Experimental Study on Switching Mechanism of a Flip-Flop Jet … · 2019. 5. 23. · 3), a flow...

15th International Conference on Fluid Control, Measurements and Visualization 27-30 May 2019, Naples, Italy

Extended Abstract ID:147 1

Experimental Study on Switching Mechanism of a Flip-Flop Jet Nozzle using

Single-Port Control

Katsuya Hirata1,*, Noriaki Tauchi1, Tatsuya Inoue2, Fumiaki Nagahata1, Takashi Noguchi1

1Department of Mechanical Engineering, Doshisha University, Kyoto, Japan

2Environmental Engineering Division, Railway Technical Research Institute, Tokyo, Japan *corresponding author: [email protected]

Abstract Our purpose is to elucidate the oscillation mechanism of the flip-flop jet nozzle (hereinafter, referred to as FFJN). In the present study, we focus upon a dominant jet-oscillation frequency of the FFJN, based on the measurements of pressures and velocities in the connecting tube and inside the FFJN, and attempt to find out the universal number which determines the jet-oscillation frequency. The measurements are carried out varying: 1) the inside diameter d of the connecting tube; 2) the length L of the connecting tube and 3) the jet velocity VPN from a primary-nozzle exit. We assume that the jet switches when a time integral reaches a certain value. At first, as the time integral which can be the universal number for the jet’s switching, we introduce the accumulated flow work of pressure, namely, the time integral of mass flux through a connecting tube into the jet-reattaching wall from the opposite jet-un-reattaching wall. Under the assumption, the trace of pressure difference between both the ends of the connecting tube is simply modeled on the basis of measurements, and the flow velocity in the connecting tube is computed as incompressible flow. Second, in order to discuss the physics of the accumulated flow work further, we conduct another experiment in single-port control where the inflow from the control port on the jet-reattaching wall is forcibly controlled by a blower-and-value system and the other control port on the opposite jet-un-reattaching wall is sealed by a plug, instead of the experiment in regular jet’s oscillation using the ordinary nozzle with two control ports in connection. As a result, it is found that the accumulated flow work is adequate to determine the dominant jet-oscillation frequency. In the experiment in single-port control, the accumulated flow work of the inflow until the jet’s switching well agrees with that in regular jet’s oscillation using the ordinary nozzle. Keywords: Flip-Flop Jet Nozzle, Flowmeter, Fluidics, Mixing, Flow Control

1. Introduction The flip-flop jet nozzle (hereinafter, referred to as FFJN) is regarded as one kind of fluidic oscillator, which

is oscillating devices among the fluidics. The fluidics, or the elements in fluid logic, is applications of the Coanda effect where a jet reattaches to a solid side wall. The FFJN retains useful features as well as other flow-induced-vibration devices: namely, 1) low production cost and high reliability due to non-mechanically-moving parts; 2) usability due to a linear frequency response in proportion to flow rate; and 3) robustness against fluid density, temperature, pressure and composition. Owing to the above features, the FFJN is applicable for such products as flow meters, fuel injectors, micro mixers and various control devices to disturb the shear layer or to enhance heat transfer, not only for singlephase flows but also for multi-phase flows [1]-[23]. Thus, the FFJN is often called a “fluidic oscillator” or “oscillatory-jet-type flowmeter” in different applications. However, the oscillation mechanism of the FFJN has not been fully understood yet. In general, it is still difficult to predict the jet-oscillation frequency, which depends upon such various parameters as connecting-tube length, connecting-tube volume, flow rate, nozzle’s geometries and so on. Our purpose is to elucidate the oscillation mechanism of the FFJN. In the present study, we focus upon a

dominant jet-oscillation frequency of the FFJN, based on the measurements of pressures and velocities in the connecting tube and inside the FFJN, and attempt to find out the universal number which determines the jet-oscillation frequency. The measurements are carried out varying: 1) the inside diameter d of the connecting tube; 2) the length L of the connecting tube and 3) the jet velocity VPN from a primary-nozzle exit. We assume that the jet switches when a time integral reaches a certain value. According to our recent study [23], as the time integral which can be the universal number for the jet’s switching, we found out that the most adequate one is the accumulated flow work of pressure, namely, the time integral of mass flux through a connecting tube into the jet-reattaching wall from the opposite jet-un-reattaching wall. Under the assumption, the trace of pressure difference between both the ends of the connecting tube is simply modeled on the basis of measurements, and the flow velocity in the connecting tube is computed as incompressible

15th International27-30 May 201

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flow. Second,experiment forcibly controlledreattaching nozzle with 2. Experimental 2.1. Model:Figure 1 shows

primary nozzle,with the controloscillation. experiment conduct anotherfluid from the

The chiefthe primarycorrespondingwhere b is fixedlength of thefixed to 2 andwhere ρ, VPN

fluid, respectively.cross sectionto 300, respectively.coefficient Kregular oscillation

2.2. Experimental

Figure 2 experiment.two chamberstube. The working6) of the FFJN,straight duct.= 2 m) to measured bythermocouple

International Conference2019, Naples, Italy

��

Second, in order in single-port

controlled by wall is sealed

with two control

Experimental Method

Model: FFJN shows the present

nozzle, two sidecontrol ports on

The basic dimensions in regular jet’s

another experimentthe other un-sealed

chief geometric andprimary-nozzle throat

corresponding aspect ratio fixed to the

the side walls and 4.5, respectively.PN and μ denote

respectively. In thesection with an inside

respectively. OnK (see later

oscillation experiment.

