246 KSME International Journal, Vol. 16 No.2. pp. 246- 254, 2002

Turbulence Enhancement by Ultrasonically Induced GaseousCavitation in the CO 2 Saturated Water

Seung Youp LeeGraduate School. Korea University, Seoul 135-701, Korea

Young Don Choi*Department of Mechanical Engineering, Korea University, Seoul 135-701, Korea

Recent primary concern for the design of high performance heat exchanger and highlyintegrated electronic equipments is to develop an active and creative technologies which enhancethe heat transfer without obstructing the coolant flows. In this study, we found through the LDVmeasurement that the gaseous cavitation induced by ultrasonic vibration applied to the CO2saturated water in the square cross-sectioned straight duct flow enhances the turbulence muchmore than the case of non-ultrasonic or normal ultrasonic conditions without gaseous cavitationdoes. We also found that gaseous cavitation can enhance effectively the turbulent heat transferbetween the heating surfaces and coolants by destructing the viscous sub layer.

Key Words: Ultrasonic Vibration, Gaseous Cavitation, Viscous Sub layer, LDV, Square Cross-sectioned Duct

Nomenclature-----------c : Specific heatD; : Hydraulic diameterDu : Viscous diffusion rate of Reynolds

stressesf : Ultrasonic wave frequencyk : Boltzmann constantm : Mass flow ratePa : Ambient pressurePo : Hydraulic pressurePu : Shear generation rate of Reynolds stressPe : Vapor pressure of liquidr : Distance from bubble centerR : Bubble radiusRo : Critical bubble radiusRe : Reynolds numberT : TemperatureVi : Velocity componentsUs : Streamwise bulk velocity Corresponding Author,

E-mail: ydchoi@Korea.ac.krTEL: +82-2-3290-3355; FAX: +82-2-928-1067Department of Mechanical Engineering, Korea Univer-sity. Seoul 135-701, Korea. (Manuscript Received June8.1001; Revised October 31. 1001)

U : Streamwise turbulent velocityIll" : Streamwise RMS (root mean square)

value of turbulent velocityu.u, : Reynolds stress componentsv : Normal turbulent velocity!1l : Normal RMS (root mean square) value

of turbulent velocityV : VolumeVf : Radial velocity at a distance of rVg : Radial velocity at a bubble surfaceW : Ultrasonic energy emission rateXi : Coordinate components

Greeksr : Ratio of specific heats of the gas in

bubble(J : Surface tension of liquidcPu : Pressure diffusion rate of Reynolds

stress0-0 : Local amplitude of ultrasonic vibrationCij : Dissipation rate of Reynolds stressesA : Wave lengthp : Density of liquid

Turbulence Enhancement by Ultrasonically Induced Gaseous Cavitation-- 247

1. Introduction

Enhancement of turbulent heat transfer be-tween heat sources and coolant flows has been aprimary concern for the design of high perform-ance heat exchanger and highly integrated elec-tronic equipments. In the past, passive techniquessuch as extended or rough surfaces have been usedto improve the heat transfer and thermal mixingbetween coolants and heat sources. The passivetechniques, however, obstruct the coolant flows toincrease the pumping power. Furthermore, mostof fluid flows in highly compact and integratedheat exchangers are stable laminar flows so thatthe heat transfer enhancements from high temper-ature heat sources to coolants are limited only tothe short downstream region from the heatingsources. Thus we need to develop new and crea-tive technologies to enhance the heat transferwithout obstructing the coolant flows.

Magneto-hydro-dynamic (MHD) turbulencewhich is the turbulence created by the body forcefluctuation inflicted on the flow fields has beenconsidered as the advanced heat transferenhancement technique for the nuclear fusionreactors tMontagomery, 1987). By similar process,emission of ultrasonic vibration to the turbulentflow may promote the turbulence generation byapplying the resonantly oscillating pressure fieldand thereby inducing cavitation. Bonkamp et al.(1997) reveals the effect of ultrasonic stream onboiling heat transfer. However, the enhancingeffect of ultrasonic vibration on boiling heattransfer is just limited to small values because theultrasonic vibration applied to the flowing purefluid can not induce the gaseous cavitation.Ultrasonic vibration is well transmitted throughwater and not dissipated easily. The micro-bub-ble involved in the fluid flow induces the gaseouscavitation if the bubble is resonated by theultrasonic vibration. In the present study, turbu-lence enhancement process through gaseous cavi-tation induced by ultrasonic vibration wasinvestigated experimentally in the straight ductflow with square cross-section.

