Experimental measurements of naturally occurring instability modes in the axisymmetric shear layer of high Reynolds number turbulent jet are presented. The region up to the end of the potential core was dominated by the axisymmetric mode. The azimuthal modes dominated only downstream of the potential core region. The energy content of the higher order modes (m is greater than 1) was significantly lower than that of the axisymmeteric and m = + or - 1 modes. Under optimum conditions, two-frequency excitation (both at m = 0) was more effective than single frequency excitation (at m = 0) for jet spreading enhancement. An extended region of the jet was controlled by forcing combinations of both axisymmetric (m = 0) and helical modes (m = + or - 1). Higher spreading rates were obtained when multi-modal forcing was applied

Raman, Ganesh

Reshotko, Eli

Rice, Edward J.

English

NASA Technical Reports Server

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I
NASA Technical Memorandum 104483
Control of an Axisy_etric Turbulent
Jet by Multi-Modal Excitation
17
Ganesh Raman
Sverdrup Technology, Inc.
Lewis Research Center Group
Brook Park, Ohio
Edward J. Rice
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio
and
Eli Reshotko
Case Western Reserve University
Cleveland, Ohio
i!_ ¸
Prepared for the
Eighth Symposium on Turbulent Sh_ _ws
sponsored by the Turbulent Shear FlowCommittee
Munich, Germany, September 9-11, 1991
N/ A
("_ +,-I" ..... "_'i1., .... .._, _.-' ,T> <L < " A:",i A_I._Y_;_ T, I.C
https://ntrs.nasa.gov/search.jsp?R=19910016807 2020-03-19T16:50:35+00:00Z
NASA Technical Memorandum 104483:
,i
Control of an Axisymmetric Turbulent
Jet by Multi-Modal Excitation
,_=.=.,.,- _2 _ /
Ganesh Raman
Sverdrup Technology, Inc.
Lewis Research Center Group
Brook Park, Ohio
Edward J. Rice
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio
and
Eli Reshotko
Case Western Reserve University
Cleveland, Ohio
:ill:
Prepared for the
Eighth Symposium on Turbulent Shear Hows
sponsored by the Turbulent Shear Flow Committee
Munich, Germany, September 9-11, 1991
CONTROL OF AN AXISYMMETRIC TURBULENT JET
BY MULTI-MODAL EXCITATION
Ganesh Raman
Sverdrup Technology, Inc.
Lewis Research Center Group
Brook Park, Ohio 44142
Edward J. Rice
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135
Eli Reshotko
Case Western Reserve University
Cleveland, Ohio 44106
ABSTRACT
Experimental measurements of naturally occurring in-
stability modes in the azisymmetric shear layer of a high
Reynolds number turbulent jet are presented. The region
up to the end of the potential core was dominated by the
axisymmetric mode. The azimuthal modes dominated only
downstream of the potential core region. The energy con-
tent of the higher order modes (m > 1) was significantly
lower than that of the axisymmetric and m = +1 modes.
Under optimum conditions, two-fTequency excitation (both
at m = O) was more effective than single frequency ex-
citation (at m = O) for jet spreading enhancement. An
extended region of the jet was controlled by forcing comp-
tnations of both axtsymmetric (rn = O) and helical modes
(m = +1). Higher spreading rates were obtained when
multi-modal forcing was applied.
INTRODUCTION
The study of the fundamental aspects of naturM jets
as well as their excitability and control is of great practi-
cal importance and shows promise for enhancing mixing,
controlling separation and reducing jet noise.
Although a vast body of data exists, most of the obser-
vations have been made in idealized "clean" jet flows. There
is a need for studying these phenomena in jets that are more
representative of industrial applications, i.e., high Reynolds
number, fully turbulent initial condition, and high core tur-
bulence. In addition, the focus needs to be at and beyond
the potential core. Such an understanding is essential if any
further progress is to be made in the application of these
techniques to technologically relevant situations.
