocation

method. Overall acoustic power level, Lw = 176.28dB; speed of sound and density in air at

T = 1000oC are 715.49 m/s and 0.28 kg/m

3 respectively.

Frequency, Hz

Source Strength,

Qs,b

× 107(m

3/s)

50 2.136

100 2.112

400 1.491

IV. Conclusions

The acoustic noise generated on a launch vehicle fairing during launch has been estimated for a particular

chemical rocket Engine ‘E’, which has the Mach number of 4.07 and the core length of 5.15m. The engine exhaust

noise has been assumed to originate along the exhaust flow, perpendicular to the vehicle axis, and has been

modelled using the non-unique source allocation method to determine the acoustic pressure loading at the surface of

the Representative Small Launch Vehicle Fairing (RSLVF) at each one-third octave band corresponding to centre

19

frequencies of 50Hz, 100Hz and 400Hz, respectively.

The non-unique source allocation method assumes that the exhaust flow can be represented by a number of point

sources distributed through the flow for each frequency band of interest. Using this method, ten individual point

sources were arbitrarily positioned close to the vehicle. The analytical and numerical results showed that the overall

sound pressure level reaches around 134.7 dB and 135.62 dB, respectively, for the band centred on frequency of 400

Hz, for ten individual point sources situated close to the vehicle acting as a line of point sources along the exhaust

flow. The numerical results produced similar pressure fluctuations, at each band of interest, to the fluctuations in the

analytical results. There were small differences in the pressure magnitudes between the results obtained analytically

and numerically because of diffraction around the edges of the Representative Small Launch Vehicle Fairing

(RSLVF) which was taken into account in the Boundary Element Method (BEM) analysis in contrast to the results

calculated analytically. Therefore, the pressure magnitudes of the results obtained analytically were slightly different

to the results obtained using the Boundary Element Method (BEM). Despite this little difference, it can be seen that

for non-unique source allocation technique the results obtained using the developed BEM and analytical tools agree

well. These can be the necessary inputs to evaluate noise and vibration control treatments for launch vehicles

It has been observed that the non-unique source allocation method results in a smaller acoustic pressure

magnitude compared with the unique source allocation method. The reason for this is, for each frequency band of

interest, the strength of each source calculated using the non-unique source allocation method was less compared

with the strength of a single equivalent point source calculated using the unique source allocation method.

It is intended to extend the present work in the future by including the effects of diffraction around the ends of

the cylinder in the analytical model. This will enable the development of a full analytical model of acoustic loading

on finite length cylinders, representative of geometries such as cylindrical launch vehicles.

Appendix

Table A1 Details of the ten sources for Engine ‘E’. Core length, xt = 5.15m; overall acoustic power level

of the rocket engine, Lw = 176.28dB; length of each segment, ∆x = 1m. [Data estimated from Figure 12

in NASA-SP-807212

]

Source Number

Estimated Source

Distance,

x3(m)

Source Distance From the

Nozzle, r (m)

Distance per unit

Core

Length,

txx /3

Elevation Angle,

β

(Degrees)

Directivity

Angle, θ

(Degrees)

Estimated Directivity Index, DI

(dB)

Estimated Sound Power per

Unit Core Length,

OA

)(10log10

W

rWtx

(dB)

Calculated Acoustic

Power per

Segment,

segwL , (dB)

20

1 1 1.52 0.194 77.73 102.27 -7.5 -12.7 156.46

2 2 2.31 0.388 66.50 113.50 -9.0 -10.0 159.16

3 3 3.21 0.582 56.88 123.12 -11.0 -8.0 161.16

4 4 4.16 0.776 48.99 131.01 -12.0 -7.0 162.16

5 5 5.13 0.970 42.61 137.39 -12.5 -5.1 164.06

6 6 6.11 1.164 37.48 142.52 -13.0 -5.0 164.16

7 7 7.09 1.358 33.31 146.69 -13.5 -4.5 164.66

8 8 8.08 1.552 29.89 150.11 -13.8 -3.6 165.56

9 9 9.07 1.746 27.07 152.93 -14.0 -3.1 166.06

10 10 10.06 1.940 24.70 155.30 -14.5 -3.4 165.76

Table A2 Estimated relative sound power level for Engine ‘E’ for ten sources for each 1/3

octave band corresponding to centre frequencies of 50 Hz, 100 Hz and 400 Hz. Core

length, xt = 5.15m; overall acoustic power level of the rocket engine, Lw = 176.28dB; speed

of sound in the exhaust flow, ae = 715.49 m/s; length of each segment, ∆x = 1m. [Data

estimated from Figure 13 of NASA-SP-807212

]

