Aeroacoustic Simulation of Double Diaphragm Orifices in an Aircraft Climate Control System

Fred Mendonça*, Alex Read†, CD adapco, London, UK, W6 7NL

Stephane Caro‡, Free Field Technologies, Belgium

and

Klaus Debatin§, Bastien Caruelle**

Airbus SAS, Airbus, France

Transient CFD acoustic source prediction and CA propagation studies of a double diaphragm orifice illustrate complex flow and aeroacoustics phenomena, combining shedding structures (tonal noise) and large eddy structures (broadband noise). Such studies are necessary for aircraft climate control systems because such components introduce nonlinearities in the system characterization. In this paper we investigate, through modeling, the noise signature of a given double diaphragm configuration comparing against microphone measurements the predicted noise spectra in the near field (source region) and the predicted propagated sound in the far field, some distance downstream of the source region. A second configuration is then assessed, with the spacing between the orifices doubled, so as to derive confidence that the modeling is accurate in both absolute and differential terms. A novel method is presented for estimating the mesh frequency cut-off from a steady-state CFD calculation; such an estimate gives valuable insight a priori into the local mesh refinement required for a transient CFD calculation to resolve the frequency range of interest. The work described in this paper is part of a wider evaluation into the use of CAA methods for aircraft climate control systems.

I. Introduction

design criterion of increasing importance in the transport industries is to reduce noise induced by fluid dynamics which result in discomfort and human fatigue with long exposure times. Historically, little

computational work for production-type geometries has been carried out due to the prohibitive computational cost of performing time varying CFD calculations, the necessity for advanced turbulence modeling akin to Large Eddy Simulation (LES) and their associated meshing issues. With the continued decrease in hardware cost and the increase in performance, Computational Aeroacoustics (CAA) calculations are now being performed by an ever-increasing number of industrial CFD engineers.

A

Aircraft climate control systems typically exhibits aeroacoustic noise which have broadband and narrowband characteristics, the former being closely related to turbulence and the latter to coherent structures such as vortex *Manager of CFD Engineering Services, London, CD-adapco, 200 Shepherds Bush Road, W6 7NL, UK / fred.mendonca@uk.cd-adapco.com†Aeroacoustics Project Coordinator, Professional Services Department, CD-adapco, alex.read@uk.cd-adapco.com‡Aeroacoustics Specialist, Free Field Technologies, 16 pl de l’Université, B1348 LLN, Belgium / stephane.caro@fft.be§Acoustic Manager, Airbus SAS, Klaus.debatin@airbus.com**Acoustic Engineer, Airbus France, Bastien.Caruelle@airbus.com Copyright © 2005 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission.

American Institute of Aeronautics and Astronautics Paper 2005-2976

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11th AIAA/CEAS Aeroacoustics Conference (26th AIAA Aeroacoustics Conference)23 - 25 May 2005, Monterey, California

AIAA 2005-2976

Copyright © 2005 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

shedding. For internal flows with ‘cavities’ i.e. in which an unstable separated shear layer sheds vortices which convect inside a re-circulation volume, simple analytical formulae have been developed and correlated to give insight into the narrowband flow excitations. For example, equation 1 approximates for low-speed flows the tonal frequencies, F, as a function of the mean velocity, U, length of the cavity, L, and the number of vortices, N, or modes, which are present inside the cavity at any instant,

F = 1/3 (N – 1/4) U/L (1) The designer therefore has means to understand which aeroacoustic modal frequencies potentially exist in a given component. However, absolute dB levels and the relative magnitude of these modes are only obtainable via direct experimentation or simulation [1,2]. This paper exploits the substantial potential for aeroacoustics simulation in the context of a double diaphragm configuration, a typical component used in the aircraft climate control system. The acoustic response of these systems is usable in the form of transfer functions in a network modeling of the complete climate control system. Numerical characterization has the clear benefit of reducing the need for experimental rigs, and potentially provides far greater insight into the flow phenomena involved. Responsibility therefore falls on software providers to prove appropriate modeling techniques, define ‘best practices’ and provide toolkits with which design and production engineers can work; CFD code STAR-CD [3] and CA code ACTRAN/TM [4] are applied, and their coupled output, validated against experimental data made by Airbus, France. The simulation process defined herein combines steady state and transient CFD computations, with data from the latter being used as input to a noise propagation CA calculation. A new steady-state method, presented here for the first time, is used to approximate the local mesh frequency cut-off for a given CFD mesh. Furthermore, useful insight is gained as to the effects of reducing the CFD time step on the resolved spectrum. Two double diaphragm configurations are considered, differing only in the separation distance between the two diaphragms, this being one and two pipe diameters respectively. For the 1D separation case, the complete process is exercised from the flow prediction through propagation and data comparison. For both 1D and 2D separation, direct comparisons of the CFD with experiment are possible from the microphone measurements made in the near field at locations 3 and 4.

