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Procedia Engineering

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Procedía Engineering 6 (2010) 28-37

www.elsevier.com/locate/procedia

IUTAM Symposium on Computational Aero-Acoustics for Aircraft Noise Prediction

Jet Noise Simulations for Realistic Jet Nozzle Geometries

Philip J. Morris*, Yongle Du, Kursat Kara

Penn State University, 233C Hammond Building, University Park, PA, 16802, USA

Abstract

This paper describes a methodology for the direct calculation of noise from realistic nozzle geometries. The focus of the paper is on the numerical approach to this problem to provide noise predictions to engineering accuracy in an efficient manner. In addition, issues related to grid generation are discussed. The methodology uses structured multiblock grids. The block surrounding the jet centerline has a Cartesian form and the surrounding grid blocks have a cylindrical polar form - at least for nearly axisymmetric jet nozzle geometries. Appropriate block interface conditions are used. In the case of military style jet nozzles the nozzles are not smooth in the azimuthal direction but have facets representative of the movable flaps in such variable area nozzles. These features must be included in the grid. To enable efficient calculations, in addition to parallel computation, a dual time-stepping approach is used. The sub-iterations in the fictitious time are accelerated using a two-level multigrid approach. A Detached Eddy Simulation (DES) approach based on the Spalart-Allmaras (S-A) one-equation turbulence model is used. Comparisons are made between flow predictions using the DES with the S-A model everywhere and with the turbulence model turned off in the jet external flow. Noise predictions are made with the permeable surface Ffowcs Williams - Hawkings (FW-H) solution. Noise predictions are presented for both a smooth convergent-divergent nozzle as well as a nozzle representative of a military aircraft engine. Comparisons are made with available experimental data.

© 2010 Published by Elsevier Ltd.

Keywords: Jet noise predictions; supersonic jets; Large Eddy Simulation; Military engine nozzles;

1. Introduction

The noise generated by military fighter aircraft during take-off and landing poses a health threat to ground crews and communities in the vicinity of airports. Governments have passed stringent noise regulations on the noise levels of civilian aircraft, and many efforts have been undertaken to understand and reduce their noise. The acoustics of military aircraft have not typically been subjected to the same scrutiny.

Though the noise generation mechanisms of hot supersonic jets contain some features in common with subsonic jets, the dominant noise mechanisms are quite distinct. Principally, the supersonic convection of the turbulence in the jet shear layer, relative to the ambient speed of sound, results in an efficient direct coupling between the

* Corresponding author. Tel.: +1 (814) 863-0157; fax: +1 (814) 865-7092. E-mail address: pim@psu.edu

1877-7058 © 2010 Published by Elsevier Ltd. doi:10.1016/j.proeng.2010.09.004

turbulence and the radiated noise. This is the Mach wave radiation. Very intense and highly directional, it is the dominant noise generation mechanism in the jet downstream arc. For jets that are perfectly expanded, it can be more than 20 dB more intense than noise radiated normal to the jet or in the upstream arc.

When the jet is operating off-design, however, which is often the case for military aircraft engines, two additional noise mechanisms may be present. These mechanisms are associated with the interaction between the turbulence in the jet shear layer and the jet's shock-cell structure. The first is broadband shock-associated noise. As the name suggests this mechanism generates noise at all frequencies, though its peak frequency is higher than that of jet turbulence mixing noise. The large-scale turbulent structures in the jet convect through the jet's shock cells and generate a sequence of coherent sources at these locations. The resulting constructive interference between the noise radiated by these sources yields the broadband shock-associated noise that radiates at large angles to the jet downstream axis and dominates the noise at these large angles.

The broadband shock-associated noise that radiates towards the jet nozzle can trigger turbulent structures that then propagate downstream, interact with the jet's shock cells, and radiate shock associated noise. This sequence can form a phase-locked loop and can generate an intense tonal noise source known as screech. Screech is rarely observed in single full-scale hot jets, but it can occur in twin jet configurations. When screech occurs, because of its high intensity, it can cause structural damage to the jet nozzle and nearby structural elements.

