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AMJkA 



AIAA 99-0672 

Periodic Excitation for Jet Vectoring 
and Enhanced Spreading 



LaTunia G. Pack and Avi Seifert 
NASA Langley Research Center 
Hampton, VA 



37th AIAA Aerospace Sciences 
Meeting and Exhibit 

January 11-14, 1999/ Reno, NV 



For permission to copy or republish, contact the American Institute of Astronautics and Aeronautics 
1801 Alexander Bell Drive, Suite 500, Reston, VA 20191 



AIAA 99-0672 



Periodic Excitation for Jet Vectoring and Enhanced Spreading 

LaTunia G. Pack' and Avi Self erf* 

Flow Modeling and Control Branch 

NASA Langley Research Center, Hampton, VA 23681 



Abstract 

The effects of periodic excitation on the evolution of 
a turbulent jet were studied experimentally. A short, 
wide-angle diffuser was attached to the jet exit and 
excitation was introduced at the junction between the 
jet exit and the diffuser inlet. The introduction of 
high amplitude periodic excitation at the jet exit 
enhances the mixing and promotes attachment of the 
jet shear-layer to the diffuser wall. Vectoring is 
achieved by applying the excitation over a fraction of 
the circumference of the circular jet, enhancing its 
spreading rate on the excited side and its tendency to 
reattach to that side. Static deflection studies 
demonstrate that the presence of the wide-angle 
diffuser increases the effectiveness of the added 
periodic momentum due to a favorable interaction 
between the excitation, the jet shear-layer and the 
diffuser wall. This point was further demonstrated by 
the evolution of a wave packet that was excited in 
the jet shear-layer. Strong amplification of the wave 
packet was measured with a diffuser attached to the 
jet exit. The turbulent jet responds quickly (10-20 
msec) to step changes in the level of the excitation 
input. The response scales with the jet exit velocity 
and is independent of the Reynolds number. Jet 
deflection angles were found to be highly sensitive to 
the relative direction between the excitation and the 
jet flow and less sensitive to the excitation frequency. 
The higher jet deflection angles were obtained for a 
diffuser length of about two diameters and for 
diffusers with half-angles greater than 15 degrees. 



Ajet 
Aslot 
<c > 



D 



Nomenclature 

jet cross-section area, 7ir^ 
active slot area, 7lh(2r+h)/4 
periodic momentum coefficient, 

jet diameter, 39mm 
reduced frequency, fLIU^ 



f excitation frequency [Hz] 

h slot width or height, 1mm 

J' periodic momentum at slot exit, pA,,^,M^J^, 

K 1000 

L distance from jet exit to diffuser exit, 

measured along diffuser wall 

p pressure 

r jet radius, 19.5mm 

Re Reynolds number based on diameter, f/,D/v 

RMS root mean square of fluctuating value 

S,Q Strouhal number, fDIU^ 

S,9 Strouhal number, fdlU^ 

t time 

U jet mean velocity 

Uj. wave packet convection velocity 

u' root mean square of the velocity fluctuations 

V kinematic viscosity 

V y velocity component 

X axial direction, x=0 at jet exit and diffuser 

inlet 
y vertical direction, y=0 at jet centerline 

y^. jet center of momentum 

z horizontal direction, z=0 at jet centerline 

5 jet deflection angle, [deg] 

p density 

diffuser half-angle, [deg] 

9 jet 2-dimensional shear-layer momentum 

thickness 
Subscripts 
d de -rectified 

e conditions at jet exit 

i index denoting z location 

slot condition at slot exit 
plane profiles of an entire jet cross-section 
profile jet profile at z/D=0.0 
Terminology 
X-diffuser 
R-diffuser 
Baseline 



streamwise excitation diffuser 
cross-stream excitation diffuser 
No control, f=<c^>=0.0 



Research engineer. Flow Modeling and Control Branch. 
" NRC researcher, on leave from Tel-Aviv University, member AIAA. 
© NASA and A. Seifert (NRC), 1999. Printed by AIAA with permission. 



1 
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AIAA 99-0672 



1. Introduction 

Turbulent jets are of significant engineering 
relevance for aerospace and mechanical applications 
(jet engines, combustion chambers, etc.) and to the 
environment (chimney stacks). As such, they have 
been extensively investigated over the last few 
decades. Controlled excitation was initially used in 
order to clarify the importance of coherent structures 
on the evolution of transitional and turbulent jets'-^. 
Research efforts were devoted to understanding the 
importance of coherent structures in noise generation 
and jet spreading. Controlled, far field, acoustic 
excitation was used in most of these studies to 
generate the jet coherent structures, owing to the 
strong receptivity of the jet lip. The limitations of 
acoustic excitation (power requirements, weight, 
applicability, and efficiency) led researchers to 
examine other methods for jet flow control. These 
methods include cross-stream blowing^, counter- 
flow'*-^*, self-excited resonance tubes^ and high 
amplitude periodic excitation*. Davis^ introduced 
cross-stream blowing through two circular tubes 
positioned on each side of the jet exit. It was shown 
that the radial introduction of steady momentum 
enhanced mixing for secondary jet momentum 
coefficients lower than 0.56%. For higher momentum 
coefficients, a mean flow distortion was generated. 
Vectoring was not seen since both control jets were 
always operated simultaneously. 

Strykowski and Wilcoxin"* attached a diffuser 1.0 
to 2.25 jet diameters long, to a low speed, circular jet 
and applied suction around the jet circumference. The 
application of suction modifies the jet exit velocity 
profile and turns it absolutely unstable for suction 
velocities greater than 31.5% of the jet centerline 
velocity'. Enhanced mixing or vectoring could be 
achieved depending on the fraction of the jet 
circumference to which suction was applied. Thrust 
vectoring was demonstrated at a Mach number of 2.0, 
using the jet-suction diffuser arrangement when 
suction was applied over a fraction of the 
circumference of a circular jet^ or along one wall of a 
rectangular jet''. Jet deflection angles were 
determined by flow visualization. Since the diffuser 
angles were relatively small, a bi-stable situation was 
encountered because the jet had a tendency to 
naturally reattach to the diffuser walls. 

Raman and Cornelius^ used a resonance tube 
with openings on opposite sides of a low speed 
rectangular jet to generate alternating suction and 
blowing with 180° phase shift between the openings. 
This generated a flapping mode that enhanced the 
mixing of the primary jet flow. Smith and Glezer* 
used a narrow excitation slot positioned close to the 



exit of a high aspect-ratio low-speed rectangular 
primary jet. The interaction between the jet and the 
high frequency and high amplitude excitation 
vectored the primary jet. It is not known if the 
primary jet was laminar, transitional, or turbulent. 
The magnitude of the fluctuating excitation 
momentum at the slot exit was not specified. The 
authors concluded that the mechanism responsible for 
the jet deflection was a low pressure region generated 
by the excitation between the primary jet and the 
excitation slot. 

The aim of the present investigation is vectoring 
and enhanced spreading of a circular, turbulent jet. 
The mechanism used for vectoring the jet is zero- 
mass-flux periodic excitation. Periodic excitation is 
used due to its demonstrated ability to effectively 
control separation on airfoils. Experiments performed 
on a variety of airfoils, over a large range of 
Reynolds and Mach numbers, indicate that periodic 
excitation can be used to effectively delay turbulent 
boundary layer separation and reattach separated 
flows'""'^. The introduction of periodic excitation 
slightly upstream of the boundary layer separation 
location enhances mixing between the high 
momentum fluid away from the surface and the low 
momentum fluid near the surface. Periodic excitation 
is significantly more efficient than steady suction and 
two orders of magnitude more efficient than steady 
blowing at controlling separation'""'^. This method 
can be applied to a turbulent jet by attaching a short, 
wide-angle diffuser to the jet exit and perturbing the 
separated shear-layer at the inlet to the diffuser. 

The three main advantages of using periodic 
excitation for jet flow control are: 

1) the potential weight reduction of a thrust 
vectoring system (mechanical thrust vectoring 
vanes account for as much as 30% of the weight 
of jet engines), 

2) the ability to change the aerodynamic forces and 
moments quickly without generating prohibitive 
inertial loads on the structure, and 

3) the demonstrated superior efficiency of the 
method compared to steady suction or blowing. 
The present paper demonstrates the enhanced 

controllability of a turbulent jet when a short, wide- 
angle diffuser is attached at the jet exit and periodic 
excitation is introduced at the juncture between the 
jet exit and the diffuser inlet. The results of a 
preliminary parametric study are presented and show 
how jet deflection angles were affected by the 
diffuser geometry (i.e. diffuser length and diffuser 
half-angle) as well as by variations in the control 
inputs (such as excitation frequency, its periodic 
momentum, and the relative orientation of the 



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AIAA 99-0672 



excitation). The response of the jet to generic 
control inputs was also investigated. The 

relationship between the present control strategy and 
the flow stability was examined in order to shed light 
on how the excitation interacts with the jet flow and 
the diffuser walls. In the present study we do not 
attempt to compare the effectiveness of this method 
to other jet control methods. Such a comparison 
would involve the definition and use of common 
terminology for input parameters and their 
effectiveness. To date, most published results do not 
provide enough details to make this comparison. 

