A numerical approach to aerodynamic noise of aircraft wings J.W. Delfs Institut für Aerodynamik und Strömungstechnik, Technische Akustik DLR - Deutsches Zentrum für Luft- und Raumfahrt e.V. Lilienthalplatz 7, D-38108 Braunschweig, Germany

In view of the need for quiet aircraft design, computational tools have to be developed, capable of describing the noise generation pro- cess for airframe noise correctly. A respective simulation concept based on Computational Aeroacoustics (CAA) and linearized Euler Equations is presented and discussed. In the context of airframe noise the question of linearity of sources is addressed. Employing the proposed ”vortex test” simulation concept an aeroacoustic assessment of the thickness effect of airfoils in unsteady inflow conditions is presented.

INTRODUCTION mass, momentum and energy and is usually refered to as CAA-simulation. The characteristic difference to the The sound generated in unbounded unsteady subsonic wave equation approach is, that apart from the acoustic flow is marginal in intensity compared to the excess noise degrees of freedom, the vortical (and entropic) degrees produced when such unsteady flow interacts with finite of freedom of the fluid dynamics is allowed for. In this aerodynamic bodies. In airframe noise problems, such way the conversion process from vorticity to sound and unsteadiness is usually associated with turbulence. A vice versa is incorporated into to theoretical description. body may be understood as a disturbance to the dynam- Although the CAA-approach is usually associated with ics of the unsteady flow components, associated with a quite an increase in computation cost, it has important corresponding change in the pressure field. This change advantages, namely a) that the sound generation is sim- is usually large near inhomogeneities of the boundary ulated, rather than modelled and b) that sound propaga- (edges, slots, humps, steps etc.) and it is accompanied tion through arbitrary flow fields is described properly. In by the conversion of part of the hydrodynamic -usually what follows a CAA-scheme is used to simulate unsteady turbulent- pressure fluctuation into sound pressure. More- perturbations about a given steady mean flow field, along over, sources of this kind represent particularly efficient with the sound generation near aerodynamic bodies in- sound emitters for frequencies with respect to which the side this mean flow. geometric body components appear non-compact. All these conditions are usually satisfied for the deployed high lift devices on the wing of a typical modern civil GOVERNING EQUATIONS

aircraft in approach. As verified in numerous flight- and

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¢ £ windtunnel tests the most intense sources of airframe For a given (quasi-) steady flow field q0 : ρ0 ¢ v0 p0 ,

noise are indeed found near the leading-, trailing- and with ρ-density, v-velocity vector, p-pressure, the inviscid

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ρ ¢

¤ ¤ ¤ side edges of the slat and flap when located by means dynamics of small perturbations q ¤ : v p about of microphone arrays [3] or elliptic mirrors [2]. this basic flow are governed by the linearised Euler equa- The computation of airframe noise may be approached tions for a thermally and calorically perfect gas: in different ways. The most classical one is to solve an in- 0

ρ ¤

d 0 0 0

¦ ¦ ¦

¦ ¦ ¦ ¤ ¤ ¦ ¦ ¤

homogeneous acoustic wave equation for a given source v ¤§¦ ∇∇ρ ρ ∇ v ρ ∇ v m˙ (1)

¥ ¥ dt ¥

term (e.g. Lighthill’s tensor as volume source, surface 0 ¤

0 d v 0 0 0 0

¦ ¦

¦ ¦ ¦ ¦

¤ ¤ ¤

pressure fluctuations as a surface source etc.). The issue ρ ρ v ¤ ∇v ρ v ∇v ∇p f (2)

¥ ¥ dt ¥

here is, that by definition all vortex dynamics (the orig- 0 ¤

d p 0 0 0

¦ ¦ ¦

¦ ¦ ¦ ¦ ¦ ¦

¤ ¤ ¤

inator to sound generation) lies buried inside the source v ¤ ∇p γ p ∇ v γ p ∇ v ϑ˙ (3)

¥ ¥ dt ¥ term and thus has to be known in advance. Typically, for 0 ∂

d 0

¦ ¦ ¦ ∇ simple cases the source term is modelled or -if availabe- Here, dt : ∂t v denotes the time derivative taken

extracted from DNS data. It is noted, that any domain, along a streamline¥ of the mean velocity field v0 and γ

where the wave equation is not satisfied (e.g. inside a is the isentropoc exponent (γ 1 ¨ 4 for air under normal

refracting shear layer) is to be understood as a source re- conditions). The equations are dimensionless with the

©

gion, requiring some source term. © ∞

following notation: time t t a l, lengths xi xi l,

ρ ρ ρ ©

© ∞ ∞

The second way to compute airframe noise involves density , velocity vector v v a , pressure

2

¤ ρ ¤ ρ ©

© ∞ ∞ ∞

the direct numerical solution of the balance equations for p p a∞, a mass source density m˙ m˙ l a , a

2

  body force density ff f l ρ∞a∞ and an energy (e.g. physical space. Overlapped grid systems are well suited

ϑ˙ ˙ 3 ϑ  ρ γ  ρ

 heat) source density l ∞a∞, where a p is for CAA [1] to facilitate gridding near complex geome- the speed of sound. The asterisk denotes quantities with try components, since these are the source locations of dimensions and the quantities with an index ∞ mean ref- airframe noise. erences, which typically are freestream values of the flow Very short wave length components of the signals quantities. which cannot be represented physically correctly on the The boundary condition for acoustically hard walls is given computation grid are suppressed with artificial se- equivalent with satisfying the kinematic flow condition lective damping (ASD) due to Tam&Dong [7]. For each

of the equations of the system (1-3) the same symmet-



    vn : n v 0 (4) ric linear, scalar damping operator D˜ is introduced. The where n is the normal vector on the considered wall point. source terms on the right hand side of (1-3) are identi- The wall condition is not directly implemented into the fied with these damping terms acting as sinks rather than difference scheme but indirectly via the pressure gradi- sources:

ent following[4]. Taking the dot product of the momen-

   m˙  νD˜ ρ

tum equation (2) with n and respecting (4) at a wall point

   ν 

˜ yields: f D v (8)

˙

 ν  

ϑ ˜ ∂ D p

p

 

0  0 0 0 0 ∇

 ρ ρ ∇

 v v  v v v v : n (5)

∂n with 2 2 

∂x  ∂x

"!#!#! $ % % &!'!#!  % % "!#!#! (!

The normal derivative on the pressure is the product of D˜ Dξ  Dη (9)

% % %

% ∂ξ ∂η

% % %

the momentum fluxes with the local curvature tensor of %

% % % % the wall. The derivative vanishes when the wall is plane The coefficients of the 7-point stencil numerical opera- or there is no flow present. tor D are given in [7]; the subscripts on D indicate the grid line direction along which the operator is to be ap- plied. The damping coefficient ν must be chosen such NUMERICAL SOLUTION SCHEME that i) non-physical, i.e. purely numerically caused sig- nal components are efficiently damped while affecting the physical wave components as little as possible, and ii) no The differential equation system (1-3) is solved nu- numerical instability of the overall scheme is generated. merically subject to the given boundary and initial condi- tions. The temporal discretization is done with the clas- sical fourth order Runge-Kutta scheme (RK4). Spatial gradients are approximated using the dispersion relation SIMULATION CONCEPT preserving 7-point stencil finite difference scheme (DRP) of Tam& Shen [5] and Tam& Dong[4], on curvilinear Because of the wide range of turbulence scales, the (block-) structured grids, see e.g. [6]. The physical grid numerical prediction of airframe noise for technically relevant flow Reynolds numbers is out of reach even on

is given as node sequence in the indices i  j

today’s largest high performance computers. In order to

 

 xi j x ξ i η j (6) reduce the computational effort, it has become popular to pre-compute (by CFD) the steady viscous mean ξ η where and represent a uniform cartesian system and flow field q0 and to simulate by CAA only the inviscid ξ assume integer values on the nodes. For fixed I the

perturbations q . As in the wave equation approach η grid variable defines a grid line and vice versa. Since this again requires some modeling. The modeling is

the coefficients of the DRP scheme are defined for the however reduced to an appropriate excitation of vorticity

ξ η uniform computation grid i, j the perturbation perturbations, rather than the whole aeroacoustic source.

equations (1-3) need to be transformed from the physical Here, an approach is presented in which upstream of ξ  η domain to the computation domain . This is done by the airframe component localized vorticity is introduced ∇ replacing by into the flow field. In the course of the simulation the ∇ ∇ M ξ (7) mean flow convects the perturbation past the airframe ∇∇ξξ

where M is the metric of the transform. It is component upon which sound is generated. The acoustic 

1 ∇ 

 obtained by inverting M  ∇ξx ξ η , which is avail- response is measured far from the body. This simulation able with high accuracy employing the DRP differencing is repeated for varied geometry but the same initial test scheme along the grid lines. The metric is needed accu- vorticity. Comparison of the acoustic responses then rately in order that the high resolution and accuracy prop- allows for a noise assessment of airframe components erties of the DRP scheme would be transferred into the in the following sense. The less efficient it converts Linearization of Lilley’s equation about a parallel mean

0 0

- /.; ; < steady flow field v 4:9 u y 0 0 shows that the linear part of Q vanishes identically, of which follows immedi- ately that sound generation in a parallel mean flow field is a fundamentally nonlinear problem. This in turn means that the evolution of a linear vortex in a parallel shear layer is perfectly silent even while initiating a Kelvin-Helmholtz instability. This situation was simulated using the linearized Euler equations (1-3)

p' 0 / in a parallel shear layer with a realistic profile u - y

taken from a RANS-CFD simulation. The shearlayer is

> > =

located in 1 = 1 y 1 1; below there is no flow and

+ = above there is a constant flow of Mach number M 4 0 4.

Localized vorticity is introduced at simulation time t 4 0

; 4 =

and position x 4 2 y 0 5. As a result a downstream + convecting unstable wave packet evolves representing the classical Kelvin-Helmholtz instability. The upper

part of Fig. 1 shows the respective linear pressure field

; ; 4 / p ?@- x y t 70 , which consists of purely hydrodynamic (i.e. non-propagating) components indicating complete silence and thus confirming the statement of Lilley’s equation. Next, the effect of the presence of a wedge

on the pressure field is considered. For this purpose a

; 4 =

sharp vertical wedge with vertex at x 4 10 y 1 4 is +

FIGURE 1. Linear pressure field evolving from localized vor- originally placed below the shearlayer and the simulation ) tex, seeded at t ) 0 and x 2. Above: no wedge, below: with is repeated for otherwise identical parameters. In this wedge at x ) 10. Wedge causing generation of sound. case, shown in the lower part of Fig. 1, sound is generated by scattering of the wave packet’s linear hydrodynamic pressure field at the wedge although the mean flow does vorticity into sound, the quieter the design. Note, that a not even touch the wedge. The example shows that in property of a body (in fact a response function) is sought, rather than an absolute pressure level in dB. 0.5 Note on linearity

Before turning to examples a short note on the math- y 0 ematical character of airframe noise sources is in place, because the question arises, whether it is justified to use -0.5 -1 -0.5 0 x 0.5 1 1.5 linearized perturbation equations (1-3) for the descrip- v' tion airframe noise generation or whether airframe noise 3 v’: -0.5 -0.4 -0.3 -0.2 -0.1 0.1 0.2 0.3 0.4 0.5 sources are fundamentally nonlinear. In order to address 2 this issue reference is made to Lilley’s equation, whose wave operator is known to describe sound propagation 1 through parallel shear flows. It reads

y 0 * 2

d d Π ∇ 2∇ t∇ ∇ 2∇

,

,.- /1032 - /54 ∇ , a ∇∇Π 2 ∇v:∇ a ∇∇Π dt dt2 + -1

t∇ ∇ ∇ /62 2 ∇v : - ∇v∇v Ψ (10)

+ -2

1 p'

7 - 8 / where Π 4 γ ln p p∞ is the acoustic variable, super- -3 p’: -0.1 -0.05 -0.025 -0.01 0.01 0.025 0.05 0.1 Ψ script t means ”transpose” and denotes terms of vis- -3 -2 -1 0 1 2 3 4

cous friction and entropy, which are negligible for high x

) D E

Reynolds numbers. The remaining aeroacoustic source FIGURE 2. Vortex-airfoil interaction. above: v ACB t 3 5 , be-

) D E

t∇ ∇ ∇ low: p ACB t 3 5 .

- /

term due to Lilley is therefore Q 4 2 ∇v : ∇v∇v . + the presence of edges the sound generation by vorticity lower part of the figure depicts the acoustic pressure prop- becomes a linear problem and it is reasonable to study agating away from the airfoil. airframe noise generation using linear equations (1-3). At DLR, a first CAA-design study on the influ- ence of airfoil thickness on the sound generation in ”dirty” inflow conditions was carried out in three APPLICATION TO GUST-AIRFOIL dimensions[6]. Joukowski-airfoils (span along z- INTERACTION direction, flow along x) with different thicknesses were subjected to the same localized test vortices with

2 2 2 2 Q

F

H IWHXG J'N J I M&N G I.G O O IYP L

The presented simulation concept for a computational v G t 0 y x 0 exp ln 2 x y z 0 1 .

I H assessment of airframe noise using CAA is applied for Pressure time histories p FZG t in the z 0-plane on the example of noise generated by an airfoil due to in- a circle with a radius of 1.5 chord lengths l around coming gusts. When a vorticity perturbation strikes the the airfoil nose were Fourier-transformed. The Fig.3

leading edge of an airfoil, sound is generated. A 2D- shows radiation directivities for two Strouhal numbers P

case is presented in Fig.2, showing the vertical veloc- Sr H f l U∞ with frequency f referenced w.r.t. the F ity v F and the pressure field p well after a test vortex freestream velocity U∞. The transformed pressure is was seeded into the Mach-0.5 flow one chord length up- related to the maximum initial perturbation velocity

stream the airfoil. The initial, circular perturbation ve- vmaxF and thus appears formally as an impedance. The

H I locity field v F@G t 0 is derived from the stream function diagrams show that under the same inflow conditions

2 2 2 Q

J J H IKH L M"N G I.G'G O L I O I'P L ψ G x y t 0 0 21exp ln 2 x 1 5 y 0 15 thick airfoils are much quieter than thin airfoils. and is normalized such that the maximum perturbation speed is equal to one. The upper part of Fig.2 shows the CONCLUSIONS divided vortex field, while the pressure distribution in the Inviscid perturbation equations may be used to simulate the generation mechanism of airframe noise employing high resolution CAA codes. Essential part 0 % of airframe noise generation rests on linear dynam- 1.2e−03 y 6 % ics. The presented ”vortex-test” serves as a method

ϕ 12 % to support low-noise design of airframe components RSRSRSRSRSRSRSR

TSTSTSTSTSTST 18 % RSRSRSRSRSRSRSR

TSTSTSTSTSTST x theoretically/numerically.

RSRSRSRSRSRSRSR TSTSTSTSTSTST 8.0e−04 ^ p sin ϕ ACKNOWLEDGMENTS v’ max 4.0e−04 Part of the work, leading to the present paper was sponsored by Deutsche Forschungsgemeinschaft DFG as part of the SWING+ project, which is gratefully 0 % acknowledged. 1.2e−030.0e+00 6 % 0.0e+00 5.0e−04 12 %1.0e−03 ^ REFERENCES p cos ϕ 18 % v’ max 8.0e−04 1. Delfs, J.W., AIAA Paper No. 2001-2199 (2001). p^ sin ϕ 2. Dobrzynski, W.; Nagakura, K.; Gehlhar, B.; Buschbaum, v’ max A., AIAA Paper No. 98-2337 (1998). 4.0e−04 3. Michel, U.; Helbig, J.; Barsikow, B.; Hellmig, M., AIAA Paper No. 98-2336 (1998). 4. Tam, C.K.W.; Dong, Z., Theoret. Comput. Fluid Dynamics, Vol.6, pp. 303–322, (1994). 0.0e+00 0.0e+00 5.0e−04 1.0e−03 5. Tam, C.K.W.; Shen, H., AIAA Paper No. 93-4325 (1993) p^ cos ϕ 6. Grogger, H.A.; Lummer, M.; Lauke, Th., AIAA Paper No. v’ max 2001-2137 (2001). FIGURE 3. Radiated pressure from airfoils of different thick- 7. Tam, C.K.W.; Dong, Z., Journal of Computational Acous- ness in Mach-0.5 flow, referenced to free field impedance. tics, Vol.89, pp. 439–461 (1993).

