Euromech Colloquium 467: Turbulent Flow and Noise Generation July 18-20, 2005 – Marseille, France

Numerical Prediction of Noise from Round and Beveled Nozzles

K. Viswanathan

1

Mikhail Shur

2

k.viswanathan@boeing.com

mshur@rscac.spb.ru

Mikhail Strelets

2

Philippe R. Spalart

1

strelets@mail.rcom.ru

Philippe.r.spalart@boeing.com

1

The Boeing Company, PO Box 3707, Seattle, WA 98124, USA

2

St.-Petersburg State Polytechnic Univ., 29, Polytechnicheskaya str., St.-Petersburg 195251, Russia

Abstract

Numerical simulations of the flow field and the noise generated by round and beveled nozzles are carried out.

The objective of this study is to gain insights into the flow characteristics that yield a noise reduction for the

beveled nozzle. For aircraft applications, the geometry of the nozzles must be optimized both for

aerodynamic and acoustic performance. Results from both RANS and LES computations are presented. The

aerodynamic predictions from RANS are in very good agreement with experimental measurements. The

noise predictions from LES agree with the trends observed in the measurements. Given the complexity of the

problem and the extreme grid requirements, good spectral predictions are obtained, albeit with a strict limit

on the maximum Strouhal number. For the subsonic jets, the noise is consistently under-predicted close to the

jet direction. The results are encouraging and this study is a part of on-going efforts to better understand the

flow physics, and possibly derive fresh ideas from a broad visibility of the turbulence.

Keywords: Jet Noise, Computational Aeroacoustics, Large-Eddy-Simulation, Beveled Nozzle

1 Introduction

Jet noise continues to be the dominant noise component during takeoff, even for modern commercial aircraft.

Despite significant research carried out over the last fifty years, there is no accepted complete theory for the

generation and radiation of jet noise, and no methodology capable of predicting the spectra at all angles and

over the wide frequency range of interest to the aerospace industry. Therefore, there is a heavy reliance on

experimental measurements, which tend to be very expensive and limited in the quantities that are measured.

Detailed knowledge of the entire turbulent flowfield is necessary in order to predict noise; there are

significant challenges in accomplishing even this first step. Only in recent years have non-intrusive optical

techniques been developed that permit the measurement of the turbulent fluctuations, and their accuracy is

limited. Even if all the requisite flow information were known, there would remain the twin challenges of

identifying the noise sources and actually predicting farfield noise to the required accuracy. The problem of

relating subtle changes in the flow field, say due to modifications to the nozzle geometry, to the radiated

noise is formidable. Significant gaps remain in our understanding of turbulence and noise.

Numerous recent studies have addressed the issue of turbulence-generated noise with the goals of obtaining

better insight into the flow and improving our ability to predict noise. With the advances in computing

capability, the use of Large Eddy Simulation (LES) for this purpose is becoming attractive. Many researchers

have adopted this approach; for example, see Bogey and Bailly [1], Bodony and Lele [2], Paliath and Morris

[3], Shur et al [4], and Uzun et al [5]. The other approach of using the steady-state solution from a Reynolds

Averaged Navier-Stokes (RANS) as input to a noise prediction methodology suffers from severe limitations,

see [4]. In most of the past LES studies, the nozzle is not included. Instead, a simple inflow profile is

specified. This practice is not satisfactory, especially for the geometries considered here.

Recently, Viswanathan [6, 7] proposed the beveled nozzle for jet-noise reduction and presented experimental

evidence of significant benefit, relative to a conventional round nozzle, in the peak radiation sector. Detailed

analyses of the aeroacoustic measurements from single jets in [6] indicated that the noise reduction is due to

the modification of the noise generated by the large-scale turbulent structures. Recall how there is no explicit

accounting for these structures in a RANS simulation. There is vectoring of the jet plume due to the beveled

trailing edge, and the static pressure in the exit plane is non-uniform. Therefore, the nozzle geometry and the

flow inside the nozzle must be included in the computations. A brief overview of the methodology, and

sample results are presented now.