2. Background

2.1 Realization of violent gaseous cavitationThe meaning of cavitation concerned here is the

formation of bubbles in liquids; cavities.Ultrasonic wave is a mechanical disturbancewhich consists of pressure oscillations above andbelow the pressure of the liquid. A reduction inpressure encourages a submicroscopic bubble togrow. A pressure above that of the pressure in theliquid will discourage bubble growth or cause thecollapse of one that has started to grow so that itproduces the characteristic effects usuallyassociated with cavitation. Growth of the bubbleoccurs at the interval corresponding to one-fourthof the period of the sound wave and collapseoccurs in a small fraction of that time. Because ofthe rapidity of the collapse, large instantaneouspressures and temperatures are developed at thecenter of the bubble. Usually the nuclei which arethe sources of the cavitation bubbles remain afterthe bubbles collapse. They will then serve againas nuclei for new bubbles.

These bubbles may be of two types: (I) thosethat have been dissolved or trapped in minutebubbles in the liquid, and (2) vapors of the liquiditself. (Ensminger, 1988)

The first type of cavitation, called gaseous cav-itation, may form a cavitation of relatively lowintensity. Choi (1979) proved by analysing the gasbubble dynamics for the minute bubblesoscillating under ultrasonic vibration that thereexists a critical resonant bubble size whichgenerates cavitation for a given ultrasonic waveintensity and frequency. Thus, if the bubble size isdeviated from the critical resonant size, the vio-lent cavitation cannot occur.

The second type, called vaporous cavitation, isof fairly high intensity. This is the process ofexpansion and subsequent violent collapse, underthe action of a varying ambient pressure. Thisexplosive formation of transient cavities, whichare largely filled with vapour, occurs when theinstantaneous pressure decreases to such an extentthat the nucleus bubbles cannot remain stablesimply by an increase of volume to a new equi-

248 Seung Yaup Lee and Young Don Choi

vaporous cavitation region

2.2 Turbulence generation by ultrasonic vi-bration and thereby induced cavitation

Generally, the heat transfer coefficient is pro-portional to the square of turbulence intensity, soif the turbulence intensity of the fluid decreases,the heat transfer coefficient will decrease accord-ingly. Therefore, turbulence enhancementtechniques have been the most important factorfor the design of high performance heat exchangerwhich requires high heat transfer coefficient be-tween coolants and heat sources. Ultrasonic vi-bration has relatively high frequency, smallamplitude and short length scale compared tonormal turbulence. By the way, turbulence can begenerated by the ultrasonic vibration through theinteraction of Reynolds stresses and mean sheargradients produced by the ultrasonic vibrationand thereby induced cavitations. Reynolds stressequations which involve the turbulence genera-tion rate term by ultrasonic vibration areexpressed as the following relation (Lounder,1975; 1989).

D~tUj =Pij+Dij+ij-cij+Pffltra (I)where pffltra is the turbulence generation rate byultrasonic vibration and thereby induced cavi-tation.

Ultrasonic energy will be dissipated to directlyheat or consumed to generate turbulence, but thetheoretical study on the interaction between tur-bulence and ultrasonic vibration reveals that theultrasonic stream does not contribute directly tothe turbulence generation while ultrasonicallyinduced cavitation may significantly enhance tur-bulence generation.

Ultrasonic vibration applying to the flowingliquid may produce turbulence through the fol-lowing three mechanisms. The first is the turbu-lence generation through the interaction betweenthe density fluctuation induced by ultrasonic vi-bration and the inherent Reynolds stresses.Ultrasonic vibration generates the rapidoscillation of fluid pressure so as to raise the localfluid density fluctuation. But the period andamplitude of ultrasonic vibration are too small togenerate turbulence. We cannot find any evidence

2.01.51.0cycles

0.5-1+--....-+----+---+--+----1

0.0

E'2~D.. 1

Fig. 1 Generation of vaporous cavitation for thenormal ultrasonic vibration condition

librium value. In order to produce vaporous cav-itation by ultrasonic vibration, the amplitude ofultrasonic wave, Po should be larger than Pa- Pvso that liquid pressure around the bubble shouldfall below Pv as shown in Fig. 1. Therefore,vaporous cavitation can be generated only in thecondition of requires high intensity ultrasonicvibration.

