A holographic study of cavitation on axisymmetric bodies and the influence of polymer additives

A .:HOLOORAPHIC. STUDY OF

CAVITATION ON AxisYmmETRic

BODIES AND THE.INFLUENCE

OF 13mA:wk. AppMyts

DR.-I

.

J. H. J. VAN ,bEk mEuf,EN.,

PUBLICATION No 509

NETHERLANDS SHIP MODEL BASIN

WAGENINGEN. THE NETHERLANDS

AMSYMMETRIC BODIES AND THE INFLUENCE OF POLYMER ADDITIVES

A HOLOGRAPHIC STUDY OF

CAVITATION ON AXISYMMETRIC

BODIES AND THE INFLUENCE

OF POLYMER ADDITIVES

DR. IR. J. H. J. VAN DER MEULEN

PUBLICATION No. 509

NETHERLANDS SHIP MODEL BASIN

WAGENINGEN, THE NETHERLANDS

INTRODUCTION 1

THE ORIGIN OF CAVITATION 3

1.1. Introduction 3

1.2. Gas bubbles stabilized in cracks or pores of solids 4

1.3. Gas bubbles stabilized by surface films 5

1.4. Gas bubbles stabilized by small particles 7

1.5. Weak intermolecular linkages 7

1.6. Inhomogeneities generated by cosmic rays 8

1.7. Conclusions 9

BASIC DEFINITIONS 10

EXPERIMENTAL METHODS 12

3.1. Description of test facility 12

3.2. Test models 14

3.3. Turbulent-flow rheometer and surface-tensionmeter 16

3.4. Holographic method 19

3.5. Flow visualization techniques 24

EXPERIMENTAL PROCEDURE AND RESULTS 28

4.1. Procedure 28

4.2. Flow visualization studies 28

4.2.1. Newtonian flow 28

4.2.2. Non-Newtonian flow 34

4.3. Cavitation studies 37

4.3.1. Newtonian flow 37

4.3.2. Non-Newtonian flow 41

4.4. Cavitation inception measurements 43

4.5. Friction reduction and surface tension 45

_

V. DISCUSSION OF FLOW VISUALIZATION

iNeWr.oriian:-f.low

5.2; !Noh7Netatonian flow

DISCUSSION OF CAVITATION STUDIES- .

-,

6,.1-.:correlation with bound,Aili-.1,4ier:,f.1Ta',

.6 .:i.Influence of polymer a:cisi.i'tives:

A

'.$711:MARY AND CONCLUSIONS

.;-.LfST.',OF

SYMBOLS.-

-- . REFERENCES 4 7. I ! 57

INTRODUCTION

Cavitation, or the formation of vapour bubbles in a liquid by pressure reduction, is a phenomenon restricted to liquids. Cavitation is concerned with both the appearance and disappearance of bubbles or cavities. Two major areas may be recognized where cavitation is involved, namely the flow of liquids where cavita-tion is produced hydrodynamically (ship propellers, hydraulic machinery, pumps) and sound fields in liquids where cavitation is

induced acoustically (sonar systems, cell disruption).

In flow systems and propulsive devices cavitation is feared for its detrimental effects such as erosion, noise and vibrations. These and other effects are caused by the high temperatures and pressures arising from the spherical collapse of vapour bubbles, or by the formation of microjets, having speeds up to 1000 m/s, during the non-spherical collapse of vapour cavities. In most cases, model tests are made prior to building a new hydrodynamic device to predict or avoid the difficulties related to cavitation. In some cases, due to the failure of the device, such tests have to be made afterwards. However, the proper scaling or transference of model test results to the prototype may be obscured by the large number of factors involved in the origin, initiation, growth and collapse of bubbles or cavities. To derive appropriate scaling laws, considerable experimental research has been conducted in water tunnels on certain "simple" bodies. These studies are mainly concentrated on the onset or inception of cavitation since,

according to the terminology applied by Plesset /1/, this state of flow may be seen as the limiting case for a non-cavitating flow and a cavitating flow. Usually, the effects on cavitation incep-tion are studied by varying the parameters related to the liquid flow (velocity, turbulence, air content, pressure history) or related to the body (size, surface roughness, wettability). These studies provided an extensive overall knowledge of cavitation and cavitation effects but a proper understanding of many cavitation phenomena was still lacking.

At this point reference should be made to an invited lecture by Professor A.J. Acosta at the 1974 Edinburgh Conference on

'Cavitation /2/. In this lecture, Acosta emphasized the need for a thorough understanding of the basic fluid mechanics of the liquid flow surrounding the bodies in which cavitation takes place. This statement was based on an earlier study by Arakeri and Acosta /3/ in which the boundary layer flow was visualized by the employment of the schlieren method. Cavitation inception could be correlated with the occurrence of laminar flow separa-tion. Unawareness of this important flow phenomenon has obscured the results of comparative cavitation studies with "simple" bodies, made in the past.

In the present work, cavitation and flow phenomena are studied by using holography, a three-dimensional imaging tech-nique. The employment of this method for the observation of cavi-tation inception phenomena has been reported before by Van der Meulen and Oosterveld /4/. A new technique, based on holography, was developed for the purpose of flow visualization. Two axisym-metric bodies were investigated, one having laminar flow separa-tion, the other not having it. The implications of this feature on incipient and developed cavitation are studied.