Finally, the levels of noise generated by hot supersonic jets can be so high that nonlinear acoustic mechanisms occur. In particular, a phenomenon called "crackle," which is identified by shock-like features in the noise time history is observed. In addition, the propagation of the sound is nonlinear, and simple linear extrapolation of the sound in the near field results in an under prediction of high frequency noise.

In the next section the overall flow and noise simulation strategy are described. A detailed description of the equations is not given, though some new implementation analysis is provided. Results are then given for the flow and noise generated by high speed jets issuing from smooth convergent-divergent nozzles as well as facetted nozzles, more typical of military jet aircraft nozzles. The emphasis is on the effects of the grid resolution as well as the methods to reduce the total computation time.

2. Simulation Strategy

The ideal choice for jet noise simulations (and other aeroacoustic problems) would be a direct simulation approach, in which all details of the unsteady flow and the radiated sound field are resolved at the same time. Because of the wide range of time and length scales of unsteady turbulent structures and sound waves in high speed jets, such simulations would require an extremely fine mesh and a very small time step. Because of this, the computational cost of these simulations is very high and only very simple flow configurations have been studied using this approach.

Under the constraint of limited computer resources and the desire for a relatively rapid turnaround time, a hybrid method combining advanced CFD technology with an acoustic analogy is the most practical strategy at present for realistic jet noise simulations. In contrast to the direct simulation method, the hybrid method does not aim to capture all details of the flow. Instead, a primary simulation is employed to resolve the major noise sources in the near-field, and, based on this information, a secondary calculation is performed for far-field noise predictions using an acoustic analogy approach. An acoustic analogy is a rearrangement of the fluid dynamic equations into a form where the right-hand side represents equivalent sound sources, and the left-hand side is a partial differential operator that represents the sound wave propagation. Once the unsteady flow solutions from the URANS/LES computations are known on an acoustic data surface surrounding the jet, the partial differential operator can be inverted to predict the radiated sound field.

2.1. Multiblock meshes and mesh singularity treatment

Most previous research excluded the nozzle geometries in the jet noise simulations. The inlet flow conditions are imposed at the nozzle exit by using the steady flow simulation result with the nozzle geometry included. As a result, the interaction of the nozzle and the flow was not considered directly. To better simulate the development of the boundary layer inside the nozzle and its effect on the jet plume, the nozzle geometry is included in the present computations. The finite nozzle thickness is also taken into account in the simulations. This triggers the unsteady flow downstream of the nozzle lip, since the wake downstream of the nozzle lip exhibits an intrinsic instability.

The unsteady jet flow simulations are run on structured multiblock grids. The typical mesh, for example for the military style facetted nozzle, is shown in Figure 1, where a multiblock topology is used to avoid the centerline singularity in the cross section. The computational domain extends to 60Dj downstream the nozzle exit, and 30Dj in the radial direction at the downstream boundary. The mesh is significantly refined around the jet core to capture the smaller turbulent structures. Based on the assumption that 10 grid points are required to resolve the shortest wave component, the grid spacing is set as 0.01Dj, and gradually stretch to 0.02Dj at the end of jet core, so that the highest frequency which can be resolved is expected to be St=1.5 - as discussed below, where the Strouhal number St=f*Dj/Uj, Uj is the fully expanded jet velocity, which is calculated from the total pressure and temperature ratios based on one-dimensional isentropic flow.

Since the spatial derivatives of the flow variables along the block interface are not continuous, special treatments are required. Kim and Lee [1] proposed a Characteristic Interface Condition (CIC) based on Thompson's characteristic boundary conditions [2]. In this method, a one-sided difference scheme is employed to approximate the spatial derivatives of the fluxes in the normal direction to the block interface for each block, and then the derivatives are corrected using the variables from its neighbor if the characteristic waves are propagating into this block. The corrections are made such that the time derivatives of the flow variables are the same for each pair of matching grid points on the block interface.

