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Inlet streamwise vorticity effects on jet evolution and far field sound generation

Marios Soteriou *, Ramons Reba, Thierry Maeder United Technologies Research Center, 411 Silver Lane, MS 129-65, East Hartford, CT 06108, USA

Abstract

A computational aero-acoustics model consisting of a vortex filament based flow solver and Lighthill's analogy is presented and employed in a study of inlet streamwise vorticity effects on flow and noise generated by a high-speed subsonic jet. The model shows that, in the presence of small amounts of inlet streamwise vorticity, the flow large-scale structure is drastically changed and is characterized by coherent structures that are related to the imposed inlet streamwise vorticity pattern. These changes are accompanied with increased spreading, mixing and turbulence of the jet. The inlet streamwise vorticity field achieves these effects by reorienting the predominately azimuthal vorticity at the inlet. The far field sound is reduced at low and increased at high frequencies. These trends are related to suppression of low-order modes and enhancement of higher-order ones.

Keywords: Jet flow; Jet noise; Vortex dynamics; Streamwise vorticity; Aero-acoustics; Vortex methods; Acoustic analogy; Flow simulation; Computational aero-acoustics

1. Introduction

Noise generation by commercial aircraft has been a problem of substantial concern in recent years and has resulted in increasingly stringent governmental noise reg­ulations. One of the main sources of aircraft noise is that associated with the turbulent mixing of the jet engine ex­haust — commonly referred to as "jet noise". Since the noise generation in this case occurs outside the engine, the main approach towards its suppression relies on mod­ifying the flow condition at the nozzle exit. Traditionally, jet-noise suppression research has relied heavily on exper­imental testing (e.g. [1-3]). Through these efforts it has been shown that passive devices such as tabs or chevrons that introduce streamwise vorticity at the jet nozzle exit can impact the jet flow and the far-field sound field in a significant way. Specifically, they tend to introduce coher­ent structures in the flow and to modify the sound field by suppressing/augmenting low/high frequencies [4]. In the recent past, computational modeling has also been revealed as an effective tool in jet noise research (e.g. [5-8]). In this work we employ a computational model based on the Vortex Filament Method (VFM) [9] and Lighthill's Acous-

* Corresponding author. Tel.: +1 (860) 610-7678; Fax: -hi (860) 610-7134; E-mail: soterimc@utrc.utc.com

tic Analogy (LAA) [10] for the simulation of the flow and far-field sound, respectively. The objective of the research is to investigate the impact of inlet streamwise vorticity on the jet flow and the far-field noise.

2. Numerical model

Details of the VFM-LAA numerical model can be found in Ref. [11]. Herein only a brief description of its salient features will be presented. The VFM provides 3D and unsteady solutions of the equations governing the mo­tion of an incompressible inviscid fluid. A non-primitive variable formulation in which vorticity is the principal variable is used and the solution is obtained in a La-grangian frame of reference. Specifically, the VFM exploits Helmholtz's and Kelvin's theorems of inviscid vortical flow to evolve vortex/material lines, commonly known as "vor­tex filaments". A desingularized vorticity field associated with the filaments is obtained via the introduction of a spherically symmetric redistribution function, f̂ , that is characterized by a length scale the core radius, 8. In this work fs is defined as a fast decaying polynomial. The velocity field is computed via a Biot-Savart convolution. Evolution in time is achieved by advecting each of the filaments with the local velocity vector while maintaining

© 2003 Elsevier Science Ltd. All rights reserved. Computational Fluid and Solid Mechanics 2003 K.J. Bathe (Editor)

1518 M. Soteriou et al. /Second MIT Conference on Computational Fluid and Solid Mechanics

their circulation fixed. This typically leads to significant stretching of the filaments, and necessitates filament re­finement. Finally, in order to account for the impact of turbulent diffusion, the filament core is expanded in time. Circular filaments are used to represent the azimuthal vor-ticity at the jet inlet and enforce the inlet top hat velocity profile. Streamwise filaments are added to represent stream-wise vorticity when necessary. An exit buffer region within which the solution unsteadiness is numerically dissipated is used to implement the exit boundary condition.

For the LAA solution the flow is assumed to be isen-tropic so that the source term in the analogy reduces to Lighthill's velocity gradient tensor. Numerical solution is performed in the frequency domain in order to avoid the numerical errors associated with the numerical differentia­tion of the VFM velocity fields. Spatial windowing of the source is employed at the outflow boundary using a Gaus­sian function and azimuthal averaging is used to improve the statistical quality of the computed spectra.