II. Experimental setup

Figure 1: Double Diaphragm Orifice Schematic (1D separation) and microphone locations Figure 1 illustrates the baseline orifice configuration, with the two diaphragms separated by a spacing of 1 pipe diameter, D. A silent air supply provides the airflow to avoid acoustic interference from the air-cycling machine. A fully developed turbulent pipe flow profile is established before entering the test section by enough inlet length of the air supply ducts.

In the test geometry shown, microphones 2, 3 and 4 are located in the aeroacoustic source region between the diaphragms and immediately downstream thereof. They are flush mounted so that direct comparisons can be made with the CFD predictions of the pressure spectra. Microphones 1 and 5 are placed far upstream and far downstream of the diaphragms so as to measure propagated noise in the duct, enabling comparison with the coupled CFD-acoustic prediction.

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III. CFD Computations

A. Turbulence modeling For aeroacoustics applications in STAR-CD, the now standardized and well validated [1,2] k-ε based Detached Eddy Simulation (DES) model [6] is applied. For most flows of industrial interest, constructing a mesh suitable for wall-functions everywhere is non-trivial because of y+ constraints. These may be relaxed with the combined use of Low-Reynolds Number turbulence models and special wall boundary treatment sometimes termed hybrid [1], used for these computations.

B. Discretisation practices Centered second-order discretisation practices in the detached flow regions are realized in STAR-CD through an advection-scheme blending practice [7]. An upwinded second-order scheme is applied elsewhere. Temporal discretisation using the PISO algorithm in STAR-CD is demonstrated to be fully second-order, and is sufficient for capturing acoustics sources.

C. Mesh and boundary conditions The CFD model consists of approximately 1.0 million cells (0.9 million for the 1-Diameter separation case and 1.1 million for the 2-Diameter separation case), created by successive 2x2x2 structured refinements down to a minimum cell dimension of 0.01D and using the trimmed-cell meshing tool in pro-STAR. Figure 2 shows the computational domain in the vicinity of the diaphragms. Upstream and downstream pressure boundaries are placed 2 and 10 diameters from the diaphragms. A steady, fully developed velocity profile with a mean velocity equal to the experimental supply is applied at the inlet.

Figure 2. CFD geometry and mesh (left – center section; right – 3D view).

D. CFD solution procedure The CFD simulation was carried out in two parts. First, a steady-state RANS calculation was performed to assess the locations of maximum shear-noise source generation and to determine an approximation of the upper limit of frequency resolvable by the mesh, termed the Mesh Cut-off Frequency (see below). The steady solution is then used as an initial guess for the fully compressible transient DES simulation; a useful technique for optimizing the computational time of the transient simulation by providing a representative initial field

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thereby reducing the computed time needed to reach a limit-cycled solution. Finally, after statistically steady conditions are reached in the acoustic source region, data is stored for transfer to ACTRAN/TM. An assessment is made of the effects of time-step size on the computed acoustic source spectrum. The larger time-step size of 1x10-4sec is based on the authors’ preferred criterion of resolving the highest frequency ‘of interest’ (here nominally 1000Hz) by 10 points. The spectrum is then compared directly with that at a smaller time-step size of 1x10-5sec. 1 second of elapsed simulation time takes 36hrs on 8xHP Itanium II processors at the time-step size of 1x10-4sec.

E. CFD steady state results

1. Acoustic Source location The Lilley Source term plots in Figure 3 confirm that the largest shear-related acoustics sources are located around the separated shear-layer downstream of the diaphragms, and justify the choice of local refinement in these locations.

Figure 3: Lilley Source relative source magnitudes (left – 1D separation, right – 2D separation).

2. Mesh Cut-off Frequency Given a cell dimension ∆ and velocity perturbation u’, the smallest length scale of a turbulent eddy structure captured by the mesh is 2∆. Therefore the maximum frequency FMC reasonably resolved by the local grid spacing ∆ is;

FMC = u’ / 2∆ (2) Since this measure is derived from a steady-state solution, some limitations are inherent. The frequencies associated with time varying large-scale motions such as vortex shedding, which convect through the mesh, will not be accounted for. Instead, its usefulness is to approximate the frequencies of the turbulence scales which are modeled with RANS, and which become resolved in Large Eddy Simulation. In other words, this measure is more valid for the broadband and less so for narrowband excitations. Figure 4 shows the approximate localized mesh cut-off frequency through the center-section of the geometry. It clearly indicates that frequencies up to 3kHz are resolvable in the bulk flow, and up to 1kHz near the pipe walls.