The phenomenon of turbulent-flow friction reduction by polymer additives of high molecular weight has been known for almost thirty years. In recent years an increased interest is

shown on the effect of polymer additives on cavitation. The phy-sical mechanisms which control this effect had not yet been

determined. In the present work the influence of polymer additives on the flow about the test bodies is studied and related with the

CHAPTER I

THE ORIGIN OF CAVITATION

1.1. Introduction.

Cavitation is frequently considered to occur as soon as the pressure falls below the vapour pressure of the liquid. This would be true if liquids could not withstand tensions. However, liquids can withstand very high tensions, or negative pressures, under certain conditions. Fisher /5/ calculated the tensile strength of liquids from a nucleation theory and found a value of 1360 kg/cm2 for water. This value is an order of magnitude smaller than that required for a simultaneous separation of all atomic bonds cut by a plane surface. The tensile strength of liquids is hardly affec-ted by dissolved gases as derived by Kuper and Trevena /6/. They calculated the reduction in the tensile strength of water caused by saturating it with air at a pressure of one atmosphere to be less than 0.5 percent. Many experiments have been done to show that negative pressures may exist in liquids without the develop-ment of cavitation. A maximum limiting negative pressure of 282 kg/cm2 was found by Briggs /7/ using distilled water at a tem-perature of 100 C. The negative pressures were produced by spin-ning a small Z-shaped capillary tube open at both ends and filled with water.

In most cases of hydrodynamically or acoustically induced cavitation it has been found that the pressures do not differ much from the vapour pressure of the liquid. This rather unexpec-ted behaviour of a liquid can only be explained by postulating the existence of nuclei, or weak spots, in the liquid from which the formation of vapour bubbles is initiated when the pressure falls below the vapour pressure. The most simple explanation would be to assume the existence of free gas bubbles. To examine this possibility, let us consider a spherical gas bubble of ra-dius R in a liquid. Let the liquid pressure be P1 and let the bubble be filled with gas and vapour. Pressure equilibrium re-quires that

2S

Pv Pg = P1 R '

where Pv is the vapour pressure, Pg the gas pressure and S the surface tension. From Eq. (1.1) it is found that the surface tension tends to dissolve small bubbles. By analyzing the dif-fusion process and considering the effect of the surface tension, Epstein and Plesset /8/ derived an expression for the time. re-quired for complete solution of air bubbles in water. For .example, an air bubble of 10 pm radius requires only 6.6 seconds to dis-solve completely in saturated water at 220 C.

Ina non-flow system, large bubbles rise to the surface and, as shown above, small bubbles are forced into solution by the surface tension. Hence, the free gas bubble hypothesis is unten-able. It should. be emphasized, however, that in recirculating water tunnels free gas bubbles may be generated by turbulence or cavitation itself and thus may act as nuclei. When such circum-stances do not exist, there still must be some stabilizing effect which prevents bubbles from dissolving or perhaps some other me-chanism Which initiates cavitation. Several hypotheses have been proposed to explain the. stabilization of nuclei. A review of these hypotheses will be given below.

1.2. Gas bubbles stabilized in cracks or pores of solids.

The most plausible hypothesis on the stabilization of nuclei is due to Harvey and his collaborators /9/

in

their study of bubble formation in animals. They first pointed out that two conditions must be fulfilled for a nucleus to be stable: a,

pressure equilibrium and a gas diffusion equilibrium. A spherical nucleus can only exist in an unstable equilibrium; the slightest disturbance causes either growth or dissolution of the nucleus. However, a nucleus attached to a surface. may be stable under certain conditions of surface geometry, shape of gas-

liquid-solid junction and advancing and receding contact angles between gas and solid. As a special case, a gas nucleus in a conical

cavity of apex angle lp and receding contact angle er is con-sidered. Whenr>90o + 4)/2 the gas nucleus will have a concave surface and, according to Eq. (1.1), the surface tension tends to stabilize the nucleus against the liquid pressure Pl. Such a nucleus satisfies all conditions necessary to fulfil pressure and gas diffusion equilibrium. The solid .material which acts as

a host for the gas nuclei can either be a body in the liquid or small particles which are always present in liquids. This was demonstrated by Liebermann /10/ who noticed deposits which re-mained on a microscope slide after the collapse of a small air bubble which was introduced in a droplet of distilled water.

In a container filled with water, the solid particles tend to fall to the bottom of the container, and so aging of the water may be expected. This phenomenon has been confirmed by Strasberg /11/ who studied acoustically induced cavitation in a glass con-tainer. Flynn /12/ pointed out that the motion of particles smal-ler than about 1 um is dominated by the Brownian motion; this limits the effect of aging. Harvey and his collaborators /9,13/ have done many experiments on the elimination of gas nuclei in liquids. They used centrifuging, filtering, boiling and pressuri-zation techniques and found a remarkable elimination of nuclei by pressurizing the liquid. They concluded that high pressures forced most gas pockets which remained in cracks and pores, into solution. Another study on the effect of pressurization was made by Knapp /14/. He found an increase of the effective tensile strength of water by previous pressurization. The amount of this increase varied with the level of pressurization, but seemed to reach an upper limit at about 150 to 200 kg/cm2. The physical concept or model of the nucleus which was most consistent with Knapp's investigations is that of Harvey: "a nucleus is a pocket of undissolved gas in the re-entrant crack in the surface of a solid particle of impurity which is hydrophobic to the liquid".