It should be noted that Kim and Lee's original formulas are not easy to implement, especially when the mesh-orientation is not the same across the block interface. Therefore, the following modifications have been made to directly manipulate the residuals of the conservative form of Navier-Stokes equations. This modification results in a simple formulation regardless of the mesh orientations.

The conservative form of corrections at the block interface can be written:

dQ/dt + PS (L + Sc) = 0 (1)

where an asterisk is used to denote the value after correction.

Res* = PS (L + Sc) - PS( L + Sc) + PS(L + Sc) = PSAL + Res (2)

where,

Mi = (Lri + Scl - Scl) - Lt = (S"P"1 Re s)r - (S^P-1 Re s)1 (3)

2.2. Unsteady jet flow simulations

The unsteady compressible Navier-Stokes equations are solved numerically to predict the development of the unsteady turbulent jets. The Dispersion-Relation Preserving (DRP) scheme introduced by Tam and Webb [3] is used in the spatial discretization. In order to circumvent the very small physical time step when the mesh is greatly refined near the wall, the dual time-stepping method [4] is used for efficient unsteady flow simulations. A two-level multigrid method [5] is used accelerate the convergence rate at the sub-iterations in the fictitious time to further improve the computation efficiency.

The dimensionless physical time step is chosen to resolve the highest frequency up to a Strouhal number St=1.5, if 10 physical time steps are required to resolve the shortest wave component. The unsteady flow simulation runs for about1.5 x104 physical time steps, to advance the unsteady jet flow to a statistically stable state before the flow sampling on the Ffowcs Williams and Hawkings (FW-H) integration surfaces is initiated. This corresponds to 15 times of the time for the turbulent eddies to travel through the jet core, based on the conservative assumptions that the average convection speed of the turbulent eddies is 50% of the jet velocity and that the jet core extends to a distance 10D,- downstream of the nozzle exit.

Figure 1: Computational mesh of the GE facetted nozzle

The Detached Eddy Simulation (DES) [6] variant of the Spalart-Allmaras (S-A) model [7] is used for the turbulent flow simulation. Although it behaves much better than the original RANS version, computations show that it still adds too much dissipation into the flowfield. An example of the difference between the instantaneous flowfield obtained using the DES with the S-A turbulence model and results where the turbulence model is turned off when away from solid boundaries is shown in Figure 2. It is clear that using the grid alone to provide the removal of turbulent energy enables much smaller features of the flow to be identified. However, it should be noted that the mesh used in this 2D example jet simulation is very coarse, and that further refinement of the mesh should capture the smaller eddy structures, as evident in the following 3D realistic jet simulations described below.

2.3. Noise predictions

The acoustic analogy theory developed by Ffowcs Williams and Hawkings [8] is used for the far-field noise predictions. Several grid surfaces in the computation mesh are used as the FW-H acoustic data surfaces. The surfaces extend to 25Dj downstream of the nozzle exit. The flow variables on those surfaces are sampled at each physical time step, and more than 5000 samples are recorded for noise predictions.

The time signals of the acoustic pressure at far-field observers are broken into several 1024-sample segments to calculate the noise spectrum by using the Fast Fourier Transforms (FFTs). Each segment is a half overlapping with the adjacent ones, to provide a more appropriate average when a Hanning window is used.

It should be noted that the noise spectrum produced in this way is still too "noisy". This would decrease as the total sample time, and hence the number of averages, increases. So, the Savitzky-Golay [9] smoothing filter is used to smooth the computed noise spectrum. Unlike other filters that use a simple averaging procedure, which introduces too much bias and smoothing of the spectral peaks, the Savitzky-Golay filter tries to preserve those features. A

comparison of an unsmoothed and smoothed noise spectrum is shown in Figure 3 with the experimental measurements, for an observer at 30 degrees to the downstream jet axis and a distance 100Dj for a smooth convergent-divergent nozzle operating at an off-design condition.

(b) Simulation with deactivated turbulence model in the DES region

Figure 2: Comparison of instantaneous Mach contours with two DES approaches (2D jet simulation).