∆ V Above: Sr=1, Below: Sr=3; Bandwidth Sr U 0 2; [6].

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Thermoacoustic devices use the phase relationship between the pressure and particle velocity in the Stokes boundary layer near surfaces to transport heat from cold to hot heat exchangers. For thermoacoustic devices to be optimized, an improved understanding of unsteady minor losses is required. In this paper a parallel numerical simulation of the minor losses in a sudden expansion in a resonator is described. The Navier-Stokes equations are discretized in space and time with high-order accurate numerical schemes. These schemes, that are also used in computational aeroacoustics, minimize numerical dispersion and dissipation errors. A high amplitude standing wave is generated in a resonator with a sudden change in cross-sectional area. The details of the unsteady flow in the vicinity of the sudden expansion are provided. It is shown that mean recirculating flow regions are established in the two sections of the resonator. The average pressure losses across the expansion are determined and the relative contributions of the Bernoulli pressure and the total pressure losses due to the generation of vorticity are estimated.

INTRODUCTION Fortran 90 with the Message Passing Interface (MPI) as the parallel implementation. A domain decomposition Thermoacoustic devices can be either prime movers or method is used, in which the physical domain is decom- heat pumps. Swift [1] provides a description of the basic posed into sub-domains and message passing is only em- physical processes involved as well as examples of dif- ployed at the sub-domain boundaries. In addition, a par- ferent thermoacoustic engines. Recently built thermoa- allel multiblock grid structure is used. This is appropriate coustic engines, such as the Stirling heat engine designed for the present problem of a resonator with two sections by Backhaus and Swift [2], have efficiencies that rival the of different cross sections. The geometry and computa- common internal combustion engine. This is achieved tional domain used in the present two-dimensional sim- through the use of a traveling acoustic wave, that has the ulations are shown in Fig. 1. The lengths are nondimen- correct pressure/volume phasing of the Stirling cycle, in sionalized by the length of the larger resonator. Differ- one part of the engine. This wave is maintained at a high ent blocks are used for the grids in the two parts of the amplitude by a standing wave in another section of the resonator in order to insure the grid orthogonality. The engine. To prevent a net mean flow in the traveling wave loop of the device, that reduces the system’s efficiency, a “jet-pump” is used. The average minor losses across the jet-pump eliminate the mean flow. Minor losses are well- Line Source documented for steady flows (see Idelchik [3]): however, 0.03 this is not the case for the unsteady flow in a thermoacous- tic engine. The purpose of the research described here is 0.05 to address this lack of understanding.

TECHNICAL APPROACH 1.0

In order to describe the interaction between the acous- tic wave in the resonator and the resonator walls the

Navier-Stokes equations are used. They are written in a 0.025 generalized coordinate system. The total energy equation x A is used as well as the equation of state for a perfect gas. B The coefficient of viscosity is related to the thermody- 0.025 namic properties using Sutherland’s formula. A Prandtl 0.5 number of 0.72 is used to relate the coefficients of viscos- ity and thermal conductivity. No turbulence model is used y in the present simulations. The equations are discretized 0.003 using the Dispersion Relation Preserving algorithm of Tam and Webb [4] in space and a fourth-order Runge- Kutta scheme in time. The computer code is written in FIGURE 1. Sketch of the computational domain. Not to scale. calculations are performed on a PC cluster. The compu- are associated with two recirculating regions that fill both tational time on 32 processors is 2.8µsec/grid point/time parts of the resonator.The instantaneous pressure differ- step. A companion experimental resonator (see Doller et ence between point A in the larger channel and point B al. [5]) is driven by either a shaker or a loudspeaker. In in the smaller channel (shown in Fig. 1) reaches a steady order to model the effect of the driver, a source term is value after the transient period. This pressure difference introduced into the continuity equation. It has a Gaussian has contributions from the Bernoulli pressure (see Wang distribution in the x-direction and is located a distance of and Lee [7]) and losses due to the generation of vorticity. 0.05 from the closed end of the larger channel, as shown The former is a second order effect associated with the in Fig. 1. A source term is also introduced into the energy finite amplitude of the acoustic pressure and particle ve- equation to insure that only acoustic disturbances are gen- locity. It’s contribution is estimated to be 25% of the total erated. No slip and no penetration conditions are applied pressure difference. Thus, the larger contribution may be at all walls. Either adiabatic or isothermal wall boundary associated with the generation of vorticity at the sudden conditions are enforced. expansion/contraction. The simulations described here represent a prelimi- RESULTS AND DISCUSSION nary examination of the ability of numerical simulations, based on methods from computational aeroacoustics, to After an initial transient period, a standing wave is es- aid in the understanding and optimization of fluid dy- tablished in the smaller resonator channel. In the com- namic phenomena in thermoacoustic devices. Much work panion experiment, the resonant frequencies are estab- remains to be done. In particular, more realistic three- lished with a broadband excitation. In the present calcu- dimensional geometries that match the actual jet pumps lations, a single frequency that generates a quarter wave- should be examined. The acoustic driver needs to be length standing wave in the smaller channel is used. Mor- modeled more accurately. Also, at high amplitudes, the ris et al. [6] show how the system settles into a periodic boundary layers may be alternately laminar or turbulent. state after approximately twenty periods. Near the change This is caused by the periodic variation of the pressure in the cross section, there is a periodic shedding of vor- gradient from favorable to adverse. This is a very chal- tices associated with the jet-like part of the cycle. In- lenging turbulence modeling problem. Some preliminary stantaneous streamtraces are shown in Fig. 2. The flow is efforts by the authors suggest that an unsteady Reynolds- symmetric about the channel centerline. This is due to the averaged Navier-Stokes method could be useful. plane wave excitation. Two pairs of vortices of equal rota- tion sense are seen. In addition, a pair of vortices with the ACKNOWLEDGEMENTS opposite sense form in between them. The vortices move away from the contraction by a process of mutual induc- This work was supported by the Office of Naval Re- tion. In addition, a net mean flow is generated. Immedi- search. ately at the contraction there is a very small mean flow on the channel centerline towards the smaller channel. REFERENCES A stronger centerline mean flow away from the contrac- tion is observed in the larger channel. These mean flows 1. G. W. Swift, Journal of the Acoustical Society of America 84, 1145 (1988). 2. S. Backhaus and G. W. Swift, Nature 399, 335 (1999).

0.59 3. I. E. Idelchik, Handbook of Hydraulic Resistance, 3rd ed.

0.58 (Begell House, New York, 1994).

0.57 4. C. K. W. Tam and J. C. Webb, J. Computational Physics 107,

0.56 262 (1993).

0.55 5. A. Doller, A. A. Atchley, and R. Waxler, Journal of the

0.54 Acoustical Society of America 108, 2569 (2000).

0.53 6. P. J. Morris, S. Boluriaan, and C. M. Shieh, Computa-

0.52 tional Thermoacoustic Simulation of Minor Losses Through

0.51 a Sudden Contraction and Expansion, AIAA/CEAS Paper 2001/2272, 2001. 0.5 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 7. T. G. Wang and C. P. Lee, in Nonlinear Acoustics, edited by M. F. Hamilton and D. T. Blackstock (Academic Press, New FIGURE 2. Streamtraces of the instantaneous flow in the res- York, 1998), Chap. 6, pp. 177Ð204. onator. Aeroacoustic studies and tests performed to optimize the acoustic environment of the Ariane 5 launch vehicle D. Gély, G. Elias and C. Bresson Office National d’Etudes et de Recherches Aérospatiales 29, avenue de la Division Leclerc BP 72, 92320 Châtillon Cedex - France

To decrease the acoustic levels inside the Ariane 5 fairing and to reduce the excitation applied to the payload, it was necessary to investigate a method for reducing substantially the acoustic environment during the lift-off. The highest-noise radiating regions were identified by analyzing the signals from a microphone array implemented on the launch vehicle. It is to our knowledge the first time such a technique is used on a launch vehicle. The MARTEL facility was then used to characterize the efficiency of a horizontally extension of the lateral flues. Based on test results and applying similarity criteria, it was possible to determine the length of this extension necessary to achieve the required noise attenuation inside the fairing. The acoustic measurements made on the launch vehicle after the flue extension construction in Kourou confirmed the reduced scale predictions obtained at MARTEL facility.

INTRODUCTION TESTS AT THE MARTEL FACILITY

The more and more powerful launch vehicles, such as Ariane 5, MARTEL facility, installed in CEAT at Poitiers involve an increase of the external Sound Pressure Level (SPL). University, has been developed as part of the Research and As the confort of launch vehicle at lift-off may become a quite Technology program lead by CNES [1]. The air-hydrogen important commercial argument for the customers in the future combustor generates subsonic or supersonic jets, cold or therefore, a continuous effort must be kept in order to obtain hot, up to 1800 m/s and 2100 K. A test campaign has been “low” acoustic levels in the payload bay. The acoustic analyses carried out with a 1/47 mock-up representative of the ELA3 made during the V503 qualification flight of Ariane 5 confirmed launch pad. Only a single jet being available in MARTEL, the possibility to reduce the acoustic levels inside the fairing the mock-up simulates only the half part of the Ariane 5 when the launch vehicle goes through the altitude from 10 to 20 pad with its SRB flue (figure 2). meters. This study has been supported by the Ariane Program and the Research & Technology program of CNES. MEASUREMENTS DURING V503 FLIGHT For the V503 flight, a microphone array has been implemented around the fairing to perform noise source localization (figure 1). For the launcher altitude of 20 m, the acoustic map shows only three main source locations appearing, one in the middle of the uncovered central engine flue, and the two others at the Solid Rocket Booster (SRB) flue outlets.

Figure 2: Ariane 5 launch pad mock-up in MARTEL facility SRB flue outlet The absolute acoustic levels measured in MARTEL facility are not representative of the full scale but the relative levels between several test configurations can be extrapolated. The first approach to obtain noise reduction was to improve SRB flue outlet the efficiency of the water injection devices [2]. Unfortunately, the gains were too low to implement this solution. The second method investigated was an extension Central flue of the SRB flues. In practice, three extensions were tested namely 10, 15 and 30 meters at full scale.

Figure 1: Acoustic sources localization V503 flight. Alt. 20 m The tests were conducted for several simulated altitudes, between 0 and 20 m. The noise spectra measured for the Based on the relative levels of the SRB and central engine three extensions are shown in the figure 3. These results sources and on the NR index, it appeared necessary to reduce the were obtained for a critical altitude of 10 m. In each case, a acoustic sources at the SRB flue outlets by at least 6 dB to noise reduction was observed over a wide frequency band. achieve the required noise reduction inside the fairing. Thus, The noise reduction increases with the flue extension CNES decided to perform tests at the MARTEL facility, length. However, based on results not presented herein, the conducted by ONERA, in order to find a solution allowing to reduction decreases as the launcher climbs. Indeed, the decrease the acoustic levels in the payload bay and then to extension of the flue gradually masks the jet near the final improve the specification applied to the payload. section. dB No flue extension (V503) the lift-off up to an altitude of 60 meters. It is interesting 10-meter flue extension to quote that, with the new flues, the contribution of the 15-meter flue extension 30-meter flue extension SRB to the noise during this period seems to have disappeared, the levels being the same before and after their ignition. This result is confirmed by noise source localization, presented for V504 flight in figure 6, where no acoustic source remains at the SRB flue outlets at an altitude of 20 meters. 5 dB

Third octave band (Hz) SRB flue outlet

Figure 3: Flue extensions effect The noise attenuations are due to the masking effect of the flue and to the change in the direction of the jet subsequent to the horizontal extension of the flue. The main jet emission direction SRB flue outlet is thus farther from the top part of the launcher. The extrapolation of the attenuation predictable at full is based on Central flue similarity criteria. Applying a 2 dB safety margin to take into account the measurement error and the reproducibility of the tests shows that a 30-meter horizontal extension of the SRB flues Figure 6: Acoustic sources localization V504 flight. Alt. 20 m satisfies the requirement. The acoustic measurement performed in Kourou fully MEASUREMENTS DURING V504 FLIGHT agrees with the predictions made using the MARTEL facility and the final noise reduction objective has been EADS, CNES and ARIANESPACE decided to perform the flue reached. extension on the Kourou site just before the V504 flight, as seen in figure 4. CONCLUSIONS

V504 flight: The test campaigns conducted by ONERA on the 30-meter extension flue MARTEL facility allowed efficient solutions to be found for optimizing the noise level during lift-off of the Ariane 5 launch vehicle. The SRB flues were extended by 30 meters just before V504 flight. The acoustic measurements made during this flight confirmed the predictions. An attenuation of about 5 dB was measured on the fairing and the localization of the noise sources using a microphone array on board has shown that the noise source at the SRB flue outlet has been dramatically eliminated. The MARTEL facility and expertise in advanced signal processing techniques prove to be excellent performing tools for Figure 4: SRB flue extension in Kourou site successfully conducting experimental studies which can be The comparison between V503 and V504 flights appears in extrapotated at full scale. figure 5, where the mean SPL of flush-mounted microphones located on the fairing has been plotted. ACKNOWLEDGMENTS This study was supported by CNES (Ariane Program). The SRB IGNITION V503 Flight authors thank the companies EADS and Arianespace for their help. We would like to extend a special note of thanks to the 5 dB MARTEL team. REFERENCES V504 Flight 1 H. Foulon, D. Gély, J. Varnier, E. Zoppellari, Y. Marchesse MARTEL: Simulation of Space Launchers Aeroacoustic Ambience 12th European Aerospace Conference (AAAF/CEAS) 0 10 40 100 Altitude (m) Paris (France), November 29-30 - December 1, 1999 2 Figure 5: V503-V504 Ariane 5 flights. Acoustic data comparison D. Gély, G. Elias, C. Bresson, H. Foulon, S. Radulovic Reduction of supersonic jet noise. Application Ariane 5 Before the lift-off, the central engine is running alone and no 6th AIAA/CEAS Aeroacoustic conference. difference is observed. In contrast, a 5 dB reduction appears from Lahaina (Hawaii – USA), 12-14 june 2000 Influence of compartment size on radiated sound power level of a centrifugal fan

Leping Feng

MWL, Department of Vehicle Engineering, KTH, SE-100 44 Stockholm, Sweden e-mail: [email protected]

The influence of the compartment size on the radiated sound pressure level of a centrifugal fan is investigated experimentally. The measurement set-up consists of a commercial centrifugal fan and a cavity with adjustable walls and ceiling. The inflow condition is adjusted indirectly by adjusting the geometry of the box, in order to avoid the difficulties to describe and measure the inflow conditions quantitatively. The tests are performed for a range of typical situations of ventilation systems. The sound pressure levels in a few typical positions are measured in a semi-aechoic room. Some useful results, and an empirical relation between the sound power level and the geometry of the cavity in a certain range, are obtained from the measurements.

INTRODUCTION 2 m Fan The radiated sound power level of a centrifugal fan 0.5 m Duct compartment is strongly influenced by the inflow condition. An Mic. 2 example of this is that a fan usually radiates 3 dB or (inlet side) more sound power when located inside a ventilation Mic. 1 system than in a free condition. There are several (outlet side) different parameters that may influence the inflow conditions. In this paper, we only deal with one Figure 2. Illustration of microphone positions situation: the change of the cross section of the compartment where the fan is located. The opening of the outlet, which is a 0.3 X 0.3 m square duct, is covered with a perforated panel ∼ DESCRIPTION OF TEST SET-UP (perforated ratio 30%) in order to make the fan working in practical working point. Two microphones are employed to register the sound pressure levels. The tests were performed in the semi-anechoic One is located at the same plane of the outlet, 0.65 m room of the Department, with the test set-up shown in Figure 1. The positions of the walls and roof are from the centre of the duct. Another is located at the adjustable to make variable cross sections of the fan centre line of the inlet side, 2 meters away from the compartment (see Figure 2). The tests are performed compartment. The centrifugal fan tested is SAMI GS in four different (motor) speeds: 700, 1000, 1500 and with 11 blades manufactured by ABB. 1900 rpm. Eleven cross sections of the compartment, varying from 0.22 to 0.596 m2, or from 2.443 to 6.622 times of the area of the outlet duct, are tested.

