NASA / TM--2002-211807

Computing Jet Screech_A Complex

Aeroacoustic Feedback System

Ching _s: Loh

'Ihitech, Inc., Brook Park, Ohio

Lennart S. Hultgren

Glepa_ Research Center, Cleveland, Ohio

August 2002
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NASA/TM--2002-211807

Computing Jet Screech_A Complex

Aeroacoustic Feedback System

Ching _s: Loh

'Ihitech, Inc., Brook Park, Ohio

Lennart S. Hultgren

Glepa_ Research Center, Cleveland, Ohio

Prepared for the

Second hi_ternational. Conference on Computational Fl.ui.d Dynamics

cosponsored by NASA, Dassault Aviation, DSTO, the School of Aerospace,

Mechanical, and Mechatronic Engineering, University of Sydney, and

the Institution. of Engin.eers, Sydney, Australia, Ju.ly 15-19, 2{){)2

National Aeronautics and

Spa ce Ad.minis tration

Glelm Research Center

August 2002
Acknowledgments

The authors wish to thank Dr. ]. Panda for fruitful discussions. The Supersonic Propulsion Technology

Project Office at NASA Glenn Research Center supported this work.

This report is a formal draft or working

paper, intended to solicit comments and

ideas from a technical peer group.

The Aerospace Propulsion and Power Program at

NASA Glenn Research Center sponsored this work.

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Available electronically at http://gltrs.grc.nasa.gov
Computing Jet ScreechmA Complex

Aeroacoustic Feedback System

Ching Y. Loh

Taitech, Inc.

Brook Pro'k, Ohio 44142

Lermm't S. ttultgren

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Abstract. The space-time conservation-element and solution-element method is employed to numerically study the near-field axisymmetric screech-tone noise of a typical

underexpanded circular jet issuing from a sonic nozzle. For the computed case, corresponding to a fully expanded Mach number of 1.19, the self-sustained feedback loop is

established without artificial means. The computed shock-cell structure, acoustic wave

length, screech tone frequency, and sound pressure levels are in good agreement with

existing experimental results.

1 Introduction

Underexpanded supersonic jets radiate mixing noise, broadband shock-associated

noise, as well as very loud discrete screech tones under certain conditions. Screech

is of particular interest not only because of general noise-reduction concerns, but

also because of potentially destructive structural interaction leading to sonic fatigue. Many experimental and theoretical investigations of jet noise have been

carried out, see the review papers [1,2] for a comprehensive discussion. Mixing

noise is directly associated with large-scale structures, or instability waves, in

the jet shear layer; whereas, broadband shock-associated noise and screech tones

are associated with the interaction of these waves with the shock-cell structure in

the jet core. The screech tones arise because part of the acoustic waves generated

by the wave/shock-cell interaction propagate upstrearn and re-generate the instability waves at, or in the vicinity of, the nozzle lip. This feedback loop leading

to distinct screech tones is sensitive to small changes in the system conditions,

and its explanation is to date mostly based on experimental observations, see

[1,2].

Jet noise is a challenging topic in computational aeroacoustics in particular,

near-field noise computation in the presence of shock cells in the jet core

and reliable direct numerical simulation of jet screech noise has up to quite

recently not been feasible. It imposes stringent requirements that the scheme

must be able to: (i) handle shock waves, (ii) resolve acoustic waves with low

dispersion and dissipation errors, (iii) resolve the instability waves in the jet

shear layers and their interaction with the core shock-cell structure and (iv) have

an effective non-reflecting boundary condition. Successful direct computation of

screech for circular jets have been carried out by Shen and Tam [3,4] using the

well-known DRP scheme and by the present authors [5] using the recent space

time conservation element and solution element method, CE/SE, [6,7]. Further

NASA/T_2002-211807 1
direct simulation of screech is presented below using the axisymmetric CE/SE

Navier-Stokes scheme. The method is described in detail in [5,6].

2 Numerical Method

In general, the CE/SE method systematically solves a set of discretized (secondorder accurate in both space and time) integral equations derived directly from

the physical conservation laws and naturally captures shocks and other discontinuities in the flow. Both dependent variables and their derivatives are computed

simultaneously. As a consequence, the flow vorticity can be obtained without reduction in accuracy. Non-reflecting boundary conditions (NRBCs) are also easily

implemented because of the flux-conservation formulation.