1.3. Gas bubbles stabilized by surface films.

In 1954, Fox and Herzfeld /15/ proposed the hypothesis that gas bubbles stabilized by an organic monomolecular skin act as cavitation nuclei. The skin was supposed to be an elastic shell which prevented diffusion of gas. Working with acoustically in-duced cavitation, they defined the cavitation threshold as the sound pressure at which the skin cracked and so permitted dif-fusion. The appearance of surface films on water has been known for many years. Goldacre /16/ found surface films on practically all natural waters he tested. In 1956, the organic skin hypo-thesis was abandoned by Herzfeld /17/. In his opinion there

should be a lower limit to the effect of pressurization and, cording to Strasberg /11/, there was no such lower limit, since the tension necessary for cavitation to set in under the influ-ence of ultrasonic waves increased smoothly with the amount of pressure previously applied. Knapp /18/ also rejected the organic skin hypothesis. In his opinion the crushing strength of the or-ganic skin was about equal to the surface tension of water. To explain the results of his pressurization experiments, the crushing strength of the organic skin should have been several orders of magnitude greatexthan the surface tension of water.

The above considerations were not actually based on experi-ments with surface films. In 1964, Bernd /19,20,21/ started an experimental study on the formation of surface films of gas nuclei. He first studied the dissolving rate of nuclei in various waters using acoustic means to induce cavitation; a high dissol-ving rate corresponding to a high tensile strength gain in a short time. Next, surface films were deliberately produced about nuclei by adding small quantities of hydrocarbons or proteins to the water, and a marked reduction of the dissolving rate was found. These and other results clearly demonstrated the influence surface films can have. The film material may be composed of long-chain, surfactant hydrocarbons. One end of the molecule must be polar, or attractive to water such as an OH or COOH group, the other end must be non-polar, such as a cH3 group. According to Bernd, proteins seem. the most important materials in the creation of surface films These films are strong, elastic and durable to a greater degree than a hydrocarbon film.

Further confirmations of the organic skin hypothesis are due to Sixotyuk /22,23/. He actually correlated the content of sur-face-active materials in water with the cavitation strength. Be also calculated the strength of a surfade-active, film about small bubbles and found a value of 130 kg/cm2. Further experiments were made with acoustically induced cavitation. The cavitation threshold pressure was measured as a function of the hydrostatic pressure previously applied or still present. A rather small in-crease in the hydrostatic pressure produced a sharp inin-crease in the cavitation threshold to a maximum value of about 130 kg/cm2. This value is consistent with the calculated strength of a sur-face film.

1.4. Gas bubbles stabilized by small particles.

Another version of the organic skin hypothesis was proposed by Turner /24/ in 1963. He suggested a nucleus to be a gas

bubble stabilized by a compressed wall of particles. This nucleus will have a degree of elasticity and may achieve a neutralization of buoyancy. However, due to the Brownian motion, neutral buoyan-cy is not a necessary condition for small nuclei. Turner's argu-ment that a rising bubble will intercept small particles and that a continuous surface of particles will form as a consequence of bubble shrinkage, is confirmed by the experiments by Liebermann /10/.

1.5. Weak intermolecular linkages.

In the preceding sections, three hypotheses have been dis-cussed which are all based on stabilized nuclei filled with gas. In 1947, Pease and Blinks /25/ distinguished between cavitation from pre-existing gas nuclei, which they called "false" cavita-tion, and cavitation in the absence of any gas phase, which they called "true" cavitation. In order to study true cavitation, they used three procedures to remove all gas nuclei. Under these cir-cumstances they found that cavitation depended upon the nature of the solid-liquid interface. Water-glass systems would not

cavitate unless negative pressures of at least 100-200 kg/cm2 were applied. On the other hand they found easy cavitation when molecules with non-polar groups were fixed on solid surfaces.

Similar findings are reported by Harvey et al /13/. They obser-ved the rapid movement of a blunt glass rod in a narrow tube fil-led with water. If the rod surface was hydrophobic and free of gas nuclei, cavitation occurred at the rear end when the veloci-ty was less than 3 m/s, but if the rod surface was hydrophilic, the velocity could be 37 m/s without cavitation. Experiments by Weyl and Marboe /26/ on the release of gas supersaturation from water resulted in similar conclusions.

The role of weak intermolecular linkages in the origin of cavitation was nicely demonstrated by Horton /27/, who investi-gated the killing rate of ultrasound on bacteria in water. The killing rate of the bacterium E. coli was decreased by the

addition of the bacterium M. phlei, which is surrounded by a very heavy waxy capsule. The linkage between the waxy bacterium and the surrounding water is much weaker than that of the normal bac-terium. Hence, cavitation first occurred at the bacteria M. phlei and thus decreased the killing rate of the bacteria E. coli. Many other studies were made on the effect of liquid-solid interfaces; among which the work by Bernd /20/ should be mentioned.

