Boundary integral calculations of scattered fields: Application to a spacecraft launcher

Malbéqui, P.; Candel, Sébastien; Rignot, Eric

doi:10.1121/1.395794

Cited by 6 publications

(3 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Malbequi et al [8] also considered the empirical source allocation technique to analyse the scattering of incident acoustic waves by the surface of the Ariane IV space launcher, using boundary integral methods. However, this analysis examined the sound field in the vicinity of the launcher rather than at the launcher surface and so could not be used to determine the acoustics loads at the surface, which are necessary for predictions of sound transmission into the payload bay.…”

Section: Introductionmentioning

confidence: 99%

“…The technique presented in the manuscript provides improved accuracy over NASA-SP-8072 [4] and other previous work [1-3,5-8] in this area because the effect of the scattered sound field is included, as well as the spreading of the sound field with distance from the source. This is possible using the presented analytical and numerical approach which permits convergence of the external pressure field calculations at the surface of the launcher, which is not possible using techniques presented previously [1][2][3][4]8].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Prediction of Acoustic Loads on a Launch Vehicle Fairing During Liftoff

Morshed

Hansen

Zander

2013

Journal of Spacecraft and Rockets

View full text Add to dashboard Cite

During liftoff of a launch vehicle, the acoustic pressure fluctuations caused by the engine exhaust gases produce high noise levels inside the fairing cavity and can damage the payload. Work presented in this paper investigates the nature of the external acoustic pressure distribution, in the frequency range from 50 to 400 Hz, on the fairing of a launch vehicle during liftoff. The acoustic pressure acting on a representative small launch vehicle fairing was estimated from the complex acoustic field generated by the rocket exhaust during liftoff. The estimation procedure involved the use of a 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. Nomenclatureof sound in the exhaust flow, m=s D e = nozzle exit diameter, m d = projected distance, m E = total number of surface elements E i = element shape function F = thrust of rocket engine, N f = frequency, Hz f b = frequency bandwidth, Hz G = Green's function H = coefficient matrix H m z = Hankel function or Bessel function of the third kind of mth order and argument, z I N = identity matrix J m z = Bessel function of the first kind of mth order and argument, z k = wave number L P;b; = sound pressure level on the circumference of the vehicle, dB L P;OA; = overall sound pressure level, dB L w = overall acoustic power level, dB L w;b = sound power level for each frequency band, dB M = total number of terms M e = Mach number m = term number n = number of nozzles, and particle outward velocity direction P = field point or observation point p, p = acoustic pressure, Pa p i = incident sound pressure, Pa p i = constant nodal pressure on ith element, Pa p o = incident sound pressure amplitude, Pa p s = scattered sound pressure, Pa p t a = total sound pressure at the surface of a cylinder, dB p 0 = spatially dependent factor Q = projection point, and integration point on the boundary Q s = source strength, m 3 =s R = distance between the integration point and observation point, and resultant oblique distance, m r = radial distance, and distance of the source from the nozzle exit, m r P = distance of observation point, m r Q = distance of integration point, m S = cylinder surface area, m 2 U e = exhaust velocity, m=s u n = outward normal particle velocity, m=s V = volume of a problem geometry, m 3 V e = exterior volume, m 3 V i = interior volume, m 3 W b = acoustic power for each frequency band, Watt Wf = sound power per Hz, Watt W OA = overall acoustic power, Watt X = X component of the cylindrical coordinate axes x 1 = axial distance of the observation point on the vehicle from the nozzle exit, m x 2 = vertical distance from the nozzle exit of the sources along the flow axis, m x 3 = distance of the source from the vehicle axis along the flow axis, m Y = Y component of the cylindrical coordinate axes Z = Z component of the cylindrical coordinate axes z = elevation height, m = incline angle between the line joining the observation point to ...

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Prediction of Acoustic Loads on a Launch Vehicle Fairing During Liftoff

Morshed

Hansen

Zander

2013

Journal of Spacecraft and Rockets

View full text Add to dashboard Cite

show abstract

“…This is partly due to the developments in digital computer technology and also partly due to the ever-increasing demand in the defense/commercial sector to obtain more faster/accurate field predictions. As a result, several formulations/algorithms have been developed based on the T-matrix approach, 1-4 boundary integral equation method, [5][6][7][8] and the method of moments ͑MoM͒. [9][10][11][12][13][14] Although all these formulations work well with varying degrees of complexity, all of them break down at certain frequencies of the incident field.…”

Section: Introductionmentioning

confidence: 99%

Acoustic scattering from rigid bodies of arbitrary shape—Double layer formulation

Bhamidipati

Rao

2004

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

In this work, a numerical method is presented, based on the well-known method of moments ͑MoM͒, to calculate the acoustic fields scattered by a three-dimensional, arbitrarily shaped, acoustically rigid body subjected to a plane wave incidence. The mathematical formulation is based on the potential theory and, in this work, the numerical method is applicable to the so-called double layer formulation ͑DLF͒. The scattering body is approximated by planar triangular patches. For the MoM solution using triangular patch modeling, edge-based basis functions are utilized to approximate the source distribution efficiently. These basis functions along with an appropriate testing procedure generates a simple numerical algorithm that is versatile enough to be applicable to closed, as well as open bodies. Finally, the present solution method is validated with several representative examples.

show abstract