SOME RESULTS

In order to check the general trend of the sound pressure/power level in function of the size of the compartment, the registered sound pressure levels at the four different rotating speeds are “normalised”. That is, the total sound pressure levels at different rotating speeds are set to be equal to that of the sound pressure level when the rotating speed is 1000 rpm. The sound pressure level at each frequency band is Figure 1 Illustration of the test set-up then calculated as 95 95

90 800 90 1000 85 85 1250 80 outlet 1600 inlet 80 75 2000 70 75 2500 3150 65 70 4000 60 65 100 200 400 800 1600 3150 A- 5000 weghted 234567A Frequency, Hz Normalised area

Figure 3 Typical spectra at the two positions Figure 5 Sound pressure levels at microphone 2 as a function of area: high frequencies L = L + (L − L ) (1) i normalised i 1k r In order to get a general picture of the influence of the cross section on the radiated sound pressure level, where subscript “i” denotes 1/3 octave band number, linear regression is made for all measured data, in “1k” and “r” are rotating speed. decibel, according to equation Typical spectra of sound pressure levels measured at the two microphone positions are shown in Figure 3. L = A + Bs 2 ≤ s ≤ 7 (2) They have different shapes. The differences at low frequencies could be due to flow, since the flow speed where s is the normalised area and A and B regression at outlet side is much higher than that at inlet side. The coefficients. Figure 6 shows the coefficient B, which is high frequency components, on the other hand, might the increase of the sound pressure level when the size be due to the interaction between the flow and the of the compartment increases the area of one cross perforated panel. Since the microphone at the inlet section of the outlet duct. For both microphones, this side is directly pointed to the fan and the cross section value is almost always negative, indicating that at this side is much larger, the signal registered by reducing the compartment size will increase sound microphone 2 might more correctly reflect the changes pressure levels at all frequency bands. Although there of the fan due to the size change of the compartment. is a big difference for 1/3 octave band values, the The test situations of the cross section are coefficient B is almost same for A-weighted sound normalised by the area of the outlet duct in order to get pressure levels measured at both microphone positions. a non-dimensional measure. Figure 4 & 5 shows the third octave band sound pressure level at microphone 2 CONCLUSIONS as a function of the normalised area. As a general tendency, sound pressure levels decrease when the area Reducing cross section of the fan compartment will is increased, with the value dependent on frequencies. increase the radiated sound power level. This increase Results from microphone 1 show the same tendency. seems not as big as we expected.

90 0.4 0.2 100 85 0 125 -0.2 100 200 400 800 1600 3150 A-weghted 80 160 -0.4 200 -0.6 75 250 -0.8 315 -1 70 400 -1.2 500 65 -1.4 630 234567 -1.6 Normalised area Frequency, Hz

Figure 4 Sound pressure levels at microphone 2 Figure 6 Regression coefficients B as a function of area: low frequencies Solid: inlet side; Dotted: outlet side Effects of Blade Material on Sound Radiation by Attached Cavity in Unsteady Flow

a b S. Kovinskaya and E. Amromin

aSeagate Technology, 10323 West Reno, Oklahoma City, OK73127, USA bMechmath LLC, 2109 Windsong,Edmond,OK73034, USA

Sound radiation by a cavity attached to a blade under unsteady flow excitation is analyzed. It is shown that cavity volume oscillations and radiated sound power are sensitive to variations in ratio of blade material Young’s modulus to product of fluid density on square of flow speed. These variations change both frequencies and levels of peaks in spectra of radiated sound.

MATHEMATICAL FORMULATION OF 2 ! 2 R 1 U F  1    "( )  2 2 (4) PROBLEM S # Rt 3 2 S Prediction of sound radiation by cavitating 3 blades/hydrofoils is currently based on model tests. Because of differences between flow-induced sound in Here B is the cavity thickness, S1 is a cavitation-free model and full-scale flows, extrapolations of blade surface, S2 is the cavity surface, S3 is projection experimental data to full-scale conditions are not of S2 on down surface of blade;  is potential of time- completely satisfactory, especially in low-frequency averaged flow around the blade. Cavitation number band [1]. =2P/(U2), where P is a difference between Selection of appropriate similitude criteria is an pressure in incoming flow and within the cavity. The important problem that can be clarified by the system (1)-(4) must be completed by Joukovski-Kutta numerical analysis. A realistic analysis must take into condition that defines the blade lift. For periodic account simultaneous oscillations of cavity thickness excitations that correspond to boundary condition it and length under periodical excitations of incoming RRxYxJAJ0 and RRyYxJAJAe (where A=const; flow, and represents a nonlinear problem with a  is excitation frequency), Eq.(1) can be rewritten as varying boundary. Theory [2] allows such analysis for R2 R2 elastic blades with the use of 2-D numerical modeling. V 2 hV F JK(1 i)  St R
For a blade (hydrofoil) at a given time-averaged angle Rx2 Rx2 C 2 2 of attack, periodical perturbation of incoming flow can be caused by turbulence. The perturbation magnitudes Here C is the blade’s chord (see Fig. 1); K=E/(U2), are much smaller than free-stream speed. The vibration R=*/, and St=C/U are dimensionless parameters of blade with attached cavity in unsteady flow (Fig.1) that affect vibration. is described in 2D approach by equation for beam in bending motion: L 2 2 2 2 R R V R V U a E(1 i)J   * h
F (1) Rx2 Rx2 Rt 2 2 Here U is free-stream speed; V is transverse displacement of the blade;  is its loss factor; E is its Young’s modulus; h and J are thickness and inertia moment of its sections; * and  are densities of blade material and water; F is the hydrodynamic load U coefficient. The coefficient F depends on velocity C potential  that is a solution of Laplace equation 
0 with the following boundary conditions: Fig. 1. Flow around a blade section.

RV R R (V  B) R Mechanical boundary conditions of rigid clamping  ;
(2)-(3) in a middle part of the blade (where V=dV/dx=0) and R t R y R t R y of free edges (where d2V/d2x=d3V/dx3=0) are sufficient S1 S 2 for integration of Eq. (1) and determination of blade cavity response at every frequency  includes the vibration. Estimating cavitation-induced sound response on excitation at the same frequency (first radiation, it is important to keep in mind that an harmonic), second harmonic of its response on oscillation of the cavity volume D is its principal cause, excitation at /2, third harmonics of the response at 2 2 and sound power level Sp~d D/dt [1]. This volume, /3, etc. One can see in Fig.2 that the prominent however, depends on blade elastic properties, because frequencies of sound radiation are found satisfactory in boundary conditions for  include V. Therefore, sound numerical analysis based on Eqs.(1)-(4). power can be found by computing d2D/dt2 after solving Eqs.(1)-(4). For any periodical excitation of incoming flow, the cavity thickness oscillates simultaneously with the cavity length L. As a result, the cavity volume oscillation accumulates both length and thickness oscillation. The volume oscillation is nonlinear and has high harmonics. Therefore, the blade response is multi- frequency, and significant nonlinear effects appear [3].

Numerical Analysis Although the current analysis is assigned to simplified flow geometry, this analysis is able to clarify some physical aspects. There are five dimensionless parameters in Eqs. (1)-(4): St, , R, L/C and K. The similitude by using R=*/, St and  is evidently attainable for model tests, but there are at least three effects that are different for full-scale and model flows. First, the ratio of cavity length L to the blade chord C depends on blade’s scale; this is an implicit viscosity Fig. 3. Effect of blade material on sound radiation (Sp) of effect [4]. Second, real incoming flow spectra are cavitating hydrofoil NACA-0015. The curve 15-S broad band and usually unknown [5]. Third, the blade corresponds to incoming flow speed 15m/s for steel hydrofoil P 8 admittance in the actual flow affects its sound (K=0.9 10 ), 9-S (marked by *) –to 9m/s for steel hydrofoil P 9 radiation. This effect can be modeled by keeping K and (K=2.5 10 ), 9-A (marked by o) -to 9m/s for aluminum hydrofoil (K=0.9P108). Cavity length L=0.6C. R, but it is usually impossible for model tests to fix both K=E/(U2) and R=*/. Selection of the similitude criterion for modeling of a material effect must depend on frequency band (St 6 values). For large St, the ratio */ is more influent, but K=E/(U2) is more important for moderate and low frequencies. The dependencies of sound power from frequency for different values of K are plotted in Fig.3. 3 The performed analysis allows conclusion that cavity p volume oscillations and the radiated sound power are S

g sensitive to variations of K. These variations change

Lo both frequencies and levels of spectrum peaks. 0 0.2 0.6 1 1.4 REFERENCES 1. Blake WK. Mechanics of Flow-Induced Sound and -3 Vibration. Academic Press, 1986 2. Amromin E & Kovinskaya S. Journal of Fluids and Log S t Structures, 2000, v14, p735-751. 3. Koinskaya S, Amromin E & Arndt R.E.A. Seventh International Congress on Sound and Vibration, Fig..2. Effect of cavity length on sound radiation S by steel P Garmisch-Partenkirchen, 2000, vIII,p1417-1424 hydrofoil NACA-0015. Solid curve –computation for Amromin E. Applied Mechanics Reviews. 2000, v53, L/C=0.75, dashed – for L/C=0.15. X -measurements for 4. p307-322 L/C=0.75,  - for L/C=0.15 5. Arndt R.E.A. ONR 23rd Symposium on Naval Hydrodynamics, Val-de-Reul, 2000 The incoming flow spectrum is accepted as white noise in the presented computations. A computed Line source radiation over inhomogeneous ground using an extended Rayleigh integral method F.-X. Bécota,b, P. J. Thorssonb and W. Kroppb aTransport and Environment Laboratory - INRETS, F-69675 Bron, France – [email protected] bDepartment of Applied Acoustics - Chalmers, S-41296 Gothenburg, Sweden

The method presented in this paper is proposed as an alternative to standard boundary integral equations for the sound radiation of a line source over grounds of arbitrary impedance and profile. Valid for any kind of source, it takes advantage of the Rayleigh integral formulation to yield a minor computational effort for flat surfaces. The calculation time, optimized according to the Fresnel zone principle, is expected, however, to be similar to boundary element methods for the case of non-flat grounds. The extended Rayleigh integral method is validated here for multipole sources radiating over homogeneous grounds. This proves its reliability for the prediction of strongly directional sound fields.

INTRODUCTION respectively dipoles, on the ground surface. The desired boundary condition on the ground surface is The general case of a source radiating above a ground expressed using the definition of the normal acoustical

of arbitrary impedance and profile is usually handled impedance of the ground, p ¢ Zvn. Including the corre- by integral equation methods, often to the expense of sponding Green’s functions for the velocity, the boundary the computational effort. Therefore, an original method value equation of the problem can be expressed as

for such cases has been developed on the basis of the §

ξ ξ (v,y) ξ ξ

¤ ¡ ¡ ¤ ¡ Rayleigh integral method for flat surfaces (see also [1]). Q ¡©¨ G x Z x G x d

Γ

Like BE methods, to which it is an alternative, this (v,y)

¨ ¤ ¡¦¥ ¡ ¤ ¡ method is valid for sound propagation above grounds of ¢ Q0 G0 xs x Z x G0 xs x (2)

arbitrary impedance and profile, and it handles any kind 

where the superscript v y ¡ indicates the velocity Green’s of primary source.

functions in the y direction, normal to the surface at the Firstly, the boundary value problem is briefly derived. point x. The amplitude of the sources on the ground, The specificity of the present work is explained in a sec- ξ

Q ¡ , are the unknwowns of this integral equation. ond part. Finally, numerical examples are presented to Eq. (2) holds for any shape of the surface Γ. However in prove the reliability of the method. the following, only sound propagation over flat surfaces will be examined because it results in a major simplifica- tion of the problem. For uneven terrains though, the com- THEORETICAL BASIS putational effort using the present method is expected to be equivalent to that resulting from BE approaches. The main idea is to estimate the sound field above an arbitrary impedance ground from the pressure field of the same source radiating above either rigid or totally soft THE EXTENDED RAYLEIGH ground (this approach is also that of the study in [2]). To INTEGRAL METHOD account for the ground effects, a number of sources are placed at the ground level. Thus, at a point xr in the half Eq. (2) can be simplified if, for instance, a rigid pri- Γ space above the surface , the total radiated pressure can mary boundary condition is assumed to be fulfilled. In be written (v,y) this case, according to the Rayleigh integral, G0 is

§ (v,y)

zero on the ground surface. G is also zero at all points

ξ ξ ξ

¤ ¡¦¥ ¡ ¤ ¡ p xr ¡£¢ Q0 G0 xs xr Q G xr d (1) ξ Γ of the surface, except for x ¢ , which represents a sin-

gularity.

¡ where G0 xs ¤ xr is the free-field Green’s function at a Thus, in Eq. (2), the evaluation of the integral at the

ξ ¡ point xr due to a source located at xs. G ¤ xr are the singular points is performed by determining the Cauchy

ξ ¡ analogue Green’s functions for the sources located at a principal value: it is zero for G ¤ x and a finite value for

ξ (v,y) ξ ¡ point of the ground. According to the Rayleigh inte- G ¤ x . At other points of the surface, a numerical gral for a flat surface, if a rigid, respectively soft, primary integration, for instance, using a Gauss-Legendre quadra- boundary condition is chosen, they represent monopoles, ture, can be performed with arbitrary accuracy as long as the singularity itself is not chosen. As a result, the bound- including both negative and positive orders (cf Fig. 1, ary value problem can be formulated as left). The pressure fields from these two sources are com-

puted using the Extended Rayleigh integral method. As £

Q ¢ x

ξ £ ¢ ξ ¤ £ ξ ¥ ¢ £ ¢ ¤ £ ©

Q ¢ G x d jZ x Q0G0 xs x (3) solutions in [2] are accurate for rather rigid grounds, a ρω ¦¨§ ¡ 2 quad normalised acoustical admittance of β=0.2 is chosen. As Once the source strengths are determined, the pressure a guideline, the exact analytical solution for rigid ground field including the ground effects, can be calculated at any is also shown in Fig. 2 (left). Despite discrepencies point in the above half space. 35 Extended Rayleigh 40 30 Exact rigid solution Extended Rayleigh Modified Chandler−Wilde 30 Modified Chandler−Wilde NUMERICAL EXAMPLES 25 Exact rigid solution 20 20 15 The method has also been presented in [1] and was 10 10 5 0 relative free field (dB)

shown to yield good predictions of relative pressure fields relative free field (dB) p 0 p L L for monopoles above homogeneous and inhomogeneous −5 −10 0 30 60 90 0 30 60 90 grounds. Special attention is paid here to the case of a Receiving angles (°) Receiving angles (°) high order source radiating above homogeneous surfaces. FIGURE 2. Dipole radiation above a flat surface of acoustical As in [1], receiving points are placed on a quarter circle admittance β=0.2, f =1kHz, low source position – left : arbitrary of radius 1.2 m, from the perpendicular vertical to the length of ground, right : Fresnel zone principle. surface (0 degree) to directly on the ground (90 degrees). The source is placed on a 1.2 m radius quarter circle op- for steep incidence angles, which were expected due to posite to the receivers, with an angle of 5 degrees (low the limitations of solutions from [2], the agreement is source position) or 45 degrees (high source position) with fairly good. In Fig. 2 (right), limitations of the Fresnel the direction of the surface. This geometry allows the in- zone principle are exemplified due a considered portion vestigation of the near field and the far field of the source. of ground, which is too small. Thus, the method seems For the discretization of the ground surface, a number of applicable to sound propagation due to the superposition 10 elements per wavelength was chosen, on a portion of of sources above finite impedance grounds, at least for ground corresponding to the first Fresnel zone, to opti- grazing angles of incidence. mize the calculation time. Furthermore, a 10:th order Gauss-Legendre quadrature was used to insure good con- CONCLUSIONS vergence of the solution. First, normalised pressure fields Due to a substantially lower computational effort for 10 40 Extended Rayleigh flat surfaces, the Extended Rayleigh integral method was 30 Exact soft solution 0 proved to be advantageous regarding standard BE ap- 20 −10 proaches. This applies for any source type (or super- 10 position of sources), radiating above arbitrary impedance −20 0 relative free field (dB) relative free field (dB) grounds. p Extended Rayleigh p L Exact soft solution L −30 −10 0 30 60 90 0 30 60 90 Receiving angles (°) Receiving angles (°) ACKNOWLEDGMENTS FIGURE 1. Radiation above totally soft, flat ground (Z=0) : 60:th order multipole, high position, f =5kHz (right) – dipole in- The authors wish to thank Région Rhône-Alpes and cluding positive and negative order, low position, f =1kHz (left). the Swedish Transportation and Communication Re- search Board (KFB) for their financial support. from a high order line source are compared with exact an- alytical solutions available for the radiation above totally soft surfaces (see Fig. 1). The good correspondance ob- REFERENCES tained for both low and high source positions proves this 1. Bécot, F.-X., Thorsson, P. J., and Kropp, W., “Noise prop- method to be reliable for the radiation from such sources. agation over inhomogeneous ground using an extended Secondly, to test the method for sound propagation above rayleigh integral method”, in Proceedings of inter.noise partially soft ground (Z finite and different from 0), a 2001, The Hague, The Netherlands, 2001. dipole pressure field is reproduced by the superposition 2. Chandler-Wilde, S. N., Hothersall, D. C. , “Efficient calcu- of two monopoles pressure fields, which were obtained lation of the green function for acoustic propagation above according to [2]. (Simulation of a source of higher order a homogeneous impedance plane”, Journal of Sound and than 10 would fail due to numerical limitations). Mathe- Vibration, 180, 705-724 (1995). matically, the obtained solution is equivalent to a dipole Experimental Investigations on Rijke Tube Y. Zhu, K. Liu, M. Chen, J. Tian

Institute of Acoustics, Chinese Academy of Sciences 17 Zhongguancun St. P. O. Box 2712Beijing 100080, P. R. China

To investigate the principle of thermoacoustic interaction, a series of experiments on a heat duct (Rijke tube) are studied. The influence of heat source location and temperature on the sound pressure and frequency in Rijke tube is provided. Besides the linear characteristics, the nonlinear phenomena in Rijke tube are presented, such as instantaneous character, heat source temperature saturation, and how the variation of inlet velocity, outlet acoustical condition, and outlet temperature affects the acoustic field in tube. The results show that the acoustic change in Rijke tube can be highly nonlinear.