2. Experiment Set-up 

2.1 Jet 

The jet facility consists of a DC fan connected to 
a 76.2 mm diameter settling chamber, followed by a 
3.15:1 contraction and a straight aluminum pipe with 
an inside diameter of 38mm and an outside diameter 
of 40mm. The thickness of the pipe wall, at the jet 
exit, was machined to bring it gradually to 0.5mm, in 
order to reduce the gap between the jet flow and the 
excitation slot. The jet exit diameter is therefore 
39mm (Figs, la and lb). The jet was surrounded by a 
1mm wide segmented slot. Each segment of the slot 
was connected to a cavity allowing independent 
excitation of every 45° of the jet circumference. 
Although steady blowing and suction could be 
introduced through the slot, the results presented here 
are for zero-mass-flux periodic excitation (i.e. no 
steady component). The excitation was introduced 
through the slot surrounding the upper 90° of the jet 
circumference, as shown in Figures la and lb. The 
divider between the two cavities connected to the 
excited region of the slot was removed, resulting in 
one continuous cavity over a 90° region of the jet. 
Trip grit (#36) was placed inside the aluminum pipe 
200 mm from the jet exit to ensure that the flow at 
the jet exit was turbulent over the velocity range of 
interest (8 m/s- 18 m/s). 

2.2 Diffusers 

A short, wide-angle diffuser could be attached to 
the exit of the jet. The effect of diffuser length on jet 
deflection angle was studied by testing diffusers of 
length, L=0.58D, l.OD and 1.85D. Diffusers with half- 
angles of 0=30° were used to study the effect of 
diffuser length. The effect of diffuser half-angle on 
jet deflection angle was also examined. Diffusers 
with half-angles of 0=15°, 22.5°, and 30° were tested. 
For the diffuser half-angle study, the diffuser length 
remained fixed at L=0.58D. The 0=30°, L=1.85D 
diffuser was designed such that periodic excitation 



could be introduced in the streamwise and cross- 
stream direction. The diffuser that introduces the 
excitation in the stream-wise direction will be 
referred to as the X-diffuser and the diffuser that 
introduces the excitation in the cross-stream direction 
will be referred to as the R-diffuser. 

2.3 Actuator 

A Piezo-electric actuator, that resonated near 
700Hz, was used to produce the periodic excitation. 
The velocity fluctuations, u', exiting the slot were 
measured using a hot-wire positioned at the slot exit. 
Since hot-wires can not sense flow direction, the 
velocities obtained at the slot exit, in the absence of 
jet flow, had to be de-rectified using the procedure 
described in Ref. 12. The maximum u' of the actuator, 
u'l^jijj, when operated at 700 Hz using the X-diffuser, is 
about 18 m/s. u'^^^^ is about 10% lower when the R- 
diffuser is used. When the actuator operated at 
300Hz, using the X-diffuser, u'^^^^, was about 7m/s. 
The hot-wire measurements were used to determine 
the relationship between the input RMS voltage to 
the actuator and the resultant velocity fluctuations. 
The linear relationship that was found between the 
actuator input RMS voltage and u' was used to 
determine u' when the hot-wire was removed. In 
addition, a dynamic pressure transducer was flush- 
mounted in the collar surrounding the jet to monitor 
the state of the actuator and serve as a phase 
reference (Figure lb). The actuator did not show 
signs of performance degradation during four months 
of experiments, as indicated by the dynamic pressure 
transducer monitoring the actuator output and 
occasional calibration checks at the slot exit using a 
hot-wire 

2.4 Instrumentation and Data Acquisition 

Most of the jet flow field measurements were 
acquired using a single-wire hotwire. Hot-wire 
calibrations were performed frequently to ensure that 
there were no significant drifts and data repeatability 
was checked often. The normal data sequence, or 
run, included acquiring data of the jet baseline flow 
field before and after acquiring data of the jet 
controlled flow field. A check of the two baseline 
data sets also served as a check of the hot-wire 
calibration. In addition to hot-wire measurements, a 
small amount of data were acquired using a 5-hole 
probe". 

Hot-wire and static and dynamic pressure data 
were acquired using a 16 bit A/D converter. The 
dynamic pressure data were always low-pass filtered 
at 2KHz and amplified prior to digitization. The 
sampling rate of the hot-wire and the dynamic 



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AIAA 99-0672 



pressure data was either 6KHz or 12KHz, and all hot- 
wire data were low-pass filtered at the sampling rate 
divided by 2.56. The hot-wire frequency response was 
always better than 20KHz. The dynamic pressure 
transducer also has a frequency response in excess of 
20KHz. The hotwire and the 5-hole probe were 
mounted to a three-axis traverse system. The traverse 
controller, the A/D converter, the hot-wire 
anemometer and the power supply for the DC fan 
were interfaced with a desktop computer. This helped 
simplify hot-wire calibrations and jet flow field 
measurements. 

2.5 Experimental Uncertainty 

The velocity measured with the hot-wire is 
accurate to within 2% of the local value. The hot- 
wire position (x, y, or z) is accurate to within +0.04 
mm, the Rcp is accurate to within 3% of the local 
value, the <c > is accurate to within 20% of the local 
value, and the jet deflection estimates are accurate 
to within +0.5° of the local value. 

3. Discussion of Results 

3.1 The Baseline Jet 

3.1.1 Reynolds Number Effect 

The flow field of the baseline jet was carefully 
documented over the Reynolds number range of 
interest to verify that the flow was turbulent and to 
assess the effect of Reynolds number, especially in 
the near exit region. Turbulent, Reynolds number 
independent flow was desired for this flow control 
experiment to eliminate transition effects thereby 
reducing the number of variables affecting the results. 
By tripping the flow five diameters upstream of the 
jet exit it was assured that the effects produced by 
using periodic excitation were not transition related 
and would be applicable to higher Reynolds numbers. 
The mean and fluctuating velocity profiles close to 
the jet exit, at x/D=0.1, are presented in Figures 2a 
and 2b. The shapes of the mean velocity profiles are 
identical over the Reynolds number range tested. 
The peak turbulence level in the shear-layer 
increases slightly as Reynolds number decreases, as 
shown in Figure 2b. The differences in the turbulence 
levels for the three Reynolds numbers could be due to 
the fact that the flow is not fully developed for the 
lowest Reynolds number, ReQ=2.1xlO''. The spectra of 
the velocity fluctuations measured at y/r=0.97 (Fig. 
3), indicate slight differences in the slopes for the 
three Reynolds numbers. This is another indication 
that the flow is not fully turbulent for the lower 
Reynolds numbers but is Reynolds number 
independent for higher Reynolds numbers. The "two- 



dimensional" momentum thickness of the jet shear- 
layer, 9, at x/D=0.1 doubles between Uj=6m/s and 
8m/s, indicating that transition from laminar to 
turbulent flow occurs. Between 8m/s and 18m/s 
(ReQ=2.1xlO**-4.7xlO**), the 9 has a mean value of 
1.68mm and varies by no more than +3.0% 

3.1.2 The effects of the attached diffuser 
The flow field of the baseline jet, close to the jet 
exit, with and without diffusers at the exit was also 
carefully examined. The velocity profiles without a 
diffuser and with the L=1.85D X-diffuser and R- 
diffuser at x/D=1.6 are presented in Fig. 4. It shows 
that the presence of the diffuser has very little effect 
on the shape of the jet mean velocity profiles. The 
initial thickness of the jet shear-layer, 9, is about 
D/25 (Fig. 5). This value is significantly higher than 
the published values for laminar jet exit boundary 
layers'* (D/200) as well as for turbulent boundary 
layers''* (D/190). However, the elimination of Re^ 
effects seems more important for the present 
investigation, than allowing a closer comparison with 
a two-dimensional mixing-layer. A significant 
increase in 9 occurs between the jet exit and 
x/D=0.2, with a diffuser present (Fig. 5). Further 
downstream, the jet spreads linearly for all three 
cases. The spreading rate of the jet shear-layer 
momentum thickness, d9/dx, increases from 0.03 to 
0.031 when a diffuser is placed at the jet exit (Figure 
5). The values of the present d9/dx are about 20% 
larger than those found by Husain and Hussain'** for a 
turbulent jet at Re[3=7.8xl0''. The effect of the 
increased initial thickness of the jet shear-layer is to 
increase the required input momentum for a required 
modification (in this case jet deflection angle), based 
on airfoil separation control experiments. The high 
initial momentum thickness is also expected to 
reduce the most amplified frequency based on linear 
two-dimensional mixing layer theory. The velocity 
profiles in the near exit region of the jet are not self- 
similar, nor is the flow parallel. This indicates that 
linear parallel stability approaches are not applicable 
to this type of flow. Furthermore, the challenge here 
is to generate a mean flow modification that is 
inherently non-linear and non axis-symmetric. 