In the present study, we are trying to realize thegeneration of violent cavitation even in the con-dition of relatively low intensity ultrasonic vibra-tion by applying it to the CO 2 saturated waterflowing in the straight duct. If ultrasonic vibra-tion is applied to the CO 2 saturated water, nu-merous CO2 gas bubble nuclei may appear anddisappear and some of them may grow in thedepressurizing phase, in which the water pressurefalls below P. due to the supersaturation of C02gas bubble in the water. Then the growingbubbles are collapsed and produce violent cavi-tation in the subsequent pressurizing phase inwhich the water pressure rises above Ps.

The mechanism of this gaseous cavitationinduced by the application of the ultrasonic vi-bration to the CO 2 saturated water is the evapo-ration of dissolved to the CO 2 gas from thesupersaturated water in the depressurizing phaseand the subsequent collapse in the pressurizingphase.

Turbulence Enhancement by Ultrasonically Induced Gaseous Cavitation->- 249

(2)

(4)

(5)

(3)

(6)

2.4 Gaseous cavitation in the CO 2 saturatedwater

Generally, there are many micro-gas bubbles intap water. However, there is a critical bubble sizewhich produces gaseous cavitation for a givenfrequency and amplitude of ultrasonic vibration.Choi (1979) revealed that only the bubbles diam-eter smaller than Itffil could generate gaseouscavitation under ultrasonic vibration. Therefore,there is little possibility to produce gaseous cavi-tation by applying the ultrasonic vibration to thetap water.

CO 2 can be easily dissolved to water, and thedissolving rate increases as the liquid pressureincreases. CO2 dissolved in water can formembryos but the embryos disappear at oncebecause the embryo sizes are too small to growover the critical size for bubble formation and thegas pressures in embryos are too large for the CO 2gas existing as micro-bubbles. However, ifultrasonic vibration is applied to the CO 2saturated water, the water becomes super-saturated with CO 2 gas during the depressurizingphase of ultrasonic vibration. This super-saturation of CO 2 gas may lower the activation

If the cavitation occurs, the local mean velocitygradient of fluid is so large enough to generateturbulence by the relation (6) which representsthe turbulence generation through the interactionof mean velocity gradient, sv.i, and theReynolds stress component in radial direction, v~in the spherical coordinate.

pultra = -11 aVtr ar

Then the local mean velocity gradient can bewritten as following equation.

aVt 2R 2 Vgar=--r-3-

is denoted to Vg , then the fluid velocity at thearbitrary position of distance r from the center ofthe bubble may be given by (4).

V;_aRU)g--a-t-R2VI (r) ::::::: Vg---:Tr

_ R aVg (r) 3 V; ( )2=1.-{p -p,at 2 g r p v a

+Posinwt-~+(Pa-Pv+~)( 1?nIf the radial fluid velocity of the bubble surface

2.3 Cavitation dynamics in the ultrasonicvibration field

On the assumption that the gas nuclei givingrise to cavitation are merely very small freebubbles, simple relations have been derived forthe pressure and other conditions of cavitationdynamics in the ultrasonic vibration field. Theequation of motion for bubble dynamics inultrasonic vibration field of sin cot is as follows.

of this kind of turbulence generation from thepresent experimental study. However, we canexpect that the ultrasonic vibration may affect theturbulence cascade process through promoting thestretching of small eddies.

The second is the turbulence generation by theinteraction of ultrasonic vibration and meanshear gradients, for example, the turbulence gen-

. b 2 aUi. h C' dieration y rr u; aXi in t e artesian coor mate.This kind of turbulence generation can not beexpected to occur in the plane channel flow or thestraight duct flow which has no acceleration ordeceleration of flow.