Figure 3: Comparison of smoothed and unsmoothed noise spectra with experiment for an observer at ^=60° and R/D/=100 (Md=1.5, M/=1.7, TTR=2.2).

3. Results and Discussion

In this section, jet noise simulation results for two nozzle geometries are presented. The first one is the NASA axisymmetric converging-diverging nozzle (smc016), with an exit diameter of 2 inches [10]. The second one is a

model of military-style facetted nozzle. Both nozzles have a design Mach number Md = 1.5 . Experimental data was at the NASA Glenn Research Center as well as in the Penn State Anechoic Jet Facility for both nozzle geometries.

Two jet operation conditions are simulated for each nozzle. For the NASA nozzle, one is a perfectly expanded unheated jet (M=1.5, TTR=1.0) and the other is an under-expanded, heated jet (M=1.7, TTR=2.2). For the facetted nozzle, one is a strongly over-expanded jet (M=1.05, TTR=2.12), and the other is a slightly under-expanded jet (M=1.56, TTR=3.02). Only a sample of the predictions is presented in this paper.

3.1. Computation with a Coarse Mesh and a Fine Mesh for the NASA Nozzle

In the jet noise simulations of the NASA nozzle, a coarse grid was created first. Simulation results showed that, compared with measurements, the noise spectrum dropped rapidly at high frequencies (St>0.1) for all observer angles and a distance from the nozzle exit R/D=100. Considering that for most cases, the noise peak appears around St~0.2~0.5, this simulation result is not acceptable.

Analysis revealed that the problem was caused by the large grid spacing in the jet core region. Therefore, for the subsequent simulations, a criterion was established to determine the appropriate grid spacing around the jet core. Assume that we need to capture the highest frequency up to St=1.0 and that N=10 grid points are required to resolve the shortest wave component, since St = (c ■ Dj) / (N -Ax -Uj), an estimate of the required grid spacing is given by Ax = (c• Dj)/(N■ St■Uj), where, c is the local speed of sound. Based on this criterion, it is estimated that the earlier coarse mesh could only resolve a highest frequency St^0.2, and that the newer fine mesh could resolve a highest frequency St~1.0. From the comparison of the predicted noise spectra in Figure 4, one can see that the criterion gives a good estimate of the grid spacing requirements for the jet noise simulations.

Pre<J iction (coarse me iction (fine mesh' riment (PSU) sh)

Prad Exp

\ !v

Strouhal number, fDJU,

Figure 4: Comparison of predicted unsmoothed noise spectra with experiment [10] from coarse and fine mesh simulations for an observer at 0=60° and R/Dj=100 for the NASA nozzle with M=1.7,

3.2. Instantaneous flow solutions

Figure 5 shows the instantaneous density gradient contours at both operating conditions for the facetted nozzle. For both jets, periodic shock cell structures are formed in the jet plume. Large and small eddies are observed in the shear layers. For the strongly over-expanded jet, a small separation region is observed near the nozzle exit.

A series of 'numerical' probes are inserted into the shear layer along the lip line for both jets, with an interval of approximately 0.5Dj. The flow variables are sampled at the probes every physical time step to estimate the convection speed of the turbulent structures. Figure 6 shows the cross-correlation of the axial velocity component along the lip line, with the reference probe at XDj=2.05, from which the convection speed can be estimated. The convection speed is Uc~0.585Uj, or the convective Mach number Mc=U/e,¡=0.809 for the over-expanded jet, and Uc~0.466Uj, or Mc~l.03 for the under-expanded jet. However, only the unsteady solutions at 2500 time steps are available in the calculation, small oscillations can be observed in the cross-correlation curves.

<a)il4=1.05,TTR=2.12

(b)A/;=1.56, TTR=3.02

Figure 5: Instantaneous density gradient contours for the facetted nozzle

¡0.2 o

-0.4 -0 6

tN'UJ/Dj

(a) M=1.05, TTR=2.12

1 str

\ - X/Dj=2.53 - X/Dj=3.0d

X/Dp4_07

y V—-

' h \/ / *

(H'UJ/Dj

(b) M=1.56, TTR=3.02

Figure 6: Cross-correlation of axial velocity fluctuations along the lip-line for the facetted nozzle.