3.2 General Aspects of Periodic Excitation 

3.2.1 Baseline & Controlled Cross-section Planes 
Hot-wire surveys of the jet flow field were made 
at a cross-stream plane at x/D=2.5 and Re[3=3.1xlO''. 
The baseline mean and fluctuating velocity contours 
are shown in Figures 6b and 6e. The circular shape 
of the baseline contours indicates that the flow is 
axis-symmetric. The maximum turbulence level of 



American Institute of Aeronautics and Astronautics 



AIAA 99-0672 



the baseline jet is about 15% and the u' contours are 
also axis-symmetric. Controlled mean and fluctuating 
velocity contours using streamwise excitation are 
shown in Figure 6a and 6d. The excitation is 
introduced through the portion of the slot surrounding 
the upper quarter of the jet circumference. The flow 
is no longer axis-symmetric. The enhanced mixing 
between the excited jet and the surrounding ambient 
flow leads to higher flow rates on the upper side of 
the jet. The increased mixing causes the mean 
velocity contours to be elongated in the vertical, y, 
direction and contracted in the horizontal, x, 
direction compared to the baseline. The spanwise 
contraction indicates that the jet is also vectored due 
to forces exerted by the upper 90° of the diffuser wall 
and not only due to enhanced mixing at the upper 
side. The jet center of momentum shifts upward, 
indicating the jet flow is vectored up by about 6° (see 
analysis to follow). The maximum fluctuating 
velocity of the controlled flow using streamwise 
excitation (Figure 6d) is about O.I8-O.2IU5 and has a 
horseshoe-like shape on the upper side of the jet. 

Controlled excitation was also introduced in the 
cross-stream direction (Figs. 6c and 6f). This mode 
of high amplitude excitation results in a deflection of 
the jet away from the excitation slot. The jet cross 
section is now elongated in the spanwise direction. 
This type of excitation does not increase the 
spreading rate nor the turbulence level as much as 
the streamwise excitation does. Similar excitation 
modes were identified by Smith and Glezer*, as the 
"push" and "pull" modes. As will be shown later, the 
presence of the diffuser at the jet exit significantly 
enhances the effectiveness of the streamwise 
excitation. Its effect on the cross-stream excitation 
has not been studied yet. 

3.2.2 Determination of Jet Deflection Angle 
Jet deflection angles were estimated from single 
profiles measured along the jet centerplane and from 
complete cross-section planes. The momentum rather 
than the flow rate was used since it is better related 
to the forces that are the purpose of the control 
strategy. The total momentum at a given spanwise 
location, z/D, was computed using 

Mi = \U'dy (Eq. la) 

where U is the jet mean velocity at a given vertical, 
y, position in the profile and i is an index denoting 
the increment in the horizontal, z, direction. The 
data were integrated in y, over the valid range of the 
hot-wire calibration velocities. The center of 
momentum of the jet at a given spanwise location, 
z/D, was determined by 



yc., 



\lfydy_ 
\U-dy 



(Eq. lb). 



The deflection angle based on one profile measured 
at z/D=0 is defined as 

■/ c , profile 



5,„,„ = tan-' ^^ (Eq. 

2), 
where x is the distance from the jet exit to the 
measuring station. The center of momentum of the 
jet at a given cross-stream location, x/D, was 
determined using 

._ = -^ (Eq.3). 

The deflection angle based on a whole cross-section 
plane was determined by assuming the jet began 
deflecting at x/D=0.0 and computing jet deflection 
angle, 5pi,„e, using 

5,„„,„ = tan-{^^^^l (Eq. 4), 



where x is the distance from the jet exit to the 
measuring station. Although data of complete cross- 
section planes of the jet flow field provide a more 
comprehensive description of the flow, the time 
required to acquire profiles of the entire cross section 
is excessive and the amount of data is enormous. A 
parametric study at this pace would have been 
prohibitive. A comparison was made between the 
deflection angle, 5p„f,ie, computed using a single 
profile measured on the jet plane of symmetry, and 
the deflection angle, Spi^n^, computed using the entire 
cross-section, in an attempt to find one profile in 
space that would be representative of the entire jet. 
Figure 7 shows the comparison between the two 
methods of computing jet deflection angles at various 
x/D locations. Most of the results are for the X- 
diffuser, but the filled symbols are for the R-diffuser 
(with the sign inverted). It is assumed that the jet 
center of momentum, at the jet exit, remains at 
y=z=0. The deflection angles computed for the X- 
diffuser, using single profiles and entire cross- 
sections, agree to within +0.5°. The deflection angles 
computed for the R-diffuser (filled symbols, 

deflection sign inverted. Fig. 7) using a single profile 
and a complete plane, are also in very good 
agreement. For the remaining results presented in 
this paper, profiles measured at z/D=0.0 and x/D=2.5 
are used to determine jet deflection angles. This 
location always corresponds to a plane of symmetry 
of the excited flow and enables an efficient 
parametric study that is conservative based on the 
results shown in Figure 7. The observation that the 
jet deflection angle decreases with x/D (Figure 7) 



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AIAA 99-0672 



implies that the jet actually started to deflect about 
ID upstream of the jet exit. To clarify this point, 
additional measurements were made using a five-hole 
probe '^. This probe enables the acquisition of three 
velocity components and provides an independent 
measure of jet deflection angles. The jet deflection 
angles for the 5-hole probe were computed using the 
local flow angle 

5,.=tan-'(y./f/.) (Eq. 5a), 

and a weighted averaging over the entire profile in 
the form 



^5, profile ~ 



^u, 



(Eq. 5b), 



where j is an index in the vertical direction, y, and 
the local mean velocity, U, serves as a weighting 
function. Data where the local velocity, U, was 
greater than O.I5U5 were included in the average. 
The deflection angles obtained with the 5-hole probe 
are within +0.5° of the deflection angles based on 
single hot-wire profiles. The close agreement verifies 
the validity of the present approach in defining the jet 
deflection angles. Furthermore, the jet deflection 
angles to be presented should be used as trends of the 
effects of the various parameters, while absolute 
angles should preferably be measured with a force 
balance. 

3.3 Parametric Study 

3.3.1. The effect of Reynolds number 
To study the effect of Reynolds number on the 
evolution of the controlled jet, data were acquired at 
three jet speeds corresponding to Rej3=2.1xl0\ 
3.1x10'' and 4.2x10**. Streamwise excitation with a 
frequency of 700Hz was used for this study. As will 
be shown later, the effect of the corresponding 
change in F* with Rcp is small. Figure 8 shows jet 
deflection angles versus periodic momentum 
coefficient, <c^>, for the three Reynolds numbers 
tested. The jet deflection angles for the two higher 
Reynolds numbers are in excellent agreement, 
indicating weak Reynolds number dependence. At 
Rej3=2.1xl0'', the jet has lower deflection angles for 
lower <c^>, and higher deflection angles for <^> 
above 2%. This could be a result of the developing 
nature of the turbulent boundary layer upstream of the 
jet exit as shown for this Re^ in Fig. 2b and Fig. 3. 

3.3.2 The effect of the excitation frequency 

To study the effects of F"^ without varying Rcp, 

the actuator was operated at two frequencies, 700Hz 

(actuator resonance) and 300Hz, generating F*=4.2 

and F*=1.8, respectively, and <c^> was gradually 



increased. The jet deflection angles presented in Fig. 
9, indicate a very low sensitivity to forcing 
frequency, in the range of available parameters. An 
F*=4.2 is slightly more effective than an F*=1.8 for 
the range of <c^>'s produced by the present actuator. 
Figure 9 also includes results obtained using the five- 
hole probe. These results agree very well in the 
shape of the mean velocity profiles (not shown) and 
in the resulting deflection angles (using Eq. 5). The 
shape of the baseline and controlled velocity profiles 
are also insensitive to F"^. Examination of the 
velocity spectra where U/Ue=0.5 (not shown), does 
not reveal any distinct frequencies with or without 
control. The power levels are almost identical below 
the excitation F* and the levels increase slightly 
above the excitation F"^. The lack of distinct peaks, 
even at the forcing frequencies, indicates that the 
excitation momentum was transferred to the mean 
flow and to smaller scales upstream of x/D=2.5. The 
overall behavior of the jet response at different Re^ 
and frequencies indicates low sensitivity to both Re^ 
and F"^ for this range of parameters. 