With an unstructured grid, the CE/SE procedure is easily adapted to complicated geometries. Here, an unstructured triangle grid is used. Figure I shows

a typical triangle cell, AABC, with O being its center and D, E, F being the

centers of its three neighboring cells. The flow variables at the current time level

F' C' E'

time level n+l

II I

time level n

Fig. 1. CE/SE unstructured grid: hexagon cylinder ADBECFA-A'D'B'E'C'F'A' conraining three CEs OADBO-O'A'D'B'O', OBECO-O'B'E'C'O', OCFAO-O'C'F'A'O'

n are stored at the center of each triangle cell. Three quadrilateral cylinders

(conservation elements, CEs) are formed by the edges that connect the vertices

and the center of the triangle and its three neighbors. The solution elements,

SEs, are the interfaces between the CEs. An integral form of the conservation

laws is applied to the hexagon cylinder that consists of these three quadrilateral

cylinder conservation elements and explicitly determines the full solution at O'

at the new time level n + 1 using only information stored at D, E, and F (no extrapolations/interpolations across a stencil of cells are needed). Discontinuities

are allowed to occur in a conservation element. Details about the unstructured

CE/SE method can be found in [8]. The weighted a-e CE/SE scheme is used

with the weighting parameter c_ = I and e = 0.5 in the present computations.

NASA/T_2002-211807 2
3 Computation and Comparison with Experiment

Figure 2(a) shows the geometry of the convergent nozzle in Panda's experiment

[9]. The flow is choked (i.e. Mach nmnber M = 1) at the nozzle exit. The jet

Mach nmnber which represents the plenum/ambient pressure ratio for the simulation is Mj = 1.19 [9]. The computational domain, see Fig. 2(b), spans between

14.3D

. D-25,4

'_105 _'= 59 _387

flange/nozzle

Fig. 2. (a) Geometry of the convergent nozzle and flange in Panda's experiment

(dimensions in mm). (b) Computational domain

-8.3D < x < 6D and 0 < r < 11.7D, with x and r being the streamwise and radial coordinates and D being the jet nozzle diameter. The flow inside the nozzle

is not computed, rather the steady flow conditions are prescribed at the nozzle

exit which is located at x = 0. This inflow plane is recessed by two cells so as not

to numerically restrict or influence the feed-back loop. There are totally 230,000

triangle cells. Non-reflecting boundary conditions are applied to the upper and

outflow boundaries and a symmetry condition is applied at the center axis. The

last 10 streamwise cells have exponentially growing size and serve as a buffer,

or sponge, zone to essentially eliminate any small remaining numerical reflection

from the downstream outflow boundary. Initially, the entire flow is at rest and

at ambient conditions; the jet flow is then impulsively started. The Reynolds

number Re = Dao/U = 570,000, where ao is the ambient speed of sound (used

as velocity scale) and u is the kinematic viscosity at the ambient conditions. Figure 3(a) displays numerical pressure contours and numerical Schlieren contours,

outside and inside of the jet core respectively, well after the start-up transients

has passed out of the computational domain. Distinct screech waves are observed

to emit from the 3rd to the 5th shock-cell and are reflected at the flange/nozzle

body. The screech wavelength (1.6D) and the shock-cell structure (0.SD spacing) agree well with the experiment [9]; for the latter see Fig. 3(b). Spectral

analysis yields a computed screech frequency of 8513 Hz, which agrees well with

the experimental value of 8525 Hz. The sound pressure level (SPL) along an

inclined line at the outer edge of the shear layer is shown in Fig. 4. This figure

NASA/T_2002-211807 3
isobars at t=410,000 steps

flange/nozzle

Fig. 3. (a) Isobars at t=410,000 steps, showing screech waves and shock cell structures.

(b) Experimental Schlieren picture showing the shock-cell structure [9]

shows Panda's [9] data for the A2 axisymmetric screech mode, the corresponding

result from the simulation as well as the computed total SPL and subharmonic

of the A_ mode. Even though the A2 SPL level in the vicinity of the nozzle lip is

190.

160.

co

13o.

100.

.,S,_,,'ff---""{"_=_"_ ....... .....................

_') Panda A 2 mode, 9828 Hz

::i: f_ CE/SE A 2 mode, 8513 Hz

CE/SE A 2 subharmonie

(_ 4- CE/SE total SPL

0:0 _:0 4:0 6:0

_D

Fig. 4. Comparison of computed and experimental SPL along the shear layer edge

NASA/T_2002-211807 4
too low, its early streamwise growth rate is, however, well predicted indicating

that the jet shear layer is in general well resolved. Nonlinearity in the shear layer

limits the amplitude that can be obtained and once the SPL level 'catches up'

the agreement is very good, in particular the SPL level in the streamwise region

where the backward radiating acoustic waves are generated is well predicted. The

strong subharmonic that appears further downstrearn is due to (axisymmetric)

vortex pairing in the shear layer and as a consequence a second streamwise peak

at the A2 frequency occurs due to nonlinear effects. However, a-D effects are

most likely to have come into play in the experiment at these streamwise locations leading to suppression of the subharmonic. The reason for the low initial

SPL values in the simulation is currently being pursued.

