International Symposium on Advanced Fluid/Solid Science and Technology in Experimental Mechanics, 11-14 Sept 2006, Sapporo, Japan

PHASE-AVERAGED MIXING CHARACTERISTICS OF MULTI-JETS
MODIFIED BY CYCLIC PERTURBATION
E. Shinohara*, K. Tatsumi, M. Mizuno and K. Nakabe
Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan* Toyota Industries Corporations, Kariya, Aichi 448-8671, Japan
It was also found that, in certain cases of the central jet
perturbation, a good mixing was found in the near-field of
the jet nozzle while a poor mixing was in far-field,
compared to the case without the perturbation. In order toelucidate this mixing tendency of the jet array perturbed
by the pulsatile jet, detail investigation on the mixing
characteristics of the jet array is performed experimentallyin the present study.
EXPERIMETAL SET-UP
Experimental Apparatus

ABSTRACT
Effects of a jet perturbation on mixing performance of an
air-jet array were investigated experimentally. The jetarray consists of three same-sized parallel jets, and themass flow rate of the central jet is perturbed in a pulsatileor sinusoidal cycle with the frequency, fr = 0, 1 or 2Hz.
The jet array discharged simultaneously without the jet
perturbation (fr = 0Hz) shows good mixing performance incomparison with the jet array of three arithmeticallysuperimposed single jets. The flow condition with the jet
perturbation (fr = 1 or 2Hz), on the other hand, isalternately changed, laminar or turbulent, in one cycle ofthe central jet perturbation. The time-averaged velocity
profiles of the jet array obtained under certain perturbed
conditions demonstrate an adverse change of the mixing
performance at the locations near the nozzle and far
downstream. Phase-averaged velocity profiles were
thoroughly examined in order to understand such a mixing
mechanism of the multiple jet flow.
INTRODUCTION
Mixing of fluids is a key technology of thermo-fluid
engineering, for example, to control chemical reaction
processes in industrial plants, to enhance heat transferfrom target surfaces of energy devices and to reduce air
pollution of exhaust emissions from burners of boiler andfurnaces. In chemical reactors, heat transfer units or
combustors, turbulent jets are typically used to enhance
the mixing of chemical agents, fuels, oxidizers, etc. The
detail characteristics of the jet flows in turbulent Reynolds
number regimes have been considerably investigated andknown well in engineering literature. Recently, the sizesof channels and nozzles in the reactors and combustors are
required to become small, which is combined with
gradually popularizing distributed energy systems, e.g.
micro gas turbines (MGT) or fuel cell (FC), and also
developing an ultra-fine processing technology, i.e. micro
total analysis systems (P-TAS) and power micro electromechanical systems (power-MEMS). In the cases of such
millimeter- or sub-millimeter-scale hardware, therepresentative jet Reynolds number becomes small
because of the limitations of jet nozzle size and jet flow
rate. Thus, the jet flows are situated in the laminar flow
regime, and the mixing performance of the jets is
restrained excessively in comparison with turbulent jet
mixing.
In order to control the mixing of laminar jets, theauthors have been focusing on the interaction of laminarjets and also on the jet perturbation with a pulsatile orsinusoidal cycle. We previously investigated on the
mixing characteristics of a triple laminar jet array andquantitatively showed that the jet array discharged
simultaneously attained better mixing than the jet array of
three arithmetically-superimposed single laminar jets [1].

Fig. 1

Experimental apparatus.

Figure 1 shows the experimental apparatus of the triple
jets issuing into the stationary atmosphere with a room
temperature. The atmosphere was an open, wide and calm
space which was surrounded by 100-mesh wire gauze(0.1mm in diameter) to suppress disturbances from outside.
Air, as the working fluid, was supplied from a compressor
to three jet nozzles. The nozzles were situated in parallelwith the same inner diameter of d = 4mm, constituting a
triple jet array. The jet flow from the nozzle located in thecenter of the array was generated pulsatingly by amechanically-rotating valve system. This system wascomposed of a cylindrical chamber and two identical rounddisks piled inside the chamber. Two holes, 20mm indiameter, were drilled symmetrically with respect to thecenter in each disk. One disk was rotated by a DC electricmotor while the other was held in the chamber. Thus, theflow rate was periodically changed with the pop-out
discharge, depending on the disk rotation. Time-averaged
volume flow rate of the jet supplied to each nozzle wasmonitored with a flow meter, and the maximum flow rate
was obtained when the hole locations of the two disks
match with each other. This system was alternatively
replaced with the other device, which was invented by
Durst et al. [2], in order to feed the jet fluid with a precise
sinusoidal change of the flow rate.