3.3.3 The effect of the diffuser length 
There is no consensus among researchers, 
regarding the relevant length scale that determines 
the effective forcing frequency, along with the 
velocity scale that is easily selected. One possibility 
is a local parameter based on the thickness of the 
shear-layer, perhaps 9, its momentum thickness. 
Another option is the jet diameter. These two 
parameters dominate the near and far field evolution 
of a transitional free jet, as identified by Drubka et. 
al.". Presently, we introduce an additional length 
scale, the length of the diffuser. As will be shown 
later, the presence of the diffuser significantly 
enhances the effectiveness of the streamwise 
excitation. The effect of the diffuser length was 
investigated using X-diffusers with L/D =0.58, 1.0 and 
1.85 corresponding to F*=1.3, 2.3, and 4.2 
respectively. F"^ was shown in the previous section to 
have little effect on jet deflection angles over this 
range. Figure 10 shows the deflection angles versus 
<c^> for the three diffuser lengths tested. The 
deflections measured using the L=0.58D diffuser were 
slightly lower than the deflections measured using the 
L=1.0D diffuser. The L=1.85D diffuser produced 
smaller deflections than the shorter diffusers at low 
<c^>'s. However, for Kcp- above 2% the longer 
diffuser (L=1.85D) generated higher deflection 
angles. It is assumed that the diffuser length plays an 
important role in the non-linear process leading to jet 
deflection, since the sensitivity to the forcing 
frequency is low (see Fig. 9 and Fig. 10). 



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The mean velocity profiles for the three diffuser 
lengths when <c^>=0% and 3.2% are shown in Figure 
11. The shift of the mean velocity profile for the jet 
with the L=1.85D diffuser on the lower side of the jet 
indicates some differences in the deflection 
mechanism for the longest diffuser. It also indicates a 
lower mixing in the excited shear-layer. The 
turbulence profiles (not shown) indicate that the jet 
velocity fluctuation levels for the L=1.85D diffuser 
are higher in both shear-layers and lower in the core 
of the jet, compared to the turbulence levels found for 
the shorter diffusers. 

3.3.4 The effect of the diffuser half-angle 

The effect of the diffuser half-angle, 0, was 
studied using X-diffusers with half-angles, 0=15°, 
22.5°, and 30°, while fixing L at 0.58D. Figure 12 
shows how the jet deflection angle varies with <c^> 
for the three diffusers. Clearly, the 0=15° diffuser is 
the least effective of the three. The differences 
between the 0=22.5° diffuser and the 0=30° diffuser 
are small, but the 0=30° diffuser appears to be the 
most effective over the range of parameters tested. 
The mean velocity profiles, shown in Figure 13, 
indicate that the 0=15° diffuser is less effective at 
entraining the flow on its upper side than the 0=22.5° 
and 0=30° diffusers. It also deflects the jet less. The 
turbulence levels of the 0=15° diffuser are higher than 
the other two diffusers (not shown). This is true for 
both shear-layers. The differences between the U and 
u' profiles for the 0=22.5° and 30° diffusers are small, 
but still higher deflection angles as well as larger 
turbulence levels at the jet core were obtained using 
the diffuser with a 30° half-angle. 

3.3.5 The effect of the excitation direction 

It is well known that when linear stability is valid 
and low amplitude excitation is used, the method of 
excitation is not important. At a certain distance 
from the source, typically a few wavelengths 
downstream, the excitation will be independent of the 
source details. On the other hand, when high 
amplitude excitation is considered, and non-linearity 
plays an essential role, the source characteristics 
could dominate. This is especially important when 
the whole interaction length between the controlled 
jet and the diffuser is about five wavelengths long. 
Two extreme options for the relative direction 
between the excitation and the jet flow direction 
were considered. The excitation was introduced in 
either the streamwise or cross-stream direction. As 
already shown in Figures 6c and 6f, the high 
amplitude cross-stream excitation deflects the jet 
away from the excitation slot. This causes the jet 



cross section to be elongated along the z-axis rather 
than along the y-axis. This type of excitation does 
not enhance the spreading rate nor does it elevate the 
turbulence levels as much as the streamwise 
excitation. 

Figure 14 shows jet deflection angles versus <c^> 
for streamwise (X-diffuser and no diffuser) and cross- 
stream (R-diffuser) excitations. For small <c^>'s, the 
jet is deflected in the same direction (upward) for 
both types of excitation with a diffuser present. The 
introduction of low <c^> excitation into the upper 
shear-layer causes enhanced spreading and 
interaction of that shear-layer with the diffuser wall. 
As the level of <c^> increases, the streamwise (X- 
diffuser) introduction of periodic momentum 
continues to gradually deflect the jet upward, towards 
the excited shear-layer, while the jet is deflected 
downward when using cross-stream excitation (R- 
diffuser) with <c^> greater than 0.5%. Note that for 
both the X-diffuser and the R-diffuser the excitation is 
introduced through the slot surrounding the upper 
quarter of the jet circumference. Figures 15a and 15b 
show a comparison of the mean and turbulence 
velocity profiles for the baseline and controlled 
(<c^>~ 3%) jet using the X-diffuser, the R-diffuser, 
and without a diffuser present. The effect of 
introducing the excitation in the streamwise direction 
without a diffuser is to increase the spreading rate of 
the excited shear-layer (Fig. 15a and 15b). This was 
accompanied by significantly smaller jet deflection 
angles, compared to the deflection angles found for 
the X-diffuser (Fig. 14). The X-diffuser causes 
enhanced spreading on the side of the excited shear- 
layer that interacts with the diffuser wall to deflect 
the entire jet to that side (Fig. 15a). High level <c^>, 
introduced in the cross-stream direction (R-diffuser), 
deflects the jet very effectively towards the opposite 
diffuser wall, without enhancing its spreading rate in 
a comparable manner (see also Fig. 6c and 6f). This 
might be important from an application point of view. 

3.4 The response of the jet to pulsed excitation 

A wave packet is generated when a strong and 
concentrated disturbance, in both space and time, is 
introduced into an unstable shear-layer. The 
concentrated excitation produces a complete 
spectrum of disturbance modes. The unstable shear- 
layer will selectively amplify the most unstable 
modes and dampen the rest. This approach was first 
introduced by Gaster'* to study linear instability of 
the Blasius boundary layer. It was later applied to 
free-shear layers by Balsa". Very good agreement 
between linear stability theory and experiments was 
found in the initial stages of transition. Further 



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downstream, various modes interact to promote 
breakdown. Gaster, et. al."* demonstrated that linear 
stability theory could be applied to predict the 
evolution of two-dimensional harmonic wave trains 
introduced into a turbulent shear-layer. The 

interaction between the linearly unstable modes and 
random turbulence could also be incorporated using 
an eddy viscosity model to improve the agreement 
between theory and experiment". Once the 
magnitude of the excitation is strong enough (at least 
1% of the reference velocity), linear theory fails to 
predict the evolution and non-linearity dominates the 
evolution of the disturbance^". In transitional boundary 
layers this type of excitation generates turbulent spots 
and in pipe flow it generates puffs and slugs. 
Zilberman et. aP' used an electric spark excitation to 
generate a turbulent spot and study its evolution in a 
fully turbulent boundary layer. A similar approach is 
presently used to study the frequency content, the 
effect of the excitation direction, the disturbance 
convection speed and the relationship between the 
excitation and the non-linear instability mechanism. 

The results presented thus far clearly demonstrate 
that periodic excitation could be used to vector a 
turbulent jet and enhance its spreading rate. The 
results of the parameter study indicate that the jet 
deflection angle is only weakly affected by F"^ and 
Rcp. The diffuser half-angle, diffuser length, and 
excitation direction have a strong effect on the 
evolution of the jet. It was also demonstrated that the 
presence of the diffuser has a strong effect on the 
effectiveness of the streamwise excitation. Wave 
packet studies were performed to understand how 
periodic excitation interacts with the jet flow and 
with the diffuser. A wave packet was generated by 
introducing a single cycle of the 700Hz excitation, 
through the slot surrounding the upper 90° of the jet 
circumference. The actuator and the data acquisition 
sequence were triggered simultaneously. The data 
were sampled at 6 KHz and 2500 records containing 
512 points were acquired at each measurement 
station. The large number of data records were 
needed because of the low ratio between the wave 
packet signal and the background turbulence. Data 
were acquired for two different excitation input levels 
that differed by about a factor of two in the amplitude 
of the pressure fluctuations, as measured in the 
actuator cavity. Data were acquired in the jet upper 
shear-layer, where U/Ue= 0.75, at six axial locations, 
x/D=0.1, 0.2, 0.4, 0.8, 1.2, 1.6, inside the diffuser 
(when present). This was repeated three times using 
the X-diffuser, the R-diffuser and without a diffuser. 
Even though 2500 realizations were ensemble 
averaged, the low amplitude wave packet signal is 



hardly detectable (not shown). However, with the 
diffuser present, the wave packet generated by the 
streamwise excitation is amplified and detectable. 
Figures 16a, 16b and 16c show the jet response to the 
high amplitude pulsed excitation. Note that the data 
signal are separated by u'/Ue=0.05 for clarity. The 
resulting wave packet is clearly seen for all three jet 
exit configurations. Forx/D=0.1 and 0.2 and time, t< 
6msec, the signals are identical showing the response 
to the one cycle 700Hz pulse. Further downstream, 
the amplitude of the wave packet generated by 
streamwise excitation (X-diffuser Fig. 16b) is the 
highest of all three cases. The wave packet, 
generated in the absence of a diffuser (Fig. 16a), 
appears sooner at the measuring station and has only 
weak negative velocity perturbations in front of it. 
The cross-stream (R-diffuser) excited wave packet 
(Fig. 16c) is the least amplified of the three cases. 
The amplitude of the wave packet as a function of x 
was computed by integrating the time histories shown 
in Figures 16. The amplitude. Amp, is expressed in 
terms of total fluctuating momentum in the form 