In a jet excited by' naturally occurring disturbances,
the large scale coherent structures occur over a band of fre-
quencies and over various azimuthal mode numbers. The
nature of these structures has frequently been characterized
using correlation functions (Drubka, 1981: Sreenivasan,
1984; Chan, 1977; Gutmark et al., 19881). Correlations of
streamwise velocity with circumferential separation can in-
dicate the relative dominance of the axisymmetric or the
azimuthal waves. For example, the correlations are inde-
pendent of circumferential separation if the flow consists
of circular vortex rings. If the correlations show a circum-
ferential dependence, they may be due to azimuthal waves
developing on the circular vortex rings, or by a transvers("
flapping of the jet. The modal spectrum representation
provides the capability of resolving the naturally occurring
axisymmetrie and azimuthal modes over a range of frequen-
cies.
Sample mode spectra have been reported previously
(Petersen et al., 1987) but have not been used to charac-
terize the evolution of the various instability, modes trig-
gered by natural disturbances. Drubka (1981) examined
the evolution of modes in an unexcited jet for both lami-
nar and turbulent exit conditions at various levels of core
turbulence. However, most of the measurenn'nts reported
were for x/D < 1 at a Reynolds number of 42,000. From
the standpoint of practical applications there is a need to
study the evolution of modes over an extended region of
the jet and at more representative Reynolds numbers.
There have been several other investigations of insta-
bility modes in jets (Kusek et al., 1989; Corke et al., 1991).
In these studies, a very low level of excitation was used to
organize shear layer instabilities and to raise the large scale
coherent structures over the background levels, in addition
to providing a phase reference for the measurements. Even
though the levels of excitation were of the same order as the
naturally occurring fluctuations, the jet displayed different
characteristics. For example, in the work of Corke et al.,
1991, low arnplitude acoustic excitation of the jet at the
natural fundamental frequency of the axisymmetric mode
suppressed the occurrence of the helical modes observed by'
Drubka, 1981, in the same jet facility. For this reason, it is
necessary to document the evolution of natural instability
modes without any aeoustic excitation.
Cohen and Wygnanski (1987-a) calculated the natural
evolution of disturbances in the axisymmetric mixing layer.
Linear stability, analysis was applied to a family of mean
velocity profiles for the first seven azimuthal modes after
assuming that the flow is inviscid and quasi-parallel. These
calculations showed that at x/D = 0.125 the amplification
rates of the first four azimuthal modes are almost indistin-
guishable from one another. As the .:fixing layer widens the
relative importance of the azimutiml modes diminishes and
at the end of the potential core, only tile m = 1 and the
m = 0 modes remain amplified. Their calculations reveal
that at tile end of the potential core, mode 1 emerged as the
dominant instability. This was also predicted by Michalke
and Hermann (1982) and Batchelor and Gill (1962), and
reported by Mattingly and Chang (1974) and Zaman and
I4ussain (1984). It is suggested, thereh)re, that the m = 1
azimuthal mode is prevalent at the end of the potential core.
and one expects this mode to control the evolution of the
fully developed jet. However, the experimental evidence for
the existence of spinning modes in high Reynolds number
jets has been rather sketchy. Direct proof, through detailed
measurements, has yet to substantiate these findings.
The degree of jet spreading offered by' single frequency
plane wave excitation may not seem attractive enough to
pursue for practical applications. However, when the "pre-
ferred mode" frequency becomes neutrally stable, its sub-
harmonic, which is then amplifying near its maximum rate,
can be used to cause further mixing enhancement. The de-
velopment of a subharmonic in a free shear layer has been
observed by several researchers. An analysis was presented
by Kelly (1967) which showed that there exists a mecha-
nism for the generation of a subharumnie wave in the ease
of a flow with a hyperbolic tangent velocity profile. It was
fer function associated with the system (amplifiers, cables,
acoustic drivers, and tubes) caused the input phases and
amplitudes to be different from those measured at the jet
exit. The radial traversing ring is used to traverse 8 single
or x-wires simultaneously in the radial direction.