Experimental Apparatus shows the

experiment. The main partchambers (Nos. 11

working fluidFFJN, through

duct. The rectification suppress theby the flow

thermocouple and a pressure

Conference on Fluid Control,Italy

��

to discuss theport control where a blower-and

sealed by a plug, ports in connection.

Method

present modelside walls, two

on the side wallsdimensions ofjet’s oscillation

experiment in singlesealed controland kinetic parameters

throat and the ratio A (≡ S/s same as s in are denoted

respectively. A soledenote the density

the regular-oscillationinside diameterOn the other for its definition)

experiment.

Apparatus for Regular schematic diagrampart of an ordinary

11 & 12) and fluid is air, which

through an air dryerrectification duct

the pulsation meter is compensated

pressure transducer

Figure

Control, Measurements

the physics ofwhere the inflow

and-value systemplug, instead of theconnection.

model of a FFJN, two control ports,

walls are linkedof the FFJN

oscillation using thesingle-port-control

control port. parameters are nozzle spans ) is equal toin the present

denoted by GSW andsole kinetic parameter,

density of fluid, theoscillation experiment,

diameter d . Their redother hand, in

definition) varies

Regular Oscillationdiagram of the

ordinary FFJN the connecting

which is provideddryer (No. 2), a

in the upstream included in

compensated usingtransducer which are

Figure 1. Model:

Measurements and

of the accumulatedinflow from

system and the the experiment

FFJN, together withports, two chambers

linked to each otherFFJN are determined

the ordinary FFJNcontrol where we

are as follows.span S are fixed

to 5. The controlpresent study. The

and LSW, respectively.parameter, thethe mean velocity

experiment, thereduced forms the single-port

varies from 1 × 10

Oscillation the present with a primary

connecting tube (No.provided by an air compressor

pressure regulatorupstream of the primary

in primary- nozzleusing both the

are placed adjacent

Model: a flip-flop jet

and Visualization

accumulated flow the control the other control

experiment in regular

with its main dimensions.chambers and a

other by the connectingdetermined according

FFJN with two seal one control

follows. In a characteristicfixed to 0.01 m

control port withThe gap between

respectively. Theirthe Reynolds

velocity at a primarythe connecting

forms d/s and L/port-control 10-4 to 3.5 ×

experimentalimary nozzle (No.(No. 5) consists

compressor (No.regulator (No. primary nozzlenozzle jet. Volumetricthe temperature

adjacent to the

jet nozzle (FFJN).

Visualization

flow work further, port on the

control port onregular jet’s oscillation

dimensions. connecting tube.connecting tube,

according to Vietstwo control

control port by

characteristic lengthm and 0.05 m,with a breadth

between the side wallsTheir reduced forms

number Re ,primary-nozzle

connecting tube with a/s vary from experiment,× 10-4 according

experimental apparatus (No. 6 in Figure

consists of acrylic-(No. 1) into 3), a flow meter

nozzle is straight Volumetric flow

temperature and the flow meter.

(FFJN).

further, we conductthe jet-reattaching

on the oppositeoscillation using

The FFJN consists tube. The twotube, to cause

Viets [8]. In addition ports in connection, a plug and forcibly

length scale the m, respectively.

breadth b is on eachwalls and the

forms GSW/s and, is defined by

nozzle exit and thea length L has 1.2 to 1.4 and

experiment, a flow-incrementaccording to the results

in a regularFigure 2), two control

-resin plates the primary meter (No. 4)

straight and enoughflow rate into

the pressure detected Pressures and

�

conduct anotherreattaching wall is

opposite jet-un- the ordinary

consists of atwo chambers

cause regular jetaddition to theconnection, we

forcibly feed

spacing s ofrespectively. So, the

each side wall,he streamwiseand LSW/s areby ρVPN s /μ,

the viscosity ofhas a circularand from 100

increment rateresults in the

regular-oscillationcontrol ports,

plates and a PVC nozzle (No.

4) and a longenough long (200 s

into the FFJNdetected by aand velocities

her is -

ordinary

a chambers

jet the we

feed

of the

wall, streamwise

are ,

of circular

100 rate the

oscillation ports, PVC (No. long

s FFJN

a


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at several pointsand two hotspecifically,of the four inside the FFJN.inside the connectingoutside the apparatus foranalyzed by

2.3. ExperimentalFigure 3 showssingle controlthe oppositeexperiment,primary nozzlemeter and compensatedtransducer whichblower throughexperiment,Then, we forcecontrol port.transducers recorded and

In the singlevolumetric flowat the tube endneed the calibration


��

points are simultaneouslyhot-wire anemometers

specifically, two (Nos. 7 is in the upstreamFFJN. One ofconnecting-tube, FFJN exit. Thefor each measurement

by a spectrum

Experimental Apparatusshows the schematic

control port insteadopposite side is sealed

experiment, the workingnozzle (No. 20)

a long straightcompensated using both

which are placedthrough a tube (No.

experiment, the jet fromforce the jet

port. Pressures (Nos. 15 &

and analysed bysingle-port-control

flow rate QT

end adjacent calibration between

Figure 2. Experimental apparatus for regular oscillation in ordinary FFJN operation.