Estimated relative sound power spectrum level,

e

oear

aU

rW

rfW

)(

),(log10 10 , dB

Source Number

1 2 3 4 5 6 7 8 9 10

50 Hz -19.00 -17.00 -16.00 -15.00 -14.00 -12.70 -12.60 -12.55 -12.50 -12.48

100 Hz -16.00 -15.50 -12.65 -12.55 -12.45 -10.50 -9.81 -9.70 -8.70 -8.50

400 Hz -10.60 -8.65 -7.00 -6.75 -6.57 -6.80 -7.48 -7.65 -8.60 -8.70

Table A3 Calculated acoustic power level for Engine ‘E’ for ten sources corresponding to

ten segments for each 1/3 octave band corresponding to centre frequencies of 50 Hz, 100 Hz

and 400 Hz. Core length, xt = 5.15m; overall acoustic power level, Lw = 176.28dB; speed of

sound in the exhaust flow, ae = 715.49 m/s; length of each segment, ∆x = 1m.

Calculated acoustic power level in each band for each segment, bsegwL ,, (dB)

Source

Number 1 2 3 4 5 6 7 8 9 10

50 Hz 118.85 125.37 129.79 132.92 136.73 138.89 140.14 141.65 142.70 142.87

100 Hz 124.86 129.88 136.15 138.38 141.29 144.10 145.94 147.51 149.52 149.87

400 Hz 136.28 142.75 147.82 150.20 153.19 153.82 154.29 155.58 155.64 155.69

Table A4 Descriptions of sixty circumferential nodes at a height of z = 2.17 m

from the bottom face of the RSLVF. Node

order

Node

no.

Azimuthal

angle,ϕ

(Degrees)

Node

order

Node

no.

Azimuthal

angle, ϕ

(Degrees)

Node

order

Node

no.

Azimuthal

angle, ϕ

(Degrees) 1 112 0 21 800 120 41 1461 240

2 124 6 22 812 126 42 1473 246

3 137 12 23 825 132 43 1406 252 4 149 18 24 837 138 44 1633 258

5 162 24 25 770 144 45 1646 264

21

References

1Mayes, W. H., Lanford, W. E., and Hubbard, H. H., “Near Field and Far Field Noise Surveys of Solid Fuel Rocket Engines

for a Range of Nozzle Exit Pressures,” NASA TN D-21, 1959.

2Tedrick, R. N. “Acoustical Measurements of Static Tests of Clustered and Single-Nozzled Rocket Engines”, Journal of the

Acoustical Society of America, Vol. 36, No. 11, 1964, pp. 2027-2032.

3Lassiter, L. W. and Heitkotter, R. H. “Some Measurements of Noise from Three Solid-Fuel Rocket Engines”, NASA TN-

3316, 1954.

4Cole, J. N., Von Gierke, H. E., Kyrasis, D. T., Eldred, K. Mck. and Humphrey, A. J. “Noise Radiation from Fourteen Types

of Rockets in the 1,000 to 130,000 Pound Thrust Range”, WADC TR 57-354, 1957.

5Eldred, K. M., Roberts, W. and White, R. “Structural Vibrations in Space Vehicles”, WADD TR 61-62, December, 1961.

6Morgan, W. V., Sutherland, L. C. and Young, K. J. “The Use of Acoustic Scale Models for Investigating Near Field Noise

of Jet and Rocket Engines”, WADD TR 61-178, Wright Paterson AFB, Ohio, USA, April, 1961.

7Franken, P. A., Kerwin, E. M., and Staff of Bolt Beranek and Newman Inc., “Methods of Space Vehicle Noise Prediction,”

Wright Paterson AFB, Ohio, USA, WADC TR 58-343, 1960.

8Potter, R. C., and Crocker, M. J., “Acoustic Prediction Methods for Rocket Engines, Including the Effects of Clustered

Engines and Deflected Exhaust Flow,” NASA CR-566, 1966.

9Mel'nikov, D. A., Komarov, V. V., Dumnov, G. E. and Dement'ev, V. K. “An Experimental Investigation of the Acoustic Field

Appearing During Rocket Ascent from a Launching pad”, Proceedings of Launch Vehicle Vibrations, First European Conference on

Launcher Technology, Centre National D’Etudes Spatiales, France, 14-16 Dec, 1999, pp. 147-155.