INTRODUCTION occur only when the heater is located in a given region where 3cm aerodynamics, combustion and acoustics to 340C°. When the heat source temperature is 140C°, This paper presents the experimental results of the only even harmonic can be activated. By increasing the influence of heat source location, temperature on sound electric power, all the harmonics will be stimulated. In pressure and frequency. The nonlinear phenomena are the mean time, the oscillation frequency will rise. It also illustrated. shows that not only the intensity but also the frequency of sound is strongly dependent on heat source Experimental Apparatus temperature.

The Rijke tube is composed of a copper tube (55cm The instantaneous character of Rijke long) and an earthenware pipe, (40cm long) with an tube inner diameter of being both 5cm. They are connected by a nut. The pipe is held vertically. The heater is made Since the heater is in the tube and the top of the tube of heating wire winding on quartz cross. The diameter is closed, the convective air doesn’t exist. When the of the plane heated gauze is the same as the internal temperature of heater rises up to a constant, the cover diameters. The temperature of the heat source is is put off. Then the acoustic pressure oscillation will adjusted by a voltage regulator. The heat source is appear immediately. With the air flowing and the placed in the tube, attaching a pair of thermo-couples temperature decreaseing, the sound will attenuate, and which measures the temperature near the heat source. come to be silent finally. The frequency varies greatly This temperature is obtained from a thermometer. The according to different heater temperature. With V=50V, voltage, current, sound pressure level and sound L=12cm, and different heater temperature, the frequency are also measured. frequency spectrum which is measured at t=0 (first second to sound) is as below. EXPERIMENTAL RESULTS The frequency spectrum becomes abundant, when the temperature increases. When Tc=200C°, only even The characteristics of heater position harmonic can be stimulated. Along with the temperature rising, odd harmonic appears. When At the same voltage (the voltage V=99.6V, the electric Tc=240C°, the odd harmonics in frequency spectrum power W=371W), by changing the heat source are 30dB lower than the even harmonics in adjacence. location, the oscillation region can be obtained. At this The odd harmonics will not appear until temperature electric power, the thermo-acoustic oscillation will reaches a standard value. Therefrom, the odd At lower heater temperature, if some cold air is harmonics increase quickly, and the pressure level of blown to the tube outlet vertically, the sound will be every harmonic decreases in turn. But in this condition, suppressed at once. When cold air is blown again, the the sound pressure level of fundamental harmonic is oscillation will be stimulated. At high heater always a little lower than that of second harmonic. In temperature, when cold air is blown too, the oscillation this experiment, the second harmonic is the easiest to will stop for a while. Then the oscillation is excited be stimulated, and its pressure level is the highest. The again, but the temperature at the outlet will increase. frequency of fundamental and second harmonic is still Keep this for several times, and the temperature will in proportion to heat temperature. The second order rise until it reaches a constant, then it is maintained. harmonic frequency rises from 385Hz to 400Hz, with These phenomena are very interesting, but the reason the heater temperature increasing from 200C° to isn’t found. 400C°. This trend is the same as it in the steady state.

The influence of flow velocity on the 150 sound 100 When the electric power is settled, steady natural convection is established in the tube. Then the inlet Lp(dB) 50 area is changed. Due to restriction on flow, the sound 0 pressure level decrease, and the excitation of high harmonics are suppressed. Although the heater 2004006008001005120514051605 temperature is nearly the same, the sound pressure f(Hz) level and frequency spectrum change greatly. The fundamental harmonic frequency also decreases by Figure 1. frequency of maximum oscillation 5Hz. Greater intensity sounds are provided when the velocity is increased. But if the flow velocity is too 150 large, the acoustic oscillation will not be maintained. )

B 100

The heat source temperature saturation (d 50 The heat source is at 1/4 of the tube length. The 0 oscillation will be maintained with the heat source sound pressure level temperature increasing. But when the electric power 189199225 306343426 528 rises from 306W to 528W, the sound pressure level electric power will not rise accordingly, instead it will decrease a little. The saturation phenomena are that the sound Figure 2. heater temperature saturation pressure level does not increase with electric power in proportion. There is a maximum when heater is at a Conclusions given location. In order to investigate the mechanism of thermo- The influence of outlet condition acoustic oscillation and to provide a theoretical base for pulsating combustion, the influence of parameters A piece of sound absorbing material is placed near the on the sound pressure and frequency in Rijke tube is top of the tube, and the heat temperature is relatively studied experimentally. Some interesting nonlinear low. If the acoustic oscillation has been excited, the phenomena are observed and reported. absorption function can’t destroy the energy balance in the tube and suppress the instability. But if the initial REFERENCES condition is silent, the sound absorbing material will play an important role, and the thermo-acoustic 1. C.-C. Hantschk, D. Vortmeyer, “Numerical simulation of self- oscillation will not be established, even when the excited thermoacoustic instabilities in a Rijke tube”, J. Sound and Vibration, 277(3),511-522 (1999) heater temperature is the same. 2. S.Karpov, A.Prosperetti, “Linear thermoacoustic instability in The influence of the outlet temperature the time domain”, J. Acoust. Soc. Am, 103(6), 3309-3317 ,1998 Experimental study of the thermal sources contribution to the acoustic emission of supersonic jets

Y. Gervaisa, Y. Marchessea and H. Foulonb aLaboratoire d’Etudes Aérodynamiques, Université de Poitiers, 40, av. du Recteur Pineau, 86022 Poitiers, France bCentre d’Etudes Aérodynamiques et Thermiques, Université de Poitiers, 43 rue de l’aérodrome, 86036 Poitiers Cedex, France

An experimental investigation was conducted in order to determine the effect of jet temperature in supersonic jet noise. Jet velocities from 900 m/s to 1700 m/s and static temperatures from 330 K to 1110 K were used. Acoustic results (Acoustic power, directivity analysis) showed that heating the jet leads to a decrease of jet noise. In a second part, mean and fluctuating temperatures in jets are investigated. Therefore, a two beam Schlieren system based on the measurement of angular beams deflection across the flow is developed. The mean temperature is obtained by the Abel transform using the Gladstone approximation. Fluctuating temperatures are estimated by statistical processes on beam deflections. Finally the Schlieren method is successfully applied on jets approaching space launcher conditions.

Studies related to supersonic jet noise have received 150 considerable attention to reduce acoustic environment in the vicinity of space launcher. In the work described 145 here, we take an interest in the temperature dependence of jet noise. Therefore, in a first part, acoustic measurements (Acoustic power level, 140 directivity) carried out on two jets with the same jet velocity for different temperatures are introduced 135 (Table 1). Afterwards, mean and fluctuating temperature in the flow are measured in order to provide a better understanding of their influence. 130 OASPL (dB − Ref. 2e−5 Pa)

ACOUSTICS MEASUREMENTS 125 20 50 80 110 140 θ (°)

The experiments were performed on MARTEL facility FIGURE 1. Effects of temperature on directivity, (O),

[1] fit out with a 50 mm diameter nozzle designed to jet 1 (Ts=860 K) ; ( ), jet 2 (Ts=1110 K) provide a perfectly expanded jet for stagnations It appears that the noise radiated by jet 1 is more conditions Pi =30 Bar and Ti=1900 K (Jet 1 on table 1). important than the noise of jet 2 (Tab. 2) which Table 1. Jet test conditions. presents a higher temperature. Moreover, one notices Jet Vj (m/s) Ts (K) that this can be observed whatever the direction of 1 1700 860 observation (Fig. 1) except in the upstream direction 2 1700 1110 where the broadband shock associated noise is

dominant for the non perfect expanded jet. Far field sound pressure, directivity and acoustic power (Lw) have been measured with 12 microphones The effects of temperature are many-sided as it (ρ (1/4’’) located on semi circle (R=84D) centered on the influences the fluctuating stress Reynolds uiuj) and 2 nozzle exit. also the entropy fluctuating source (p-ρc0 ) in Lighthill’s stress tensor [2]. Nevertheless, our results Table 2. Acoustic Power Level. confirm that in the case of high exhaust speed, it Jet Lw (dB) mainly appears that the increased contribution of noise 1 124.9 due to entropy fluctuations source is compensated by 2 119.4 the decreased contribution from the Reynolds’s stress. 900 1100 120 120 b X=3D a 1000 c X=4D 800 100 100 X=6D 900 X=8D 700 80 80 X=10D 800 X=12D

600 60 60 700 d 600 (r) (K) 40 40 500 S M

500 R T(r) (K)

400 T 20 20 400

300 300 0 0 0 0.5 1 1.5 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 r/D 1 2 r/D r/D r/D FIGURE 2. Mean temperature, jet 1 (a) and jet 2 (b) ; Quadratic temperature, jet 1 (c) and jet 2 (d)

MEASUREMENTS OF MEAN AND theoretical values and profiles spreading out due to FLUCTUATING TEMPERATURE the extent of the mixing layer (Fig. 2.a and 2.b). Fluctuating profiles show that a peak appears in the middle of the mixing layer corresponding to a The temperature has been estimated with Schlieren maximum of turbulence (Fig. 2.c and 2.d). Quadratic optical method based on the measurements of angular temperatures estimated in jet 2 are more important deflections of two perpendicular crossed LASER beams than those measured in jet 1 because of the use of the through the flow (details of this method can be found same ratio of length scale in the two jets which is not in [3]). Mean transverse angular deflections may be adapted in jet 2. Unfortunately, none previous work written as an Abel’s integral of the form : propose value of these length scale.

∞

It appears that fluctuating temperature doesn’t greatly

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θ = − affect the noise level. Moreover, the role of mean

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¢ £ − ¤ − temperature is not certain. Indeed, the identification of the physical phenomenon at the origin of the where r and y denote radial and axial distances of experimental results is delicate. As one can’t separate LASER beam from the centerline and n the refractive the two contributions in Lighthill’s tensor, it is then index of the medium. An inversion of this relation difficult to conclude that the temperature influences allows an estimation of the refractive index and the first term while the second one remains unaffected.

temperature profile with Gladstone relation :

    

   

   −  = (2) ACKNOWLEDGMENTS where J is constant and depends on the flow This work was supported by CNES. characteristics. Quadratic temperatures may also be

estimated from a statistical process with the two



fluctuating longitudinal beam deflections θ  , θ and # # REFERENCES

" ζ ξ ! η, the turbulent length scales in the x, y and z directions: 1. H. Foulon, D. Gely, J. Varnier, E. Zoppellari and Y. Marchesse., MARTEL facility : Simulation of space

launcher aeroacoustic ambiance, 29 Nov. – 1 Dec. 1999, -

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+ ) ' ) ' -

( #

* 12 European Aerospace Conference (AAAF/CEAS). $ γ− $

. ξ

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+ ) ' ≈ θ θ (3) * π η ζ 2. J. Lighthill., On sound generated aerodynamically, Proceedings of the Royal Society of London, A211, pp. After a satisfactory validation was carried out in a 654-687 (1952). subsonic flow with classical thermocouple data, temperature are estimated on the two former jets (Fig. 3. M.R. Davis, Measurements in a subsonic turbulent jet 2). One notices axial temperatures similar to using a quantitative Schlieren technique, J. Fluid. Mech. 46(3), pp. 631-656, 1971. On the Use of the Divergence Theorem in the Derivation of Curle's Formula for the Amplitude of Aerodynamic Sound

A. Zinovieva

aDepartment of Mechanical Engineering, Adelaide University, North Terrace, Adelaide, 5005, Australia

Curle’s formula establishes that the amplitude of aerodynamic noise radiated by turbulent flow near solid boundaries depends upon the surface distribution of the total pressure in the fluid. In this work, the mathematical algorithm, used by Curle in the derivation of his formula, is analyzed. A new understanding of the use of the divergence theorem in this algorithm, different from the traditional one, is proposed. This new understanding leads to the conclusion that the amplitude of density fluctuations in the acoustic wave radiated by turbulent flow in the presence of a solid body depends on the surface distribution of density and its normal derivative rather than pressure. The new expression for the amplitude of density fluctuations is shown to take the form of the well-known formula, which claims that a potential field is a sum of three fields generated by three kinds of sources: volume distribution of sources, surface distribution of monopoles, and surface distribution of dipoles.

FORMULATION OF CURLE’S Lighthill in his famous work [1]. It describes the THEORY generation of sound by turbulence in volume V without boundaries. The second term in Equation (1) describes the Lighthill [1] and Curle [2] showed that the amplitude generation of sound that occurs in turbulent flow on of density fluctuations ρ − ρ in an acoustic wave 0 the solid boundaries S. It states that the sound is radiated by turbulent flow in the presence of solid generated by a layer of dipoles on the solid boundaries boundaries is determined by a sum of two integrals: and its amplitude is determined by the surface  ∂ 2 T ∂ P  distribution of the total pressure. Equation (1) can be ρ − ρ = 1 ij − i () 0  dy dS y  (1) considered the fundamental result of Curle’s work. 4πc 2 ∂x ∂x ∫ r ∂x ∫ r 0  i j V i S  According to Curle, the second term in Equation (1) ρ ρ where is the density of the fluid, 0 is the density can be simplified, if the following conditions are satisfied: of the fluid at equilibrium, c0 is the speed of sound in x >> λ, L << λ 2π , (4) the fluid at rest, r = x − y , x = ()x , x , x is the 1 2 3 λ coordinate of the observation point, y = ()y , y , y is where is a typical wavelength of the sound 1 2 3 generated, x is the coordinate of the observation point, the coordinate of the source point. and L is the largest dimension of the solid object. If the Tij is Lighthill’s stress tensor determining conditions (4) are true, the surface integral in Equation turbulence. (1) can be written as 2 ∂ T = ρv v + p − c ρδ , (2) 1 xi ij i j ij 0 ij F ()t , (5) 2 ∂ i where v is the i-th component of the velocity of fluid c0 x t i () where the i-th component Fi t of the total force particles, pij is the compressive stress tensor in the δ acting upon the fluid is determined by fluid, and ij is the Kronecker’s symbol. F ()t = P (y,.t )dS (y ) (6) P is determined by i ∫ i i S = − Pi l j pij , (3) Equations (5) and (6) represent the well-known where l are the direction cosines of the outward result of Curle. They state that sound generated by j turbulent flow on the surface of a small solid object ()= normal n from the fluid, i.e. l1 ,l2 ,l3 n ,and pij is has dipole characteristics and its amplitude is the compressive stress tensor in the fluid. proportional to the total force exerted upon the fluid by The first term in Equation (1) has been obtained by the object. Curle’s Use of the Divergence Theorem bounded by the surface S. Consequently, it is not sufficient to consider the surface S of the solid body in While deriving Equation (1) Curle [2] used the the surface integrals in Equations (7) and (8). Instead, divergence theorem to make possible the following the integration must be carried out over a surface transformations of volume integrals into surface enclosing all turbulence. integrals: The integral over such a surface can be evaluated as ∂ ∂ follows. If the size of the surface is large, there is no ∂  Tij 1 Tij dS()y  dy = l , (7) turbulence on the surface and the integral over the ∫ ∂y ∂y r ∫ i ∂y r V i  j  S j surface disappear and thevolumeintegralsin Equations (7) and (8) are equal to zero. ∂  1 dS()y T dy = l T , (8) As a result of the above consideration the second ∫ ∂y  ij r  ∫ j ij r V j   S term in Equation (1) will take the following form: where V is the total volume external to the solid  1 ∂ρ ∂ 1  boundaries and S is the surface area of the solid c 2  l dS()y + l ρ dS()y  (11) 0  ∫ i r ∂y ∂x ∫ i r  boundaries.  S i i S  Equation (11) shows that the amplitude of density fluctuations in a sound wave generated on the surface FORMULATION OF THE of a rigid body depends upon the surface distribution DIVERGENCE THEOREM of density and its normal derivative rather than pressure. Thus, Equation (5) will not hold and the Formulation of the divergence theorem with two amplitude of aerodynamic noise cannot be determined extensions and necessary proofs and definitions can be only by the force exerted upon the fluid by the object. found, for instance, in the book by Kellogg [3]. Equation (11) together with Equation (1) is a direct The divergence theorem can be written as: consequence of the well-known formula from the theory of potential [4], which establishes that the  ∂X ∂Y ∂Z   + + dV = ()X l + Y l + Zl dS ,(9) solution of a linear differential equation can be ∫ ∂ ∂ ∂  ∫ 1 2 3 V  x y z  S represented as a sum of three potentials: a) potential of or, alternatively, a volume distribution (Lighthill’s solution); b) div F()r dV = F ()r ⋅ n ⋅ dS, (10) potential of a simple layer, or a layer of monopoles, ∫∫ (first term in (11)); c) potential of a double layer, or a VS where V is the volume of a regular region of space layer of dipoles, (second term in (11)). According to Curle’s theory, the term describing the bounded by a surface S, F = ()X ,Y, Z , functions X, Y layer of monopoles vanishes due to the boundary and Z are continuous in V and have partial derivatives conditions on the surface of a solid immoveable of the first order which are continuous in the interiors object, and the sound radiated has dipole of a finite number of regular regions of which V is the characteristics. However, it needs to be noted that sum, and the volume integral in the left-hand part of investigation of the properties of the sound determined Equation (9) is convergent. by Equation (11) is outside the scope of this work. A set of points is said to be bounded if all its points lie in some sphere. Equations (7) and (8) can be shown to take a form ACKNOWLEDGMENT equivalent to (9). Differentiation is carried out with respect to the source point y . The author is grateful to Professor Colin H. Hansen for his support and encouragement. A VIEW OF THE DIVERGENCE THEOREM IN CURLE’S WORK REFERENCES