Figure 5 shows computed SPL contours for the A2 mode. As in the experiment [9], a standing wave structure can be observed along the edge of the jet

shear layer. The results are in general agreement with the experimental ones

except, as pointed out earlier, that the computed SPL levels are too low in the

vicinity of the nozzle lip and the existence of a second, or extended, region of

elevated values further downstream (x/D > 4).

6.30

4.40

2.50

0.60

0.0 2.0 4.0

158.0

155.0

152.0

149.0

146.0

143.0

140.0

137.0

134.0

131.0

128.0

125.0

122.0

119.0

116.0

113.0

110.0

6.0

x/D

Fig. 5. Computed A2-mode SPL levels for Panda's experiment

Figure 6 displays the computed SPL at the nozzle exit lip wall, z/D = O,

r/D = 0.6. The SPL shows a distinct spike corresponding to the A2-mode screech

tone observed in Panda's [9] experiment. Note that in our previous work [5],

which had a much simplified description of the nozzle external geometry, the

Al-mode screech tone (not observed in [9]) was also obtained at this condition.

This illustrates the sensitivity of the screech phenomenon to geometry changes.

NASA/T_2002-211807 5
140.

120.

J_

69

100.

80.

O. 5000. 10000. 15000. 20000.

frequency (Hz)

Fig. 6. SPL at nozzle exit (x/D = O, riD = 0.6), 75 Hz digital binwidth

4 Summary

It is concluded that the simulation shows a reasonably good agreement with

experimental data in the streamwise region where the flow is expected to be predominantly axisymmetric and, hence, that jet screech is successfully simulated

using the CE/SE scheme.

References

1. C.K.W. Tam: Ann. Rev. Fluid Mech. 27, 17-43 (1995)

2. G. Raman: Prog. Aerospace Sci. 34, 45-106 (1998)

3. H. Shen, C.K.W. Tam: AIAA Paper 98-0283 (1998)

4. H. Shen, C.K.W. Tam: AIAA Paper 2001-0820 (2001)

5. C.Y. Loh, L.S. Hultgren, P.C.E. Jorgenson: AIAA Paper 2001-2252 (2001).

6. S.-C. Chang, X.-Y. Wang, Chow, C.-Y. Chow: J. Comp. Phys. 156, 89-136 (1999)

7. C.Y. Loh, L.S. Hultgren, S.-C. Chang: AIAA J., 39, 794-801 (2001)

8. X.-Y. Wang, S.-C. Chang: C.F.D.J. 8, 309-325 (1999)

9. J. Panda: J. Fluid Mech. 378, 71-96 (1999)

NASA/T_2002-211807 6
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August 2002 Technical Memorandum

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Computing Jet Screech--A Complex Aeroacoustic Feedback System

6, AUTHOR(S)

Ching Y. [,oh and Lennart S. Hultgren

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

John H. Glenn Research Center at Lewis Field

Cleveland, Ohio 44135 - 3191

WU-708-90-43-00

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E----13502

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AGENCY REPORT NUMBER

National Aeronautics and Space Administration

Washington, DC 20546-0(101 NASA TM------.2002-211807

11. SUPPLEMENTARY NOTES

Prepared for the Second International Conference on Computational Fluid Dynarmcs cosponsored by NASA, Dassault

Aviation, DSTO, the School of Aerospace, Mechanical, and Mechatronic Engineering, [ Jniversity of Sydney, and the

Institution of Engineers, Sydney, Australia, July 15-19, 2002. Ching Yi Lob, Taitech, Inc., Brook Park, Ohio 44142,

and Lennart S. ttultgren, NASA Glenn Research Center. Responsible person, Ching Y. Loh, organization code 5800,

216-433-3981.

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12b. DISTRNBUTION CODE

13. ABSTRACT (Maximum 200 words)

The space-time conservation-element and solution-element method is employed to numerically study the near-field

axisyimnetric screech-tone noise of a typical underexpanded circular jet issuing from a sonic nozzle. For the computed

case, coI_'esponding to a fully expanded Much number of 1.19, the self-sustained feedback loop is established without

artificial means. The computed shock-cell structure, acoustic wave length, screech tone frequency, and sound pressure

levels are in good agreement with existing experimental results

14. SUBJECT TERMS

Jet screech noise; Aeroacoustic feedback loop; CE/SE method

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