-433-

International Symposium on Advanced Fluid/Solid Science and Technology in Experimental Mechanics, 11-14 Sept 2006, Sapporo, Japanburst signals of the scattering light from the tracer particles
back to the probe were recorded and analyzed by a signal
processor (DANTEC, BSA F50), which was linked to andcontrolled by a personal computer.
Flow Conditions with and without Jet Perturbation
The steady jet flows without the central jet
perturbation were visualized, as shown in Fig. 3. These
three images in order from left-hand side correspond tothe cases of single, twin and triple jets, respectively. All
the flow rates of the jets were fixed at the same, thecorresponding jet Reynolds number of which was Re =1,500. The definition of the jet Reynolds number isdefined as follows:
U d
Q
(1)
Re { m , U m
SQ
Um and Q indicate a mean axial velocity of jet and akinetic viscosity of air, respectively. Um was calculatedwith a time-averaged volumetric flow rate, Q, and a crosssectional area of the nozzle, S. Q was estimated using thevelocity profile obtained experimentally in the vicinity of
the nozzle exit, at x/d = 0.25, which quantitatively agrees
well with the theoretical profile assumed on the basis ofHagen-Poiseuille’s law. The deviation from the theoreticalvalues was estimated within less than 1.6%.

For both the flow visualization with a high resolution
CCD camera and the velocity measurement with a twodimensional laser Doppler anemometry (LDA) system, aparticle generator (TSi, model 9306) was installed at thelocation between the flow meter and the nozzle discharging
the jet fluid as a visualizing object.
The arrangement of the jet nozzles is shown in Fig. 2.
Three jet nozzles were aligned closely to each other. As isconvenient for further discussion, hereafter, the center jet
will be referred to as C-jet and the two other side jets as Sjets. The left-hand side jet is named more specifically as SLjet and the right-hand side jet as SR-jet. The separation
distance between the centers of C-jet and SR-jet (or SL-jet)
was fixed at L = 5.9mm in the present study. The nozzle tip
was sharpen and tapered by 45q.

Fig. 2Jet array arrangement.

The schematic illustration of the laser sheet to visualize
the jet flows is also shown in Fig. 2. A small amount of oil
mist, DEHS (Di-Ethyl-Hexyl-Sebacate), used as tracer
particles, was produced by the aforementioned particle
generator and was mixed into the air upstream of the jet
nozzle. The nominal diameter of the oil mist particle was
1.0µm. The mist-laden jet flows were illuminated by a lightsheet of an Nd:YAG pulsed laser through a cylindrical lens,and the snapshots of the flow patterns were taken using the
CCD camera. The wavelength of the laser was 532nm. The
picture frame of CCD camera was synchronized with thelaser pulse and the maximum frame rate was 30frames per
second. The spatial velocity vector maps were also obtainedusing PIV system when the Nd:YAG laser was emitted
twice in a short series of the pulse every 1/15 seconds.
Time-dependent local velocity of the jet flow wasmeasured using the LDA system, instead of the Nd:YAG
laser and the CCD camera. In this system, two pairs of laser
beams, emitted from an Argon-ion laser having the
wavelengths of 488nm and 514.5nm, were guided through alaser light fiber probe (DANTEC) which was used at thelocation similar to that for the CCD camera. The Doppler

Fig. 3

Snapshots of steady jet flows (Re = 1,500).