2 Methods and Results

A comprehensive description of the objectives of the numerical approach, a review of the state-of-the-art and the

pros and cons of the various choices/assumptions invoked by the different research groups, the rationale for the

choice of the numerics and the integral method for noise computation, the grid topology, the effect of the location

and shape of the Ffowcs-Williams-Hawkings (FWH) surface, the effect of the closing disc in the downstream

direction, etc., are given in [4]. The turbulence is treated by LES and the Navier-Stokes equations are solved with

a slightly upwind-biased high-order differencing for spatial discretization and implicit time integration. The

Sub-Grid-Scale (SGS) model is de-activated, and the approach is viewed as “Implicit LES”. The far field noise is

calculated using the permeable FWH formulation, with the FWH surface having a funnel shape and a closing disc

at the downstream end; since turbulence crosses this disk, the accuracy depends on a change of variables in the

FWH equation. Computations with the finite-volume code and on multi-block structured grids are performed on

personal computers with two processors capable of 2.8 gHz each. Therefore, the number of grid points is

somewhat lower than on mainframe machines: fewer than 2 million, compared with at least 10 million. However,

the resolved frequency range is not dramatically narrower: the highest resolved Strouhal number is around 1.5,

while it is ≤2.0 even for simulations carried out on supercomputers. Reference [4] also presents results for a wide

range of jets, with various Mach numbers, temperatures, and co-flow levels, and some with chevrons.

Three different nozzle geometries are analyzed: a round conic, and two beveled nozzles with bevel angles of 45º

(bevel45) and 33º (bevel33). The flow regimes are considered with the jet stagnation temperature ratio 3.2 and

different nozzle pressure ratios corresponding to the fully expanded Mach numbers [M] 0.6, 1.0, and 1.56. A

complete LES simulation of the nozzle internal flow and the external plume is not quite feasible yet. A RANS

simulation is first carried out for the internal and external plume on a grid of ~2.2 million points that provides an

accurate resolution of the nozzle boundary layer. A LES is performed in a second step for the external plume on a

coarser grid in the radial direction near the nozzle wall edge (resolving the viscous sublayer not being necessary),

with the velocity field from the RANS simulation interpolated and specified as the inlet boundary condition. The

inlet pressure for the subsonic jets is calculated from a standard non-reflecting boundary condition. It has been

verified that the time-averaged pressure field from the LES matches that from the coupled RANS simulation, thus

validating the two-step approach. The LES grid is more uniform in the streamwise direction, which is essential for

simulations aimed at noise predictions. It has ~1.5 and ~3.0 million nodes for the subsonic and under-expanded

supersonic jets respectively. The computational domain extends to 75D in the axial direction [D is the nozzle

diameter]; in the radial direction, the grid extends to 15D upstream of the nozzle exit and progressively widens in

the axial direction to accommodate the spreading jet, reaching 48D at the last axial station. First, the accuracy of

the RANS nozzle internal calculations is verified with the experimental measurements of [6]. The measured

nozzle discharge coefficient is ~13% less for bevel45 compared to the round nozzle, and the difference is 13.6%

from CFD. The computed plume deflection angle at M=1 is 11º, while it is ~10º in the measurements. Thus, the

predicted integral quantities are in good agreement with measurements. The discharge coefficient is 0.895 and the

deflection angle is 8.5º for bevel33. Though no measurements are available, it is noted that these values for

bevel24 are 0.92 and 7º, respectively.

For the stringent case of the beveled nozzle, issues of grid clustering in LES, shape and location of the FWH

surface, etc. had to be investigated afresh. To accommodate the plume deflection from the beveled nozzles, the

FWH surfaces, like the grid, are turned towards the shorter side of the beveled nozzle. Sample LES and noise

results are presented now. Figure 1 shows vorticity contours for M=1 bevel45 flow in two different planes. The

azimuthal angles (φ) are measured as follows: 0º corresponds to the longer lip direction and 180º the shorter lip;

see [6]. The development of the shear layer is similar to those in [4], with a relatively fast transition to turbulence

even without unsteady inflow perturbations. The development of the two shear layers in the XZ-plane (plan view)

is symmetric, while the plume deflection is evident in the XY-plane. However, a closer examination of the

vorticity field immediately downstream of the nozzle, shown along with the grid in Figure 2, indicates that the

grid used this far is somewhat too coarse in the axial direction, and is not aligned with the shear layer. This could

well be the reason for the observed smooth roll-up and vortex pairing and more rapid damping of the turbulence in

the upper shear layer. This example highlights some of the issues with grid and numerics that come with beveled

nozzles. This deficiency will be remedied, and should be kept in mind when examining the noise results.