The third is the turbulence generation due tothe interaction of mean velocity gradient inducedby the cavitation and inherent Reynolds stresscomponents surrounding the bubbles. Thefluctuating velocity induced by the cavitationbubble is so large enough to be compared withturbulent velocity scale, so that the thirdmechanism is the most promising mechanism forturbulence enhancement by ultrasonic vibration.We could realize the violent gaseous cavitation byapplying relatively lower intensity ultrasonic vi-bration to the C02 saturated water compared tothat for vaporous cavitation. The aim of thepresent study is to investigate experimentally theevidence that ultrasonically induced gaseous cav-itation may be the most efficient turbulenceenhancement technique.

250 Seung Youp Lee and Young Don Choi

.

raver seCorurcner

Fig.3 Test Loop

2.01.51.0cycles

gas bubble growing region

0.5

gasbubble collapsing region

0+----'

-1+---+----+----+---~0.0

Fig. 2 Generation of gaseous cavitation by applyingthe ultrasonic vibration to the CO2 saturatedwater

F:cw Cnanoer

..:.:l:....r.,er 'veeS,;r.C:! ?Oc.t~ssor';':':;",~r Soooiv ~'1o:c- '-C...c~~,~~::;:,,,,.

. 3r?oc eel: ~_ _____. IJ

______C0~.::'l;O' ,,/ ~'I==--:-- ---f ----=:::....-=::::::::.::::: _---',y

'iii _~?--'~' ~ J-~--" ::;:::- -

Seam Senner Trar3;;'jr~,;'Q cens

roc-Loser scc.ce

3. Experimental Method

energy for the formation of the gas bubbles. Thus,probability of the embryos to grow over thecritical sizes for bubble formation may increase.

Fig.4 Schematic of LDV systemFigure 3 shows the test loop which is composed

of a closed circuit for experimental measurementof turbulent characteristics using LDV system, astorage tank, chemical pump, chiller, controlvalve, bypass valve, OVAL flowmeter, 0.04 X 0.04nr acrylic test-section, ultrasonic vibrator andgenerator. Water in the storage tank is circulatedby the chemical pump. I" PVC pipes are arrangedto compose a closed circuit. The temperature ofcirculating water is set to io'c and controlled bychiller. THIS-IOOONAF-typed chiller involves adigital temperature controller, which can controlthe variation of circulating water temperaturewithin 0.5e.

The flowrate of circulated water in the closedcircuit is controlled by a control valve and abypass valve, and measured by a OVALflowmeter. The LSV52A3-30 type OVALflowmeter has the flowrate range of 0.4- 3 m3j hand uncertainty of O. 35%. Water flows throughthe test-section from the bottom toward the top.

When ultrasonic vibration is exerted on thenatural water, the cavitation occurs by the gase-ous .bubble naturally dissolved in the water.However, the turbulence enhancement by the

cavitation is restricted by the number of trappedgas bubbles that resonate to the ultrasonic vibra-tion. CO 2 can be easily dissolved to water, but itcan also be easily formed to gaseous bubble byexternal disturbances. In the present study, CO 2 issupplied to the circulating water for one hourwith constant pressure, 1.6kgjcm2, to saturate thewater by the dissolved CO2 gas before theexperiment.

Turbulence enhancement by ultrasonic vibra-tion is measured by LDV. The LDV system usedin the present study is two-components ion lasertype manufactured by Dantec. Lens focus lengthis 160mm and the maximum output of laser beampower is 6kW. The LDV system is composed of a-laser beam, fiber flow components, processor,feeding system, etc. as shown in Fig. 4.

A two-dimensional traversing mechanism isused to move the measuring volume. Themaximum traversing length of the measuring vol-ume is 690mm and increasing width is capable ofminimum O.lmm.

Generally, if tap water is used as workingmaterial, dispersion light can be obtained without

Turbulence Enhancement by Ultrasonically Induced Gaseous Cavitation->- 251

4. Results and Discussions

In the present study, we measured the emissionrate of ultrasonic energy by temperature gradientof water in an adiabatically closed volume usingfollowing formula.

any particle suspension in the fluid, but in thepresent experiment, we can obtain more clear datasignals by suspending SiC part icl es (di amet er :1.5.um, density: 3.2g/cm3) . The number of datameasured in the present experiment are 30,000 per30 seconds and the data are averaged to calculatemean values. Signals obtained from photo-multi-plier are analyzed by correlation type processorwhich is composed of frequency filter, digitalsampler, D/A converter, etc.

I0.50025

vi,

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