3.3. Mean flow solutions

Figure 7 shows the time-mean Mach number contours at the two operating conditions for the NASA nozzle. Very weak shock cells appear in the plume of the nearly perfectly expanded jet, and periodic shock cell structures are clearly visible in the plume of the under expanded jet.

(a) Mj=1.5, TTR=1.0 (b) Mj=1.7, TTR=2.2

Figure 7: Time-mean Mach number contours for the NASA nozzle computations

Figure 8 shows comparisons of the simulated and measured total pressure distributions for the on-design NASA jet case. The measurements were made by Miller et al. [11]. Figure 8(a) shows radial profiles close to the jet exit and Figure 8(b) shows the profiles at downstream locations. The agreement between the predictions and measurements is reasonable.

(a) From x/D,=0.0 to x/Dj=1.0

10 12 2.5 x/D

(b) From x/D,=1.0 to x/Dj=6.0.

Figure 8: Comparison of predicted (lines) and measured (symbols) radial profiles of total pressure (NASA nozzle, M,=1.5, TTR=1.0)

Pt2 / Pt0 + 2.5 x/D

3.4. Far-field noise predictions

The flow sampling for the noise predictions is started after the unsteady jet flow becomes statistically stationary, and more than 5000 samples are recorded on the FW-H acoustic data surfaces. The noise prediction is made with the same physical time step as the unsteady flow simulations. Figures 9 and 10 show a comparison of measured and predicted noise spectra for all jets at three observer angles with the distance of 100Dj to the nozzle exit. All noise spectra are smoothed by a Savitzky-Golay filter. In the peak frequency range, the agreement between the predictions

and measurements is satisfactory. A rapid decay at high frequencies can be observed. In light of the comparison of the noise spectra from the coarse and fine computations in Figure 4, it is expected that the agreement at high frequencies could be improved significantly by further refinement of mesh in the jet core.

(a) M=1.5, TTR=1.0

(b) M=1.7, TTR=2.2

Figure 9: Comparison of predicted (lines) and measured (symbols) noise spectra at three observer angles with the distance of 100Dj to the nozzle exit, NASA nozzle

(a) M=1.05, TTR=2.12 (b) M=1.56, TTR=3.02

Figure 10: Comparison of predicted (lines) and measured (symbols) noise spectra at three observer angles with the distance of 100Dj to the nozzle exit, facetted nozzle. Because the measured noise spectra at the same operating conditions are not available for the over-expanded jet, measurements at two other conditions are provided for comparison. One has an acoustic Mach number Ma=Uj/c-=1. 31, (squares) and the other has an acoustic Mach number Ma=1.54, (filled triangle). The over-expanded jet has an acoustic Mach number Ma=1.38.

4. Conclusions

The present simulations represent preliminary calculations of the flow and noise from nozzles with realistic geometries. Additional simulations are being run for longer sample times and further comparisons with flow and noise measurements are being conducted. The present approach has focused on simulations with moderate grid requirements with an aim to resolve the noise generated in the peak noise direction. It can be argued that the noise at other angles is more effectively and efficiently predicted using methods based on steady flow simulations and acoustic analogies, or related formulations.

Acknowledgements

This research was supported in part by the Strategic Environmental Research and Development Program under task WP-153. The program manager is Mr. Bruce Sartwell. Support was also provided through an STTR under a subcontract to Innovative Technology Applications Company, LLC, funded by the Naval Air Warfare Center. The technical monitor is Dr. John Spyropoulos. The authors are grateful to Dr. James Bridges at the NASA Glenn Research Center for supplying the experimental measurements for the NASA nozzle and to Dr. Dennis McLaughlin and Mr. Ching-Wen Kuo for the Penn State noise measurements.

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