��

simultaneouslyanemometers KANOMAX

7 & 8) of theupstream of theof the two hottube, and theThe hot-wire

measurement whose analyzer (No.

Apparatus for Singlschematic diagraminstead of dual control

sealed by a plug,working fluid is air,

20) of the FFJN,straight duct. Volumetricboth the temperature

placed adjacent(No. 1), which

from the primary to switch by

Pressures and velocities& 16) and twoby a personal

control experiment,T from the control to a chamber

between QT and


Figure 3.


simultaneously measured byKANOMAX 7000the four pressurethe primary nozzle,

hot-wire anemometersthe other one

wire anemometerswhose duration

(No. 17) and a

Single-Port Controldiagram of the present

control ports,plug, being

air, which is providedFFJN, through

Volumetric flowtemperature and

adjacent to the flowwhich is regulated

primary nozzle is reattachedby the inflow,

velocities at severaltwo hot-wire anemometers

personal computer (No.experiment, we quantitatively

control port throughchamber and the control

nd hot-wire anemometer


3. Experimental

Measurements and

by four pressure7000 with I-type

pressure transducersnozzle, and the

anemometers (No. (No. 14) is

anemometers are calibratedduration is less

personal computer

Control present apparatus

ports, as in the regular flush with provided by an air dryerflow rate into the pressure

flow meter. Theregulated by a flow

reattached toinflow, from the

several points areanemometers (No. 7).

quantitatively through the tube,

control port. So,anemometer signal


Experimental apparatus for

and Visualization

pressure transducerstype probes

transducers are near thethe other (No.

(No. 13) is for the for the measurement

calibrated using a than 2 hours.

computer (No.

apparatus in the singleregular oscillation a side wall. an air compressor

dryer (No. 11), ainto the FFJN

pressure detected The inflow from

flow-control valueto the side wall side wall toare simultaneously (Nos. 17 &

characterisetube, which isSo, prior to thesignal VT.


for single-port

Visualization

transducers KYOWA (Nos. 13 & the connecting

(No. 10) of thethe measurement

measurement ofa Pitot tube outside

hours. These signals18).

single-port experiment.oscillation experiment.

wall. As well ascompressor (No.

a pressure regulatorFFJN measured

by a thermocouplefrom the control

value (No. 4). Inwall with the to the opposite

simultaneously measured& 18), respectively.

characterise the magnitudeis detected bythe single-port


port control.

KYOWA PGM-G (Nos. 14), respectively.

connecting-tube ends,the four is on

measurement of the flowof the flow velocityoutside the experimental

signals are recorded

experiment. Theexperiment. The control

as the regular 10 in the figure)

regulator (No.measured by the flow

thermocouple andcontrol port is

In the single- control port

opposite side wall measured by two

respectively. These

magnitude of the inflowby a hot-wire

port-control experiment,


�

(Nos. 7 - 10),respectively. More

ends, one (No. 9) the sidewallflow velocityvelocity justexperimentalrecorded and

The FFJN has acontrol port on

regular-oscillationfigure) into a

(No. 3), a flowflow meter is

and a pressure driven by a-port-control in advance. without the

two pressureThese signals are

inflow using anemometer

experiment, we

10), More

9) sidewall velocity

just experimental

and

a on

oscillation a

flow is

pressure a

control advance.

the pressure

are

ing anemometer

we


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3. Results and 3.1. RegularThe frequency

industrial viewpoint.connecting-still difficultIn the presentdetected at ones in additiongeometric parametersinner diameterdimensional

��

where φ denotesnumber St ,

�� All the symbols

= 100 - 300,to lower stabilityexperimental1) St monotonicallythat 3) St monotonically �� with experimentalare determinednote that L/spresent test empirical formula

The empiricalranges of theconsider morethe present tube ends atwhich are commonly

Figure 4. Strouhal


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and Discussion

Regular Oscillation:frequency f of jet’s

viewpoint. According-tube length,

difficult to predict fpresent study, we

the FFJN exitaddition to mean

parameters arediameter d of a connecting

imensional analysis, we

��

denotes an arbitrary instead of f

�� .

symbols in Figure300, d/s = 1.2 andstability of the

experimental apparatus.monotonically decreases

monotonically

��

experimental constantsdetermined using the

L/s is the mosttest ranges. The

formula almostempirical formula

the governingmore generally

experiments;at L/s = 100,commonly seen

Strouhal number


��

Discussion

Oscillation: Jet-Oscillationjet’s oscillationAccording to

h, connecting-f even in the

we get the experimentalexit (No. 14 in

mean velocity VPN

are the spacingconnecting tube.we get

� ��

arbitrary function. . The definition

Figure 4 representand Re = 7000 present periodic

apparatus. From the results,decreases with increasing

monotonically increases with

��

constants such asthe least-squares

most influentialThe curves in Figure

almost agrees withformula Equation (3)

governing parameters,generally focusing upon

experiments; that is, the100, d/s = 1.2 and

seen in all the

number St against Reynoldsdenote experiments


Oscillation Frequencyoscillation is important

to Raman et-tube volume,

the present stage.experimental value

in Figure 2). PN at a primary

spacing s of a primarytube. We regard

function. In this Equationdefinition of St is given

represent an example7000 - 20,000. Whileperiodic flow phenomenon

results, we canincreasing L/s

with increasing

,

as C = 0.068, αsquares method based

influential upon St amongFigure 4 show

with the experiment.(3) is practically

parameters, but restrictedupon the jet-oscillation

the time historyand Re = 13,000. present experiments;