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This approximation is validated later by direct comparison of the same measure derived from the transient calculation.

Figure 4: Mesh Cut-off Frequency Approximation (left – 1D separation, right – 2D separation).

F. CFD transient results 1. Flow fields Typical pressure perturbations from the CFD calculation and the associated spectrum, plotted in Figure 5, have been taken from a location between the two diaphragms for the 2-diameter separation case. The pressure trace is demonstrably broadband, with superimposed tones due to the structures shed from the edge of the orifices.

Figure 5. Wall pressure trace (Pa) and spectrum (SPL) between the diaphragms

In Figure 6, shed structures are clearly visible from the pressure plot whilst the velocity contours illustrate well the LES-nature of the predicted flow field. This plot depicts the presence of two main vortices in the length-wise direction between the two diaphragms. Closer inspection, not shown here, reveals smaller structures typical of an

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energy cascade down to the sub-grid scales. With successively smaller scales, one would expect a series of modes with diminishing magnitudes to be present in the spectrum – their presence in the simulation is assessed together with the analytical formula (equation 1) and experimental data in a later sub-section.

Figure 6. Flow-field snapshots (left – velocity magnitude; right – pressure). 2. Effects of time step size Figure 7 contrasts the CFD pressure spectra at a point along the wall between the two diaphragms for the 1-diameter separation case. An interesting observation from the larger (1.0x10-4sec) time-step result is the noticeably abrupt kink in the mean slope towards the horizontal between 1 and 2kHz, and loss of resolution thereafter. The energies associated with the higher-frequency, smaller-scale structures are smeared out across the unresolved timescales. Contrastingly, at the smaller time increment (1.0x10-5sec) the high frequency resolution is improved.

Figure 7. Effect of time step size on SPL (1x10-4 sec versus 1x10-5 sec)

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These figures support the assertion that the CFD time-step size should be at least one tenth of the inverse of the maximum frequency required to be resolved.

3. Comparison of the modal behavior of the CFD predictions. Table 1 compares the measured and CFD predicted modal behavior for both cases with the analytical expression, equation 1, for which the mean velocity through the diaphragm orifice is taken to be 17.5ms-1 and L is the separation between diaphragms.

1-Diamater separation 2-Diamater separation Mode

Eqn. 1 (Hz) CFD (Hz) Expt (Hz) Eqn 1 (Hz) CFD (Hz) Expt (Hz) 1 87.5 110 - 43.75 - - 2 204 - - 98.6 100 108 3 321 310 336 155 - 155 4 437.5 - - 211 - - 5 554 550 - 600 553 268 270 278 6 671 - - 324 - 319 7 787.5 - 805 380 - - 8 904 920 - 437 420 434 9 1021 - - 493 - -

10 1137.5 - 1108 549 520 546

4. Direct comparison of the CFD and experimental Sound Pressure Level – 1D diaphragm separation.

Figure 8 shows a good overall broadband predictions compared with experiment. The small differences in tonal frequencies could be due to uncertainties in the applied inlet velocity profile. It is shown in previous work [1,2] that the relative magnitude of the modes is dependent on the flow three-dimensionality, and therefore that it is critical that the boundary condition at inflow in terms of velocity profile and turbulence levels are correct. The over-predictions in SPL at the lower frequencies could be due to the nature of prediction of the separated shear layer, where the DES model transitions in its behaviour between RANS and LES modes. Any over-prediction in the thickness of the separated shear layer will result in a too-high energy transfer to the separated part, resulting in an over-predicted spectrum.

Figure 8: CFD versus expt SPL at microphones 3 and 4 - 1D separation case

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The kink in the predicted spectra towards the vertical at approximately 1500Hz, where it deviates from the

experimental spectrum, is notable by the fact that this is close to the value suggested by the mesh cut-off frequency estimation as shown in Figure 4; it provides a useful validation of the method. The energy contained in scales smaller than those resolvable by the mesh are lost to the spectrum, hence the abrupt drop in the SPL. 5. Direct comparison of the CFD and experimental Sound Pressure Level – 2D diaphragm separation. Figure 9 shows similar trends to the 1D diaphragm separation case where the broadband content is very well predicted up to 1500Hz, and with reasonable correspondences of the tonality.