1.6. Inhomogeneities generated by cosmic rays.

Another hypothesis which might explain the origin of cavita-tion was proposed by Briggs /28/ in 1958. In his opinion, cosmic radiation might be responsible in part for the widely scattered values obtained in cavitation measurements. He referred to Glaser /29/ who had shown that, when a highly energized cosmic ray passes through a superheated liquid, bubbles are formed and the liquid explodes (bubble chamber). This

opinion

was not shared by Knapp /18/ in his study on the effect of pressurization. Knapp con-sidered the effect of cosmic rays and concluded: "No correlation was found between the average tensile strength at failure and the duration of the tension even though this duration varied over several orders of magnitude between the different tests. This result implies that cavity formation in liquids under tension

cannot

be explained by nucleation resulting from cosmic rays or other high energy radiation received by the liquid while under tension".

The hypothesis got a new impulse from the work by Sette and Wanderlingh /30/. They studied ultrasonic cavitation in water and found a remarkable effect by enclosing the tank, in which the liquid was

contained,

with lead or paraffin screens. In their opinion, these findings prove that the nucleation responsible for ultrasonic cavitation is connected with cosmic radiation. In another study, Sette and Wanderlingh /31/ proposed a theory on the creation of microbubbles in liquids by

ionizing

particles. They concluded: "It would seem that the process suggested will ensure a statistical lifetime of the microbubbles in the liquid for a time sufficient to reach a condition at which the bubble may remain indefinitely stable: e.g., by adhering to a dust

"Since organic impurities present at the interfaces or in the form of clusters of molecules are oxidized to CO2 by the trans-mission of 1 rays through water, the gas formed causes a growth of the bubbles already existing and the generation of new ones".

1.7. Conclusions.

A comparison between the above-mentioned hypotheses leads to the conclusion that no single hypothesis can explain all phenomena which have been observed with experiments on the ori-gin of cavitation. It just depends upon the conditions of the liquid, such as its purity, or upon the surface characteristics of solid bodies, which type of nucleus or weak spot prevails and causes cavitation. According to Darner /32/, the complexity of the stabilization of nuclei in water is due to the complex na-ture of water itself, a property which seems to be absent in other liquids /33/.

In flow systems, one usually distinguishes between surface nuclei adhering to the wall of a solid submerged body, and stream nuclei which are present in the flow. Much work has been devoted to correlating cavitation inception with either stream

or surface nuclei. Also in this case, one must conclude that such factors as the conditions of the liquid or the surface characteristics of solid bodies decide which class of nuclei prevails and causes cavitation.

and

Po - P v a

h _{p Vo2}

where Po denotes the static pressure, and Vo the uniform flow ve-locity of the liquid at a great distance from the body. Pv is the vapour pressure of the liquid and p its density. According to Plesset /1/ three flow conditions for a given body may be indi-cated. A large value of o corresponds to a non-cavitating flow and a small value to a cavity flow where a large cavity is attached to the body. The third condition is reached at the transition between these flow conditions and is mostly charac-terized by small bubbles or cavities near the body. This state of limited cavitation can be attained in two different ways: starting from a non-cavitating condition and decreasing Po (or increasing Vo) which leads to the incipient state of cavitation and starting from a cavitating condition and increasing Po (or decreasing Vo) which leads to the desinent state of cavitation. Accordingly, two cavitation numbers are defined /35/: the incipient cavitation number CTi and the desinent cavitation number ad given by

Poi - Pv - Pod - Pv ad p Vo2 CHAPTER II BASIC DEFINITIONS

In 1924, Thoma /34/ derived the law of similarity for cavita-tion in a water turbine and defined the dimensionless parameter a. This parameter has been widely used since to characterize ca-vitation in a fluid flow and is called the caca-vitation number. Its definition is

(2.1)

(2.2)

p Vo2

where P denotes the static pressure on the body. If the pressure coefficient is related to the minimum static pressure Pmin on

the body, the minimum pressure coefficient Cpmin is given by

Po - Pmin

Cpmin - (2.5)

p Vo2

According to

Holl

/36/, the classical theory of limited cavita-tion states that

cipient and desinent cavitation respectively.

Holl

/36/ distinguished between three physical phenomena which can cause a bubble or cavity to grow. The first phenomenon

is evaporation of liquid which is a rapid process but still takes place at a finite rate. This form of cavity growth is called vaporous cavitation. It can occur only when the pressure is lower

than the vapour pressure of the liquid. The second phenomenon is

siMply

based on Boyle's law which states that the volume of a given quantity of gas or vapour increases when the pressure

de-creases. This form of cavity growth is called pseudo cavitation. The third phenomenon is diffusion of gas dissolved in the liquid

into the cavity. This form of cavity growth is called gaseous cavitation, Pseudo and gaseous cavitation can occur above or below

the vapour pressure of the liguid. Extending the Pease and Blinks /25/ concept of bubble formation, vaporous cavitation may be called true cavitation and pseudo or gaseous cavitation may be called false cavitation. Experimentally, it is difficult to distinguish between the various types of cavitation that can occur. Besides, the cavity growth phenomena described earlier may all contribute to the ultimately observed cavitation.

A characteristic parameter for the pressure distribution around a (streamlined) body is the pressure coefficient Cp defined as

Po - P

(2.4)

°I

= crd = CPmin. (2.6)

CHAPTER III

EXPERIMENTAL METHODS

3.1. Description of test facility.

The facility used is the high speed recirculating water tun-nel of the Netherlands Ship Model Basin. Originally, the maximum speed in the 40 mm circular test section was 65 m/s and the maxi-mum allowable tunnel pressure was 35 kg/cm2. A detailed des-cription of this tunnel set-up and its air content regulation system is given in Refs. /37/ and /38/. Later on, a 30 mm x 90 mm rectangular test section was made for studying cavitation on hydrofoils. The same section was used for a holographic study of cavitation inception on a hemispherical nose /4/. An advantage of the shape of this section was that the distance between the glass windows was only 30 mm, which favoured the quality of the holograms. A disadvantage, however, was that the influence of the tunnel walls on the flow about the model became noticeable.

