Aeroacoustics of LV

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Aeroacoustic of the VEGA Launcher Wind Tunnel Tests

and Full Scale Extrapolations

B. Imperatore *

CIRA – Italian Aerospace Research Centre, 81043 Capua (CE), Italy

G. Guj† University 'Roma 3', 00146 Rome, Italy

A. Ragni‡ CIRA – Italian Aerospace Research Centre, 81043 Capua (CE), Italy

A. Pizzicaroli§ AVIO S.p.A, 00034 Colleferro (Rome), Italy

and

E. Giulietti** University 'Roma 3', 00146 Rome, Italy

This work describes the main aspects of the extended experimental campaign aimed at

the characterization of the aeroacoustic environment created by the external aerodynamics

around the VEGA launcher, the expendable launch system developed by the European

Space Agency (ESA). In the frame of the VEGA program, a collaboration between AVIO,

CIRA and DIMI of University “Roma 3” has been established for the evaluation of the

pressure fluctuations on the launcher external surface in order to determine the vibro-

acoustic loads on its structure. This issue is accomplished by extrapolating at full scales the

results obtained on the test model by utilizing proper analytical models reproducing themain properties of the pressure fluctuations. The wall pressure fluctuation characterization

was addressed through wind tunnel tests at transonic and supersonic flow conditions on a

1:30 scaled model. In the present paper a specific attention is focussed on the technical

aspects and on the proposed analytical models for the full scale extrapolations and on the

acoustic behaviour of the full scale launcher, while in the companion paper the aspects

regarding the behaviour of the pressure wave at transonic flow conditions has been

addressed.

Nomenclature

Capital Roman

F = generic function;H = generic function; Ma = Mach number;

* Ing., Aeronautical Ground Testing Facilities Dept., Transonic Testing Group, Via Maiorise 1, Capua (CE)† Prof., Mechanical and Industrial Engineering Dept. (DIMI) University 'Roma 3', via della Vasca Navale 79, 00146,

Rome, Italy, [email protected]‡ Ing., Aeronautical Ground Testing Facilities Dept., Icing Wind Tunnel, Via Maiorise 1, Capua (CE)§ Ing., AVIO S.p.A – Propulsione Aerospaziale, Corso Garibaldi 22, Colleferro (Roma)** Ing., Mechanical and Industrial Engineering Dept., Via della Vasca Navale 79, Roma

American Institute of Aeronautics and Astronautics

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1th AIAA/CEAS Aeroacoustics Conference (26th AIAA Aeroacoustics Conference)23 - 25 May 2005, Monterey, California

AIAA 2005-291

Copyright © 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


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P = static pressure;

Re = Reynolds number;S = Power Spectral Density;St = Strouhal Number;

U = velocity;UC = convection velocity;

Small Roman

a = constant exponent;c = local velocity of sound;

f = frequency;

h = the launcher axis elevation with respect to the U∞ direction;

j = imaginary unit ( j = 1− ) p = acoustic and dynamic pressure fluctuation;q = dynamic pressure;

s = the azimuthal curvilinear coordinate (s= θ r);u = velocity component in x direction;

v = velocity component in y direction; x = x=z-1006.54 aeroacoustic abscissa;

r, θ , z = cylindrical coordinates;

Capital Greek

Λ = length scale of the launcher (=1006.54 mm);

∆ = difference between two values;

Small Greek

α = incidence angle;δ = boundary layer thickness;

δ 1 = displacement thickness;

γ = coherence function;

η = curvilinear distance between two transducers (η =si’-si);

ν = kinematic viscosity;

ρ = density;

τ = generic ∆τ ;

ω = 2π f ;

ξ = axial distance between two transducers (ξ =zi’-zi);

Subscripts

∞ = quantities in unperturbed flow;

Superscripts

* = dimensionless quantities;


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I. Introduction

Acoustic environments, created by the rocket motors and the external aerodynamics of the launcher vehicles in

lift-off and flight conditions, are extremely important in view of the intensive acoustic pressure fields which can

excite the structures. The study of these excitations, of the resulting vibrations and noise transmission is of great

importance for the survival of the payloads and of the launcher equipments. Therefore a very good understanding of

the interaction between temporally & spatially random pressure fluctuations is needed. As matter of fact the fullscale experimental campaign is out of possibility and so a proper extrapolation mathematical model has to be

proposed to scale in a proper way the wind tunnel experiments, which allow the tuning of the coefficients, in theextrapolation to full scale launcher.