Amp = J — dt (Eq.6a), 

'=0 Ul 

where the velocity perturbation, u'(t), is given by 



u'(t) = U(t)-— \U{t)dt 

T (=50»,sec 



(Eq. 6b), 



and the integration period, T, is 30msec, after the 
response to the wave packet has passed. The times 
of integration were chosen because the flow returns to 
its undisturbed state at about t=50 msec as shown in 
Figures 16. Integrating the perturbation momentum 
beyond this point would only add noise. The total 
fluctuating momentum of the wave packet can also 
be viewed as a magnitude of the mean flow 
distortion. Figure 17 shows how the total fluctuating 
momentum of the wave packet varies with x for the 
three jet exit configurations examined. The initial 
fluctuating momentum is identical for the three 
configurations, indicating that the input is not 
sensitive to the presence of the diffuser or to the 
excitation direction. Figure 17 clearly shows that the 
disturbance resulting from the pulsed excitation in the 
streamwise direction (X-diffuser) is the most 
amplified. A factor of about two in the ratio of the 
integrated fluctuating momentum is seen between the 
X-diffuser and the no diffuser wave packet. This ratio 
increases to almost three at x/D=1.6. The disturbance 
resulting from the cross-stream excitation is the least 
amplified of the three configurations. Further 
analysis, experimentation, and theoretical 

considerations are needed to clarify the physical 



American Institute of Aeronautics and Astronautics 



AIAA 99-0672 



mechanism leading to these differences. Figure 17 
also shows the Amp values integrated across the 
entire y range. The ratio of about three between the 
R- and X- modes indicates that the results presented 
in Figure 17 for 11/11^=0.75 are of a global nature. 

Wave Packet surveys were also made at 
x/D=1.6, the diffuser exit, using the X-diffuser (Fig. 
18a) and the R-diffuser (Fig. 18b) across the entire y 
range of the jet at its plane of symmetry, z/D=0.0. 
The wave packet generated by streamwise excitation 
(X-diffuser) is of significantly higher amplitude in the 
excited shear-layer than in the non-excited layer (3% 
and 0.5% respectively). The cross-stream excitation 
(R-diffuser) affects the entire jet cross-section, 
generating comparable amplitudes in both shear- 
layers. The maximum amplitude of the X-diffuser 
wave packet is much higher than the maximum 
amplitude of the R-diffuser wave packet. This 
demonstrates how much more receptive the excited 
shear-layer is to streamwise excitation. It also shows 
that the cross-stream excitation generates a more 
global response rather than the response generated by 
the streamwise excitation. This pattern clarifies why 
the jet is effectively vectored towards the excited 
shear-layer side when using the X-diffuser (Fig. 14). 
It also indicates that the excitation using the R- 
diffuser is not related to an instability mechanism 
when high amplitude is applied, but does not reveal 
the reason why it is effectively deflected to the 
opposite direction. The mechanism responsible for 
the jet deflection away from the excitation slot, using 
the R-diffuser, is similar to the mechanism 
responsible for the modification in the jet cross- 
section measured by Davis' using two steady control 
jets. 

The convection speeds of the wave packet (Fig. 
19) were computed by determining the wave packet 
appearance time at each x location for the three 
types of high amplitude excitation. The wave packet 
was thought to be in the initial stages of development 
at x/D=0.1 and 0.2, therefore these two points were 
omitted from the convection speed computations. All 
convection speeds were calculated by applying a 
linear fit to the data shown in Fig. 19. The 
convection speeds are around 60% of the jet exit 
velocity. This value corresponds favorably with 
convection speeds of coherent structure in turbulent 
shear-layers^', and with linear stability theory 
predictions (Ref. 15 and references therein). The 
convection speed of the wave packet generated by 
streamwise excitation (X-diffuser) is slightly higher, 
even though the mean flow speed is lower when the 
jet is spread more towards the excitation slot. This 
indicates that this mode of excitation should result in 



faster response to changes in the excitation <c^>. 
The reason for the earlier appearance of the wave 
packet when there is no diffuser at the jet exit is not 
clear. It might be connected to slight differences in 
the nature of the interaction between the excitation 
and the shear-layer very close to the excitation slot, 
in the absence of the diffuser 

Analyzing the frequency content of the wave 
packet reveals that the most amplified frequency for 
the free jet (no diffuser attached) is around 100 Hz. 
This frequency corresponds favorably with both shear- 
layer modes'^ Ste=0.02, and with the column mode, 
StQ~0.2-0.6. However, the limited frequency scans 
performed (Fig. 9) indicate that the 300Hz excitation 
did not generate higher deflection angles than the 
700Hz excitation in the range of parameters studied. 
The most amplified frequency is reduced to 50-70Hz 
when the X-diffuser and R-diffuser are used. These 
frequencies combined with a convection speed of 
0.6U^ result in a disturbance wavelength of about 3 
jet diameters. It seems that this wavelength is too 
long to interact with a diffuser that is about half this 
length. It remains to be seen if longer diffusers and 
lower frequencies will be more effective. 

3.5 Jet response to step changes in <c ^> 

3.5.1 General 

The response of the flow to step changes in the 
magnitude of the excitation, <c^>, was also 
investigated. Studying the response of a system is a 
fundamental step in identifying the dynamics of the 
control process. For this investigation, data were 
acquired with the actuator toggled between off, on 
and off again. Data acquisition and the initial 
actuator on command were triggered simultaneously. 
For each flow condition, 512 records, containing 6000 
data points acquired at 12KHz, were ensemble 
averaged. The excitation was again introduced 
through the slot surrounding the upper 90° of the jet 
circumference, and the frequency of the excitation 
when the actuator was on was 700Hz. All 
measurements were made at an axial location 
corresponding to the diffuser exit, x/D=1.6 and the 
plane of symmetry of the excitation, z/D=0.0. In the 
cases where a diffuser was attached to the jet exit, 
the length of the diffuser, L, was 1.85D and the half- 
angle, 0, was 30°. 

3.5.2 Effect of the excitation direction 

The effect of the excitation direction on the jet 
response was studied at Rej3=3.1xlO'* resulting in an 
F*=4.2 when a diffuser was present. The <c^> when 
the actuator was on was 1.6% and 2.2% for cross- 
stream (R-diffuser) and streamwise (X-diffuser and no 



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AIAA 99-0672 



diffuser) excitation, respectively. Such a variation in 
<c^> should not have a significant effect on the 
results since measurements acquired for different 
<c^> levels did not lead to changes in the transient 
jet flow response when normalized by the steady- 
state jet flow conditions. The hot-wire was positioned 
in the excited shear-layer, at a y location 
corresponding to UAJj=0.50, y^^. Figures 20a and 20b 
show the ensemble-averaged velocities, normalized 
by the jet exit velocity. At time t=0.0 the actuator is 
switched on. It operates for 0.49 seconds before being 
switched off The on and off times of the actuator 
have been subtracted to align the on and off times at 
t=0. The abscissa of Fig. 20a and 20b has the 
actuator toggle time multiplied by the convection 
speed determined in Section 3.4, producing a 
response convection length. This length scale, 
Uj.*time, is normalized by the jet diameter, D, 
relating the jet response time to distance in terms of 
jet diameters. When control is switched on, the flow 
responds in a matter of milliseconds to the change in 
<c^> in all cases. The response of the jet to switching 
the streamwise excitation on without a diffuser 
attached is the fastest, in agreement with the wave 
packet convection results shown in Figure 19 and 
with the higher frequency content of that wave 
packet. Switching the streamwise excitation (no 
diffuser and X-diffuser) on results in an initial 
vectoring of the jet below the baseline state followed 
by an upward deflection of the jet above the 
controlled state before converging to the controlled 
steady-state. The jet response to switching the cross- 
stream excitation (R-diffuser) on is smoother but is 
the slowest among the three cases studied. The jet 
response to switching the streamwise excitation off, 
in the absence of a diffuser (Fig. 20b), is the fastest 
and is accompanied by a slight deflection above the 
controlled steady-state. The jet response to switching 
the cross-stream excitation off is smooth, fast and is 
accompanied by only a small deflection above the 
baseline state before converging to the baseline 
steady-state. Figure 20b indicates that the jet 
response to turning the streamwise excitation off (X- 
diffuser), is initially accompanied by a deflection 
higher than the controlled steady-state at 2D and a 
deflection lower than the baseline steady-state 
centered around 4.5D. The effect of different diffuser 
lengths on the response of the jet to step changes in 
the excitation level has not been studied yet. Looking 
at the normalized response times, the jet starts to 
respond at a convection distance of about 2D and the 
transition stage also takes about 2D-4D (Fig. 20). 

