Euromech Colloquium 467: Turbulent Flow and Noise Generation July 18-20, 2005 – Marseille, France
Numerical Prediction of Noise from Round and Beveled Nozzles
Philippe R. Spalart
The Boeing Company, PO Box 3707, Seattle, WA 98124, USA
St.-Petersburg State Polytechnic Univ., 29, Polytechnicheskaya str., St.-Petersburg 195251, Russia
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
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 , Bodony and Lele , Paliath and Morris
, Shur et al , and Uzun et al . 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 . 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  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 . 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  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 . 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 . The development of the shear layer is similar to those in , 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 . 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
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.
 Bogey, C., Bailly, C., Investigation of subsonic jet noise using LES: Mach and Reynolds number effects,
AIAA Paper 2004-3023, 2004.
 Bodony, D. J., Lele, S. K., Jet noise prediction of cold and hot subsonic jet using large-eddy simulation,
AIAA Paper 2004-3022, 2004.
 Paliath, U., Morris, P. J., Prediction of noise form jets with different nozzle geometries, AIAA Paper
 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.
 Uzun, A., Lyrintzis, A. S., Blaisdell, G. A., Coupling of integral acoustics methods with LES for jet noise
prediction, AIAA Paper 2004-0517, 2004.
 Viswanathan, K., Nozzle shaping for reduction of jet noise from single jets, AIAA Paper 2004-2974, 2004.
 Viswanathan, K., An elegant concept for reduction of jet noise from turbofan engines, AIAA Paper
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 .
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
for the round and bevel45 jets at
round and bevel45 jets at M=1.56. M=1.56 with data .