DISCUSSION OF RESULTS
Naturally Occurring Modes in a Jet
The modal decomposition representation at a discrete
frequency of the spectrum can be used to characterize the
flow as consisting of various modes of motion of the vorti-
cal structures at that frequency. The modal spectrum was
determined by measuring the unsteady streamwise velocity
using 8 hot-wires positioned at intervals of 45 ° about the
circumference of the jet cross-section. Linearized signals
from the hot-wires were input to a spectrum analyzer to
obtain cross-spectra. The cross-spectra are randomly trig-
gered ensemble averages over a long time interval. Using
the signal from hot-wire number 1 as reference, 7 cross-
spectrum magnitudes and phases were evaluated at each
frequency with the 7 cross-spectra (magnitudes and phases)
as input the magnitude and phase of the first 3 modes in
the clockwise direction and the first 3 modes in the counter-
clockwise direction were determined, by solving the 7 simul-
taneous complex equations. To generate the modal spec-
trum, the decomposition is performed at every frequency
in the chosen range. The modal spectrum then consists of
the amplitude of the mode plotted as a function of the fre-
quency. The modal decomposition was performed at every
5 Hz up to 2000 Hz using 8 circumferential measurement.q
providing the magnitude of modes m = 0, 4-1, -4-2, 4-3 as a
function of frequency.
x
z
...s
m = +3
m = +2 m = -2
¢-
:' J_L,J:_':Imlr!i'' r 'c ! ir +Itl,r,],r i[, [
E
+.
J :1 I_ I ,I
m = -3
(a) x/D = 2.
K =
+:- m = +3 _ m = -3
__ ............... _.,...,++,,,,..,,.++,. u+. +..... : .
m = +2 :- m = -2
E =
m = +I m = -I
//.,; " m = 0
0 2000
FREOUEIKY, Hz
(b) x/D = 4.
Figure 2.--Axial evolution of the natural modes in a
circular jet, turbulent initial boundary layer,
velocity measurement at U/UCL : 0.8, M = 0.2,
Re(D) = 400 000.
Results will be shown for one case at M = 0.2
(Re(D) = 400,000), with a core turbulence intensity of
0.1% and a turbulent nozzle exit boundary layer. The
data in Figure 2(a-d) show that the energy content of the
higher order modes (m > 1) was significantly lower than
the rn = 0 and m = -F1 modes. The initial region of the
jet is dominated by the axisymmetric mode, whereas the
region downstream of the potential core is dominated by
helical modes. Drubka (1981) found that when the distur-
bance level in his laminar exit boundary layer was of the
order of 5% the probability of finding either mode (0 or 1)
was 0.5, near the nozzle exit (x/D < 1). The present work
(Figure 2) shows that the axisymmetric mode is dominant
in the initial region. But beyond the end of the potential
core (z/D _ 6) the helical modes dominate. The damping
of the axisymmetric mode beyond the potential core is in
agreement with the predictions of Batchelor and Gill (1962)
and Morris (1976).
The stability analysis of Strange and Crighton (1983)
predicted that helical waves would be more amplified than
a,xisymmetric waves at the preferred frequency. Even
though the helical modes have a higher growth rate (Raman
(1991)), the initial region of the jet is dominated by the ax-
isymmetric mode. This result is attributed to the type of
natural disturbances occurring at the jet lip. For the 8.89
cm nozzle used, the cutoff frequency for all nonaxisym-
metric modes was 2270 Hz (Skudrzyk (1971), page 431).
Thercfore, acoustic disturbances in the frequency range of
0 - 1000 Hz arriving at the jet lip through the nozzle are ax-
isymmetric. Some of these disturbances are of a relatively
high amplitude (due to plenum resonances) and the.v couple
x
K-
r-
1_ m= +3., m = -3
- L_,_ m = +2 m = -2
_ "_,'_'0,,,,,,,..,,.,_.. .............. th'_-,,,.,¢.-,+,..,_.... .........
_',t,, +
I m= 1 -1
r 0%+.'.+_,,+.....+-•_ _ : .... ,,
+
E m= o
_:A_t._,,_.._ ...._...... _...,
(C) x/D = 6.
.8
_- K
. m = +3 _ . m = -3
, m= +2 _- , , m = -2
L nl= 0
2000
FREOUENCY,HZ
(d) x/D = 8.