Several models have been proposed in literature1,2,3,4,5,6 to reproduce the shape of the pressure auto-spectrum at

the wall in a turbulent boundary layer. The main problem encountered in the present applications is the significantvariation of the flow physics that may occur along the model due to the different flow conditions, e.g. attached

boundary layer, intermittent shock, separated flow. The shape of the pressure auto-spectrum in different flow

conditions may vary significantly7. Thus, it is not possible to determine a priori a model that is able to reproduce the

shape of the pressure spectrum independently of the pressure transducer position.

The knowledge of cross-correlation and cross-spectrum functions allows for the forcing functions to be correctlycomputed in the evaluation of the structural dynamics and the flow induced vibrations of the launcher panel

surfaces8; as matter of fact the cross-correlation function globally characterizes the propagation of the pressure

perturbation close to the wall surface of the launcher

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. The cross-spectra models proposed in literature

10,11,12

assumethat the boundary layer is fully turbulent and the pressure field over the outer surface may be characterized astemporally stationary with spatially homogeneous statistics. Therefore, the pressure field may be expressed by a

cross-correlation function that is decaying with spatial and time separation and is convected with the flow. The

common feature of the empirical models for the TBL developed so far is the separation of variables approach to

represent the correlation function dependence on the stream wise separation (ξ ) and the cross flow separation (η ). It

should be stressed that the axisymmetry of the geometry and flow is not explicit in the formulations but it isaccounted for through the adjustable coefficients13.

The objectives of this paper are the development of an analytical dimensionless model for the external

aeroacoustics of the VEGA launcher and the simulation of the full scale behaviour.

A selected set of the most relevant results obtained from the post-processing of the experimental data is

presented and discussed along with the main properties of the boundary layer (BL) obtained on the launcher modelfrom the numerical simulations. The experimental data base for the transonic and supersonic conditions has been

developed in the framework of the collaboration among AVIO, CIRA and University “Roma TRE”.

II. Experimental set up and test matrix

The scaled model, the same for both the experimental campaigns, has been equipped with 32 miniature KULITE

pressure transducers (Fig.1), flush mounted along the model surface in several positions in order to minimize the

intrusivity effects. The transducers location was organized into clusters in order for cross-correlations and cross-spectra to be computed as well. In this way the validity of classical cross-spectra models was verified. Four

accelerometers have been located, grouped by two, in the vicinity of the model nose and trailing edge respectively;

they were respectively oriented along orthogonal directions.

In all the cases here considered, the adopted scaled model refers to the 4 stages clean configuration.

Transonic measurements have been carried out at the T1500 transonic wind tunnel of FOI (The Swedish DefenceResearch Agency) in Stockholm. The selected Mach numbers spanned from Ma=0.83 up to Ma =0.98, while

different angles of incidence, up to 6°, were considered.Supersonic measurements were conducted in the DNW SST facility. The selected Mach numbers spanned from

Ma=2.0 up to Ma=3.0, while two angles of incidence have been considered (0° and 5°). The sampling rates have

been fixed to 100kHz and 130kHz for transonic and supersonic flow conditions respectively, with an anti aliasing

filtering at half of the sampling rate.


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Figure 1. The sketch shows the number of transducers which are organised in cluster with different layout.

III. Dimensionless fluctuating pressure model

Dimensional analysis permits the dimensionless representation of the original problem of the fluctuating pressurespectrum in terms of independent, significant dimensionless parameters. A dimensional analysis has been performed

for the general representation of the original problem and for the definition of the analytical model of the type

proposed in literature7,14, which guarantees the extrapolation to the full scale; the considered reference quantities are

given in the sketches reported in Fig.2.

Figure 2. Sketch of the launcher model.