For the present study a new test section was made. It has a 50 mm square cross section with rounded corners (radius 10 mm), to limit the influence of the walls. The models, having a dia-meter of 10 mm, occupy 3.25 percent of the cross-sectional area of the test section. Injection of polymer solutions from the nose of the models is made by a Hughes Centurion-100 pump unit. The unit consists of a drive mechanism fitted with two pump heads. A pulse-damper is used to minimize flow variations due to the restricted number of pump heads. Further details on the injection of polymer solutions are given in Ref. /39/. A schematic diagram of the tunnel with the polymer injection system is shown in Figure 1. A detail showing the contraction, test section and diffuser is given in Figure 2. A Van Slijke gas-analysis appara-tus was used to measure the total air content of the tunnel water. In this apparatus the air content in a 10 cc water sample is extracted under a Torricellian vacuum and the pressure of the extracted air is measured upon recompression to a volume of 2 cc. Prior to testing, the tunnel was calibrated. Velocity surveys in

=-7 PUMP UNIT _ PULSE -DAMPER CENTRIFUGAL pumP GLASS BEAKER

POLYMER INJECTION LINE

VilLEUE7

D.CMOTOR 1000 COOLING -WATER. HEAT EXCHANGER

I

Dri-NC-71s s. N\ .NWsc: WATER SUPPLY PUMP BEAERATION LINE

Win

'911100100ww..----L--wwWAIM.

_alAirA'

ENV%

_Now

diitigAMACk

Alp

4k

NOwehmkomm"--d

MODEL

FT TEST SECTION NTR TION

Figure 2. Cross section of contraction, test section and diffuser.

the central part of the test section were made by using a Pitot rake. The maximum deviations in axial velocity were found to be within 0.2 percent of the mean axial velocity.

3.2. Test models.

According to Arakeri and Acosta /3/, most axisymmetric models used in cavitation inception studies, such as the

hemi-spherical nose and the I.T.T.C. standard headform, exhibit a laminar boundary layer separation. It means that the laminar boundary layer is unable to overcome the adverse pressure

gra-dient and the flow separates from the wall. Schiebe /40/ intro-duced a standard series of axisymmetric models which, theoretical-ly, should not exhibit laminar boundary layer separation. To distinguish between these two classes of axisymmetric models, a hemispherical nose and a blunt nose, selected from Schiebe's standard series, were used in the present investigations. In the absence of wall effects, the minimum pressure coefficient for the hemispherical nose according to Ref. /41/ is

9.755.

The blunt nose, selected from Schiebe's standard series, has a minimum pressure coefficient of

0.75.

The contour of the blunt nose is derived from the combination of a normal source disk and a uni-form flow. Schiebe /40/ calculated the dimensionless coordinates and pressure coefficients for a series of models in the range Cpmin = 0.33 (point source) - 1.0. The coordinates for the blunt nose having a minimum pressure coefficient of

0.75

are given in Table 1. The diameter D of the cylindrical part of the

hemisphe-Table 1. Coordinates of blunt nosewith minimum pressure coef-ficient C = 0.750. min Axial coordinate: over diameter ' x/D Radial cbdrdinate over diameter ' r/D Surface coordinate over diameter s/D 0 0 0 0 0.0180 0.0180 0.005 0.1451 0.1453 0.01 0.1995 0.1999 0.02 0.2654 0.2666 0.03 0.3037 0.3062 0.04 0.3264 0.3310 0.05 0.3407 0.3485 0.06 0.3511 0.3629 0.07 0.3594 0.3759 0.08 0.3665 0.3882 0.09 0.3727 0.3999 0.1 0.3784 0.4114 0.12 0.3882 0.4337 0.15 0.4003 0.4661 0.2 0.4163 0.5186 0.25 0.4286 0.5701 0.3 0.4385 0.6210 0.4 0.4532 0.7221 0.5 0.4636 0.8227 0.6 0.4710 0.9230 0.7 -0.4766 1.0231 0.8 0.4808 1.1232 1.0 0.4865 1.3232 1.2 0.4901 1.5233 1.4 0.4925 1.7233 1.6 0.4941 1.9233 2.0 0.4961 2.3233 2.2 0.4968 2.5233 2.4 0.4973 2.7233

rical nose is 10.00 mm. Theoretically, the diameter of the blunt nose increases smoothly to an asymptotic value D, with increasing axial distance x. This value was set at 10.00 mm. However, for the manufacture of the blunt nose a minor deviation from the theoretical contour had to be permitted. Thus, the actual con-tour coincides with the theoretical concon-tour over a distance x/D = 0 - 1.6 and next changes smoothly into a circular cylinder with a diameter of 9.88 mm. Further dimensions of the-models are given in Figure 3.