In each snapshot of Fig. 3, the meandering area of thejet column is seen, and this area approaches the nozzle
exit as the number of the jet increases. This implies
qualitatively that the interaction of multiple jets enhances
the fluid mixing. The time-averaged axial velocity
distributions of the triple jet case of Fig. 3 are shown in
Fig. 4 to quantitatively examine the mixing performanceenhanced by the multiple jet interaction. The velocity
profiles were measured in the spanwise direction at six
different streamwise locations, i.e. x/d = 0.25, 10, 20, 25,
30 and 40, and were normalized by U0 which is the timeaveraged central streamwise velocity of C-jet measured at(x/d, y/d) = (0.25, 0). The x-y spatial coordinate system isoriginated at the center of the C-Jet nozzle exit. The
centers of SR-jet and SL-jet are located, respectively, at y/d= ±1.48. The solid circle (•) indicates the result obtainedin the case that all three jets are simultaneously discharged.
The open diamond (¡) depicts the result obtained bylinearly superimposing the velocity distributions of a-434-

International Symposium on Advanced Fluid/Solid Science and Technology in Experimental Mechanics, 11-14 Sept 2006, Sapporo, Japan

0.63 and 078 makes the central jet a transition between
laminar and turbulent flows, resulting in a better mixing
performance in the near-field of the nozzle.
Table 1 Conditions of jet perturbation by MFC.

single jet assuming that each jet is independent of theothers.
At the locations of x/d = 0.25, 10 and 20 in Fig. 4, thevelocity distributions of the two cases, • and ¡, are almost
the same, pointing out that no interaction occurs among
the jets near the nozzle exit. At x/d = 25, the maximum
peak of each jet decreases in the case of the simultaneouslydischarged triple jet, and the velocity distribution exhibits asomewhat wider pattern due to laminar jet diffusion and its
interaction. At x/d = 30, a noticeable difference between thetwo distributions was observed, where the peak of thevelocity profile in the simultaneously-discharged caseconspicuously lowers and the outside flank of the
distribution rises, namely, a flatter distribution wasobserved in this case because of the transition from laminar
to turbulent of the flow. The superimposed jet casepredicted a similar trend further downstream, at around x/d= 40. This comparison demonstrates that the interaction ofmultiple jets causes nonlinearly an early transition fromlaminar flow to turbulent one and a better mixing of fluids.

Type

Re

C-jet

1.5u103

Frequency
fr [Hz]0
1
2

Amplitude
A/U0
0
0.27
0.63
0.78
0.27

Following the above-mentioned examination, themechanically-rotating valve system was used toemphasize the transition of the central jet from laminarflow to turbulent one and to expect a better mixing
enhancement. The typical time-sequential flow patterns inthis case are shown in Fig. 5. The disk of themechanically-rotating valve system made a full turn withthe rate of rotation, 30rpm, and then a high-speed pop-out
C-jet flow was discharged twice at a regular interval in
one rotation of the disk. Thus, the frequency of jet
perturbation, fr, is equal to 1Hz. 10 images of Fig. 5 weretaken with the time interval of 0.2s. The number assigned
to each image in Fig. 5, #1 ~ #5 or #6 ~ #10, denotes thephase, 1/(5fr), 2/(5fr), ~ , 5/(5fr) of the first half or thesecond half of one disk rotation, respectively.

Fig. 4 Velocity profiles of steady triple jet flow (•:Simultaneous discharge, ¡: Superimposition,
Re = 1,500).
Next, in order to investigate the fundamental flow
characteristics of the triple jet influenced by the central jet
perturbation, the MFC which can feed the jet fluid
precisely in a time-dependently sinusoidal fashion wasused to perturb the C-jet flow. The data obtained using
MFC was referred to for the hereinafter-described resultsin the following section. The flow conditions of C-jet are
tabulated in Table 1. The jet Reynolds number was fixedat Re = 1,500 with the constant time-averaged flow rate.
The parameter, A, used in Table 1 indicates an amplitudeof the sinusoidal jet velocity fluctuation. In the case of A =0.27, the flow field showed no mixing patterns within theaxial distances, 0 d x/d d 20, independent of theperturbation frequency, fr, since the velocity of the central
jet in this case changed only within the laminar flow
regime. An increase of the amplitude in the cases of A =Fig. 5 Time-sequential images of the triple jet flow
with perturbation in one period of the disk
valve rotation (fr = 1Hz, Re = 1,500).
Mixed-up regions of the triple jet as cloud-like shapes
were clearly visualized in each image of Fig. 5, showingthat the bottom edge of the mixed-up region moves up anddown in response to the time-dependent flow rate of C-jet.
It could be confirmed that the neighboring S-jets are
significantly influenced by the pop-out C-jet perturbation.
At the phases which have a maximum flow rate of C-jetwith an every 1.0s interval, the three jet fluids were mixed-435-

