The effectiveness of jet unsteadiness in enhancing flow entrainment was assessed. It was conducted that entrainment depends on the type and amount of jet unsteadiness. Apparently, the mere introduction of jet unsteadiness by small sinusoidal flow angle variations is insufficient to enhance entrainment but, it should be noted that the results were obtained at measuring stations which are all many nozzle widths downstream of the jet nozzle. Thus, no fully conclusive statement can be made at this time about the entrainment close to the nozzle. The high entrainment of the fluidically oscillated jet was caused by the high-frequency content of this square wave type of oscillation but more detailed measurements are clearly needed, in particular for the fluidically oscillated and the pulsed jets. Practical ejector application requires the proper trade-off between entrainment and primary nozzle thrust efficiency

Bremhorst, K.

Platzer, M. F.

Simmons, J. M.

English

NASA Technical Reports Server

ENTRAINMENT CHARACTERISTICS OF
UNSTEADY SUBSONIC JETS
M. F. Platzer
U. S. Naval Postgraduate School, Monterey, California
and
J. M. Simmons and K. Bremhorst
University of Queensland, Brisbane, Australia
A revised version of this paper was published in the AIAA
Journal, Vol. 16, No. 3, pp. 282-284, March 1978.
Permission to include in the workshop proceedings has been
granted by AIAA.
311
https://ntrs.nasa.gov/search.jsp?R=19800001885 2020-03-21T02:14:28+00:00Z
I NTRODUCTION
The entrainment mechanismin turbulent jets has been a subject of con-
siderab]e basic and applied interest for manyyears. Recently, this problem
has received increased attention because of the need to develop compact, yet
1highly efficient thrust augmenting ejectors for VSTOLapplications Several
new techniques have been introduced or proposed to increase the jet entrain-
ment e.g , hypermixing 2. , swirling 3, acoustic and unsteady jetinteraction 4
5techniques . It is the objective of this paper to present recent results on
the entrainment characteristics of two types of unsteady jet flows, i.e.,
oscillating jets with time-varying jet deflection and pulsating jets with
time-varying mass flow.
The use of oscillating jets for enhanced flow entrainment was first
advocated by Viets 5 who also developed a rather ingenious fluidic jet actua-
tion device. Other oscillating jet studies have been reported 6'7'8'9 but
they do not contain entrainment measurements.
The favourable effect of pulsating jets on flow entrainment seems t:o
have ]teen first recognized during the development of the pulse jet
engineI0'II']2. LockwoodI0 also noted the generation of ring vortices due
to pulsating [low, an effect later verified more clear]y by Curtet and
Cirard 13• Further pulsating jet studies are those of Johnson and Yang14
l)ide]le et el. 15,16, Binder and Favre-_.Larinet17, , Crow and Champagne18 and,
very recently Bremhorst and Hatch19.
The fo]lo:eing section is a report of three different experiments which
were c_,nducl:ed to assess the effectiveness of jet unsteadil_ess in enh_nc_nf;
i 1o_ cntr_iltn_crlt.
312
EXPERIMENTS
Definition of the edge of a turbulent jet raises suhtleties which are
18
di';cussed by Crow and Champagne in terms of the turbulent (or inner rota-
tional) region and the induced potential flow (or potential tails). In the
experiments mean volumetric flow rates Q(x) in the turbulent region of
unsteady subsonic jets were determined at a number of distances x from
the nozzle by integration of mean jet velocity distributions. A constant
temperature hot-wire anemometer was used in all cases and the mean of its
linearized output was assumed to be proportional to the mean velocity in the
direction of the center line of the nozzle. Errors arising from estimation
of the edge of the turbulent region and from the influence of high ratios of
rm_; to mean velocities near the edge of the jet are regarded as tolerable in
this investigation.
Various measures of entrainment are defined in the literature. Here,
entrainment is defined as (Q(x) - QR)/QR where QR is a reference flow
rate and is properly taken as the mean volumetric flow rate QE at the
nozzle ex.it in two of the experiments. In the third experiment QR is taken,
for lack of precise nozzle flow rate information, as the volumetric flow rate
Q1 at a station near the nozzle in a steady jet. This still enables com-
par[sons and is discussed later in more detail. Clearly, the entrainment