10Dumnov, G., Mel'nikov, D. and Komarov, V. “Acoustics Loads on Rockets During Launching”, 36th

AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Huntsville, 17-19 July, 2000, AIAA 2000-3742, pp. 1-11.

6 174 30 26 1000 150 46 1658 270 7 89 36 27 1013 156 47 1671 276

8 364 42 28 1025 162 48 1683 282 9 377 48 29 1038 168 49 1616 288

10 389 54 30 1050 174 50 1846 294

11 402 60 31 983 180 51 1859 300 12 414 66 32 1210 186 52 1871 306

13 347 72 33 1223 192 53 1884 312

14 577 78 34 1235 198 54 1896 318 15 590 84 35 1248 204 55 1829 324

16 602 90 36 1260 210 56 2022 330

17 615 96 37 1193 216 57 2035 336 18 627 102 38 1423 222 58 2047 342

19 560 108 39 1436 228 59 2060 348 20 787 114 40 1448 234 60 2072 354

22

11Dementjev, V. C., Koudriavtsev, V. V., Rybak, S. P., Safronov, A. V. and Troclet, B. “Technique for Predicting the

Acoustical Environment Resulting from a Launch Vehicle Engine Jets Interaction with Launch Pad”, Proceedings of Launch

Vehicle Vibrations, First European Conference on Launcher Technology, Centre National D’Etudes Spatiales, France, 14-16 Dec,

1999, pp. 169-178.

12NASA SP-8072, “Acoustics Loads Generated by the Propulsion System,” NASA Space Vehicle Design Criteria

(Structures), 1971.

13Morshed, M. M. M., Hansen, C. H. and Zander, A. C. “Prediction of Acoustics Loads on a Launch Vehicle Fairing During

Lift-off”, Journal of Spacecrafts and Rockets (JSR), Vol. 50, No. 1, January, 2013, pp. 159-168.

14Juhl, P. M., “The Boundary Element Method for Sound Field Calculations,” The Acoustic Laboratory, Technical University

of Denmark, Report No. 55, Aug. 1993.

15Morshed, M. M. M., Zander, A. C. and Hansen, C. H., “Two-Dimensional and Three-Dimensional Acoustic Loadings on

Cylinders Due to a Point Source”, Journal of American Institute of Aeronautics and Astronautics (AIAA), Vol 49, No. 11,

November, 2011, pp. 2421-2429.

16Morse, P. M., Vibration and Sound, 1st ed., McGraw-Hill Book Company, New York, London, 1936. Chap. 7.

17Fahy, F., Sound and Structural Vibration : radiation, transmission and response, 1st ed., Academic Press Inc. Ltd., London,

1987.

18Morshed, M. M. M., “Investigation of External Acoustic Loadings on a Launch Vehicle Fairing During Lift-off”, Ph.D.

Dissertation, School of Mechanical Engineering, The University of Adelaide, SA, Australia, 2008.

19Marburg, S. and Nolte, B., Computational Acoustics of Noise Propagation in Fluids- Finite and Boundary Element

Methods, 1st ed., Springer, German, 2008. Chap. 0.

20Marburg, S., “A Review of the Coupling Parameter of the Burton and Miller Boundary Element Method”, Inter-noise,

Melbourne, Australia, 16-19 November, 2014, pp. 1-6.

21Marburg, S. and Amini, S., “Cat’s Eye Radiation with Boundary Elements: Comparative Study on Treatment of Irregular

Frequencies”, Journal of Computational Acoustics, Vol. 13, No. 1, 2005, pp. 21-45.

22Bies, D. A., and Hansen, C. H., Engineering Noise Control, 3rd ed., Spon Press, London, 2003. Chaps. 1,5.

23Howard, C. Q.,Hansen, C. H. and Zander, A. C., “Vibro-acoustic Noise Control Treatments for Payload Bays of Launch

Vehicles: Discrete to Fuzzy Solutions”, Applied Acoustics, Vol. 66, No. 11, November, 2005, pp. 1235-1261.

24Howard, C. Q.,Hansen, C. H. and Zander, A. C., “Noise Reduction of a Rocket Payload Fairing Using Tuned Vibration

Absorbers with Translational and Rotational DOFs”, Proceedings of Acoustics, Busselton, Western Australia, Australia, 9-11

November, 2005, pp. 165-171.