Extreme care has to be exercised in manufacturing models for cavitation studies. An accurate similarity of the model contour is essential, but a smooth surface is even more critical. The drastic effects of surface roughness, in particular isolated irregularities, on cavitation inception have been demonstrated by Holl /42/ and Arndt and Ippen /43/. In a study on the influ-ence of polymers on cavitation inception /39/ some of the measure-ments were strongly affected by isolated irregularities on the stainless steel models. The present models were made by Instru-mentum T.N.O. in Delft. The models, made of stainless steel, were inspected by an optical comparator (magnification 50x). For the hemispherical nose, the maximum deviation from the true con-tour is within 5 pm. For the blunt nose, the maximum deviation for x/D <0.3 is within a few microns and for x/D > 0.3 within 10 pm. The mean surface roughness height for both models is 0.05 pm.

3.3. Turbulent-flow rheometer and surface-tensionmeter.

To measure the influence of polymer additives on the fric-tion factor and the surface tension of the solufric-tions, a turbulent-flow rheometer and a surface-tensionmeter have been used. The rheometer shows a close resemblance to the one first described by Hoyt /44/. A schematic diagram is shown in Figure 4. A fluid sample with a volume of 184 cc is stored in the cylinder. When

the piston moves upwards, the fluid is forced through the test

pipe. The test pipe has a length of 800 mm and an inner diameter of 2 mm, the entrance being well rounded off. The pressure dif-ference across the test pipe is measured by which the friction factor follows. With this rheometer, an extensive test program

1O 09.88

cn co

HEMISPHERICAL NOSE BLUNT NOSE

Figure 3. Cross section of axisymmetric test models (dimensions

in. mm).

has been carried out 145/ to measure the friction reduction and degradation properties of guar gum, CMC, Separan NP-10 and Polyox WSR-301.

Surface tension measurements were made at the Chemistry Department of the Agricultural University in Wageningen. The instrument used is the Dognon-Abribat surface-tensionmeter. Its principle is as follows. A thin platinum plate with length L is partly dipped into the liquid, as illustrated in Figure 5. The liquid creates a. meniscus on both sides of the plate and pulls

Figure:A. Sohematic diagram of turbulent-flocheometer.',

'o.rithe,:iplate with a force K which equals the product of the

sur=

face-t&iiiOn,,S and the total wetted length Thus.,-

for iero

con-tact angle;'Whave

,

Other .Methods to measure the surface tension are given in ,Adamson's'book /46/. FILIJNG CUP

0

U.

CYLINDER PISTON MEMBRANE ELECTRO-MAGNETIC

MONCLUTCH AND :BRAKE

PRECiSION' MANOMETERS ROTARY -CURRENT 1/3,HP MOTOR TEST PIPE AinauAit' FILL' NG PIPE , DRAIN 'COCK

-0

-;2

5C

1111

21

gRIARO GEA BOX

Figure 5. Schematic diagram of surface-tensionmeter.

3.4. Holographic method.

In the present work, holography has been used for studying cavitation and flow phenomena about the test models. The method consists of making photographic records containing detailed in-formation on the cavitation and flow patterns.

Holography has become one of the most important areas of modern optics since the invention of the laser as a new light

source. Holography is usually described as a method for storing wavefronts in a record from which the wavefronts may later be reconstructed. The record, formed in photo-sensitive material, is called a hologram. In forming holograms two sets of waves are involved, the reference wave (usually a simple plane wave) and the subject wave (usually a rather complicated set of waves

is-suing from the scene). The hologram is the photographic record of the interference pattern generated by these two sets of waves. Let us consider how a simple hologram, that of a point source of

light, is created when the light source is placed in front of a photographic plate and the plate is also illuminated by a beam of laser light. The plane reference waves will interfere with the

spherical waves issuing from the point source. The photographic record will show a pattern of circular interference fringes. This record is almost identical to an optical device known as a zone

plate, a set of concentric annular rings which cause wave energy to be diffracted. The open spaces of a zone plate permit passage of that energy which will add constructively at a desired focal point, and the opaque rings prevent passage of energy which would interfere destructively at the point (see Ref. /47/). The holo-gram is the recording of the interference pattern in a sensitive material, where the darkening of a unit volume of photo-graphic emulsion is a function of the energy absorbed by that volume. When the plate is developed, and the hologram is illumi-nated by a beam of laser light, the diffraction process causes converging and diverging waves to be produced, creating a real and virtual image of the original point source. Since any scene can be looked upon as being made up of many individual sources of light, the hologram of an actual scene will, when illuminated, generate a real and virtual Image of the original scene. The real image can then be studied or photographed through a microscope.

A schematic diagram of the optical system used for making the holograms is shown in Figure 6. The light source is the Korad K-1QH pulsed ruby laser of the Institute of Applied Physics TNO-TH. A pulsed ruby laser instead of a continuous-wave laser was used because of its short-duration pulses having a high intensity. Originally /4/, the wave length of the red light emitted was 0.694 pm. However, to improve the quality of the holograms, a KDP (Potassium dihydrogen phosphate)-crystal was used, by which under phase-matched conditions the frequency of the light was doubled (second harmonic) and, consequently, the wavelength was reduced to 0.347 pm (ultraviolet light). The pulse duration is 25 nanoseconds. The laser beam is focussed on the KDP-crystal by the lens Ll. Next, the beam is enlarged to a parallel beam with a diameter of 30 mm by the lenses L2 and L3. A mirror

re-flects the beam into the test section of the tunnel. In the walls of the plexiglass test section, two highly polished glass windows with a diameter of 30 mm have been inserted. The location of the models in the test section is such that the nose of one of the models is illuminated with the laser beam over a length of about