A common case where a solid object is surrounded 1. Lighthill, M. J., Proc. Roy. Soc. A, 211,564–586 by a fluid with turbulent flow is considered below. It is (1952). assumed that turbulence occupies a finite region of 2. N. Curle, Proc. Roy. Soc. A, 231, 505 – 514 (1955). space. The volume integrals in Equations (7) and (8) can be 3. O. D. Kellogg, Foundations of the Potential Theory, evaluated in the following way. As stated above, for Berlin, Verlag von Julius Springer, 1929 pp. 84 – 121. the divergence theorem to hold the volume V must be 4. G. A. Korn and E. M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill, 1968, p. 488.

On the Use of Linear and Non-linear Source Terms in Aeroacoustics - A Comparison of Different Approaches

Ricardo E. Musafir

School of Engineering & PEM/COPPE – Universidade Federal do Rio de Janeiro C.P. 68503, Rio de Janeiro, 21945-970, Brazil [email protected]

The equations of Lighthill, Lilley and Howe are compared with respect to the use of terms linear and non-linear in the fluctuations. It is shown that apparent inconsistencies are due to the fact that the forms of the equations normally used correspond to different levels of approximation, having thus different ranges of application. It is important that this be properly considered when choosing the equation to model a particular problem.

INTRODUCTION EQUATIONS AND SOURCE TERMS

A marked difference between the successful Lighthill’s equation can be written aeroacoustic approaches of Lighthill [1], Lilley [2] and 2 2 2 Howe [3] is the use made of terms linear and non- ∂ ρ/∂t − ∇ p = ∇.∇.(ρvv) (1) linear in the fluctuations. Lighthill’s analogy, in its ρ original form, is given by a linear equation with a where is density, p is pressure and v is velocity. The source function containing terms linear and non linear source term above involves linear and non-linear parts, in the fluctuations. Being based on the equation for an usually called – density fluctuations neglected – shear homogeneous medium at rest, the equation is generally and self noise terms, respectively. Some of the source valid although, unless direct simulation is intended, it density fluctuations, however, refer to convection of cannot be solved without the introduction of sound waves by the mean flow and are relevant if the simplifications in the source function, which amounts equation is to be transformed into a convected wave ρ∂ ∂ ∂ ∂ to abandoning propagation effects which are hidden equation. The linear term 2 Ui/ xj uj/ xi, where U is therein. Lilley’s equation is based on the identification the mean and u the fluctuating part of v, includes, even of source terms as those involving non-linear for constant density, interaction of the sound field with interaction of fluctuating quantities, while linear terms the mean flow. are associated with sound propagation. Although the Lilley’s equation is obtained when all variables are source identification scheme is independent on mean decomposed into mean and fluctuating parts (which flow assumptions, the assembling of a wave equation will be noted, except for v, by the suffix 0 and primes, with these properties is possible only if the mean flow respectively) and all linear terms are transferred to the is no more complex than a parallel shear flow. Howe’s left side. A relevant step in its derivation is equation, on the other hand, chooses to define as 2 –1 [D0 {(ρc ) D0 p/Dt}/Dt – ∇.(∇p/ρ)]’ = sources the terms involving vorticity and entropy inhomogeneities. As a consequence, both sides of the ∇.∇.(uu)’ + ∇.(u.∇U) + ... (2) equation, which, as Lighthill’s, is generally valid, present terms linear as well as non linear in the where D0/Dt = ∂/∂t + U.∇, c is sound speed and fluctuations. This, of course, generates a difficulty to ∇ p0 = 0 was assumed. The omitted terms, –∇.(u∇.u)’ its solution, which is usually faced by linearizing in the 2 and [–D0 {u.∇p/(ρc )}/Dt]’, refer to the interaction of fluctuations the wave operator and, frequently, also the sound with turbulence and can be neglected. The linear source function. Thus, in practical terms, one is left term on the right side can be eliminated with the use of with the picture of three linear wave equations with the momentum equation, yielding, in turn, linear and forcing functions sometimes described by both linear non-linear components. A linear wave equation with an and non-linear terms, or, instead, exclusively by one exclusively non-linear source function can be obtained type or the other. In what follows, the differences in only if the mean flow is, at most, a parallel shear flow. these approaches will be examined. For simplification, In this case, the resulting equation for the logarithmic an inviscid isentropic flow will be assumed. 2 pressure π, defined by dπ = d p/(ρc ), is third order. Only if there is no mean shear a second order equation

with this property can be obtained. mean flow than Lilley’s. Howe’s equation is based on the equation for the The fact that, in a free shear flow, the homogeneous time derivative of the velocity potential φ, in an form of Lilley’s equation is satisfied to first order in irrotational homoentropic mean flow (a situation for the fluctuations supports the idea of second order terms which all field variables can be written in terms of φ). as responsible for sound generation in this case [2, 6, An intermediate step in its derivation is 7]. In the presence of solid boundaries, however, the first order coupling of vorticity and sound modes gives ∂ [(ρc2)–1 Dp/Dt]/∂t – ∇.(∇p/ρ) = ∇.(v.∇v) rise to linear source terms [7]. The fact that Howe’s formulation is employed preferably for problems = ∇.(w x v) + ∇2|v|2/2 (3) involving surface generated vorticity justifies then the where w = ∇ x v. use of the linear source term only. For free flows, In order to have the chosen dependent variable, the however, the non-linear terms would have to be stagnation enthalpy B = h + |v|2/2, where h is the included. enthalpy, in the first term on the left, one has to add to That approximations in Howe’s equation can be (3) derivatives of a multiple of the momentum tricky can be exemplified with Mohring’s exact form equation, what answers for refraction-like terms, of the equation, which, for homoentropic flows, is [8] containing the factor c-2 Dv/Dt, in both sides of the -2 resulting equation. Alternative approaches, where this ρD(c DB/Dt)/Dt – ∇.(ρ∇B) = ∇.(ρw x v) (5) factor is replaced by –∇h/c2 or –∇ρ/ρ, have been derived by Doak, Mohring and Musafir, having been Since equation (5) is, in the appropriate limit, ∇ ρ∇ 2 ∇ ρ discussed in [4]. Although Howe’s equation is equation (1) with .[ |v| /2 + v .( v)] shifted to the generally valid (as are the alternative ones), it is left side and, for homoentropic flows with no external ∇ρ ∇ 2 = ρ -2 usually not employed in a form more complex than sources, = p/c – c Dv/Dt, one can conclude that density fluctuations were not completely removed -2 2 2 2 c0 D0 B/Dt – ∇ B = ∇.(w x v – T ∇S) (4) from the source function in Howe’s approach, persisting still in the terms containing c-2Dv/Dt. where T is temperature, S is entropy and all non-linear The analysis shows that the forms of the equation of terms in the operator, as well as the terms containing Lilley and Howe normally used correspond to different c-2Dv/Dt, have been neglected. In most applications the levels of approximation and so, cannot be strictly source function is also linearized in the fluctuations, compared. Howe’s equation seems to be closer to being frequently reduced to ∇.(w’ x U). The relevance Lighthill’s than is usually thought. The choice of the of the entropy terms is discussed in [4, 5]. Indeed, it is equation to be used in a particular problem must rely frequent to neglect altogether convection effects in the on the satisfactory degree of approximation. This operator, the equation being then effectively reduced to suggests that different equations will always coexist in Lighthill’s equation with the density removed form the Aeroacoustics. source function (or, actually, taken as constant therein). REFERENCES DISCUSSION 1. Lighthill, M. J., Proc. Royal Soc. London, A211, pp. 564-587 (1952). Equations (2) and (3) can be seen as different stages in 2. Lilley, G.M., Lockheed Georgia 4th Month. Progr. the process of obtaining a convected wave equation by Report, Contract F-33615-71-C-1663, Appendix, 1971. shifting parts of the source term in (1) to the left side. 3. Howe, M. S., J. Fluid Mech. 71(4), pp. 625-673 (1975). The approximation leading to equation (4), for the 4. Musafir, R.E., “On the Use of the Stagnation Enthalpy case of a uniform mean flow, makes Howe’s operator as an Acoustic Variable”, in Proc. 7th Int. Congr. Sound basically identical to the corresponding form of and Vibration, edited by G. Guidati et all., Garmish- Lilley’s, although the right hand side, in the former Partenkirchen , 2000, pp. 1275-1282. equation, contains linear terms, while in the latter it is 5. Aurégan, Y., Starobinski, R., J. S. V. 216(3), pp. 521- 527 (1998). given in terms of quadratic quantities only. A partial 6. Goldstein, M.E., Ann. Rev. Fluid Mech. 16, pp. 263-285 explanation is that, while Lilley’s equation holds to (1984). second order in the fluctuations (it can be shown, by 7. Goldstein, M.E., Aeroacoustics, MacGraw-Hill, N.Y., changing the dependent variable to π + π2/2, that the 1976. combined effect of the neglected second order terms is 8. Mohring, W., Obermeier, F. “Vorticity, the Voice of actually of third order [6]), the approximate Howe’s Flows”, in Proc. 6th Int. Congr. Sound and Vibration equation (4), holds only to first order. Being less edited by Finn Jacobsen, Coppenhagen, 1999, pp. 3617- ‘exact’, however, it is subject to less restrictions on the 3626.

Analysis of Sound Filed of Ultrasonic Transducer in Air with Temperature Variation by FDTD

N.Endoh, Y.Tanaka, and T.Tsuchiya

Department of Electrical, Electronics and Information Engineering, Kanagawa University, 221-8686 Yokohama, Japan [email protected].

The Finite Difference Time Domain (FDTD) method is proposed for calculation of acoustical characteristics of an ultrasonic transducer in air. An aerial-sonar projected a 40kHz pulse sound whose pulse-width was about 0.15ms. The sound pressure field of sonar was calculated in constant temperature of 30 degrees. We also calculated sound pressure field in air with temperature variation of 20 degrees. There was little difference between these two contour patterns. FDTD method enabled the visualization of propagation pulse projected from the transducer as a function of propagation time. The reflected echo signals from the target were also calculated as a function of its height. The amplitude and propagation time of the reflected pulse changed a little with temperature variation. These results show the validity of the FDTD method.

INTRODUCTION propagates in x-direction, substitutions of two An aerial-sonar for an automobile is very useful to equations into Eq. (1) yields the next equation detect the object in the rear of a car. In this paper, the R 22P . Finite Difference Time Domain (FDTD) method [1] is  /jP 0 (4) R 22 2 proposed to calculate the propagation of sound in air. xc c0 The recent development of computer system enables 
 PP012exp j ( j ) x (5) the FDTD to be applied in the acoustics.[2] To   confirm the validity of the FDTD, the sound pressure where P0 is the constant and 1 and 2 are the wave number and attenuation constant, respectively. The field of sonar was calculated in constant temperature velocity of sound c and resistance coefficient are of 30 degrees when the 40kHz pulse was projected. A 
series of propagated pulse waveforms were obtained obtained where is angular frequency: because the FDTD was capable of calculating the c
/ 22 (6) instantaneous sound pressure along the propagation of 12 2 pulse. The reflected echo signals from the target were 
12 c (7) also detected in air with temperature variation. 22 12 The finite differential equations are obtained as a function of discrete positions x, y in space and a FDTD CALCULATION METHOD discrete time t as shown below. [3] Wave Equation for FDTD The basic equations of the FDTD method, which is taking account of attenuation, are given as follows: RR Rv 1 pvx y nn
1 nn

1/ 2 1/ 2  (1) pij(, )
p (, ij )
C [(1/2,)(1/2,)vi
 jvi j ctxy2  RRR px x

nn

1/ 2 1/ 2 RR vijyy(, 1/2) vij (, 1/2)], vpx v (2) nn
1/2 1/2 nn x vij(, 1/2) Cvij (,  1/2) Cpijpij!1 (,  1) (, ) , RRtx yvyv12#3 vinn
1/2(1/2,) jCvi 1/2 (1/2,) jCpijpij!1 nn (1,)  (,), R R xvxv12#3 vy p v (3) 2 y where Cc
 tx/ . RRty p where p is sound pressure, v is the particle velocity,  In these equations, superscripts show the time and i is the density and t is time. The second part of the and j are the grid-numbers in the x and y directions in right hand side in Eqs. (2) and (3) show an attenuation space, respectively. For simplification, x = y. In of the medium. If the only plane sinusoidal wave this paper, the resistance coefficient  that is proportional to the particle velocity is ignored because FIGURE 2. Received waveform. (Height of object is 0.2m, of low attenuation in air. 0.4m and 0.7m from top to bottom) Calculation Results 0.7 The FDTD method calculated the sound field in air 0.5 changing the sound velocity from 349 to 361m/s. A sound source placed at 50cm above the earth projected 0.3 a pulse sound of 40kHz. Target was at x=1.5m. We Height[m] 0.1 decided that the increments in space x=y=0.8mm and in time t=0.8 s for obtaining accurate results. 0.0 0.5 1.0 1.5 2.0 To eliminate the reflection wave from the outer 0.7 boundary of the calculation space, Mur’s first order 0.5 absorbing boundary conditions were provided. The contour patterns were almost the same in various 0.3 temperatures from 30 to 50 degrees. Figure 1 shows Height[m] 0.1 the propagating sound to and from the target in constant temperature of 30 degrees. It is clearly shown 0.0 0.5 1.0 1.5 2.0 that there are not only direct and reflected echo pulses 0.7 but also diffracted wave behind the target. Figure 2 0.5 show the receiving echo signals of the target as a function of its height. There is always the same echo 0.3 pulse at t=10.2ms from the corner of the target and the Height[m] 0.1 earth. The first echo from the upper-left corner of the target increases with its height. The amplitude and 0.0 0.5 1.0 1.5 2.0 propagation time of the echo pulse changed a little Range [m] with temperature variation. The maximum amplitude of the first echo decreased with temperature. When FIGURE 1. Snapshots of sound propagation.
(3.2ms, the temperature was 50 degrees, traveling time to and 4.8ms and 5.6ms after radiation of the pulse sound) from the target became 0.1ms shorter than at 30 degrees.