differs by unity from the dimensionless local flow rates Q(x)/QR which
are presented in this paper.
F[uldicallv Oscillated Three-Dimensional Jet
The fluidic nozzle illustrated in figure 1 was used by the first and
second authors to exhaust a jet of air with oscillating angle into still air.
313
Tile nozzle was based on a design by Viets 5. Flow from a plenum chamber and a
contraction emerges from a 6.2 x 49.0 mm rectangular section into a rapid
diffusion section where it is bistable because of the proximity of the walls.
The flow is illustrated at the moment it attaches to the lower wall A. This
sets up an entrainment process and generates compression and rarefaction waves
in the feedback tube connecting control parts A' and B T. Continuous jet
oscillation results at a frequency which depends on the length of the feedback
tube.
In both the oscillating and the steady tests the nozzle was operated at
a pressure ratio of 1.13 to produce a mean mass flow rate of 0.0188 kg/s as
measured with an upstream orifice plate. The jet oscillated through about 7
dogrees e[ther _i.de of the nozzle center line and with a fundamental frequency
of 52 ]Iz. IIowever, higher harmonics were appreciable because of the flip-flop
mode of operation. Viets 5 showed that velocity fluctuations at the half-width
position of the mean velocity profile have almost a square wave shape.
The values of volumetric flow rate Q(x) used in figure 2 were obtained
by integration of the mean velocity distribution across the jet cross-sections.
The limits of integration were stations at which the mean velocity was
bet_een 5 and l0 percent of the maximum value in a distribution. This
necessitated mild extrapolation of the distribution furthest downstream so
thCLt the value of Q(x) there has a possible error of about I0 percent.
For the two cases of oscillating and fixed jet angle, Q(x) is normal-
ized by the mean volumetric flow rate QE at the nozzle exit. Mass flow
raI-_ upstream of the nozzle (measured with an orifice plate) was used to
determine QE The hydraulic diameter of the nozzle (4 x area/perimeter)
i:_ tm,,clas the length scale because of the essentially three-dimensional
314
nature of the flow. The change in slope of the curve of Q(x)/QE for the
steady jet is attributed to the transition from a high aspect ratio three-
dimensional flow to a more axisymmetric meanflow.
Mechanically Oscillated Two-Dimensional Jet
Recent two-dimensional studies of flow past an airfoil at zero incidence
and with an oscillating trailing edge jet flap have been extended by the first
and second authors to measurements of entrainment. Details of the mechani-
cally oscillated nozzle have been reported previously 9'20. In these tests
the nozzle was oscillated through 5.2 degrees either side of the airfoil
ehordline and at frequencies of 4 and 20 Hz. The free stream velocity was
29.2 m/s and the nozzle exit velocity of 137 m/s was estimated, using the
results of Bradbury and Riley 21, from measurements of the velocity profile
close to the nozzle with the jet held parallel to the free-streamo
20
The instantaneous velocity profiles measured in a previous study
were averaged over a cycle of nozzle oscillation to obtain mean velocity
profiles and hence mean volumetric flow rates. Because nozzle velocity was
not measured directly the measurements in figure 3 for the oscillating and
the steady cases are both normalized by the volumetric flow rate in the
steady jet across the measuring section nearest the nozzle (Joe. 35 nozzle
widths downstream). The use of a small nozzle width (0.38 ram) and measurin[;
stations many nozzle widths downstream is a legacy of the preceding stud:ies
of jet flaps and leads to an uncertainty in Q(x)/QI which increases to
about I0 percent at the downstream limit. Nevertheless, the measured insen-
:;itiv_ty of Q(×)/QI over the range of x to the frequency of oscillation
i_ s:Ignif:icanto It must be stressed that the jet flowed into a moving air-
5 t. FC_Im.
315
Axisy_etric Jet with Pulsed Core
Bremhorst and Harch 19 recently studied a fully pulsed axisymmetric air
jet exhausting into still air and their measurements of Q(x)/QE are
reproduced in figure 2. They used a mechanical valve connected to a pl_num
chamber by a smooth transition piece. The valve allowed flow for one third
of its period of cyclic operation. The first and third authors used the
same valve to study an axisymmetric air jet flowing into still air but with