20 mm, and its contour is imaged on the hologram. Also imaged are bubbles or cavities on the model contour and bubbles or particles in the fluid flow between the windows. The laser beam not being disturbed by the object, acts as a reference beam. This

PULSED RUBY LASER '

6.ngoamiL

\\\9 MEW

N

Irrr

UV-FILTER K DP -CRYSTAL GLASS WI NDOW TUNNEL WALLS GLASS WINDOW SHUTTER

Figure 6. Schematic diagram of optical system for making holograms: of cavitation or flow phenomena in test section of

tunnel.

method of holography is called "in-line" holography. A shutter is placed on the first window. The camera containing the holographic plate is located close to the second window. The emulsion used for hologram recording consists of extremely fine grains of sil-ver halide (diameter <0.1 um). The emulsion is coated on a glass plate. Miring the development process the exposed silver halide grains are converted to metallic. silver. For the present study, Agfa-Gevaert Scientia plates 8E56 and 8E75 were used, Which are specified to have a high resolution (3000 lines/mm).

When Observing small objects such as particles or bubbles, the distance between the object and the holographic plate Should be made as small as possible. Otherwise, a large part of the diffracted light is not recorded on the hologram and the object cannot be reconstructed. The distance may be expressed by the

z=

optical path z, equivalent to that in air. We find

- zwater zglass

z

nwater nglass + zair

(3.2 )

where n is the index of refraction. For the optical path between the centre of the test section and the holographic plate we have

+ 9.2 = 34.6 mm.

The ruby laser could be used as a multiple switched laser. Two or three pulses with pulse separations of 50 or 100 psec could be generated. This enabled multiple imaging of moving objects (particles or cavities) on one and the same hologram. The quality of such holograms depends very much upon the relative energies of the pulses. For that reason, the energy output of the pulses was visualized on an oscilloscope. At first, the re-peatability of the relative energies was rather poor. A

con-siderable improvement was obtained by replacing the flashlamp by a new one. Some recent applications of multiple exposure

holo-graphy are presented by Trolinger /48/. A photograph of the experimental set-up, showing the high speed tunnel and the holo-graphic equipment, is given in Plate 1. Further details of the holographic system used are given by Sies-Oosterveld and Van Renesse /49/.

Reconstruction of the holograms was made with a continuous-wave He-Ne gas laser (A = 0.633 pm) since this laser was readily available and since a continuous-wave laser is a necessity for a visual study of holograms. It should be noted that all distances

in the reconstruction, parallel to the laser beam, are reduced with respect to the corresponding distances of the original

ob-ject, due to the higher wave length of the He-Ne laser. A sche-matic diagram of the

reconstruction

set-up is given in Figure 7. A photograph is given in Plate 2. The diameter of the laser beam

is enlarged by the lenses Li and L2. The intensity of the light iecontrolled by a polaroid filter. The hologram is placed on a stage, fitted with guides so that the hologram can be moved in two orthogonal directions. The movement of the stage is measured on vernier scales. The reconstructed image is studied with a

25 10

L2

STAGE WITH

HOLOGRAM

Figure 7. Schematic diagram of reconstruction set-up.

microscope. The magnification of the ocular is 10x; for the magni-fication of the objective a choice can be made between 4x, 10x and 20x.

The history of the application of holography for studying cavitation phenomena is a very short one. The first efforts were aimed at the measurement of bubble or nuclei spectra in flowing liquids /50, 51, 52/. The lower limit Of the size of the nuclei, imposed by the holographic method, was found to be about 5 pm. A recent evaluation of three optical methods (holography, light

scattering and microscope) to measure nuclei spectra is given by Peterson, Danel, Keller and Lecoffre /53/. A holographic study of bubble fields, generated by acoustic waves, was made by Bader /54/. He used the "off-axis" method of holography. He also made double exposure holograms where the angle between the reference beam and the subject beam was switched from -300 to +200 during the short time lag between the two

exposures.

The first applica-tion of holography for studying hydrodynamically produced cavita-tion is given by Van der Meulen and Oosterveld /4/. They compared cavitation inception phenomena on a hemispherical nose with those reported earlier by Arakeri /55/.

The main advantages of the holographic method for the ob-servation of cavitation phenomena are (1) the extremely short duration of the ruby laser pulses and (2) the possibility to store detailed three-dimensional information on the object. The first item permits high flow speeds in the system, the second

item permits detailed analysis of the reconstructed image by microscopy. In the next section it will be shown how holography

can be used to visualize boundary layer flow phenomena in liquids.

MICROSCOPE

He- Ne GAS vPOLAROID FILTER

3.5. Flow visualization techniques.

A new technique had to be developed for the purpose of flow visualization or, more specifically, for the purpose of boundary layer flow visualization. Acosta /2/ recognized the importance of a thorough knowledge of the boundary layer flow about bodies on which cavitation takes place. The justification of this thought can be found in the results of an earlier study carried out by Arakeri and Acosta /3/. They employed the schlieren method of flow visualization and were able to correlate cavitation incep-tion on a hemispherical nose with the occurrence of laminar flow separation, a phenomenon not known until then.