CONCLUSION 0.2 The FDTD method calculated the acoustical 0.2m characteristics of an aerial-sonar. It projected a 40kHz 0.0 pulse whose pulse-width was about 0.15ms. The sound pressure field of sonar was almost the same in -0.2 various temperatures from 30 to 50 degrees. We also 0.2 calculated the reflected echo signal from the target as a 0.4m function of its height. The amplitude and propagation 0.0 time of the reflected echo pulse changed a little with temperature variation. These results show the validity -0.2 of the FDTD method. 0.4 0.7m Amplitude[arb.] 0.2 ACKNOWLEDGMENTS The authors wish to thank Professor T.Anada at Kanagawa university for his useful and constructive 0.0 comments.

-0.2 REFERENCES

-0.4 1. K.S.Yee, K.Shlager and A.H.Chang, IEEE Trans. Ant. Prop., 14, 302 (1966) 9.8 10.0 10.2 10.4 10.6 2. R.A.Stephen, J. Acoust. Soc. Am. 87, 1527 (1990) 3. N.Endoh, F.Iijima and T.Tsuchiya, Jpn. J. Appl. Phys. 39, 3200- Time[ms] 3204 (2000) Numerical calculations of sound propagation over ground surfaces O. Kr. Ø. Pettersena, V. Henriksena, M. Bjørhusb,d, U. Kristiansenc, G. Taraldsena

aSINTEF Telecom and Informatics - Acoustics, 7465 Trondheim, Norway bSINTEF Applied Mathematics - Numerical Simulation, 0314 Oslo, Norway cInstitute of Telecommunications - Acoustics, NTNU, 7034 Trondheim, Norway dTTYL, 0212 Oslo

The purpose of this study has been to develop a numerical model for sound propagation in both air and ground over long distances. A set of partial differential equations (PDEs) for wave propagation in a porous medium with a rigid frame has been used. By introducing Chebyshev spectral collocation in the spatial variable the equations have been transformed to a set of ordinary differential equations (ODEs) in time. Domain decomposition is used to divide the computational domain into sub domains of manageable sizes. The time integration is performed by a second order explicit Runge-Kutta method. Spectral collocation can only be used if the computational domain is a square of a certain dimension. To be able to calculate sound propagation in complex shaped domains a mapping is performed from the physical coordinates to the coordinates of a square domain. An approximation to the exact open boundary condition is introduced at the outer boundaries of the computational domain. Simulation results are compared to analytical results, calculations done with a Nordic calculation model and results from outdoor measurements.

RU RU RU THE DIFFERENTIAL EQUATIONS  A  A  CU
0 (5 ) Rt 1 Rx 2 Ry Sound propagation in a porous medium with a rigid frame is modeled by Eqs. (1) and (2). The vector U is defined by U = [u v p] with u and v being the horizontal and vertical particle velocity Rv p  ρ>  Rv
0 (1) components and p the air pressure. Through the Rt introduction of spectral collocation in the spatial Rp variable a discretization in space is achieved. This  ρ>c>2  v
0 (2 ) Rt means that the PDEs are transformed to ODEs in time.

R 1 R Here p is the air pressure, v a vector containing the u  D p  u
0 (6 ) particle velocity components and R the flow resistivity. Rt ρ> x ρ> Furthermore is ´ the equivalent density and c´ the R  1  R
equivalent sound speed for the porous medium and v D yp v 0 (7 ) Rt ρ> ρ> they are given by Eq. (3) and (4) respectively. R  > >2

p ρ c D xu D y v 0 (8 ) ρ k Rt ρ'
0 s (3 )  The matrixes Dx and Dy are the derivative matrixes in c c'
(4 ) the two spatial directions (see [1] for more details ks about derivative matrixes). The velocity components and pressure values at the discretization points, which are called collocation points in spectral collocation, are Here is 0 the air density, ks the structure factor,  the porosity and c the sound speed. contained in the matrixes u, v and p. The ODEs are integrated using a second order Runge-Kutta method.

SPECTRAL COLLOCATION DOMAIN DECOMPOSITION For a two dimensional Cartesian coordinate system Eqs. (1) and (2) can be written as Eq. (5). Domain decomposition is introduced to be able to calculate sound propagation over long distances. The computational domains are divided into a set of smaller non-overlapping subdomains. All subdomains contain 345 only air or ground and are in a sense homogenous. To 344.5 ensure satisfaction of the differential equations on the 344 boundaries between subdomains, a correctional method 343.5 is introduced. In this method the boundary values are Power 343 0.013 corrected between each timestep in the Runge-Kutta spectral 342.5 density time integration. These corrections are calculated on 342 of source the basis of the physical boundary conditions, Sound speed in m/s 341.5 signal continuous normal particle velocity and air pressure, 341 and implemented via characteristic boundary 340.5 0 conditions [2, 3]. 340 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 Frequency in Hz

OPEN BOUNDARIES Figure 1. Sound speed between 5 and 80 meters from the source.

In order to reduce reflections from the outer boundaries 15 of the computational domain, an approximation to the 14 exact open boundary conditions is implemented at the outer boundaries. The implemented approximation is a 13 low order approximation, but it gives very good results for normal incidence. 12 Damping in dB in Damping 11

MAPPING OF DOMAINS 10

9 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 A mapping of non-square domains is performed in Frequency in Hz order to be able to calculate sound propagation over different terrain profiles. In this mapping the physical Figure 2. Damping between 5 and 80 meters from the coordinates of the domain is mapped onto a square. source. This leads to a transformation of the spatial variables. Results from simulation where ground surfaces are introduced show equally promising results. Some of NUMERICAL EXPERIMENTS these results will be given in the oral presentation. See also [4] for more results. Some numerical experiments were performed in order to test the proposed model. A two dimensional computational domain with 66 subdomains (3x22) and REFERENCES the dimensions 15x110 meters (height x length) was used. In each subdomain 51 collocation points were 1. Canuto, C., Hussaini, M. Y., Quarteroni, A. and Zang, T. A., used in each spatial direction. This means a resolution Spectral methods in fluid dynamics. Springer-Verlag, New of 3.44 points per wavelength for a 1000 Hz signal. A York, 1988, pp. 68-70. 2. Bjørhus, M., SIAM J. Sci. Comput., No. 16, May 1995, pp. point source was implemented by trigging one 542-549. collocation point with an air pressure that varied with 3. Bjørhus, M., A computational model for outdoor sound time. A bandlimited signal between approximately 100 propagation. Part II: A spectral collocation method, SINTEF and 850 Hz was radiated from this point source. The Report STF42 A00XYZ, SINTEF Applied Mathematics, power spectral density of this signal is shown in Fig. 1. Norway, 2000, pp. 11-13. 4. Henriksen, V., Numerical calculations of sound propagation The sound speed and damping of the signal in free over ground surfaces, Diploma Thesis (in Norwegian), NTNU, field was calculated from a simulation with only air 2000. domains. The sound speed between 5 and 80 meters from the source is shown in Fig. 1. The damping of the signal over the same distance is shown in Fig. 2. The results are in good accordance with the expected sound speed and damping of 344 m/s and 12dB within the frequency band of the signal (100 to 850 Hz). Analytical Prediction of Aeroacoustic Cavity Oscillations D. B. Bliss, L. P. Franzoni, and M. A. Cornwell

Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC, USA

High-speed flow over cavities in vehicle surfaces can produce intense tonal pressure fluctuations. This problem has been of concern for decades, especially for aircraft, but the underlying physical mechanisms have not been well understood. A fairly simple analytical model has been developed that improves understanding of the oscillation mechanisms in shallow rectangular cavities. The model describes the phenomenon, and gives reasonable agreement with experimental data. The analysis is constructed from waves that exist in a system having a finite thickness shear layer dividing two acoustic media, one at rest and one in motion. The wave types can be interpreted in physical terms. The shear layer thickness has an important effect on the speed of convective waves. Only two convective waves and three acoustic waves suffice to represent the basic phenomenon. Mass addition and removal at the rear bulkhead due to shear layer oscillation plays an important role in the process. Conditions on energetics and shear layer motion at the rear of the cavity must be satisfied simultaneously for the oscillation to occur.

INTRODUCTION from the front bulkhead and also excite convective disturbances on the shear layer. The oscillation is As shown in Fig. 1, high-speed flow over cavities sustained because these aeroacoustic waves and the or cutouts in vehicle structural surfaces frequently shear layer convective waves interact with each other produces intense tonal pressure fluctuations. The and the cavity boundaries, in particular at the trailing high pressure levels can jeopardize the integrity of edge, in such a way as to draw energy from the mean nearby structural components, internal stores, and flow. sensitive instrumentation. Refs [1,2] describe the The present study was inspired by the analytical phenomenon and propose a physical explanation of approach suggested in Refs [1,2], but only now the oscillation mechanism. A semi-empirical formula carried to completion. This relatively simple analysis for resonance frequencies has been developed [3]. method has been refined, and an important model for Model studies and flight tests have provided shear layer structure has been added. The results information about the relationship of geometric and exhibit the physical behavior of cavity oscillations, aerodynamic variables to the aeroacoustic and there is good agreement with data, especially for phenomenon. Recently, CFD methods have provided supersonic flow. The most important aspect of the simulations of the oscillation phenomenon [4,5]. results is that they provide physical insight into the Nevertheless, the underlying physical mechanisms primary wave mechanics of the oscillation remain not well understood. The development of mechanism, and emphasize the important role of simple but effective means to reduce unsteady mass addition and removal at the cavity trailing edge. pressure levels continues to be a major challenge, especially given constraints on cavity geometry and FORMULATION size restrictions on suppression devices. The analysis is based on the various harmonic UA MA trailing edge mass addition wave solutions that can exist for a 2-D acoustic and removal shear layer domain of infinite extent above a rigid boundary and LE TE below an idealized shear layer. Above the shear D waves layer is a high-speed compressible flow, see Fig. 2.

L UA damping  0 MA FIGURE 1. High-speed flow over a shallow cavity.   H A (z)ei( t- x) z

The oscillation occurs because disturbances on the shear layer
shear layer impinge on the trailing edge, causing -A x +A unsteady mass addition and removal at the rear waves D bulkhead. This effect appears much like an oscillating pseudo-piston at the rear bulkhead, producing waves that propagate forward in the cavity FIGURE 2. Infinite shear layer dividing moving and and also radiate to the exterior. The waves reflect stationary acoustic media for wave analysis. Governing equations are solved in the acoustic UA MA Kutta Condition region (wave equation), the compressible flow region  shear layer (convective wave equation), and the shear layer TE LE trailing edge region. Extending Ref.[6], the shear layer is analyzed D waves mass addition it and removal Satisfy Ue modeled by in an idealized form, as a linear Mach number profile, BC's with disturbances governed by the compressible pseudo-piston L Euler equations (inviscid, rotational flow). All waves FIGURE 3. Assembling the cavity from waves are isentropic, with uniform sound speed. satisfying the appropriate boundary conditions. The compressible flow region requires special treatment to identify the physically realistic solutions RESULTS that have only outward radiation. A rigid boundary is placed above the compressible flow at H, far from the For two cases, each given an assumed frequency, shear layer. The convective wave equation is Figure 4 shows that realistic pressure mode shapes modified to include a small amount of damping, . are predicted for a cavity having L/D = 4. At the assumed frequencies, the real part of pseudo-piston For very small damping, as H A, the reflected impedance is plotted versus L/D in Figure 5. The waves from the upper boundary become negligible. large negative real part around L/D = 4 shows that a In each region, harmonic pressure wave solutions   maximum amount of energy is extracted from the p = P(z)ei( t- x) are found. At each interface, the free stream flow to drive the trailing edge mass pressure and normal velocity are matched, giving sets addition and removal process at this L/D. Figure 6 of homogeneous equations for the pair of arbitrary shows the corresponding trailing-edge shear layer constants associated with P(z) for each region. These deflections versus L/D. Maximum deflections are equations are expressed in matrix form. The obtained around L/D = 4. Overall, these results show determinant gives a transcendental dispersion relation    that the frequencies are correctly chosen for L/D = 4. D( , ) =0 relating real frequency to complex There is also reasonable agreement with experiment. wavenumber =  R + i I . Contour plots of the P/P magnitude of D(,) are used to locate the zeros in LE P/PLE the complex -plane. The roots are strongly dependent on frequency and Mach number. Roots associated with vorticity convection also depend Mach 1.2 Mach 2.0 strongly on shear layer thickness . Mode 1 x/D Mode 2 x/D Typically five roots play the most important role FIGURE 4. Typical pressure modes for L/D = 4. in cavity oscillations: a conjugate pair of amplifying 1 0.8 Real Impedance and decaying acoustic waves propagating upstream 0.6 0.5 versus L/D Real Impedance 0.4 under the shear layer; a conjugate pair of amplifying 0 versus L/D 0.2 and decaying vorticity convection waves propagating -0.5 0 -0.2 downstream on the shear layer; and a real-valued root -1 Mach 2.0 Mach 1.2 -0.4 -1.5 Mode 1 Mode 2 having fast acoustic propagation downstream. The -0.6 remaining infinite set of roots are higher acoustic 0 1 2 3 4 5 6 0 1 2 3 4 5 6 modes in the z-direction under the shear layer. At FIGURE 5. Pseudo-piston impedance versus L/D. lower cavity oscillation frequencies, these roots are 0.8 1.4 Mach 2.0 TE Shear Layer Mode 2 Displ. vs L/D evanescent, having small real parts and imaginary 0.6 1.2 parts that are integer multiples of . As frequency 1 Mach 1.2 0.4 Mode 1 increases, the smaller of these roots become 0.2 0.8 TE Shear Layer Displ. vs L/D propagating waves with higher mode structure. 0.6 0 The solution is assembled by summing waves to 0 1 2 3 4 5 6 0 1 2 3 4 5 6 satisfy boundary conditions at points in the cavity, as FIGURE 6. TE shear layer deflection versus L/D. shown in Fig. 3. The Kutta condition is applied at the leading edge, normal velocities must vanish on the REFERENCES front bulkhead, and normal velocities equal the 1. H. Heller and D. Bliss, Progress in Aeronautics pseudo-piston velocity at the rear bulkhead. A linear and Astronautics, MIT Press, 45, 281-296 (1976). system is then solved for the wave amplitudes. The 2. H. Heller and D. Bliss, USA AFFDL, TR-74-133. pressure on the cavity floor was calculated, along 3. H. Heller, et al, USA AFFDL, TR-70-104 (1970). with the mechanical impedance of the pseudo-piston, 4. N. Sinha, et al, AIAA Paper 2000-1968.(2000). and the trailing edge shear layer deflection. Using 5. C. Rowley, et al, AIAA Paper 2000-1969 (2000). only the five basic roots typically gives good results. 6. Williams, et al, AIAA J.,15, No.8, 1159-66 (1977)

Statistics of the meteorological conditions favourable to propagation according to the three definitions K. Rudno-Rudziński

Institute of Telecommunication and Acoustics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50370 Wrocław, Poland, [email protected]

Frequencies of the meteorological condition favourable to propagation according to the definitions of CONCAWE, ISO and NMPB were compared. Territories in Poland in different climate zones were chosen, in day and night time. Polar graphs of the conditions favourable to propagation show a lot of variability caused by the differences in the definitions. Variability caused by these differences is stronger than the one coming from the climate and the direction of propagation influences.