Figure 2.--Concluded.
Multi-Modal Forcing
Based on the results presented thus far, plane wave
(m = O) excitation would be expected to be effective mainly
in the region up to the end of the potential core, since be-
yond this point, the axisymmetric mode is damped. Con-
trol of the region beyond the potential core could be ac-
complished via the forcing of the helical modes. Hence, a
combination of both plane wave and helical mode forcing
would be expected to be even more effective for controlling
the jet than either excitation applied alone. Results will be
shown for one case at a Reynolds number of 400,000, with
a core turbulence intensity of 0.1% and having a turbulent
nozzle exit boundary layer.
Figure 5 shows the evolution of modes f or a forc-
ing case: m = :1:1 at St(D) = 0.15, and m = 0 at
S_(D) = 0.6. The forcing here is in tim range of the natu-
rally preferred frequencies determined from the modal spec-
trum for the unforced jet. The forcing levels measured at
U/Uc = 0.8, z/D = 0 were (_o/U)St(D)=O.6,m=o = 0.06
and (_o/YjSl{D)=OlS,m=+l = 0.0- 9. The modal decomposi-
tion technique used for generating these results is the same
as that for the unexcited case. However, only the coherent
part of the signal at the excitation frequency was used.
In the initial region, the axisymmetric mode (m = 0)
grows to about 9 percent of the jet exit velocity. Note that
the modes in Figure 5(a) are evolving in the presence of
each other. Figure 5(a) shows that the ra = 0 mode is am-
plified and saturates in the initial region of tile jet. As the
m = 0 mode becomes damped, the m = ±1 (combined and
denoted by a single curve) grow and peak around x/D = 6,
beyond which they are damped. Figure 5(b) shows the mo-
mentum thickness plotted versus axial distance.
Curves are shown for the following cases: unexcited,
plane wave (rn = 0 at St(D) = 0.6); helical modes (m =
±1, at St(D) = 0.15): and the multi-modal case (m = 0 at
St(D) = 0.6 and m = ±1 at St(D) = 0.15). The last two
cases are represented by bands bounded by 0m_, and 0mi n
since 0 varies azimuthaJly. Comparing Figures 5(a) and
(b) one observes that the local regions of higher spreading
rate (steeper curves in Figure 5(b) for r/D between 0 and
2, 4 and 6) correspond to regions of wave amplification
in Figure 5{a), and local regions of lower spreading rate
(flattening of curves in Figure 5(h), for J:/D between 2 and
4, greater than 6) correspond to regions where the waves
are damped. The jet's spreading rate is enhanced in a 2-
step process. In step 1. due to m = 0 (x/D between 0 and
2), and in step 2, due to m = ±1 (x/D between 4 and 6).
The above interpretation is also supported by the theory of
Mankbadi and Liu (1981 l.
The low frequency heiic',d modes along with the ax-
isymmetric mode of the multi-modal case (Figure 5) are
more effective in producing higher spreading rates in the
downstream region (5 < x/D < 10). Therefore, the choice
of the forcing frequencies would vary depending on the re-
gion over which maximum control is desired. From Fig-
ure 5 it is clear that the combination of a plane wave and
two opposing helical modes provides a higher degree of con
trol over the spreading rate of the jet than either excitation
applied alone. The plane wave enhances spreading up to
tim end of the potential core. and helical modes (m = ±1)
cause the jet to flap beyond the potential core.
SUMMARY AND CONCLUSIONS
The overall objective was to study natural as well as ex-
cited jets under conditions more representative of practical
applications, i.e. high Reynolds number and fully turbulent
I ,,Ii " ..... m • _l, St:D! _ 0 T5
0 _ _ 6 8 10
e_EXC]TEO J[7
m*4-*..m-*J JEI EXCll[_ A7 m - O, M:2 L_.,
....... REGION BOU_e[9 BY OMj x A_: ÷M'N F;;
...... .ET £XCITEI) AI m : *l, S! 1, ,1: :
Jl[l EXCIT[D $IRULTANEOUSLY AT ,'1,1 0
21 • .