Reynolds numberexperiments and

Measurements and

Frequency and Connectingimportant not only

et al . [12], volume, flow rate,

stage. So, we firstvalue f by the

As governingprimary-nozzle exit,

primary-nozzle regard s , VPN and

Equation (1), wegiven by

example of the experimentalWhile there exist

phenomenon butcan see the followingL/s , that 2) St

increasing Re . Then,

α = −0.72, βbased on all

among the threeshow this empirical

experiment. practically useful notrestricted due to

oscillation frequency.history of the pressure

13,000. The waveexperiments; namely,

number Re at d/s =and an empirical

and Visualization

Connecting-Tubeonly from an academic

f depends rate, nozzle’s geometries

first propose an Fourier analysis

governing parametersexit, fluid density

throat, the lengthand ρ as characteristic

we consider

experimental resultsexist minor randombut due to unknown

following threeSt monotonically

Then, we assume

(3)

β = 1.37 and γ the experimental

three non-dimensionalempirical formula

not only for to the lack offrequency. Figure

pressure differencewave form in

namely, 1) clos

= 1.2, in regularempirical formula, respectively.

Visualization

Tube Flow academic viewpoint

upon such geometries andan empirical

analysis on the flowparameters for f , we suppose

density ρ and fluidlength L of a

characteristic scales.

a normalized

results of St random scatterings,

unknown factorsthree tendencies.

monotonically increases the following

γ = 0.22. Theexperimental results

dimensional governingformula Equation (3).

the present of theoretical

Figure 5(a) showsdifference Δp between

Figure 5(a) close periodicity

regular FFJN oscillation.

respectively.

viewpoint but also

various parametersand so on. However,

formula to determineflow-velocity suppose three

fluid viscosity connecting

scales. Then, according

normalized f, namely,

plotted againstscatterings, thesefactors included

tendencies. That is, we increases with increasingfollowing power function

The experimentalresults in Figure 4

governing parameters(3). We can

FFJN in thetheoretical background.

shows a typicalbetween both the

indicates someperiodicity with high-frequency

oscillation. Symbols

�

also from anparameters asHowever, it is

determine f .velocity fluctuation

three geometric μ. The threetube and the

according to the

(1)

the Strouhal

(2)

against Re at L/sthese are not due

in the actual can see that

increasing d/s andfunction as φ .

experimental constants4. We should

parameters in the see that the

the present testbackground. Then, we

typical example ofthe connectingsome featuresfrequency

Symbols and lines

n as is .

fluctuation geometric

three the the

(1)

Strouhal

(2)

L/s due

actual that and

constants should

the the

test we of

connecting features


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random fluctuationspositive andwhenever theare characterisedwith some secondaryBy means offlow velocitysee that VT random fluctuationsit is rather d

Now, we view. ConcerningEquation (3).amplitude coefficientΔpAMP betweenkeeps a constantRe. More specificallybecause, thesuitable for as a right-angledis as follows.equations of

��

where VT denotesresistance coeffiWe numericallyaccuracy, we

Now, wewhen the accumulationcontrol port,and the connectingof mass flux,conclude JP

regarded asspeaking, itand the pressurethe same side.integrals JP

Figure 5. Time


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fluctuations andand negative signs

the wave formcharacterised by one

secondary peaksof simultaneous

velocity VT in the is closely periodic,

fluctuations superimposed.different from summarise all

Concerning the (3). Then, wecoefficient C

between the ensembleconstant value of

specifically athe experimental

further delicateangled triangular

follows. As the of motion can

��

Ȃ��

!��

denotes the flowcoefficient of

numerically solve we compare several

we consider theaccumulation

port, and/or of connecting tube,flux, in addition

P is more adequateas the accumulatedit is the product

pressure differenceside. So, we is defined as

Time histories oftube,


��

and 2) the wavesigns during

form is almost periodic.one remarkablepeaks representingeous measurements, connecting tubeperiodic, as well

superimposed. from the wave form

all the experimentsfluctuating period

we next considerCΔpAMP (Ȃ #$

ensemble mean of about 0.11at this stage,

experimental raw datadelicate discussion

triangular wave. Then, compressibility

can be described

��& ,

flow velocity of pipe flow by

Equation (4)several computationsthe physical background

accumulation of the inflowthe outflow

tube, reaches a certainaddition to the time

adequate than accumulated flow product of the accumulated

difference between hereinafter

as follows.