Measurements were also made over the entire 
center plane of the jet, at x/D=1.6, to assess the 



overall response of the jet to a step change in <c^>. 
Figure 21 presents the jet response to on-off 
excitation in the form of mean velocity contours 
normalized by the jet exit velocity using streamwise 
(X-diffuser) and cross-stream (R-diffuser) excitation. 
For both types of excitation, the jet starts to respond 
at about 10 msec from the step change in <c^>. The 
jet response to switching the streamwise excitation 
on is initially characterized by a strong downward 
deflection (below the baseline steady-state) that is 
followed by an upward deflection (above the 
controlled steady-state) of the excited shear-layer 
(Fig. 21a), before converging to the controlled 
steady-state. This response could be interpreted as 
the shedding of a counter clockwise rotating vortex 
from the upper shear-layer as a response to turning 
<c^> on. The opposite happens when the streamwise 
excitation (X-diffuser) is turned off (Fig. 21b). The 
excited shear-layer starts to bend upward 
immediately, resulting in an even higher upward 
deflection at about 10 msecs after <c^> has been 
turned off, and a small deflection below the baseline 
state at 24 msec. This response could be interpreted 
as the shedding of a clockwise rotating vortex from 
the upper shear-layer. The opposite shear-layer 
responds more smoothly, but both shear-layers have 
deflections below the baseline steady-state at about 
20 to 24 msec. 

The transients of the jet response, to turning on 
the cross-stream excitation (R-diffuser Figure 21c), 
are smoother throughout the center plane (Fig. 21c). 
Unlike the smooth response seen for switching the 
cross-stream excitation (R-diffuser) on, the transient 
stage of the jet response to switching the cross-stream 
excitation (R-diffuser) off begins with a slight 
vectoring of the jet below the controlled state 
followed by a vectoring of the jet above the baseline 
state before gradually reaching the baseline steady- 
state. 

The transient responses described above could be 
interpreted as vortices shed from the jet exit as the 
excitation is turned on and off An upward deflection 
is accompanied by a shedding of a counterclockwise 
vortex while a downward deflection is accompanied 
by a clockwise vortex. It seems that the on response 
of the streamwise excitation and the off response of 
the cross-stream excitation generate more 
concentrated vortices. More direct measurements of 
vorticity are required to validate this hypothesis. 

3.5.3 The effect of jet exit velocity 

The Reynolds number dependence of the 
response was studied by altering the jet exit velocity 
and repeating the tests described in Section 3.5.2 



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AIAA 99-0672 



using streamwise excitation (X-diffuser). The results 
for Reynolds numbers corresponding to 11^=8, 12 and 
18 m/s are presented in Figures 22a and 22b for 
actuator on and off responses, respectively. The <c^> 
when the actuator was on was 2.4% for all R%'s. 
Time is multiplied by U^ to provide a common 



angles were lower for a diffuser half-angle of 15° than 
for diffuser half-angles of 22.5° and 30°. Jet deflection 
was highly sensitive to the direction in which the 
excitation was introduced. Periodic excitation, 
introduced in the streamwise direction, vectored the 
jet towards the diffuser wall where the excitation was 



convection length for the 



response. Thisintroduced. Low amplitude excitation introduced in 



normalization collapses the data very well, indicating 
Rcj, insensitivity and a typical response time of 
O.4AJ5 for the present geometry. Assuming that the 
convection speed is independent of Rcp, and looking 
back at Figure 20a and 20b, it is safe to assume that 
the jet will respond within a convection distance of 
about 3-4 diameters regardless of Re^, jet diameter, 
and its exit velocity. 

The fast response and its independence of Re^ 
are very encouraging for control purposes. However, 
the strong transients identified in the jet response, 
mainly of the streamwise excitation are a concern 
from an application point of view. This is especially 
important since the streamwise excitation is the most 
effective as it requires the minimum <c^> to generate 
effective spreading and vectoring, at <c^> levels of 
about 1%. This is probably the upper limit of what 
can be achieved in high subsonic speed applications. 

4. Summary and Conclusions 

Periodic excitation was introduced through a slot 
surrounding the upper quarter of the circumference of 
a circular jet to vector it and enhance its spreading 
rate. A diffuser, attached to the jet exit, promoted 
attachment of the jet shear-layer to the diffuser wall 
in a similar manner to that found in airfoil 
experiments using periodic excitation. 

The boundary layer upstream of the jet exit was 
tripped to achieve turbulent flow at the jet exit. 
Data were acquired for Rg between 1.6x10^* and 
4.7x10"*. The tripped boundary layers of the jet 
generated a Reynolds number independent flow, the 
desired effect. The turbulence level in the jet core 
was 3%. 

The use of periodic excitation and a diffuser at 
the jet exit in a flow control experiment introduced 
additional parameters such as frequency, excitation 
momentum and its direction, diffuser length, and 
diffuser half-angle. The jet deflection angles were 
insensitive to the excitation frequency, in the range 
of parameters studied. The jet deflection angles were 
independent of the Reynolds number, although some 
differences were noticed in the jet behavior when at 
Re[3=2.1xl0'', close to the transition Re^. Diffusers of 
length to diameter ratio between 0.58 and 1.85 were 
tested. The longest diffuser, L/D=1.85, generated 
somewhat higher deflection angles. Jet deflection 



the cross-stream direction vectored the jet in the 
same direction, but high amplitude excitation 
introduced in the cross-stream direction vectored the 
jet away from the wall where the excitation was 
introduced. 

Pulsed excitation was used to generate wave 
packets in the jet shear-layer in order to study the 
frequency content, the effect of the excitation 
direction, the disturbance convection speed and the 
relationship between the excitation and an instability 
mechanism. These studies revealed that the presence 
of a diffuser at the jet exit significantly amplified the 
pulsed excitation introduced in the streamwise 
direction. The favorable interaction between the 
excitation, the jet flow and the diffuser wall explains 
the higher jet deflection angles obtained with the 
diffuser when exciting the shear-layer in the 
streamwise direction. The wave packet excited by 
introducing a pulsed excitation in the cross-stream 
direction evolved differently even though a diffuser 
was present. This wave packet is the least amplified 
among the cases studied. It is also of similar 
amplitude in both the excited and opposite shear- 
layers, indicating a more global effect of the 
excitation when introduced in the cross-stream 
direction. This is consistent with the jet being 
deflected towards the opposite diffuser wall when 
using high amplitude cross-stream excitation. 

The jet responded quickly, on the order of 10-20 
milliseconds, to step changes in the level of the 
excitation. The response was independent of the 
Reynolds number when the jet exit velocity was 
increased. The practical implication of this finding is 
that a proportional increase in dimensions and speed 
will maintain a similar response time. The jet 
response to turning the excitation on is quicker, when 
the excitation is introduced in the streamwise 
direction, than when it is introduced in the cross- 
stream direction. However, this is accompanied by 
stronger transients, similar to an underdamped 
system. These transients can also be interpreted as 
shedding of a vortex whenever a step change in the 
level of the excitation occurs. The sign of the vortex 
is determined by the direction of the resulting jet 
deflection. 

From this jet control study, a number of areas for 
future research were identified. One area is the use 



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AIAA 99-0672 



of simultaneous streamwise and cross-stream 
excitation on opposite sides of the jet. It is assumed 
that significantly higher jet deflection angles could 
be obtained this way. The effect of the diffuser on 
the cross-stream excitation has not been studied yet. 
More wave packet studies, where diffusers of 
different lengths would be used, are required to better 
understand how the amplification and convection 
speed of the wave packet (and the associated mean 
flow distortion) are effected by the diffuser length. 
Finally, it is planned to use periodic excitation for 
the control of a rectangular jet with an exit diffuser. 
A rectangular jet is of interest because of the longer 
shear-layers per unit area and the additional possible 
modes. One such mode is jet rotation. 

A fast responding method of altering the direction 
of the flow emanating from a low speed, turbulent 
circular jet was demonstrated. Moderate <c^>'s were 
required to produce this effect. The technique could 
be applied to a number of applications including, jet 
engine exhaust, gust alleviation, and control surface 
augmentation or replacement without moving parts. 

Acknowledgment 

This work was performed while the second author 
held a National Research Council - NASA LaRC 
research associateship. The authors would like to 
thank Mr. W. L. Sellers III, Mr. M. Walsh, Dr. R. 
Joslin and Ms. C.B. McGinley for their support. 

References 

1) Crow, S. C. and Champagne, F. H., "Orderly 
Structure in jet turbulence". Journal Of Fluid 
Mechanics Vol. 48, part 3, 1971, pp. 547-591. 

2) Zaman, K.B.M.Q, and Hussain, A.K.M.F, 
"Turbulence suppression in free shear flows by 
controlled excitation". Journal of Fluid 
Mechanics, Vol. 103, 1981, pp. 133.-159. 

3) Davis, M.R., "Variable Control of Jet Decay", 
AIAA Journal, Vol. 20, No. 5, 1982. 

4) Strykowski, P. J. and Wilcoxin, P. J., "Mixing 
enhancement due to global oscillations in jets 
with annular counterflow", AIAA Journal, Vol. 31, 
No. 3, March 1993. 