For the auto spectrum, based on the variable separation approach, the following form is proposed:

)(F ) Ma(F ) z ,St ( H ) , Ma , z ,St (S q

U S *

21

****

pp

1

2

pp

α α δ (1)

with five independent significant parameters:

1

2

*

δ ∞

∞=

q

U S S

pp

pp : non dimensional spectrum

∞

=U

f St 1

δ : Strouhal number based on the free stream velocity


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Λ

z z =* : longitudinal coordinate

c

U Ma ∞∞ = : free stream Mach number

*α : incidence angle

Under specific conditions, also the dimensionless function can be expressed through the separation

of variables approach leading to:

),( * zSt H

)()(),( *21* z H St H zSt H =

(2)

According to Camussi et al.15, the general law proposed for , that is a frequency function with unitary

integral area, has the form:

)(1 St H

( )[ ] ( )[ ] ( )[ ] ( )[ ] ( )[ ] F St E St DSt C St BSt Ast H +∗+∗+∗+∗+∗= 102

10

3

10

4

10

5

10110logloglogloglog)]([log

(3)

An analytical approximation of is very difficult to be driven, thus piece wise constant approximations are

proposed and adopted. The modulation of the spectra represented by H 2(z*) is computed by integrating over St the

equation and enforcing that the integral of H 1(St) has unity area.

)( *2 z H

The cross-spectrum assumes the form:

( ) ( ) **2

*******

' ,,,,,,U

St z j

pp pp es zU St Ma zSt S S

∆

∞ ∆∆=

π

γ α (4)

Thus three new independent dimensionless groups have been introduced for the cross-spectrum:

∞

=U

U U c

*, velocity scale ratio,

1

*

δ

ξ ∆ = z , longitudinal separation,

1

*

δ

η ∆ =s , azimuthal separation.

We have to note that the dependence upon the Ma∞ is recovered by the auto-spectrum, while the dependence on α *is

negligible. Thus the coherence function, which appears in the cross-spectrum, assumes the following form:

( )*

6*

5*

4*

3 )()()()(*** ,,,sSt MaF zF zSt MaF zF

ees zU St ∆−∆− ∞∞

=∆∆γ (5)

The possibility of using again simplified power laws has been explored on the basis of the experimental data base. Inthe latter case the equations would simplify as follows:

and( ) 34a

Ma MaF ∞∞ = ( )

5

6

a Ma MaF ∞∞ = (6)

The dimensionless equations are then obtained by various forms of best fitting on a large number of experiments.

In view of Eq.(1) the TBL displacement thickness δ 1 is a fundamental parameter but it is not measured in the

planned tests therefore it has to be determined numerically. The pressure fluctuation models require the BL integral

characteristics to be available, specifically the displacement thickness δ 1. A simplified CFD support is needed, as all

the necessary information are not available from direct measurements on the model. The proposed CFD model for

the BL characterization considers a number of simplified hypotheses, which are:

1. the geometry of the VEGA launcher is considered symmetric in cylindrical coordinates;2. due to the small angle of attack the fluid dynamic conditions are considered symmetric in cylindrical

coordinates even in presence of the maximum incidence angle (6°);

3. the fluid dynamics is in all cases 2D in cylindrical coordinates;4. the compressible BL is solved along a stream line using the external boundary conditions given by

experimental measurements (pressure coefficients) of external flow;

5. the wall of the launcher is considered adiabatic and its temperature is equal to the total temperature;

6. the flow is considered steady.The CFD code is based on the solution of the BL integral equations, and therefore provides only information on the

BL integral quantities.

An example of displacement thickness in transonic and supersonic conditions are shown in Fig.3.


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a)

b)

Figure 3. Displacement thickness in the turbulent case at Ma=0.83 (a) and

Ma=3.02 (b) for the launcher model.

IV. Full scale extrapolation

The dimensional mathematical models of the auto and cross spectra, applied for the simulation of noise emission

at full scale, are determined by properly rescaling the non-dimensional models.

The dimensional auto-spectrum (in Pa2 /Hz) is:

( )∞

∞∞∞ =Λ=

U

q Ma zSt S hcU f s zS S pp pp pp

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***

1 ),,,(,,,,,,,,, δ

α ν ρ δ (7)

where U ∞ , q∞ , Ma∞ are the full scale launcher free stream velocity, dynamic pressure, Mach number respectively

and δ1 is calculated by the TBL simulation.