of pressure differencetube, in regular


wave form characterised each jet-oscillationperiodic. In fact,

remarkable and stable representing higher

measurements, we gettube obtainedwell as Δp. Again, While the waveform of Δp in

experiments concerningperiod or the

consider the fluctuating$'()� (1/2* of the maximum

0.11 through all stage, we attemptdata including random

discussion on the switchingThen, using the

compressibility is negligibledescribed by

averaged overby Spriggs [24(4) by the

computations withbackground

inflow into a jet from the oppositecertain value. integral JM of both JM and work by pressure

accumulated volumebetween a re-circulation

refer to JP

difference Δp between FFJN oscillation

Measurements and

characterised byoscillation period.

fact, Fourier- spectrum peak harmonics due

get Figure 5(b),obtained by the hot

Again, the periodwave form of in Figure 5(a).

concerning the pressurethe fluctuating

fluctuating amplitude ��& )), which

maximum Δp and the present measurements,

attempt to purify random fluctuations

switching mechanismthe modeled Δ

negligible through

over a cross section24] and JSME fourth-order

with different time of the presentjet-switching

opposite un-jetvalue. In our previous

of momentumand JE. JP is thepressure to thevolume (or the

circulation region and as the accumulated

between both connectingoscillation at L/s = 100,

and Visualization

by the two period. The second

-transform analysespeak representingdue to the periodic(b), which is the

hot-wire anemometerperiodicity is

of VT seems to(a). pressure difference

fluctuating frequencyamplitude of Δp. To

which is the normalisedand the ensemble

measurements, these wave

fluctuations like mechanism of theΔp, we compute

through all the present

section of the JSME [25]. order Runge-Kutta

time steps. present approach.

side wall fromjet-switching

previous study [23]momentum flux and the

the accumulatedthe fluid insidethe quotient of

and the connectingaccumulated flow

connecting-tube100, d/s = 1.2 and

Visualization

similar non-second feature

analyses on therepresenting a dominant

periodic but nonthe corresponding

anemometer (No. not rigorous

to be not sinusoidal

difference Δp fromfrequency of Δp, we

To conclude,normalised half

ensemble mean of themeasurements, being independent

forms by a Figure 5(a)

the jet. At first,compute VT. The computat

present experiments,

connecting tube

Kutta method.

approach. We assumefrom the connectingside wall into

[23], we examinethe type integral

accumulated mass, whichinside the re-circulation

of the accumulatedconnecting-tube

flow work. Specifically

tube ends and velocityand Re = 13,000.

-isosceles triangles is commonly

the present resultsdominant periodicity,

non-sinusoidalcorresponding time history

13 in Figurerigorous due to high

sinusoidal but non

from a quantitative have already

conclude, the ressurehalf value of the

the minimumindependent of

a simple model and Figure

first, Δp is simplycomputational

experiments, the

tube to be exact.

To confirm

assume that the jetnnecting tube

into the other examined the timeintegral JE of energy

which could becirculation regions;

accumulated mass divided end (or the chamber)

Specifically speaking,

velocity VT in a13,000.

�

triangles withcommonly observed,

results alwaysperiodicity, together

sinusoidal wave form.history of the

Figure 2). We canhigh-frequencynon-isosceles,

quantitative point ofalready proposed

ressure-difference-the difference

minimum Δp, almost L/s , d/s and

model. This is 5(b) are not

simply modeledional procedurethe governing

(4)

exact. λ is the

confirm numerical

jet switches,tube through a

control porttime integral JP

energy flux. Tobe essentially

regions; strictlydivided by ρ)chamber) on

speaking, the

a connecting

with observed,

always together

form. the can

frequency isosceles,

of proposed

-difference

almost and

is not

modeled procedure governing

the

umerical

switches, a

port P

To essentially

strictly )

on the


��

+� where VCP denotesEquation (6

, where κ denotesspecify the t = tSW, Δp side wall fromflows in themonotonicallytoward a certainflow in the jumps fromjet-switchingconnecting-supposed integral

For convenience,

+Ȃ Figure 6 shows

at d/s = 1.3present study,So, we first +Ȃ� tends

same but dependsFortunately,

is the universal

κ =./�� (=0.01)

To conclude,influence of1.4 and Re =1) ./�� is almost

of d/s . On

monotonically

�+

Figure


��

� Ȃ 01 2 *3,��45�6

denotes the 6).

Ȃ �� : ;�

denotes a damping integral interval jumps from

from the oppositethe connecting

monotonically decreasescertain positive

connecting tubefrom zero to a certa

switching side onto -tube flow from

integral intervalconvenience, all the

Ȃ� Ȃ

<=�>?

shows the normalised

1.3 and Re = study, we have confirmed

examine thetends to decrease

depends upon Fortunately, we can find

universal number

(=0.01) attains

conclude, concerningof L/s , we summarise= 7000 - 20,000almost constant

On the other

monotonically decrease

+Ȃ��/��

Figure 6. Normalised


��

*3,��

flow velocity

: ��45C��DE> F

damping constant.interval in Equation

zero to a positiveopposite side wall.

tube from thedecreases with timepositive value, crossing

tube is reversedcertain negative the oppositefrom a certain

interval in Equationthe integrals

normalised integral

14,000. Whileconfirmed that

the influence of with increasing

L/s, the curvefind all the crosses

to determine

attains �+Ȃ��/�� (=0.2).

concerning the influencessummarise all

20,000 as follows.constant (≈0.012)

hand, 3) we

toward a constant

� �� H

Normalised integral +


velocity at the control

F

constant. We shouldEquation (5), Figure

positive value.wall. On the other

the jet-switchingtime t toward zero.crossing zero at

reversed at t = t0 andnegative value, corresponding

opposite side wall. And,certain positive value.