0 2 _ 6 8 lO
lid
Figure 5.--Multi-modal excitation results
(forcing levels, i'io/U = 0.06,
(St(D) = 0.6, m = 0) (bo/U = 0.02,
(St(D) = 0.15, m = :1:1)).
initial condition, with a focus at and beyond the potential
core. The conclusions are as follows:
(1) The evolution of instabilities resulting from naturally
occurring disturbances at the jet lip was studied using
the modal frequency spectrum. The region up to the
end of the potential core was dominated by tile axisym-
metric mode. The azimuthal modes grew rapidly but
dominated only after the potential core region. For the
jet excited by natural disturbances the ener&v content
of the higher order modes {m > 1) was significantly
lower than the axisymmetric and m = =El modes.
(2) Based on the results from the naturally occurring jet
instability mode experiments, target modes for efficient
excitation of the jet were determined. The effect of ex-
citing a high Reynolds number, initially turbulent jet
simultaneously at fundamental and subharmonie fre-
quencies was studied. The initial phase difference be-
tween the two waves was varied in steps of 45 °. The
effect of varying the initial forcing levels was also stud-
ied. It was found that at high amplitudes of fundamen-
tal and subharmonic forcing levels, the subharmonic
augmentation and the axial location of the peak are
independent of the initial phase difference. This find-
ing will have a very favorable impact on the design of
practical excitation devices. Two-frequency excitation
is indeed more effective than single frequency excita-
tion in jet spreading enhancement. Tile spreading is
quantified by:
CT?C;:'_<L _:'7_" ':"
G- ?_ .O!Jlg2P;
IU/ A
National Aeronautics and
Space Administration
Report Documentation Page
1. Report No. I 2. Government Accession No.
INASA TM- 104483
4. Title and Subtitle
Control of an Axisymmetric Turbulent Jet by Multi-Modal Excitation
7. Author(s)
Ganesh Raman, Edward J. Rice, and Eli Reshotko
9. Performing Organization Name and Address
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135-3191
12. Sponsoring Agency Name and Address
National Aeronautics and Space Administration
Washington, D.C. 20546- 0001
3. Recipient's Catalog No.
5. Report Date
6. Performing Organization Code
8. Performing Organization Report No.
E-6243
10. Work Unit No.
505-62 -52
11. Contract or Grant No.
13. Type of Report and Period Covered
Technical Memorandum
14. Sponsoring Agency Code
15. Supplementary Notes
Prepared for the Eighth Symposium on Turbulent Shear Flows sponsored by the Turbulent Shear Flow Committee,
Munich, Germany, September 9- 11,1991. Ganesh Raman, Sverdrup Technology, Inc. Lewis Research Center Group,
2001 Aerospace Parkway, Brook Park, Ohio 44142; Edward J. Rice, NASA Lewis Research Center; Eli Reshotko,
Case Western Reserve University, Cleveland, Ohio 44106. Responsible person, Ganesh Raman, (216) 826-2277.
16. Abstract
Experimental measurements of naturally occurring instability modes in the axisymmetric shear layer of a high Reynolds
number turbulent jet are presented. The region up to the end of the potential core was dominated by the axisymmetric
mode. The azimuthal modes dominated only downstream of the potential core region. The energy content of the higher
order modes (m > 1) was significantly lower than that of the axisymmetric and m = ±1 modes. Under optimum
conditions, two-frequency excitation (both at m = 0) was more effective than single frequency excitation (at m = 0) for
jet spreading enhancement. An extended region of the jet was controlled by forcing combinations of both axisymmetric
(m = 0) and helical modes (m = -+1). Higher spreading rates were obtained when multi-modal forcing was applied.
17. Key Words (Suggested by Author(s))
Turbulent jets
Stability
Acoustic excitation
18. Distribution Statement
Unclassified - Unlimited
Subject Category 02
lg. Secudty Classif. (of the report) 20. Secudty Classif. (of this page) 21. No. of pages
Unclassified Unclassified 8
_As_ FOR_ le26 oc'r _ *For sale by the National Technical Information Service, Springfield, Virginia 22161
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Control of an axisymmetric turbulent jet by multi-modal excitation

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