5) Strykowski, P.J. and Krothapalli, A., "The 
Countercurrent Mixing Layer: Strategies for 
Shear-Layer Control", AIAA paper 93-3260, 1993. 

6) Strykowski, P.J., Krothapalli, A., and Forliti, D. J., 
"Counterflow Thrust Vectoring of Supersonic 
Jets", AIAA paper 96-0115, 1996 

7) Raman, G. and Cornelius, D., "Jet Mixing 
Control using Excitation from Miniature 
Oscillating Jet", AIAA Journal, Vol. 33, No. 2, 
1995 

8) Smith, B. L., and Glezer, A., "Vectoring and 
Small-Scale Motions Effected in Free Shear 



Flows Using Synthetic Jet Actuators", AIAA 
paper 97-0213, 1997 

9) Huerre, P. and Monkewitz, P. A., "Absolute and 
convective instabilities in free shear layers". 
Journal of Fluid Mechanics Vol. 159, 1985, pp. 
151-168. 

10) Seifert, A., Bachar, T., Koss, D., Shepshelovich, 
M. and Wygnanski, I., "Oscillatory Blowing, a 
Tool to Delay Boundary Layer Separation", AIAA 
Journal, Vol. 31, No. 11, 1993, pp. 2052-2060. 

11) Seifert, A., Darabi, A. and Wygnanski, I., "On 
the delay of airfoil stall by periodic excitation". 
Journal of Aircraft, Vol. 33, No. 4, 1996, pp. 691- 
699. 

12) Seifert, A. and Pack, L.G., "Oscillatory Control 
of Separation at High Reynolds Numbers", AIAA 
paper 0214-98, 1998. 

13) Kinser. E. and Rediniotis, O.K., " Development of 
A Nearly-Omni-Directional, Three-Component 
Velocity Measurement Pressure Probe," AIAA 
paper 96-0037, 1996. 

14) Husain, Z.D. and Hussain, A.K.M.F, 
"Axisymmetric Mixing Layer: Influence of the 
Initial Boundary Conditions", AIAA Journal, Vol. 
17, No. 48, 1979. 

15) Drubka, R. E., Reisenthel, P., Nagib, H. M., "The 
dynamics of low initial disturbance turbulent 
jet". Physics of Fluids, A 1 (1), 1989, pp. 1723- 
1735. 

16) Gaster, M., "The development of three- 
dimensional wave packets in a boundary layer". 
Journal of Fluid Mechanics, Vol. 32, 1968, 
pp.173-184. 

17) Balsa, T.F., "Three-dimensional wave packets 
and instability waves in free shear layers and 
their receptivity". Journal of Fluid Mechanics, 
Vol. 201, 1989, pp. 77-97. 

18) Gaster, M., Kit, E., and Wygnanski, I., "Large- 
scale structures in a forced turbulent mixing 
layer". Journal of Fluid Mechanics, Vol. 150, 
1985, pp. 23-39. 

19) Tumin, A. and Likhatchev, O., "On Harmonic 
perturbations in turbulent shear flows". Presented 
at the 51" Meeting of the APS/DFD, 
Philadelphia, PA, 1998. 

20) Morkovin, M. V., " On the many faces of 
transition", in Wells, C.S. (ed.). Viscous Drag 
Reduction . Plenum Press, New York, Sept. 1969, 
pp. 1-31. 

21) Zilberman, M., Wygnanski, I., Kaplan, R.E., 
"Transitional boundary layer spot in a fully 
turbulent environment". Physics of Fluids 
Supplement 20 (1977) S258-271. 



12 
American Institute of Aeronautics and Astronautics 



segmented collar 

and actuator chambers jet diffuser 




Boundary layer trip 



exit 



diffuser exit 



Figure la: Schematic of jet side view. 




Region where periodic 
excitation used 

-dynamic pressure transducer 

for monitoring excitation level 

1.0 mm wide slot 



jet exit 
D=39 mm 

Figure lb: Schematic of jet front view. 

1 -. ' ;^^ ! tt 8 K i C»» l j=WS 



u/u 




Figure 2a: Baseline U profiles at x/D=0.1 and z/D=0.0. 
0.2 f 

0.15 



u7U 



0.1 



0.05 







- 


-*-R 


V21K 


: 


M 


--x--Rejj=42K 


M 


i > 










- 


^ ^^i^^^^^^^^^^' 


^ 



-1.5 



-0.5 





y/r 



0.5 



1.5 



Figure 2b: Baseline u' profiles at x/D=0.1 and z/D=0.0. 
(Dashed line indicates y location of spectra shown in 
Figure 3.) 



3 

"cO 

o 

(D 
Q. 
03 

(1) 

O 

Q. 




f*D/U 

e 
Figure 3: Baseline spectra at y/r=0.97, x/D=0.1. 

0.6 



100 




(y-yo.,)/2e 

Figure 4 : Diffuser effect on baseline profiles at xD= 1 .6, 
z/D=0.0, Rep=3. 1x104. 0=30° andL=1.85D. 

^^no diffuser, de/dx=0.030 
-^ X-diffuser , de/dx=G.031 
-x- -R-diffuser , de/dx=0.031 



e/D 




Figure 5: The effect of diffuser on shear-layer momentum 
thickness close to jet exit. Rejj=3 .IxlQf^ . 0=30° and L=1.85D. 



13 



American Institute of Aeronautics and Astronautics 




-25 25 

Z [mm] 



-25 25 

Z [mm] 



25 25 

Z [mm] 



Figure 6: U/Ug and u'/U^. contours at x/D=2.5 Rep=3.1xlO^ for different excitation directions (a) U/Ug, streamwise excitation, 
<c^>=3.3%, F+=2.3, L=1.0D (b) U/U^ , baseline (c)U/Ug cross-stream excitation <c^>=3.3%, F+=4.2, L=1.85D, (d) u'/U^, 
streamwise excitation, <c >=3.3%, F+=2.3, L=1.0D (e) u'/U^ , baseline, and (d) u'/U^, cross-stream excitation, <c >=3.3%, 
F+=4.2, L=1.85D. 

7 ts 

'■^ i' ' ' ' I j 

• I 1 



0) 


6.5 


■n 








CD 


6 


m 




r 




cc 


b.b 


r 




n 




t) 


5 


0) 




X- 






T3 


4.b 



3.5 



*^X-diffuser, plane 
^ -X-diffuser, profile 
• (-) R-diffuser, plane 
A (-) R-diffuser, profile 




1.5 



2.5 

x/D 



3.5 



Figure 7: Jet deflection angles computed using profiles on 
z/D=0.0, and cross-section planes. <c >=3.3%, F+=2.3, 
and L=1.0D for X-diffiiser. <c^>=3.3%, F=4.2 and 
L=1.85D for R-diffuser. ReD=3.1xl04 . 




Figure 8: The effect of Re^ on jet deflection angle measured at 
x/D=2.5 and z/D=0.0 ( 0=30°, L=1.0D X-diffuser). 



14 



American Institute of Aeronautics and Astronautics 



CD 
D) 

c 

TO 

C 

g 
o 



T3 



8 ^ 
7 1 
6 1 
5 1 
4 L 
3 1 



-^=^f=300Hz, F-'=1.8 

-x--f=700Hz, F-'=4.2 
♦ f=700 Hz, 5-hole probe 




Figure 
ReD=3 



CD 



o 

CD 



CD 



9: The effect of frequency on jet deflection angles. 
.1x104, x/D=2.5, z/D=0.0, 0=30°, L=1.85D X-diffuser. 



L=0.58D, F-'=1.3 
L=1.0D, F-'=2.3 
L=1.85D, F-'=4.2 




Figure 10: The effect of varying diffuser length , L, on jet 
deflection angles. 0=30° X-diffuser. Rep=3.1xl04, x/D=2.5, and 
z/D=0.0 (Dashed line indicates <c > for profile in Fig. 11). 



0.8 



0.6 



L=0.58D, F*=0.0 
L=1.00D, F*=0.0 
U1.85D, F*=0.0 
U0.58D, F*=1.3 
L=1.00D, F*=2.3 
L=1.85D, F*=4.2 



U/U 




0.4 



0.2 



c 
TO 



o 



T3 



2 1 




L_ 
0.001 



Figure 12: The effect of varying the diffuser half -angle, 0, on jet 
deflection angle. L=0.58D X-diffuser. Rep=3. IxlO'*, x/D=2.5, 
z/D=0.0 (Dashed line-profiles in Fig. 13). 

1 



U/U 




20 40 
y [mm] 

Figure 13: U profiles for different diffuser half-angles, 0, at 
Rep=3.1xl04, x/D=2.5, andz/D=0.0. <c^>~3.1% (when control 
apphed). L^0.58D X-diffiiser. 



en 

CD 

cn 

d 

CO 

g 

o 

_g 

T3 



-^;:^no diffuser 
-^ -X-diffuser 
-X -R-diffuser 



/■ 



/t 



^ 



M — 






-at . 