INTRODUCTION STATISTICS

The three classifications of meteorological condi- The calculated frequencies (percent) of the CFTP tions are likely the most popular in environmental versus the direction of propagation are shown on the acoustics: CONCAWE [1], ISO [2] and IMPB [3]. The radar graphs with the angular resolution of 30o. aim of this work was to compare the statistics of the Frequencies for the day time and the night time are conditions favourable to propagation (CFTP) accord- shown on the Figure 1 and Figure 2 for Wrocław sta- ing to above mentioned definitions. tion as an example. Graphs of CFTP for the ISO defi- nition correspond to the smoothed wind rose (180° re- DEFINITIONS versed). Frequencies according to CONCAWE are higher than to ISO, for the day and the night. For all In the ISO definition the wind velocity and direction definitions, frequencies according to NMPB are lowest decides that the conditions are favourable. In the re- for the day and highest for the night. Such a regularity maining two the atmospheric stability is the second occurs in the all stations. main factor besides of the wind. In CONCAWE the Pasquill classification and the wind velocity compo- nent in the direction of propagation are used, in the CONCAWE ISO NMPB NMPB some practical stability classes are employed 0 together with the wind velocity and direction. In spite Wrocław day of some similarity in wind and stability classes, there 40 330 30 are differences between CONCAWE and NMPB in 30 joining them in the outcoming classes of propagation conditions. 300 20 60 ANALYSED DATA 10 Meteorological observation from the three stations lying in different climatic region were chosen for this 270 0 90 research (Table 1)[4]. The data set contains the results of observation made in three-hour cycles during the one whole year. Only the observations with the wind below 5 m/s were included (67 % in Łeba, 76 % in 240 120 Warszawa and 85 % in Wrocław). Table 1. Three meteorological stations 210 150 Localisation Main climate influences Wind rose type 180 Łeba seaside breeze Warszawa continental bipolar FIGURE 1. Percent of CFTP for Wrocław in the day time Wrocław oceanic uniform according to the three definitions. Table 2. Difference between maximum and minimum fre- CONCAWE ISO NMPB quency and between the mean frequencies for night and day

0 max-min max-min mean (night)- Wrocław night station method 70 (day) (night) mean (day) 330 60 30 CONC 20,1 24,8 -2,0 50 Łeba ISO 12,7 25,2 0,0 40 NMPB 10,7 15,8 41,2 300 60 30 CONC 10,1 7,5 7,5 20 Warszawa ISO 13,8 9,7 0,0 10 NMPB 11,3 10,0 39,8 270 0 90 CONC 3,2 21,2 7,8 Wrocław ISO 14,9 22,5 0,0 NMPB 12,8 13,0 34,4 240 120 The difference between mean frequency of the CFTP for the night time and the day time equals to zero for 210 150 ISO definition, ranges from –2 to 7,8 % for CON- CAWE and from 34,4 to 41,2 % for NMPB. 180 The difference between the maximum frequency and FIGURE 2. Percent of CFTP for Warsaw in the night time the minimum frequency of the CFTP (for all the according to the three definitions. propagation directions in a given location) ranges from 3,2 to 24,8 %. Figure 3 shows frequencies of the CFTP conditions CONCLUSIONS according to NMPB for three stations, for the day (in- side) and for the night (outside). The difference between mean frequency of the CFTP Table 2 shows the difference between the maximum and for the night time and the day time equals to zero for the minimum frequency and between the mean frequencies for night and day. ISO definition, ranges from –2 to 7,8 % for CON- CAWE and from 34,4 to 41,2 % for NMPB. Łeba Warszawa Wrocław In the case of ISO definition the obvious reason of the lack of the difference between day and night is the NMPB 0 neglect of the atmospheric stability. 70 The lack of the difference in frequency of the CFTP 330 60 30 between night and day indicates the same outdoors night 50 noise attenuation what is inconsistent with the experi- 40 ence. 300 60 30 From this point of view, NMPB gives likely the best 20 classification method for the meteorological conditions of sound propagation outdoors. 10 Additional calculations indicates that CONCAWE 270 0 90 could be corrected to better differentiate day and night conditions, maintaining precision of wind velocity day quantification resulting from wind vector. 240 120 REFERENCES

210 150 1. K. J. Marsch, Appl. Acoustics, 15, 411-428 (1982) 2. Bruit des infrastructure routiere - methode de calcul 180 incluant… CERTU, CSTB, LCPC, SETRA (1997) 3. ISO 1996, 9613 4. K. Rudno-Rudziński, Meteorological conditions of sound FIGURE 3. Percent of CFTP according to NMPB for the propagation outdoors in Poland, in Proceedings of the three stations in the night time and the day time. Sixth ICSV, Techn. Univ. of Denmark 1999, pp.749-756 Split Mufflers for Improved Aerodinamic for Ventilation Systems

O.V.Plitsina, V.T.Plitsin, M.N.Kucherenko

Togliatti Polytechnical Institute, Belorusskaya 14, 445667 Togliatty, Russia

Split mufflers suggested by the authors provide equal wide-band noise reduction in air conduits of large cross-section, have stable characteristic in two-phase flows. Aeroacoustic test of split designs is presented. Their acceptability for ventilation systems with aerodynamic limitations is shown. Effective noise reduction and aerodynamic resistance decrease may be achieved by the splits orientation in parallel to the larger side of design’s cross-section.

Split mufflers were suggested for noise control of replacement sections is ended with trumpet in inlet of fans mounted in systems with large cross–section ducts the reverberant chamber 14. Air goes out the chamber (having characteristic dimensions which are larger than 14 to room through the nozzle 17. The condenser the wavelength of propagating sound). In order to microphone 16 is placed into the chamber 14 on the obtain muffler characteristics the aeroacoustic stand for support. Set of the replacement sections 13 allows to model (1 : 10) experiments was used. mount various length split mufflers between the The stand is mounted in three separate rooms reverberant chambers 8 and 14. The reverberant with 400 mm thickness brick walls (Fig. 1). chambers 8 and 14 are welded 4 mm thickness plate steel structures having ribs. All chambers’ surfaces are not parallel. The chambers have the doors 9 and 15. The doors are fulfilled from steel corners sheathed by 4 mm thickness plate steel with packing over the perimeter by sponge rubber. Each chamber is mounted on rubber shock dampers. Leads input is fulfilled in the chambers (to the microphones 10, 16 and sound columns 11) through packing glands. The chambers have nozzles for insertion of starting pistol used in reverberant time defining. The instrumentation is placed in the room situated between the rooms with the reverberant chambers. In acoustic testing the signal is FIGURE 1. Scheme of aeroacoustic stand transferred from the rose noise oscillator 21 to the amplifier 20 joint with the sound columns 11. Sound High pressure fan 1 entering into the stand has direct– oscillations arising in the reverberant chamber 8 are current motor. The motor is supplied from voltage sensed by microphone 10, sound oscillations control source 23. It allows to change flow of air in the transmitted through the testing split muffler are sensed air conduit 4 from 0 to 1000 m³/h. Fan’s aerodynamic by microphone 16. The signal is transferred from the noise is reduced in the tubular muffler 3 joined with microphones to the B&K complex of the measuring the fan by the flexible insertion 2. In order to measure apparatus 22 for precise laboratory and nature testing. flow of air the diaphragm 6 having manometer tubes 7 The complex allows to obtain noise characteristic in and micromanometer 19 are used. In order to measure frequency bands of set width in the such form as pressure of air passing through the diaphragm 6 the U– digital presentation, curve on the recorder or on the tube manometer 18 is joined to manometer tube 5. cathode – ray oscillograph. The air conduit 4 is joined with inlet of the reverberant Stand’s chambers was attested before mufflers chamber 8 in which the sound columns 11 and the testing with taking into consideration requirements of condenser microphone 10 on the support are mounted. ISO documents. The air conduit with the replacement sections 13 is It was tested on the stand: the model of one joined to outlet (in direction of stream) of the section muffler; the model of two sections muffler with reverberant chamber 8. There are manometer tubes 12 the same sections; the model of two sections muffler for the U–tube manometer 18 joining in the having sections with opposite orientation splits. replacement sections. The air conduit with the The model of one section muffler has built–up 10 (muffler with vertical splits) results in k reduction steel body of rectangular shape (Fig. 2). from 1,87·10–3 to 1,2·10–3 Pa/(m³/h)² in one section The model of two sections muffler with the muffler. Correspondingly the aerodynamic resistance same sections is successive arrangement of the decreases on 36%. In adding section the pressure loss mufflers with horizontal splits. The replacement air increases in 2 time in case of the same splits conduit 273 mm long is placed between the mufflers. orientation and in 1,6 times in case of opposite

FIGURE 2. Model of one section muffler with horizontal splits The model of the muffler having sections with opposite orientation. Hence, in order to increase aerodynamic orientation splits includes the muffler with horizontal resistance the split muffler should be designed with splits, replacement air conduit 273 mm long and the rectangular shape cross–section breaked up in parallel muffler with ten vertical splits. Section’s vertical and its larger side. In estimating acceptability of pressure horizontal splits are identical. According to acoustic characteristics split mufflers provide even broad –band noise reduction. Minimum effectiveness of the one section muffler (design is not optimized) is 4 dB; minimum effectiveness of the muffler having two sections with opposite orientation splits is 8 dB. The acoustic characteristic of muffler including the same sections coincides with the characteristic of one section muffler. Experiments show that influence of air stream moving with speed to 18 m/s through the models of muffler on acoustic characteristics is insignificant and it may be FIGURE 3. Pressure loss-air flow relation: 1- muffler disregarded. with horizontal splits; 2- muffler with vertical splits. In obtaining aerodynamic resistance in the models the air speed was being changed from 3 to 18,5 m/s and the flow was being changed from 160 to 1000 m³/h loss it was took into consideration design difference of correspondingly. Experimental data was twelve split muffler (bars) and baffle–type silencer (baffles measurements averaged. Confidence interval was with thickness about 200 mm). In increasing split calculated for probability 0,95 and instrumental error muffler rectangular cross – section in 1,5 times and 2,5 %. fulfilling suggested splits orientation pressure loss in According to experiment (Fig. 3) friction and split mufflers and in baffle–type silencer are the same. local resistance pressure loss in the split muffler ∆P, Pa Thus split mufflers may be used in systems with is aerodynamic limitations. ∆P = k Q², where k – characteristic of resistance, Pa/(m³/h)²; Q – flow of air, m³/h. The number of splits influences k value significantly. Its decrease from 13 (muffler with horizontal splits) to Acoustic Analysis Aimed At Characterizing Combustion Instability In Premixed Burners

M. Annunziatoa, G. Coppola, M. Presaghia, R. Presaghi, G. Puglisi, F. Romanello a

a ENEA Ingegneria ed Impianti di Generazione di Energia, 00060 Roma, Italia

New method to determine combustion characteristics by means of acoustic noise generated by dimensional variations of the flame due to unstable operation of the burner. The method allows to test efficiency of a burner and to deeply understand the causes that originate some problems related to the combustion.

METHOD OF ANALYSIS on which the method is based remains a valid one. The photographic series of FIG.3 (a-f) shows a A method to characterize burners used in energy typical evolution of the flame in instability conditions. generation plants is presented. The method has The most important information that are possible to demonstrated to be particularly useful to put into gain from noise are the thermal power variation and the evidence the anomalies presented by premixed burners dimensional variation of the flame, being the former in some operation regimes. In premixed burners, fuel correlated to noise amplitude and the latter to its and air are premixed before their entering combustion dominant frequency. With the aim of evidencing the chamber. Differently from other burners, the premixed effects induced by the flame on the cavity’s resonance ones operate at lower temperatures, thus emitting less quantity of pollutants, but, although having these positive characteristics, they are affected by unpredicatble operation criticities, that cause a lowering in efficiency, environmental pollution and dangerous structural stresses [1]. The method is based on the principle that the burner represents a true FIG. 3 acoustic cavity, containing both “flame fluid” and frequency, a simplified formula is reported, based on “exhaust fluid”. The different mechanical impedances the principle [3] that the resonant acoustic wave and the dimensions of such fluids, determine the propagates itself into a cavity in a time that equals ¼ of resonance frequency of the cavity. Acoustic effects of its period. The simplification concerns the disposition the said cavity move the noise band and center it on the of the two fluids (flame and exhaust gas) that occupy resonance value. Consequently, by monitoring the volumes that are adjacent, not in communication, and latter parameter, it is possible to detect its cause: the having each constant temperature, Tf e Te (FIG. 4). variation in flame’s activity. -1 é ù kR Lf L - Lf FIGS. 1 and 2 represent a schematic view of two f r = ê + ú (1) 4 dimensional aspects of the flame due to the up ëê Tf Te ûú FIG. 4 mentioned phenomenon. When dimensional variation f = resonance frequency [Hz]; L =flame length[m]; in the flame occurs with no variation in the quantities r f L=cavity length [m]; k=adiabatic index; of air and fuel entering the burner, a flame instability R= specific gas constant [J/kg K= m2/s2 K]. [2] is experienced. Such instabilities are due to a series of causes that are originated by the reciprocal 200 interaction of many parameters; for instance, pressure Tf = 1400°C 190 Te = 550°C fluctuations generated by acoustic noise, act on 180 L = 1m combustion chemistry and determine chaotic 170 evolutions in the phenomenon. However, the principle 160 Frequency (Hz) 150 flame lenght [m] 140 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 FIG. 1 FIG. 2 FIG. 5 types ofsensors:acoustic of theupmentione the phenomenonhasbeenthusconductedonbasis not relevantforouraim.Theinstrumentalanalysisof assuming frequency, amplitude)obtainedbythe combustion (microphone) andpressuregaugeconnectedto different operationcondition of thefigureshowsabar graph generatedbyfive discriminator. Theinstrument in theupperrightcorner (realized byLabView),basedontheupmentioned shows thefrontpanelof also attimesinwhicha)assumesreducedvalues. envelopment ofa)andpresentsnoticeablevariations can beevidencedhowb)hasatrendsimilartothe represents thefrequencydeviationofnoiseitself. diagram a)reproducescombustionnoise,whileb) discriminator. OneexampleisreportedinFIG.7: processing thesignalbymeansofafrequency the flameisassociatedtoachangeinitsdimensions. not alwaysanhighvariationinthethermalpowerof event associatedtohighinstability.Thisshowshow excursions arenoticed,whileonlyonceitappearsan transform statistical occurrenceofstronginstabi flame’s instabilityranges,thisinadvancetothe this way,signalb)hasthepeculiaritytodetect some noisecomingfromexternalenvironment. considering thatthemicrophonesignalcontained the combustioninstabilityphenomenon, Processed signalsareoriginatedbytwodifferent The trendof FIG. 6representsathree Similar Max min Frequency Amplitude

Frequency k technique.Inthisfiguremanyfrequen resultshavebeenobtainedwh

and chamber. Boththesignalsallowedtocatch R d considerations. tobethesameforbothfluids,thatis Time (ms) f r versus FIG. 6 FIG. 7 Time

the finalsoftwaredevice

-

dimension diagram(time, s oftheburner, L

f - electric transducer is showninFIG.5, lities. FIG.8

wavelet also

the min Amplitude Max cy en In It

3. hystogram correlated tothephenomenon. filtered astoeliminatethecomponentsthatarenot signals shownin again theirheight.Thebarsrepresenttheenergyof be themoststable condition oftheflame;thirdappearsto burner. Thehighe and 1.5aretheoperationlimitsofinvestigated air quantityandsteichiometricone). 1.3; 1.4;1.5( respectively havingthefollowingvaluesof 2. 1. This one ofitscontrolsystem. aimed attheknowledgeofburnerefficiencyand method appearstobesuitableforcarryingoutanalysis noise itself.Onthebasisofobtaine noise: thatisthevariationindominantfrequencyof induced effectsonthecombustiongeneratedacoustic cavity andthusgeneratingtheideatodetect obtained consideringtheburnertoactasaresonant compared tothealreadyknownones;thishasbeen methodology abletogivemoreinformationwhen or tocontroltheirdifferentphases. front panelisusedtosettheparametersofanalysis mixtures withaireccess). (mixtures closetothesteichiometricvalueand pubblisher, 1977 Javorskij B.M.,DetlafA.A., Energy CombustionScience,1993,vol19,pp1 of ActiveControlCombustionInstabilities McManus K.R.,Poinsot Hill, NewYork,1983. Lefebrve A.H.,

studyhasbeencarriedouttodetecta

is duetothedifferentinstabilitytypes

ll st barisreferredtothemostunstable FIG. 7,b),thathavebeenpre meaningtheratiobetweenintroduced REFERENCES Gas TurbineCombustion CONCLUSIONS one,thenthebarsstarttoincrease

FIG. 8

T.andCandelS.M.,

Every otherdeviceofthe Spravoènik pofisike

Values of

Asymmetry in

d results,the

ll , McGrow : - A Review 29. ll 1.1; 1.2;

viously , Progr. of 1.1 , Mir -

Higher mode cylindrical radiator for an aerial intense ultrasound source H. Yamanea and T. Otsukab a Department of Electrical Engineering, College of Science and Technology, Nihon University 1-8 Surugadai, Chiyoda-ku Tokyo 101-8308, JAPAN b Department of Electrical and Electronic Engineering, College of Industrial Technology, Nihon University 1-2-1 Izumicyo, Narashino, Chiba 275-8575, JAPAN

This work deals with a development of a cylindrical radiator for industrial applications such as collecting fine oil mist that floats in air. The thickness of the cylindrical radiator was selected so as to be within the range of the flexural vibration. The radiator was driven by a Bolt-Clamped Langivin transducer(BLT). The stripe mode vibration was obtained on the radiator while the flexural vibration appeared along the radiator axis. The resonance frequency of the cylinder itself and the ultrasound of a radiator in the cylinder were adjusted at the same frequency to produce a high intensity ultrasound field. As a result, the sound pressure level in the cylinder up to 170 dB was obtained. This makes it possible to use the system in the industrial application of collecting and/or coagulating fine oil mist floating in air.