International Symposium on Advanced Fluid/Solid Science and Technology in Experimental Mechanics, 11-14 Sept 2006, Sapporo, Japan

well together even near the nozzle exit, corresponding to
the visualized images, #3 and #8.

forward period before full opening, and the backward
period after full opening, with the rotational valve holes
matching. Thus, the time period, F+O+B, is regarded as
the total pop-out injection period of C-jet. An open
triangle + plotted in Fig. 6 indicates the result measured
in the case that the tracer particles were mixed in C-jet,while a solid triangle  indicates the result with the tracer
particles mixed only in SR-jet. The ordinate of the graph isthe phase-averaged streamwise velocity normalized by U0
and defined in the following paragraph.
Concerning the data processing procedure of the jet
perturbation case, an instantaneous streamwise velocity,u(t), is regarded as the addition of time-averaged velocity,U, and velocity fluctuation, Uc(t), and also as the additioni , and another velocityof phase-averaged velocity, U
fluctuation, uc(t) as described in Eq. (2). Velocity datameasured during 5 ~ 10 rotations of the disk valve wasused to calculate a phase-averaged velocity. The samedefinitions are adopted also for a instantaneous lateralvelocity, v(t).
i u' tu t U U ' t U(2)
v t V  V ' t Vi  v ' t(a) y/d = 0

In Fig. 6 (a), no data plotted with solid triangle wasobserved adjacent to the nozzle exit, at the location of x/d= 0.25, implying that no interaction between C-jet and Sjets occurs there. At the rest of the measuring x/d locations,the contribution of SR-jet data to C-jet is clearlyrecognized in O-region with a considerable coincidence of
the S-jet data with the C-jet data. Besides the O-region,
the latter half of F-region and the former half of B-region
have also some contributions of SR-jet because of thestarting and finishing periods of the laminar-to-turbulent
transition of C-jet leading to the jet interaction. In Fig. 6(b), the contribution of C-jet data to SR-jet was recognized,
as vice versa, in the same injection period of F-, O- and Bregions.
During the period of O-region, the phase-averaged
streamwise velocity becomes comparatively lower since
the C-jet of O-region is already a turbulent flow anddiffuses to the surroundings due to high momentum
exchange. In F- and B-regions, C-jet fluid flows intransition between laminar and turbulent of the flow. The
peaks observed in these two regions can be regarded as
the apparent critical velocities of the flow transition.
RESULTS AND DISCUSSION
Effects of the perturbed C-jet on the neighboring S-jets are
discussed in this section. Figure 7 (a) and (b) shows thetime-averaged streamwise and lateral velocity distributions,
U and V, of the perturbed jet case in comparison with thecorresponding steady jet case under the same jet Reynolds
number, Re = 1,500. Both velocities are normalized by U0.
The solid and open circles, x and R, represent the cases ofthe steady and perturbed jets, respectively.
In Fig. 7 (a), the perturbed jet case possesses a bit
smaller velocity near the C-jet nozzle, at x/d = 0.25, than
the steady jet case. This becomes more obvious at thestreamwise locations of x/d = 10, 20 and 25 where the jet
center velocity decreases more rapidly in the perturbed jetcase compared to the steady jet case. The corresponding(b) y/d = 1.48
Fig. 6 Time histories of axial velocity with jet
perturbation (Open triangle: tracer injection to
C-jet, Solid triangle: tracer injection to SR-jet,
Re = 1,500).
Figure 6 (a) and (b) shows the time histories of
streamwise velocity of the triple jet under the same flow
condition of Fig. 5. The monitoring locations, (a) y/d = 0
and (b) y/d = 1.48, correspond to the centers of C-jet andSR-jet, respectively. Four characters, C, O, F and B in eachgraph are assigned to the following four classified regions:the closing period of the valve, the opening period, the-436-International Symposium on Advanced Fluid/Solid Science and Technology in Experimental Mechanics, 11-14 Sept 2006, Sapporo, Japan