An analogous dimensional form is proposed for the cross-spectrum (in Pa2 /Hz, complex quantity):

( )η ξ ν ρ δ ,,,,,,,,,,,, 1'' C pp pp U hcU f s zS S ∞Λ= (8)


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V. Results

An example of an Over All Sound Pressure Level (OASPL) for the model scale at Ma=0.98 is reported in Fig.4

as a function of x, it is evident the negligible effect of α on the OASPL, while the position is extremely important,

and in contrast to Camussi et al. 15 because an universal analytical form can not be found.

Figure 4. OASPL evolution along the launcher model for Ma=0.98.

Figure 5. OASPL evolution along the launcher model for =0° in terms of microphones numbers, the

reference pressure is equal to the dynamic pressure downstream of the bow shock .

The effect of Ma, in supersonic regime, is focused in Fig.5, and, according to the Lowson law16, the OASPL

increases for decreasing Ma.


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a)

b)

c)

Figure 6. Some representative auto-spectra along the launcher model computed at =0 o:

Ma=0.83 (a), Ma=0.89 (b), Ma=0.98 (c).

In Fig.6 some representative auto-spectra along the launcher model in transonic conditions, computed at α =0o

are reported. It is evident that the shape is quite similar for groups of microphones and so all the spectra belonging to

the same group can be made to collapse if a proper dimensionless form is adopted. Analogous considerations can be

performed in the supersonic cases (see for example Fig.7).


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Figure 7. Normalized auto-spectra evolution along the launcher model for Ma=3.02 and =0 o.

In Figs.8 and 9 the experimental validation at the model scale, of one proposed analytical model is presented for

the auto and cross spectra respectively. The agreement between the analytical reconstruction and model sound

measurement is good; as a matter of fact the main features of the spectrum are well reproduced by the model.

Figure 8. Dimensional auto-spectrum measured and reconstructed through the above reported analytical

models.


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Figure 9. Dimensional cross-spectrum measured and reconstructed through the above reported analytical

models.

VI. Conclusion

Cross-spectra and overall sound pressure level represent fundamental quantities which are needed input for

estimating the structural response of the launcher and the acoustic transmission from the external field of fluctuating

pressure. They allowed us to determine the location of the most critical regions along the launcher at the different

Mach numbers analysed. The characterization of the aeroacoustic environment around the VEGA launcher at flight

conditions is obtained by analytical models which are tuned through the specific data base obtained in theframework of the present experimental campaign.

In order for the experimental data from the scaled model to be reported on the full-scale launcher, the knowledgeof some relevant quantities at full-scale conditions is required. Specifically, once the dimensionless form of the auto-

or cross-spectra has been computed, the full-scale spectra are retrieved by rewriting the dimensional expression in

account of the full-scale magnitude of the reference parameters.

In addition to the position along the launcher model, auto-spectra are affected also by both the Mach number and

the angle of incidence, the Mach number being, however, the most relevant parameter influencing the auto-spectrashape while the angle of incidence has a weak influence.

At the low transonic Mach numbers, specifically for Mach≤0.92, significant variations of the spectra shape are

observed depending on the nature of the boundary layer (e.g. close to the stagnation point, separations, shockwaves). At larger Mach (close to 1) the behaviour is much more regular and power law decays are observed.

In the supersonic condition the Flare zone is the region where the largest pressure peaks occur. This behaviour

happens independently from the Mach number. It is interesting to note that the largest peaks are obtained at thelowest Mach which, therefore, represents the most critical situation.

Concluding, the use of the dimensionless representation for auto and cross spectra allows us to extrapolate the

model test results to full scale launcher, even in the cases in which the dimensions are slightly different from those

of VEGA.

Acknowledgments

The present research has been funded by AVIO in the framework of an ESA contract.


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Graham, W. R., “A comparison of models for the wave-number-frequency spectrum of turbulent boundary layer pressures”. Journal of Sound and Vibration, Vol.206, No.4, pp. 541-565, 1997.

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