3. Results and discussion

For the VFM solution the jet mixed velocity and diam­eter are used as reference scales. The filament core radius at the inlet is selected as 5 = 0.05 and is expanded in time according to 8^{t + dt) = 8^(t) -\-Cdt with C = 0.004. A coflowing atmosphere f/ambient = 0.25 is assumed. The computational domain length is selected as Xmax = 5 with an additional exit buffer region of Axbuffer = 2. The main inlet streamwise vorticity condition considered was that of twelve, azimuthally equispaced counter-rotating vortices as shown in Fig. 1, the V12 case. The strength of the stream-wise vortices is small compared to the azimuthal vorticity shed by the nozzle; the ratio of circulations of the stream-wise and azimuthal filaments is rstreamwise/Fazimuthai = 0.01. A second inlet condition in which the streamwise vor­ticity was continuously but randomly distributed around the circumference (with maximum streamwise circulation equal to that of the V12 case) was also considered — the Vrandom case.

Fig. 1. Schematic of arrangement of inlet vortices for the V12 case. Arrows indicate induced velocity.

Figs. 2 and 3 compare the V12 and Vrandom results with those of a simulation without any inlet streamwise vorticity — the baseline case. It is evident that imposing weak streamwise vorticity has a substantial impact on the downstream evolution of the jet: it enhances jet spread and entrainment and leads to increased turbulence (Fig. 2). Moreover, the VI2 case is much more effective than the Vrandom in achieving these effects. In Fig. 3 vortex fila­ments are used to visualize the flow field. Images on the left are instantaneous visualizations of the azimuthal filaments. Images on the right are constructed by sampling the az­imuthal filament solution in time at a particular streamwise location. The figure indicates that in the presence of inlet streamwise vorticity, the flow develops a complicated spa-tiotemporal structure involving a larger range of scales and more three-dimensionality. The V12 case is seen to spread the most. It does this by creating a coherent, six-lobed vortical structure downstream. Contrasting this structure to the pattern of the inlet streamwise vorticity specified for this case (Fig. 1) leads to the conclusion that the two are directly related. The features of the inlet pattern are also important. Comparison between the V12 and Vrandom cases clearly indicates that the V12 pattern is much more effective at modifying the downstream flow.

The fact that streamwise vorticity can substantially aug­ment the mixing and growth of otherwise axisymmetric or planar shear flows such as jets and shear layers has been known for some time (e.g. [3,12]). What is different here is that the streamwise vortices introduced at the inlet are extremely weak compared to the rest of the vorticity field. Fig. 3 shows that the mechanism by which the weak inlet vorticity field impacts the flow is by reorienting the azimuthal inlet vorticity — note, for example, the side views of the scatter plots in Fig. 3 which indicate that the originally azimuthal filaments have acquired a streamwise component. Near the inlet the imposed streamwise vortic­ity, while small, is the main component in the streamwise direction and perturbs the azimuthal filaments in the radial direction. The segments of the azimuthal filaments that are not residing in the r = 0.5 cylinder are thus exposed to the jet shear and are distorted in the streamwise direction. This argument implies that the reoriented vorticity will ex­perience a maximum at the same location as that of the original streamwise vortex, hence the close relationship of the downstream structure to the inlet pattern.

We now shift our attention to the acoustic field. Pressure spectra are presented for an observer at 90 degrees to the jet axis. Results have been normalized using the jet diam­eter and the ambient pressure and the jet Mach number is specified as 0.9. Sound pressure spectra for the V12 and baseUne cases are compared in Fig. 4. The introduction of streamwise vorticity reduces the peak noise level at St = /D/t/jet ~ 0.5, and increases noise above St = 0.6. This cross-over from noise reduction at low frequencies to noise increase at high frequencies is characteristic of noise

M. Soteriou et al. /Second MIT Conference on Computational Fluid and Solid Mechanics 1519

baseline — • Vrandom - - - V12

— baseline — Vrandom - - - V12

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Fig. 3. Instantaneous (left) and scatter (middle, right) filament plots for the baseline (top), V12 (middle) and Vrandom (bottom) cases.

control devices such as tabs which introduce streamwise 4. Conclusions vorticity [4]. Mode-order/frequency analysis of the results indicates that the reduction of noise at low frequencies is A computational aero-acoustics model consisting of a related to the suppression of low order modes while the vortex filament based flow solver coupled with Lighthill's increase at high frequencies is related to the amplifica- analogy has been developed and used to simulate a free tion of higher-order modes [11]. The physical picture that round jet with weak inlet streamwise vorticity. Results indi-emerges is that noise suppression/augmentation is related cate that this vorticity alters the flow downstream dynamics to mitigation/introduction of large/small flow scales. in a significant way, enhancing the level of mixing, en-

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References

Fig. 4. Sound pressure spectra for the baseline case (dashed line) and V12 (solid line) cases.

trainment and turbulence. The degree to which these effects are manifested depends on the pattern of inlet vorticity imposed and they occur due to a reorientation of the origi­nally azimuthal vorticity. Acoustic results indicate that the impact of inlet streamwise vorticity is to reduce/increase noise at low/high frequencies.

Acknowledgement

This work is jointly funded by United Technologies Research Center and Pratt & Whitney. The authors would like to thank R. Schlinker, W. Lord and S. Narayanan for their support and fruitful discussion.

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