0.001 



0.01 



0.1 
<c > % 



10 



Figure 11: U profiles for varying L. <c >~3% when control 
appUed. 0=30° X-diffuser. Rep=3.1xl04, x/D=2.5, and 
z/D=0.0. 



Figure 14: The effect of excitation direction and presence of the 
diffuser on jet deflection angle. L=1.85D and 0=30° (when diffuser 
present). Rej-,=3.1xlO"*, x/D=2.5, and z/D=0.0 (Dashed line -profiles 
in Fig. 15a and 15b). 

15 

American Institute of Aeronautics and Astronautics 



u/u 



no diffuser, <c >=0.0% 

X-diffuser, <c >=0.0% 

V- 

R-diffuser, <c >=0.0% 

V- 

— 9 — no diffuser, <c >=3.1% 

V- 

-& - X-diffuser , <c >=3.1% 

V- 

— X--- R-diffuser , <c >=2.3% 

V- 




20 40 60 80 
y [mm] 
Figure 15a: U profiles showing effect of excitation direction and 
presence of diffuser on jet. L=1.85D and 0=30° (whffe diffuser 
present). Reo=3.1xl0'*, x/D=2.5, and z/D=0.0. 

0.25 



0.2 



0.15 



uVU 



0.1 

0.05 





«A n f^^ 




no diffuser, <c >=0.0% 

X-diffuser, <c >=0.0% 

R-diffuser, <c >=0.0% 

O no diffuser, <c >=3.1% 
-A - X-diffuser , <c >=3.1% 
—X--- R-diffuser , <c >=2.3% 



-40 -20 







20 40 60 80 
y [mm] 
Figure 15b: u' profiles showing the effect of excitation direction and 
presence of the diffuser on jet. L=1.85D and 0=30° (where diffuser 
present). Reo=3.1xl04, x/D=2.5, and z/D=0.0. 



u7U 




u7U 




Time [msec] 
Figure 16b: High amplitude wave packet for X-diffuser 
L=1.85D, 0=30° varying x/D. U/U^=0.75 and 
Reo=3.1xl04. 



u7U 




20 30 40 50 

Time [msec] 
Figure 16c: High amplitude wave packet for R-diffuser 
L=1.85D, 0=30° varying x/D. U/U^=0.75 and 
Rep=3. 1x104. 



8E-06 



6E-06 



CM 

3 



4E-06 



2E-06 



- 








▲ 


- 




Y 


no diffuser 
X-diffuser 








- 






-■■f 


- 


- 




R-diffuser 
X-diffuser, 


/ 

profile / 


- 


▲ 


- 


■ 


R-diffuser, 


profile / 




- 


~ 






/ 




~ 








/ 






- 






/ 




- 








/ 










/ 








- 




/ 






- 


- 




A 




^ 


- 






/ 


- 






- 


y 


^^ 




- 


- 


f^ 




.-^ 


.-•£> 


- 




/ 


^-"■^^""''''^ 








- 


■Jt-"^ 


— ■ 


.......a--' 




- 


:i 


B-tn n-- 


B--" 


II 


1 1 


1 


II 


1 1 1 1 



8E-05 



6E-05 






4E-05 ! 



2E-05 



0.5 



Time [msec] 
Figure 16a: High amplitude wave packet without 
diffuser, varying x/D. U/Ug=0.75 andReo=3.1xl04. 



1 
x/D 



1.5 



Figure 17: Wave packet amplitudes. ReQ=3.1xl04. 



16 



American Institute of Aeronautics and Astronautics 



u'/U 




: y=-21 .5 
~ y=-25.5 



20 30 40 

Time [msec] 
Figure 1 8a: High amplitude wave packet for X-diffuser 
L=1.85D, 0=30°. ReD=3. 1x104, x/D=1.6, z/D=0.0. 



y=26.0 



U'/U 




20 30 40 

Time [msec] 



Figure 1 8b: High amplitude wave packet for R-difliiser 
L=1.85D, 0=30°. ReQ=3. 1x104, x/D=1.6, z/D=0.0. 



0.07 
0.06 
0.05 



X m 



0.04 - 
1] 
0.03 

0.02 

0.01 







o no diffuser UJ U^= 
- ^ - X-diffuser UJ U^= 
--x---R-diffuser U^/U^= 


0.587 / 
0.603 /^ 






=0.577/ ^ 


/ / 




i ^ a/x-' 




(? ^ X 




/ //' 








/ / / 








/ '/■■ 

■,/,,, 1/ ,,- 









1.79 
1.54 
1.28 
1.03 
0.77 
0.51 
0.26 




x/D 



0.006 0.008 0.01 0.012 0.014 0.016 0.018 
Time [sec] 

Figure 19: Wave Packet detection time (Conditions 
specified in Fig. 16). 



Time [sec] 
0.011 0.022 0.033 0.043 0.054 



U/U 




U *(t-t^ J/D 

c ^ ON' 

Figure 20a: Effect of excitation direction and presence of 
diffuser on jet response to a step change in<c > (0-2.2% 
streamwise and 0-1.6% cross-stream). Rejj=3.1xl04. ON. 

Time [sec] 



1 



0.8 







0.011 0.022 0.033 0.043 0.054 



0.6 



U/U 



0.4 



0.2 



,,,,,, 


, , 1 < < < 1 < < 




no diffuser 


,.'V, ;•«•'" 


\ 
\ 


— 


- -X-diffuser 


v-y>-S»A 


\ 


— 


---R-diffuser 


w^-V \ ^ 




- 


\ ^ 




- 




1 






- 


\ ^ '-■• 




- 


- 


f^ 


^^^'V^ 


^?^^0:5?:3;^?<?^ 




1 V 






- 


- 








- 



u;(t-t„,,)/D 



1 



Figure 20b: Effect of excitation direction and presence of 
diffuser on jet response to a step change in<c > (2.2 -0% 
streamwise and 1.6-0% cross-stream). ReQ=3.1xl04. OFF. 



17 



American Institute of Aeronautics and Astronautics 



>- 




0.02 0.03 0.04 

t-toJsec] 



0.05 



a) X-diffUser, Excitation ON 



30 r 



20 - 



10 - 




E^ 
>- 



-10 - 



-20 



-30 - 




0.01 0.02 0.03 0.04 0.05 

t-topp[sec] 
b) X-diffuser, Excitation OFF 



30 



20 



10 - 



I ° 




-10 - 



-20 

-30 




_1_ 



_1_ 



_1_ 



_1_ 



J 



0.01 0.02 0.03 0.04 0.05 

t-toJsec] 
c) R-diffUser, Excitation ON 



> 



30 


; 


/ ^0 2— — — 








/xC—— 








^ /^ ^ ,.,~.~-~~^r) A. 






2U 


" 


mii^X^X^^^ 


0.6 







: 


EE^:?Eri^vf^^^^ 




0-8- 


111 










= 


==;ir5i^/ 













-^ 


-—0.9 --^^ 




- 


^-0.9 ^ 






10 


^^^^^S^= 


0.8- 

0.6- 


0.7 


20 
30 




— — — -— 0Jj;;5)i,^-'^ -0.4— 


0.2 


-0-3 

1,1 



0.01 0.02 0.03 0.04 0.05 

t-topp[sec] 
d) R-diffuser, Excitation OFF 



Figure 21: Contours of U/Ug of jet response to a step change in <c > (0-2.2% for X-diffuser and 0-1.6% for R-diffuser) at 
Rep=3.1xlO^, x/D=1.6, z/D=0.0 (Dashed-dotted line indicates center of baseline jet). 

1 



U/U 



1 

0.9 
0.8 

0.7 

J 

e 

0.6 
0.5 
0.4 
0.3 









f^^^ijOAj^^ 


fiK/IMMWn 


y>SjhUdV« 


/l 




"-'-■■•-0. 










; 








; 




- 


— Re =21K 
-Re =31K ; 






--R^D " 


=47K 



0.9 
0.8 
0.7 



U/U 







0.2 0.4 0.6 0.8 



e 
0.6 



0.5 
0.4 
0.3 









^% 


=21 K 






- 


--Rep=31K 


5wk¥\ 






- -Re^=47K 


''""" \ 






- 


\ 






; 


\ 




- 


\ 


g$^ 


i:^3i-:^^>^*'*-^;^^**f^ 


\ P^ 




- 


\f^: 




: 


'" 




; 


: 


, , ! , , ,: 



0.2 0.4 0.6 0.8 



1 



Figure 22a: Effect of Re^ on jet response to a step change in 
<c^> (0.0-2.4%) at x/D=l. I 
L=1.85D X-diffuser. ON. 



<c^> (0.0-2.4%) at x/D=1.6, z/D=0.0, and U/U^=0.5. 0=30°, 



Figure 22b: Effect of Re^ on jet response to a step change 
in <c^> (2.4- 0.0 %) atx/D=1.6, z, 
0=30°, L=1.85D X-diffuser. OFF. 



in <c^> (2.4- 0.0 %) at x/D=l .6, z/D=0.0, and U/U^=0.5 



18 



American Institute of Aeronautics and Astronautics