Figures 3 and 4, respectively, show contours of the pressure time-derivative for the beveled nozzle and

comparisons of the predicted directivities of the overall sound pressure levels (OASPL) with data. We notice in

these figures that the predicted noise radiated to the sides (φ=±90º) by bevel45 is slightly higher than that for the

round nozzle, a trend seen in the experiments. The predicted noise levels radiated to the azimuthal angle of 0º is

lower than those at both 90º and 180º, again matching the experimental trends. Furthermore, the shift in the peak

radiation angle by ~25º between φ=0º and φ=180º is captured well by the simulations. However, the peak angles

themselves remain too low, as they were in simpler cases [4]. There is good qualitative agreement between the

predictions and data. The reason for the ~3 dB over-prediction at φ=180º (at least partly) is suspected to be due to

the problem with the grid in the vicinity of the upper shear layer noted in Figure 2. Too smooth a transition and

vortex pairing could lead to increased noise levels; an examination of the spectra (not shown) indicates a false

peak at ~7 kHz due to the vortex pairing, which is not correct.

Sample illustrations of the results of the simulations for the under-expanded jets are given in Figures 5 and 6.

“Numerical schlierens” in Figure 5 reveal clearly a system of shock cells interacting with turbulence. Figure 6

demonstrates good spectral predictions of the noise caused by this interaction (broad-band shock-associated noise)

for both the round and beveled nozzles. There is very good agreement up to a frequency of ~20 kHz (St=1.57),

which is the upper limit for the grid used. Absolute predictions of the shock-peak locations and levels, without any

empirical adjustments, attest to the validity of the approach and indicate that the right physics is captured in the

simulations.

3 Discussion

This study represents our initial efforts at the prediction of the flow features and noise of beveled nozzles.

The sample results included here demonstrate good agreement between the predictions and measurements for

the effect of the bevel. New issues with grid and numerics are being addressed. Detailed results from

simulations at different jet conditions and predicted spectra will be presented in the full paper. Given the

complexity of the problem, these preliminary results are encouraging and it is hoped that a viable

computational tool for the reliable assessment and optimization of this noise reduction concept is feasible.

References

[1] Bogey, C., Bailly, C., Investigation of subsonic jet noise using LES: Mach and Reynolds number effects,

AIAA Paper 2004-3023, 2004.

[2] Bodony, D. J., Lele, S. K., Jet noise prediction of cold and hot subsonic jet using large-eddy simulation,

AIAA Paper 2004-3022, 2004.

[3] Paliath, U., Morris, P. J., Prediction of noise form jets with different nozzle geometries, AIAA Paper

2004-3026, 2004.

[4] Shur, M. L., Spalart, P. S., Strelets, M., Noise prediction for increasingly complex jets, Part I: Methods and

tests; Part II: Applications, accepted for publication in the International J. of Aeroacoustics, 2005.

[5] Uzun, A., Lyrintzis, A. S., Blaisdell, G. A., Coupling of integral acoustics methods with LES for jet noise

prediction, AIAA Paper 2004-0517, 2004.

[6] Viswanathan, K., Nozzle shaping for reduction of jet noise from single jets, AIAA Paper 2004-2974, 2004.

[7] Viswanathan, K., An elegant concept for reduction of jet noise from turbofan engines, AIAA Paper

2004-2975, 2004.

Figure 1: Snapshots of vorticity magnitude in the Figure 2: Computational grid and vorticity near the

XY- and XZ-planes. M=1.0, bevel45. nozzle exit in XY-plane. M=1.0, bevel45.

Figure 3. Snapshots of time-derivative of pressure in

Figure 4. Comparisons of polar directivities at

the XY- and XZ-planes. M=1.0, bevel45.

various azimuthal angles. M=1.0, bevel45. Data [6].

Figure 5. Snapshots of magnitude of density gradient Figure 6. Comparisons of narrow-band spectra at a

in the XY-planes (“numerical schlierens”) for the polar angle of 50

o

for the round and bevel45 jets at

round and bevel45 jets at M=1.56. M=1.56 with data [6].

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