lateral velocity of the perturbed jet case shown in Fig. 7 (b),in particular at x/d = 10, has a point-symmetric distribution
with respect to the central jet axis, deducing that the central
jet fluid was convected equally to the right and left sides by
the jet perturbation and thus a spanwisely-wider velocity
distribution was obtained.

(a) Streamwise velocity(b) Lateral velocity
Fig. 7 Time-averaged velocity distributions of triplejet (R: perturbed jet, x: steady jet, Re = 1,500).
An unexpected but interesting feature characterizing thepresent jet perturbation was observed at the location, x/d =30, where an adverse situation of the jet mixing trend
between the steady and perturbed jet cases appears. That is,
the steady jet case has a relatively flatter and wider velocity
distribution without a cusp shape than the perturbed jet case.
This implies that the steady jet diffuses more and theperturbed jet apparently suppresses the fluid mixing at thislocation. Point-symmetric distributions of the lateral-437-

velocity were distinguishably observed there and also at x/d= 25 in the steady jet case of Fig. 7 (b), confirming againthat the considerable spanwise diffusion occurs in thesteady jet case.
In order to elucidate the above-mentioned adverse
mixing situation, phase-averaged velocities of the perturbed
jet case were calculated using the same time-sequential raw
velocity data as the one for the calculation of time-averaged
velocity plotted with R in Fig. 7 (a). After calculating thephase-averaged velocities at each measuring location, thetime-averaged velocity was calculated for each
aforementioned-categorized time-period, F-, O-, B- or Cregion. Two graphs, (a) and (b), plotted with ¡ in Fig. 8
show the spanwise distributions of such phase-averaged andcategorized streamwise velocity for O-region and C-region,
respectively. The solid circle, •, denotes the steady jet caseas the reference data for the comparison to the perturbed jetcase. O-region corresponds to the time-period including theoccurrence of maximum mass flow rate of C-jet, while Cregion corresponds to the time-period of the minimum rate.
F- and B-regions were found to have relatively similar
velocity profiles to the steady jet case. Typical flow patternsof O-region were visualized as the snapshots #3 and #8
shown in Fig. 5, and the ones of C-region as the snapshots#1 and #6 (or #5 and #10).
A protruding velocity profile of C-jet in the case of thejet perturbation was seen at x/d = 0.25 in Fig. 8 (a), since
the mass flow rate becomes relatively larger during Oregion than the other regions, F, B and C. Hence, the jet
Reynolds number becomes larger and the C-jet makes thetransition from laminar to turbulent flow near the nozzle
exit. Correspondingly, the mixing of the triple jet isenhanced and the jet fluid merges into one already at x/d =20, so that the velocity distributions at further downstream
locations have a hill-like shape with a gentle and wide slope,which appears better for the mixing than the velocity
distribution of the steady jet case.
Focusing on the velocity distributions during C-region
shown in Fig. 8 (b), on the other hand, their distribution
patterns appear oppositely different from the ones during Oregion. The mass flow rate of C-jet is relatively smaller
during C-region, and the corresponding jet Reynolds
number is in the regime of laminar flow. Hence, the C-jet
remains laminar even at the location of x/d = 30. S-jets also
remain laminar with almost no interaction with thecomparatively lower velocity of C-jet, which leads to thevelocity distribution possessing two high side-peaks and a
relatively lower central peak, clearly seen at x/d = 25 and 30.
In contrast, the steady case of all the three jets
possessing the same mass flow rate exhibits a three-peakmountain-like velocity distribution of the triple jet flow
somewhat interacting and merging together at x/d = 25.
Then, at x/d = 30, an almost complete merging with C-jet
and S-jets can be clearly seen in the result plotted with •,showing that the velocity distribution of this case forms aflatter and wider hill-like pattern.
In the case where the time-averaged velocity without theconsideration of the phase is discussed, the effect of the Cjet during O-region is relatively conspicuous in the nearfield of the jet nozzle exit because of turbulent jet, and aInternational Symposium on Advanced Fluid/Solid Science and Technology in Experimental Mechanics, 11-14 Sept 2006, Sapporo, Japan