Equation (5). are usually normalised

integral +Ȃ� plotted

While we supposethat L/s is the of L/s prior to

increasing κ at each

curve with a certaincrosses in a narrow

determine the jet-oscillation

(=0.2).

influences of the other the results in

follows. being independent

we cannot ignore

constant value

H ��CJ�� L

Ȃ� against time

Measurements and

control port. In

should note thatFigure 5(c) and

value. This jumpother hand, VT

switching side to thezero. On the t = t0. Then, and afterwards

correspondingAnd, VT begins

value. In summary,

normalised as

plotted against the

suppose three governing most influential

to d/s and Re .each L/s . As the

certain L/s tendsnarrow range of

oscillation period

other two governingin the experimental

independent of both

ignore the influence

with increasing

� L ��

time constant κ,

and Visualization

In Equation (

that these integrals Figure 5(d) show

jump of Δp correspondsT is still negativethe opposite un other hand, VT becomes

afterwards continuescorresponding to the jet’s

begins to deceleratesummary, there

as follows.

the time constant

governing parametersinfluential upon St

. the decreasing

tends to cross theof κ ≈ 0.01. In

period (or St ): that

governing parametersmental ranges

both d/s and Re

influence of Re

increasing Re . This

at L/s = 100 -

Visualization

5), a decaying

integrals are amountsshow the definitions

corresponds to thenegative even at

un-jet-switchinghand, VT monotonically

becomes positive at tcontinues to accelerate.

switching fromdecelerate toward

ere exists no reversed

constant κ, in a

parameters likeSt among the three

decreasing manner of +the other curves

In other words,

that is, the jet

parameters d/s andranges such as L/s

Re , 2) (+Ȃ�)UNV

Re upon (+Ȃ�This tendency is

300, d/s = 1.3

decaying factor w

amounts per unitdefinitions of t0the jet’s switchingat t = tSW, that

switching side. Thereafter,monotonically increases

t > t0. In otheraccelerate. Finally, at

from the sidetoward the next reverse

reversed flow

range of L/s

like L/s, d/s andthree (also see

+ȂN at each L/s

curves with differentwords, we can expect

jet switches when

and Re in additionL/s = 100 - 300,

UNV is almost

� )UNV , which

is empirically

1.3 and Re = 14,000.

�

(5)

is given by

(6)

unit span. To0 and tSW. At

switching onto athat is, the fluid

Thereafter, Δpincreases with tother words, the

at t = tSW, Δpside wall on the

reverse of theflow during the

(7)

= 100 - 300

and Re in thesee Figure 4).

L/s is not the

different L/s ’s.expect that +Ȃ�when +Ȃ��with

addition to the300, d/s = 1.2 -

independent

which tends to

empirically given by

(8)

14,000.

)

by

)

To At a

fluid Δp

t the Δp the the the

)

300

the ).

the

’s.

�

with

the -

independent

to

)


��

on the basis

Equation (8consistent, as

As a result,

./��(=0.012)with the experiment.calculated the

As a result,that both CΔlike L/s , d/s

As will bereattaching un-reattachingthe details ofregion on thepossibly controlled 3.2. Single-In the previous

there exists the jet-switchingdominant. Another

oscillation frequency.

of the jet further,have confirmedexclusively

the inflow fromconnecting-

O K means aaccelerationcould increasetSW. In otheruntil the instantestimate theshows K plotted

Figure


��

basis of (+Ȃ�) for

8) are derivedas the needed

result, the predicted

(=0.012) assumingexperiment. In

the comparison

result, the standardΔpAMP and ./��

d/s and Re in thebe revealed wall is crucial

reattaching wall is notof the jet switching

the jet-reattachingcontrolled by a

-Port Controlprevious subsection,

one remainingswitching side wall

Another question

frequency. So,

further, we conductconfirmed that the

examine the

from a quantitative-tube flow, and

� ��P�DE?