pulsation restricted to the inner core by the fitting of a two-stream
coaxial nozzle downstream of the valve (figure i). The nozzle consisted
of a central reducer with 6.9 mm exit diameter to which air was supplied
solely from the pulsating valve, and an annular section of 25.4 mm diameter
wh_ich was _ed through a regulating valve with air taken from upstream oF
the plenum chamber.
The total jet flow rate was measured with a flow meter well upstream
of the plenum chamber. The inner coaxial jet flow rate for the pulsed core
was metered separately upstream of the plenum chamber. The mean exit veloci-
ties _or the steady annular portion of the jet and the pulsed core were 18.3
and 12.6 m/s respectively.
The results in figure 2 were obtained by planimeter integration of the
radi,l_ times local mean velocity versus radius profiles. These profiles
were [aired to zero in order to exclude the potential tails as was done by
18
Cr_,w a_id Chamvagne . The total volumetric flow rate across a downstream
_ection was then normmlized by the mean volumetric flow rate at the nozzle
18
exit. Measurer,_ents by Crow and Champagne for a steady axisymmetric jet
arL_ p_e_ented for comparison.
316
DISCUSSION
The results in figure 2 show the powerful effect of full jet pulsation
on entrainment. Also, the entrainment is seen to increase with frequency,
but measurements are available for only two frequencies. Pulsation of only
the jet core still provides significant entrainment benefits over the steady
jet (figure 2) and this method can be regarded as an entrainment control
device which enables the setting of the desired entrainment level for a jet
of given flow rate. The fluidically oscillated jet shows equally significant
entrainment increases (up to 55 percent increase in Q(x)/QE at the most
downstream station) when compared in figure 2 with the steady jet. Similar
results with the same fluidic nozzle operated at a higher pressure ratio
(1.33) were obtained by %eltman 22 with a cruder measuring technique
(pitot-static tube). Finally, in figure 3 the volumetric flow rate
measurements for the sinusoidally oscillated jet flap show negligible
variation from the corresponding steady jet measurements. This indicates
that any significant influence of jet oscillation on the entrainment
processes must, if it exists, be confined to the as yet uninvestigated
vicinity of the nozzle.
These results indicate that entrainment depends on the type and amount
of jet unsteadiness. Apparently the mere introduction of jet unsteadi-
ness: by small sinusoidal flow angle variations is insufficient to enhance
ent_rainment but it should be noted that the results in figure 3 were obtained
at Ineasuring stations which are all many nozzle widths downstream of the
jet nozzle. Thus, no fully conclusive statement can be made at this time
abo,t the entrainment close to the nozzle. However, the measuring stations
for the sinusoidally oscillated jet were all within less than one llalf of
317
thc :Jet wave length. Therefore, the sinusoidally oscillated jet was operated
at a much smaller reduced frequency than the other two jets. In effect, it
approached quasi-steady conditions which may well explain its low entrainment.
Indeed, in two previous papers 20'23 it was shown that quasi-steady concepts
are quite successful in explaining the major flow features.
The high entrainment of the fluidically oscillated jet woul_ appear to
be caused by the high-frequency content of this square wave type of oscilla-
tion but more detailed measurements are clearly needed, in particular for
the fluidically oscillated and the pulsed jets. Such studies are presently
in progress. Furthermore, practical ejector application requires the
proper trade-off between entrainment and primary nozzle thrust efficiency.
• . 5,22
Whil_: some information is available on the thrust efflclency of the
fluidic nozzle there seems to be none available for pulsating nozzles.
318
i. Schum, E. F., "Techniques for Increasing Jet Entrainment Rates in
Ejector Augmenters," Proceedings of the Workshop on Prediction Methods
for Jet V/STOL Propulsion Aerodynamics, Naval Air Systems Command,
July 1975, pp. 639-652. (available from DDC as AD-A024023).
2. Quinn, B., "Compact Ejector Thrust Augmentation," J. Aircraft, Vol. I0,
Aug 1973, pp. 481-486.
3. Chlgier, N. A. and Chervinsky, A., "Experimental and Theoretical Study
of Turbulent Swirling Jets Issuing from a Round Orifice," Israel J.