CYLINDRICAL RADIATOR SOUND PRESSURE DISTRIBUTION IN- SIDE THE CYLINDER The frequency of the (m,s) mode in the cylindri- 1) cal radiator is given by The Root-Mean-Square value of the sound pres- c sure level distribution inside the cylinder is given by fms = αms (1) 2πr m, s − where 1 are the number of nodal diam- P = Jm(αms r) · cos mθ (5) eters and the number of nodal circles, αms is the m Table 1 gives the dimension of the cylindrical eigenvalue given by Jm(αms)−Jm+1(αms)=0, αms radiator calculated from Eqs. (3) and (4). where Jm,Jm+1 are cylindrical Bessel functions of the m-th and (m + 1)-th order and c is the velocity of sound, r is the radius of cylinder. Table 1. Details of cylindrical radiator The m-th order of the resonance frequency of (m,s) Inside radius Thickness Length Frequency 2) the flexural vibration on the cylinder surface is r [cm] h[cm] l [cm] f[kHz] determined for the number of m mode lines as (11,5) 7.715 0.48 9.30 20.90 NmCM h fm = (2) 2π(r + h/2)2 Figure 1 shows the sound pressure level distri- m(m2−1) where Nm = √ , CM is the material con- bution inside the cylinder as calculated by equation m2+1
  E (5). There are 11 nodal diameters and four nodal stant and determined from = 12ρ(1−ν2) , where circles. E is the Young’s module of elasticity, ρ is the den- sity, ν is the Poisson’s ratio and h is the cylinder thickness. The cylinder radius at the (m,s) mode is ob- tained using Eq. (1) c r = αms (3) 2 πfms The thickness h is determined by the following methodology: Substitute fms for fm from Eq. (2) into Eq. (3) and the resulting thickness h is obtained by the following Figure 1. Sound pressure level distribution inside expression  the radiator at the frequency of 20.9 kHz by

2 NmCM NmCM Eq.(5). h = −2 r − + r − − r2 (4) 2πfms 2πfms DRIVING UNIT Fig. 4 shows the linearity of the acoustic power as measured with a 1/8 ” 4138 microphone. The The schematic of the driving unit is shown in microphone was located at the point A in Figure Figure 2. The BLT at the frequency of 20 kHz is 3. The sound pressure is proportional to one half connected to a half wavelength exponential horn, the input electric power and 5.64 kPa (169 dB) was the cylindrical radiator is driven by the horn. obtained at 200 W of input power.

7000 170 6000 5000

4000

3000

nodal lines 2000 160 Sound pressure [Pa] Figure 2. Cylindrical radiator for the frequency of Sound pressure level [dB] 20.9 kHz. The stripe mode can be observed on the inner surface of the radiator. 1000 10 100 ACOUSTIC CHARACTERISTICS Electric input power [W] The sound pressure level distribution was mea- Figure 4. Linear characteristic of the sound sured along the radius with the maximum sound pressure versus the input electric power. pressure levels occurring on the central axis inside the cylinder.

1 CONCLUSIONS

A The cylindrical radiator with radial flexural vi- bration was designed to operate at the frequency of 20.9 kHz. The radiator is made of titanium and the sound pressure levels of 169 dB were obtained at 0.5 200 W of electric power input. This system can be used in industrial applica- tions as a tool that would enable attraction and coagulation of the fine free-floating oil mist. Normalized sound pressure

REFERENCES 0 02468 1) McLanchlan, N. W., Bessel function for engineer- Distance from center axis of cylindrical ing. Oxford University Press, London 1955. radiator [cm] 2) Timoshenko, S. P., Young, D. H.,& Weaver, W. Figure 3. Normalized sound pressure distribution. Jr., Vibration Problems in Engineering. John Wiley & Sons, New York 1974. The sound pressure level was measured with a 1/4 ” condenser microphone with the probe tube when the electric power of 20 W was applied to the BLT. The probe tube is 20 cm long, has 0.15 cm inner diameter and is 0.05 cm thick. The measured sound pressure level distribution is in good agree- ment with the calculations. Variations of transverse structure of coupled acousto-gravity - Rayleigh waves in multilayered system Earth - atmosphere

G. Burlak, V.Grimalsky, S. Koshevaya

Center for Research on Engineering and Applied Sciences, Autonomous State University of Morelos,Z.P. 62210, Cuernavaca, Mor., Mexico.E-mail: [email protected]

The transverse distribution of coupled acousto-gravity waves in atmosphere and a Rayleigh wave in a layered system Earth - atmosphere is investigated. The special attention is given to a mode of strong coupling of waves in a solid substrate with the oscillations in upper medium (atmosphere) when the phase velocities of waves are close (coupling point, or a point of synchronism). Is shown that in this point the frequency shift induced by the mutual influence of waves becomes maximal. In vicinity a coupling point, a strong change of the cross structure of wave in air takes place.

system in atmosphere and the system of theory A propagation of acousto-gravity waves in of elasticity in ground should be solved jointly. atmosphere has been studied rather intensively The propagation in an atmosphere of the [1-3]. These waves are considered often as one seismically excited sound waves causes of basic channels of energy exchange between oscillations of the ionosphere - atmosphere lithosphere and ionosphere caused by different boundary. As a result, Doppler reflections of disturbances of both seismic and space nature electromagnetic waves from ionosphere layers at (see, for example, [4-6] and references therein). frequencies 10 and 25 MHz were observed [7]. The main consequence is the exponential growth of amplitude of the oscillatory velocity of particles with an altitude. Certainly, such a growth is limited by the account of such factors as viscosity of air, and also of convective nonlinearity in equations of motion. As it is shown below, the very important factor is also mutual coupling of acousto-gravity waves with another excitations in the ground, one of them is the Rayleigh wave in the Earth crust. Generally, an influence of the sound in air on a Figure 1. Geometry of the system propagation of Rayleigh waves in a substrate is very little, because of a great difference of the Those observations demonstrated that the densities of environments. However, such an Rayleigh waves can propagate to considerable influence, as it was marked in [6], becomes distances from a source (about 5000km). As this essential in the point of intersection of effect was detected rather far from a seismic dispersion branches of the Rayleigh wave in a source, it is apparent that in such conditions the substrate with the volume branch of the sound Rayleigh wave propagated as an own wave of a wave in the air when the phase velocities of layered system. During such propagation, the waves become equal. Such a point refers to as a conditions of a synchronism with waves in coupling point, or a point of synchronism. In a atmosphere can be reached. Therefore, vicinity of such a point, the mutual influence of understanding the features of interaction of a waves becomes strong. Particularly, this Rayleigh wave with acousto-gravity waves in concerns to a case when the gravity force is vicinity of a point of a synchronism is important essential and the acoustic waves in atmosphere to see over the total physical picture. However, become of acousto-gravity type. It is impossible in this case the problem becomes more complex, to investigate the wave subsystems in air and as it is necessary to take into account for both ground separately in a vicinity of a synchronism waves under equal conditions. We should solve point. In this case, the aero - hydrodynamic the coupled acousto-gravity - sound problem by a self-consistent way. (a) (c) In this report, the transverse distribution of 1.4 0.35

1.2 coupled acousto-gravity wave with a Rayleigh 0.3 1 v ↑ wave in a layered system Earth - atmosphere is 0.8 0.25 ph

Re(x) 0.6 0.2 v → investigated. The motion equations has form[8]: v, km/sec gr ϖ 0.4 ∂ ϖ ϖ 0.15 v + ∇ = −∇ + ρ ∇ 0.2 ( v ) v p g z , 0 0.1 ∂ 0 1 2 3 4 0 1 2 3 4 t kh kh 2 (b) (c) ∂ ∂ 0.1 0.5 ui pik γ = (1) 0.4 2 0.08 ∂ ∂ 0.3 t xk 0.06 )

+ 0.2 κ Im(x) The special attention is given to a mode of 0.04 Re( 0.1 0 strong coupling of waves in a solid substrate 0.02 −0.1

0 −0.2 with a sound in upper medium (atmosphere) 0 1 2 3 0 1 2 3 4 when the phase velocities of waves are close kh kh (coupling point, or a point of synchronism). We Figure 2. Dependencies of real and imagine parts of a wave frequency (a,b), phase and group use the dimensionless parameters x=ωh/ct1 and y=kh. In these variables, the dispersion equation velocities (c), and the transverse wave number κ has a general form +of the acoustic-gravity wave in the air (d) ρ (y2 −x2 /c 2 )D(x, y) = 0 x2(κ +2η )F(x,y) (2) system Earth - air versus the value of y=kh for n γ + 2 1 pointed above parameters. These dependencies Thus, the dispersion equation of sound waves in are obtained by a direct numerical solution of the examined system can be presented as dispersion equation. It is seen from the Fig.2 (b) 2 that in the left side from coupling point the κ D(x, y) = δx F(x, y)(κ + + 2η ) (3) 0 2 attenuation of waves is unessential but it δ ρ γ κ 2 2 2 where = 0/ , 0=y -x /c0n , c0n=c0/c1t. For a increases sharply in the right hand side from this -3 contact soil - air, it occurs δ=10 <<1. At δ=0, point yh=2.6. This increase is due to a more equation (3) splits into two independent deep penetration of the wave into the soil where branches: a volume wave in the air and a normal a viscosity is not equal to zero. Also one can see mode in a layered ground. We are interested in from the Fig.2(d) that in the left side from the the modes, which can intersect with a volume point of coupling the most part of the wave is wave in the air. Note that second the lowest delocalized (Re κ+<0 on z<0; in the right side branch of acousto-gravity wave [4] does not from this point the wave is concentrated mainly have intersection with the Rayleigh wave. This in the solid substrate z>0. The account of branch is not studied here. At δ≠0, the waves viscosity in soil causes weak wave attenuation become coupled. However, as δ<<1, this but does not change a general physical picture of coupling is weak and it results in the small the wave interaction. frequency shift. We found that in this point the ACKNOWLEDGEMENT frequency shift induced by the mutual influence This work is supported by CONACYT project waves becomes maximal. In vicinity a coupling #35455-A. point, a strong change of a cross structure of wave in air arises. The strong dependence of a REFERENCES factor of the exponential growth of an oscillatory 1. Hocke, K. and Schlegel, K., Ann. Geophys. velocity of acousto-gravity waves with an 12, 917 (1996). altitude due to parameters of a solid substrate is 2. Hunsucker, R.D., Rev. of Geophys. and Space demonstrated. It is shown that the frequency Phys. 20, 293 (1982). band of the exponential growth is limited on 4. Gossard, E. E. and Hooke, W. H., ''Waves in high frequencies. As a result, a wave becomes the Atmosphere'' (Elsevier, Oxford, 1975). localized near the surface of the Earth at higher 5. lngersoli, A.P., Kanamori, H. and Dowling, frequencies. The point of the change from T.E., Geophys. Res. Lett. 21, 1083 (1994). increase to decreasing is determined by a point 6. Ewing, W.M., W.S.Jardetsky, W.S. and Press, of a synchronism with a Rayleigh wave in the E., ''Elastic Waves in Layered Media'' (McGraw- ground substrate. Fig.2 presents the Hill, New York, 1957). dependencies of real and imagine parts of a 7. Weaver, P.F., P.C.Yuen, P.C., G.W.Prolls, wave frequency (a,b), phase and group velocities G.W. et al., Nature, 226, 1239 (1970). 8. Brekhovskikh, L.M., ''Waves in Layered (c), and the real part of coefficient κ of the + Media'' (Pergamon Press, Oxford, 1985). wave in the air(d) of a coupled wave in the Measurements of Aerodynamic Velocity Fields With An Acoustical Probe

V. Dewailly, F. Cohen Tenoudji, J.P. Frangi and M. de Billy

Laboratoire Environnement et Développement, Université D. Diderot, Tour 33-43, Case postale 7087, 2 place Jussieu, 75251 Paris Cedex 05, France. e-mail : [email protected]

A system using the displacement of a three-axis ultrasonic anemometer probe in the air flow within a wind tunnel is used to probe the local variations of the flow velocity. The three velocity components are calculated from the sound travel times between transducer pairs placed in opposition (three pairs ; 44 kHz frequency). For each probe location, 400 velocity vector data values are measured at 32Hz. The average velocities and their fluctuations along the main axis of the flow and in the transverse plane are pictured as images coded as false colors or vector arrows. The spatial resolution of the 22 cm x 22 cm images is in the order of 1 cm after correction of the bias brought by a particular probe orientation. The technique shows good reproducibility in the air flow characterization. Acoustical results are compared with those obtained by an optical technique for different air flow situations.

The sound scattering by a moving fluid is an important The components of the velocity vector are recorded problem which has received a considerable experimental and simultaneously in three orthogonal directions. The z- theoretical interest since many years [1-3]. The interaction of component (or axial velocity) coincides with the axis of the acoustic waves with a turbulent flow is used to visualize the propeller (see Fig.1). Because of the fluctuation of the velocity field near a square outlet at moderate Reynolds velocity of propagation of the sound in the turbulent medium, number. This experimental method is not intrusive and does the arrival time varies and for each probe location 400 not necessitate additional matter. The average field velocity velocity vector data values are measured at 32Hz. The fluctuations - which are generated by the turbulence - are turbulence is supposed to be stationary. The measurements plotted in a plane perpendicular to the flow axis and in the are achieved in a (X,Y) plane located at 4cm from the outlet. direction of the air flow. The patterns obtained with and without a grid (located at the outlet) are compared and RESULTS AND ANALYSIS analyzed. In figure 2-a are plotted the diagrams of the velocity fields EXPERIMENTAL SET-UP (represented by vector arrows) obtained in the X-Y plane and without any grid (vertical and horizontal scales are in cm). A sonic thermometer – anemometer (type CSAT 3 from Campbell-Society) is used for the measurements. It includes three non – coplanar pairs of ultrasonic transducers operating 20 about 40kHz and is attached to an X-Y linear displacement equipment which lets the transmitters to move accurately by 18 step of 10mm which determines the spatial resolution. All the 16 displacements are driven by a computer. The jet flow is 14 produced by a rotating fan placed in the central section 12 2 situated between the square (22x22cm ) inlet and outlet. 10

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FIGURE 2-a : Velocity field in the X-Y plane Air flow Fan (without grid). X Grid Y

Z On the picture we observe only one vortex the origin of which is the rotation of the fan. No such behavior is noticed in the figure 3-a which represents the velocity field diagram FIGURE 1 : Schematic diagram of the experimental when a grid is introduced between the outlet and the 3 set-up. anemometer. The dimensions of the grid are 1x1x1cm . No periodicity characteristic of the grid may be extracted from this plot. In figures 2-b and 3-b are showna gray-scale of a virtual “tube” in which the z-component velocity value is distribution of the z-component velocity measured with and zero. without the grid respectively. In the center of the first picture,

FIGURE 3-b : Gray representation of the axial velocity (with grid).

FIGURE 2-b : Gray representation of the The second figure confirms that there is no more negative axial velocity (without grid). component of the velocity.

CONCLUSION 18

16 The measurements previously described and limited to the 14 comparison of results obtained with and without grid may be 12 extended to the velocity fields measurements behind 10 axisymmetric targets. Temporal inter-correlation and auto-

8 correlation should be calculated to get additional characteristics of the fields velocity and to gather more 6 informations on the energy exchange between the different 4 components of the velocity. 2

0 0 2 4 6 8 10 12 14 REFERENCES

FIGURE 3-a : : Velocity field in the X-Y 1. Petrossian, A., and Pinton, J.F., J. Phys. II France 7, 801- plane (with grid). 812 (1997). 2. Baudet, C., Ciliberto, S. and Pinton, J.F., Phys. Rew. Lett., 67, 193-195 (1991). we may the presence of negative values of the axial velocity 3. Wen-Shyang Chiu, Lauchle, G.C. and Thompson, D.E., J. which result from the conjugated effects: the existence of Acoust. Soc. Am., 85, 641-647 (1989). high velocity components near the periphery and the presence