�

a normalisedacceleration dVT/dt ought

increase approximatelyother words, we

instant when thethe range of K plotted against

Figure 7. Flow


��

for L/s = 100

derived using the needed accumulatedpredicted St based

assuming a triangularIn order to confirm

comparison between all

standard deviation of/�� are approximatethe prediction. in the latter

crucial for jet switching,not crucial. At

switching mechanism,reattaching wall could

a certain accumulated

Control subsection, we have

remaining question wall and the outflow

question is whether

So, in this subsection,

conduct the the jet’s switching

the effectiveness

quantitative pointand define the

normalised accelerationought to be constant,

approximately with acould suppose

the jet switches. in the actual

against Re , in the regular

Flow-increment-rate


- 300 like Figure

least-squaresaccumulated flow work

based on the empirical

triangular-wave pressureconfirm the effectiveness

all the experiments

of St is less thanapproximated to

prediction. half of the

switching, whileAt the present

mechanism, it seemscould be a trigger

accumulated amount

have introduced

as to whetheroutflow from

whether��+Ȃ��/��subsection, in order

single-port-controlswitching is sensitive

effectiveness of +Ȃ� concerning

point of view. Then,the flow-increment

acceleration of fluid constant, but vary

a constant accelerationsuppose the connectingswitches. Under thisactual regular oscillation

regular oscillation

rate coefficient

Measurements and

Figure 6 at various

squares method onwork for jet switching

empirical formula

pressure differenceeffectiveness of

experiments and the

than 0.0025 be constant

present study,while the outflow

present stage, althoughseems acceptable

trigger of the jet’samount from the

introduced +Ȃ� as the

whether either or bothfrom the un-jet-

/�� is effective

order to discu

control experiments.sensitive to theconcerning the

Then, we assumeincrement-rate coefficient

in the tube.vary with time

acceleration fromconnecting-tube flow

this situation,oscillation of the

oscillation at L/s =

coefficient K against Re

and Visualization

various values

on the basis ofswitching increasesformula Equation

difference with CΔp

of the empiricalthe corresponding

for all the present without any

study, the inflowoutflow into the otheralthough we do not

acceptable that to weakenjet’s switching.the control port,

the universal number

both of the inflows-switching side

effective even in a quasi

discuss the physics

experiments. Bythe inflow, but

the inflow, below.

assume a constantcoefficient K as

tube. From a theoreticaltime t . However,from the reversedflow and the inflow

situation, K becomesthe ordinary FFJN

= 100 - 300,

Re at d/s = 1.2,

Visualization

values of d/s and

of all the results.increases with decreasing

Equation (8) for �+Ȃ�ΔpAMP = 0.11

empirical formula corresponding predictions

present results.any dependences

inflow from one other control not have exactweaken/destabilize

switching. In this context,port, such as +Ȃ

number for jet

inflows from side wall into quasi-steady situation

physics +Ȃ� , or the

some preliminarybut not to the

below. At first,

constant accelerationas follows.

theoretical pointHowever, as seenreversed time t0 to

inflow continue an appropriate

FFJN with two d/s = 1.2 and

in regular FFJN

and Re . Three

results. This formuladecreasing Re .

��/�� together

0.11 shows goodformula Equation (13),

predictions based on

results. It should bedependences upon the three

control port port on the opposite

exact information/destabilize the re

context, the jet Ȃ� .

jet switching.

the connectinginto the connecting

situation at very

the switching

preliminary experiments,the outflow.

first, we need to

acceleration of the inflow

point of view,seen in Figures

to the jet-switchingcontinue to accelerate

appropriate parameter.two control ports.and Re = 5000

FFJN oscillation.

�

constants in

formula seems

together with κ =

good agreement(13), we haveon �+Ȃ��/��.

be remarkedthree factors

port on the jet-opposite jet-

information to discussre-circulation switching is

switching. However,

connecting tube intoconnecting tube are

very low jet-

switching mechanism

experiments, weSo, we will characterise

inflow or the

(9)

view, K or the 5(b)-(d), VT

switching timeaccelerate linearly

parameter. Next, weports. Figure 7

- 25,000.

oscillation.

in

seems

=

agreement have

.

remarked factors

--

discuss circulation

is

However,

into are

-

mechanism

we l

characterise

the

)

the T

time early

we 7


��

We should can confirmvaries from 1 × 10−4 toalthough K of K is the same.

Figure 8 velocities VFFJN’s exit11 denotes thosepTE, respectively.

In Figureat t = 0 merelylinear, but almostfrom the primaryattached side.