Figure 9: CFD versus expt SPL at microphone 3 (center) – 2D separation case

G. CFD data transfer The coupling between STAR-CD and ACTRAN/LA, in this example, involves the exchange of the time varying Lighthill stress tensor divergence at all locations of the acoustic mesh nodes shown in Figure 10 for the final 0.5sec of the CFD computation. The relevant flow-field variables are interpolated onto the acoustic mesh points. The data is transferred using the open source Hierarchical Data format (HDF) developed at The National Center for Supercomputing Applications (NCSA) at the University of Illinois. A Fourier transform is then performed, using filters if necessary, before the field is passed to ACTRAN/LA. The Fourier tool used is part of the ACTRAN/LA distribution. The acoustic mode contains 72000 degrees of freedom, and 1300 free modal basis (non-reflecting) boundaries on either side of the diaphragms.

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Figure 10. Acoustic mesh (inset – center section distribution)

IV. Computational Acoustics on the 1-diameter Diaphragm Separation

A. Methodology The theory behind the ACTRAN methodology [4,5] is summarized very briefly here. Recasting of the mass and

momentum conservation equations lead to the derivation of Lighthill’s equation. Low Mach number, high Reynolds number and isentropic flow assumptions lead to simplifications, which are then adapted to a finite element, frequency domain formulation.

B. Results 1. Monopole assessment of pure acoustic resonance The Krylov-based solver methodology in ACTRAN/LA allows for quick searching of the pure acoustic resonance modes of the system. The resultant mean square pressure, Figure 11, is a measure of the acoustic response to a monopole source placed between the two diaphragms. This figure shows that there is no natural resonance in the frequency range 0-1500Hz.

Figure 11. PRMS response to monopole excitation showing no pure acoustic resonance

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10American Institute of Aeronautics and Astronautics Paper 2005-2976

. Comparison betw

ons with the measurements of the noise spectra, using standard filtering techniques, propagated to icrophones 1 and 5, which are 31 diameters upstream and downstream of the diaphragms, are presented below.

Figures 12 and 13 illustrate excellent agreement with experiment with respect to the broadband noise levels across the 0-1500Hz range, and encouraging signs regarding the tonal content which reflects the underlying CFD generated excitation. The acoustic propagation calculations with a 2Hz resolution over the range 0-1500Hz take 26 hours on a standard PC, and 5 hours using standard filtering with a 10Hz resolution.

Fig m)

Figure 13. Propagated spectrum (dB) at Microphone 5 (downstream)

2 een measurements and simulation

ComparisM

ure 12. Propagated spectrum (dB) at Microphone 1 (upstrea

V. Conclusions

. Computational Fluid Dynamics

tructures has been introduced and validated. When compared directly to microphone measurements in e

on, and comparatively well with respect to the tonal content.

B. Computational Acoustics the far-field noise signal propagated in ACTRAN compared with measured

-3303 2Allen, R., Mendonça, F., DES Validation of Cavity Acoustics over the Subsonic to Supersonic Range, AIAA-2004-2862

al, release 3.2, CD-adapco, 2004

th AIAA/CEAS Aeroacoustics Conference and Exhibition, 10-12 May 2004, Manchester, UK. 6Spalart, P. R., Jou W-H, Strelets M., and Allmaras, s on the Feasibility of LES for Wings, and on a Hybrid

RANS/LES Approach, Advances in DNS/LE, 1st AFOSR NS/LES, Aug 4-8 1997, Greyden Press Columbus Oh.

ublished in Advances in LES of Complex Flows, pp 239-254, eds. P Friedrich and W.Rodi, Kluwer Aca

A A well-constructed process towards producing reliable STAR-CD solutions for aeroacoustics has been exercised. A measure derived from steady RANS simulations for estimating the frequencies associated with resolvable turbulence sth vicinity of the aeroacoustics sources near and between the diaphragms, the predictions compare excellently with respect to the broadband noise content up to the limits of the grid resoluti

Similarly, excellent agreement of spectrum is obtained. This provides a useful validation of both the computational acoustic methodology and the data transfer mechanisms adopted.

References 1Mendonça, F., Allen, R, de Charentenay, J., Kirkham, D., CFD Prediction of Narrowband and Broadband cavity acoustics at

M=0.85, AIAA-2003

3STAR-CD Methodology Manu4Oberai, A., Ronaldkin, F. and Hughes, T., “Computation of Trailing-Edge Noise due to Turbulent Flow over and Airfoil”,

AIAA Journal, Vol.40, 2002, pp2206-2216 5Caro, S., Ploumhans, P. and Gallez, X., “Implementation of Lighthill’s Acoustic Analogy in a Finite/Infinite Elements

Framwork”, AIAA-2004-2891, 10S. R., Comment Int. Conf. On D

7Travin, A., Shur, M., Strelets, M., Spalart, P., Physical and Numerical Upgrades in the Detached-Eddy Simulation of Complex Turbulent Flows, p

demic Publishers, 2002

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