TeohnoZof/y, Vol. 4, Feb 1966, pp. 44-54.
4. Hill, W. and Greene, P., "Self-Excited Superturbulence: The Whistler
Nozzle," Grumman Research Department Rep. No. RE-488, Oct 1974,
(available from DDC as AD-A001021).
5. Viets, H., "Flip-Flop Jet Nozzle," AIAA Journal, Vol. 13, Oct 1975,
pp. 1375-1379.
6. Trenka, A. R. and Erickson, J. C., Jr., "The Determination of Un._teady
Aerodynamics of a Two-Dimensional Jet-Flap Wing," CAL AC-2260-S-I,
Cornell Aeronautical Laboratory, Buffalo, NY, April 1970.
7. K1etz, M., "Commande Asservie des Forces Aerodynamiques Instationnaires,"
Dc_ 07-44E5, Giravions Dorland, Suresnes_ France, 1973.
8. Simmons, J. M. and Platzer, M. F., "Experimental Investigation of
Inc:ompress[hle Flow Past Airfoils with Oscillating Jet Flaps," J.
Ai_'ona:'g, Vol. 8, Aug 1971, pp. 587-592.
9. S_mm_ns, J. M., "Measured Pressure Distrib_tion on an AirJoil with
Osc[]lating Jet Flap," A IAA Journal, Vol. 14, Sept 1976, pp_ ]297-1302.
319
i0. Lockwood, R. M., "Pulse Reactor Lift-PrOpulsion System Development
Program," Hillier Aircraft Company,Rep. No. ARD-308, March 1963.
ii. Foa, J. V., "Inter_ttent Jets," High-speed Aerodynamics and Jet
Propulsions, Vol. XII, Sect. F, Princeton University Press, 1958.
12. Bertin, J., "Dilution Pulsatoire sur Reacteur, C. R. Acad. Sci. P_is,
Vol. 240, 1955, pp. 1855-1857.
13. Curtet, R. M. and Girad, J. P., Visualization of a Pulsating Jet," Proc.
of ASME Symposium on Fluid Mechanics of Mixing, Atlanta, GA., June
1973, pp. 173-180.
14. Johnson, W. S. and Yang, T., "A Mathematical Model for the Prediction of
the Induced Flow in a Pulsejet Ejector with Experimental Verification,"
AS_" Winter Annual Meetin_ and Energy Systems Exposition, New Yo_k,
Paper 68-WA/FE-33, Dec 1968.
]5. Didelle, H., Binder, G., Craya, A. and Laty, R., "L'augmentation de la
pouss6e d'une trompe h jet inducteur pulsant: Project, instal]ation et
mise au point de la soufflerie, de la trompe et du banc de mesure de
pouss6e," Laboratoires de M6canique des Fluids, Univ. Grenoble, Oct 1971.
16. Didelle, H., Binder, G., Craya, A. and Laty, R., "L'augme_tation de la
pous6e d'une trompe h jet inducteur pulsant: R_sultats des essais,"
Laboratoires de M6canique des Fluides, Univ. Grenoble, J_rne 1972.
]7. Binder, G. and Favre-}_arinet, M., "Mixing Improvement in Pulsating
Turbu]ent Jets," Proc. AS_',E Symposi_Jn on Fluid Mechanic_._ of Hixing, "
Atlanta, GA., June 1973, pp. 167-172.
18. Crow, S. C. and Champagne, F. H., "Orderly Structure in J(_t Turbulence,"
J. Fguid ffech., Vol. 48, Aug, 1971, pp_ 547-591.
320
19. Bremhorst K. and Harch, W. H., "Near Field Velocity Measurementsin a
Fully Pulsed Subsonic Air Jet," Symposium on Turbulent Shear Flows,
Pennsylvania State University, April 1977.
20. Simmons, J. M., Platzer, M. F. and Smith, T. C., "Velocity Measure-
ments in an Oscillating Plane Jet Issuing into a Moving Airstream,"
J. Fluid Mech., vol. 84, part I, OP. 33-53, 1978.
2]. Bradbury, L. J. S., and Riley, J., "The Spread of a Turbulent Plane
Jet Issuing into a Parallel Moving Airstream," J. Fluid Mech._
Vol. 27, Feb 1967, pp. 381-393.
22. Veltman, R. J., "An Experimental Investigation of the Efficiency
and Entrainment Rates of a Fluidically Oscillated Jet," Master's
Thesis, U. S. Naval Postgraduate School, June 1976.
23. Simmons, J. M. and Platzer, M. F., "A Quasi-steady Theory for
Incompressible Flow Past Airfoils with Oscillating Jet Flaps,"
AIAA Journal, Vol. 16, No. 3, Dr. 237-241, March 1978.
321
t
B
ii i i m
, - 76.2 -
FLUIDIC NOZZLE
6:2
5.3 6-4
I.
9"6
dimensions in mm
steady flow (4 inlets)
;sh
8
pulsed
PULSED CORE NOZZLE
Figure i. Schematic of flui,!ic _nd pulsed core nozzles.
322
QQE
20
16
12
8
4
0
I I I I I I I I I I I I
FULLY PULSED-25
-I0 HZ
FLUIDIC- 52 HZ
x.,...,.,...._-"""__CROW 81 CHAMPAGNE-- STEADY
I I I I I I I I I I I I _
0 4 8 12 16 20 24
x/d
Figure 2. Mean volumetric flow rates Q(x) versus streamwlse distance x
for fluidic, fully pulsed and pulsed core nozzles. QE is mean
nozzle exit flow. d is hydraulic diameter of fluidic nozzle
or diameter of axisymmetric nozzles.
323
32
Q
QI
0
<)
O
I I I I I I 1
0
8
0
0
D
0
D
STEADY
4 HZ
20 HZ
I. I I I I I 1
400 800 1200
x/h
0
1600
Figure 3. Mean volumetric flow r_tL, s Q(x) versus strear_¢Ise distance x
for mechanically .scillated two-dimensional jet. Q1 is flow in
steady jet at x/h = 35 . h is nozzle width.
324


Entrainment characteristics of unsteady subsonic jets

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