Figure

Figure 9. Time


��

note that K isconfirm the dependence

1 ×10−4 to 5to 3.5 × 10−4,

in the regularsame. shows a typical

VT and VEX andexit and the pressure

those K = 3.5respectively. Figure 7(a), VT starts

merely representsalmost linear

primary nozzleside. In order to

Figure 8. Time histories

Time histories


��

is the time-meandependence of K upon

5 × 10−4. So, , keeping a constant

regular oscillation

typical exampleand a pressure

pressure at the connecting3.5 × 10−4 and

starts to increaserepresents the time

linear with a constantnozzle switches

to determine

histories of velocities

histories of velocities


mean value fromupon L/s , d/s we next conductconstant acceleration

oscillation is not the same

example in the singlepressure pTE where V

connecting-tube Re = 8800. In

increase from zerotime when eachconstant acceleration

switches from the beforehandtSW, this switching

velocities and pressure

and pressure

Measurements and

from t0 to tSW

d/s and Re . conduct the singleacceleration of

same as that

single-port-controlVEX and pTE denotetube end adjacentIn the figure,

zero with time t each measurement

acceleration duringbeforehand-jet

switching is preliminarily

pressure in single

in single-port

and Visualization

SW, because K The actual range

single-port-controlof the inflow

in the single

control experiment,denote the flow

adjacent to the chamberfigure, figures (a),

at t = t0 (=0.measurement starts. The

ing the durationjet-attached

preliminarily observed

single-port control at

port control at K

Visualization

depends uponrange of K in

control experimentsas closely as

single-port-control

experiment, namely, theflow velocity chamber and (b) and (c) represent

(=0.5 s). We shouldThe increasing

duration t = 0.5 - 0 side to the

observed by flow

at K = 3.5 × 10−4

= 1 × 10−4, d/s

upon t in a strictin the regular

experiments in a rangeas possible. To

control experiments,

the time histories near one side

and the control represent VT,

should note thatincreasing manner is

0.8 s. At t = opposite afterward

flow visualisat

10−4 and Re =

d/s = 1.3 and Re

�

strict sense. Weregular oscillation

range of K fromTo be exact,

experiments, the order

histories of twoside wall at the

port. Figure, VEX and

that the instantis not strictly= tSW, the jetafterward-jet-

visualisation using

= 8800.

Re = 20,000.

We oscillation

from exact, order

two the

Figure

instant strictly

jet -



smoke together with simultaneous measurements of VT, VEX, pTE and so on. Actually, corresponding to this jet switch at t = tSW, VEX in Figure 8(b) and pTE in Figure 8(c) step down and up toward constant values at the same time, respectively. Then, we can determine K or dVT/dt from Figure 8. To be exact, dVT/dt is time-mean which is obtained by such three data as t0, tSW and the VT at t = tSW. Of course, the above features can be seen in other cases. Figure 9 summarises all the results in the single-port-control: measured +Ȃ� ’s in the single-port-control

experiments are plotted against Re in a range of Re = 8000 -20,000 at d/s = 1.3 and various values of K. Each plot represents the ensemble mean over five trials in the single-port-control experiments. And, a solid line represents proposed empirical formula Equation (13) for �+Ȃ��/�� based on the regular oscillation using the

ordinary FFJN with two control ports in connection. We can see good agreement of the single-port control with the empirical formula for the regular oscillaton. This agreement suggests that +Ȃ� or the accumulated

flow work of not the outflow but the inflow from the connecting tube to the FFJN inside could be a key parameter for jet switching to explain the oscillation mechanism of the FFJN, in addition to the validity of +Ȃ� in practical aspects to estimate the jet frequency of the FFJN. 4. Conclusion In order to reveal the oscillation mechanism of a flip-flop jet nozzle (FFJN) with a connecting tube, we

have carried out the measurements of pressures and velocities in the connecting tube and inside the FFJN specially focusing on the jet-oscillation frequency f , varying: 1) the diameter d of the connecting tube; 2) the length L of the connecting tube and 3) the jet velocity VPN from a primary-nozzle exit. Obtained results are as follows. We have proposed an empirical formula to determine f , and confirmed its validity. Then, to consider f more generally, we assume that the jet switches when a time integral reaches a certain value. At first, as the time integral, we have introduced the accumulated flow work +Ȃ� of pressure through the

connecting tube into the jet- reattaching wall from the opposite jet-un-reattaching wall. Under this assumption, we have shown the effectiveness of JP to determine f . Second, to discuss the physics of JP further, we have conducted another experiment in single-port control, instead of the experiment in regular jet oscillation using the ordinary nozzle with two control ports in connection. As the result, we have confirmed good agreement between the single-port control and the regular jet oscillation. This agreement suggests that J P from the connecting tube to the FFJN inside can be a key parameter to explain the jet’s switching, in addition to the validity of J P in practical aspects to estimate the dominant jet frequency of the FFJN. References [1] Levin, S.G. and Manion, F.M. (1962) Jet Attachment Distance as a Function of Adjacent Wall Offset

and Angle. Fluid Amplification, vol. 5, pp 20-22. [2] Ozaki, S. and Hara, Y. (1967) Introduction to Fluid Logic. Nikkan Kogyo Shimbun Ltd., Tokyo. [3] Perry, C.C. (1967) Two-Dimensional Jet Attachment. In: Brown, F.T., Ed., Advances in Fluidics ,

ASME, New York, pp 205-217. [4] Epstein, M. (1971) Theoretical Investigation of the Switching Mechanism in a Bistable Wall

Attachment Fluid Amplifier. ASME Journal of Fluids Engineering , vol. 93, pp 55-62. [5] Drzewiecki, T.M. and Goto, J.M. (1973) An Analytical Model for the Response of Flueric Wall

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ASME Journal of Fluids Engineering , vol. 114, pp 362-366. [10] Raman, G., Hailye, M. and Rice, E.J. (1993) Flip-Flop Jet Nozzle Extended to Supersonic Flows.

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Vibration and Acoustics , vol. 116, pp 263-268. [12] Raman, G., Rice, E.J. and Cornelius, D.M. (1994) Evaluation of Flip-Flop Jet Nozzle for Use as

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Oscillating Impinging Planar Jet. ASME Journal of Heat Transfer , vol. 124, pp 770-782. [15] Hung, C.I., Wang, K.C. and Chyou, C.K. (2005) Design and Flow Simulation of a New Micromixer.

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Experimental Study on Switching Mechanism of a Flip-Flop Jet … · 2019. 5. 23. · 3), a flow...

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