better mixing among the triple jet is attained in comparison
to the steady jet case. In further downstream of the nozzle
exit, in contrary, no interaction among the individual
laminar C-jet and S-jets during C-region leads to the
suppression of the jet fluid mixing. Thus, the perturbed jetcase apparently exhibits a smaller diffusion than the steadyjet case. The r.m.s values of the velocity fluctuations werealso correspondingly reversed between the steady andperturbed jet cases, figures of which were omitted becauseof the limited space. This interesting adverse characteristicof the jet perturbation can be applicable in respect of fluid
mixing control.
CONCLUSIONS
Effects of a jet perturbation on the mixing performance of
triple air-jet array have been experimentally investigatedunder the flow conditions of Re = 1,500 and fr = 0, 1 or
2Hz in the present study. The major findings are
summarized as follows:
1) The triple jet array discharged simultaneously in thesteady case exhibits better mixing than the linearlypredicted jet array with three arithmetically-superimposed
single jets.
2) The time-averaged velocity profiles of the triple jetarray obtained in the present flow condition of jet
perturbation demonstrate that a better mixing occurs in thenear-field of the jet nozzle exit while the steady jet casehas a better mixing performance in the further
downstream, x/d  30.
3) The adverse change of the mixing performance along
the streamwise locations mentioned in the above item isrelated to the phase-averaged velocity profiles of the jet
perturbation. Alternative change between laminar flow
with smaller jet velocity and turbulent flow with higher jet
velocity in one cycle of the central jet perturbation
significantly influences and controls the time-averaged jet
mixing performance.
NOMENCLATURE

REFERENCES[1] Shinohara, E., Tatsumi, K., Okamoto, F., Kitaoka Y.
and Nakabe, K., Mixing Characteristics of multi-jets
modified by cyclic perturbation, Proc. Int’l Conf. on Jets,
Wakes and Separated Flows, (2005), pp. 255 – 260.
[2] Durst, F., Ünsal, B. et al., Mass flow rate control
system for tim-dependent laminar and turbulent flow
investigations, Measurement Sci. Technol., 14 (2003), pp.
893 – 902: Mass flow rate controlled fully developed
laminar pulsating pipe flows, ASME: J. Fluid Engineering,
127 (2005), pp. 405 – 418: Pulsating laminar pipe flows
with sinusoidal mass flux variations, Fluid Dynamics
Research, 37-5 (2005), pp. 317 – 333.

(a) Streamwise velocity of O-regionA
perturbation amplitude, m/sdnozzle diameter, mfr
perturbation frequency, HzLseparation distance between nozzles, m
Re
jet Reynolds number, Umd/Ȟ
S
cross-sectional area of nozzle, m2
Utime-averaged streamwise velocity of jet, m/s
Uc, uc streamwise velocity fluctuation, m/s
Vtime-averaged lateral velocity of jet, m/s
Vc, vc lateral velocity fluctuation, m/s
xstreamwise distance, mylateral distance, normal to jet axis, mGreek symbols
Ȟkinetic viscosity of the fluid, m2/s
Subscripts
mtime-averaged value
0
time-averaged reference value at the jet center
Superscripts~
phase-averaged value(b) Streamwise velocity of C-region

ACKNOWLEDGEMENT
This research was partially supported through Grand-inaid for Scientific Research (B) by Ministry of Education,
Culture, Sports, Science and Technology. The authors
express our gratitude to Professor Durst, F. and Dr. Ünsal,
B. for their kind support on our experiment.

Fig. 8 Phase-averaged and categorized velocity
distributions of triple jet (¡: perturbed jet, x:
steady jet, Re = 1,500).

-438-