In the present study, the original idea was to visualize the boundary layer flow about the models by injecting a sus-pension of small particles from a hole located at the stagnation point of the models. Single- or multiple-exposed holograms should provide information on the type of boundary layer flow or on

transition or separation. An important condition was that the particles should be large enough to be detected in the holograms

and small enough to essentially follow the streamlines. The only particles commercially available in a specified

concentra-tion are those delivered by Dow Chemical Company. Unfortunately, the number of sizes available in the range of interest is rather limited. The best choice seemed styrene divinyl-benzene copolymer latex particles having a nominal diameter of 5.7 pm with a medium standard deviation of 1.5 pm. The density of this material is 1.05 g/cc. The particles are suspended in water; the solid con-centration is 10 percent (9.87 x 108 particles/cc). It was ex-pected that these particles could just be detected in the holo-grams.

To investigate the effectiveness of this method, initial tests were made with the hemispherical nose. A diluted suspen-sion (solid concentration 0.2 percent) was injected by using one pump head of the Hughes Centurion-100 plunger pump. The motion of the plunger activated a relay with an adjustable time delay, by which the shutter was opened and, subsequently, the ruby laser triggered. The mean injection rate during the delivery stroke of the plunger was such that the corresponding displacement thick-ness 6.* at the location of the cylindrical shaft of the model

was between 2.6 and 4.4 pm. The velocity in the test section was 6 or 10 m/s. Several holograms were made and the

reconstructions

carefully examined but no particles could be detected. The next step was to verify that the laser pulse was correctly synchro-nized with the instant of maximum injection rate. The time delay was varied in such a way that a complete cycle of the plunger pump was passed through. Twelve holograms were made and examined but only a few isolated particles were detected. Further attempts proved to be unsuccessful and the final conclusion was that the particle size was just below the resolution of the optical system. Thus, larger-sized particles had to be used and the next diameter

size available was 25.7 pm with a medium standard deviation of 5.8 pm. Detection of these particles should not be a problem, but other problems arise. First, for the same solid concentration,

the number of particles in a unit volume is considerably lower (1.07 x 107 particles/cc). Second, upon

standing

the particles will settle in a rather short time (rate of fall about 1 mm per minute. Third, the size of the particles relative to a

charac-teristic length in the boundary layer is such that the particle trajectories may deviate from the streamlines. To meet some of the difficulties, another injection method was applied. It simply consisted of using a hypodermic syringe, operated by hand. The capacity of the glass cylinder was 10 cc. However, after a few attempts this method had to be abandoned since the particles became trapped between the plunger and the cylinder and thus prevented smooth operation. In the final arrangement, the

sus-pension

was stored in a vertical glass tube and through a valve connected to the horizontal

injection

line in the tunnel. By

lowering the tunnel pressure slightly below one atmosphere and by opening the valve, the suspension was sucked into the

tunnel.

This method worked satisfactorily, but the holograms made seemed rather inadequate to correctly interpret boundary layer phenomena

(see section 4,2.1.).

During the investigation to visualize the flow by particle injection, it was realized that in earlier cavitation experiments where water or polymer was injected with a plunger pump, a

pul-sating injection region on the nose of the models could be seen when watched through a

magnifying

glass. The explanation of this

different index of refraction from the fluid in the tunnel. This was either caused by a slightly different temperature or by the polymer additives. Based on these observations, a new method was developed to visualize the boundary layer flow.

The first step was to inject heated water with the hypoder-mic syringe. The temperature difference between the fluid in the cylinder and in the tunnel was about 240 C. However, in the injection line the fluid temperature will decrease rapidly and the final temperature difference between the injected fluid and the fluid in the tunnel will be much lower. The amount of water injected was such that the corresponding displacement thickness

i* at the location of the cylindrical shaft of the model was about 4.5 pm, Four holograms were made at tunnel velocities of 5 or 6 m/s. The quality of the holograms was such that the occurrence of laminar flow separation could just be detected

(see section 4.2.1.). The next step was to inject a solution of sodium chloride. Initially, a concentration of 5 percent NaC1 was used. The injection rate was such that di* was about 4 pm. Four holograms were made at tunnel velocities of 5 or 10 m/s. The quality of these holograms was much better than in the previous case. Next, the sodium chloride concentration was reduced to 2 percent. A final series of holograms was made at a tunnel velo-city of 5 m/s. In this case the injection rate was somewhat lower. Detailed pictures of laminar flow separation and subse-quent transition to turbulence were obtained (see section 4.2.1.).

The method of flow visualization by the injection of heated water or an aqueous solution of sodium chloride is based on arti-ficially changing the index of refraction of a small isolated volume in the flow. The velocity of light c is related to the index of refraction n by the equation

where

co is the velocity of light in vacuum. If there is a gra-dient of index of refraction normal to the light rays, the rays will be deflected since, according to Eq. (3.3 ), the light travels more slowly when the index of refraction is larger. The deflection of the light rays is recorded in the hologram, and

a) 35 -7 0 50

4540 -25 20 1.5 Index of Refraction. n

Figure S. Index' of refraction of- Water as a function of the teff- -Perature and 'ãS. a function Of the concentration of sodium Chloride...

upon reconstruction the isolated, volume with a different index, of refraction can be detected.-Thd.temPeratUre effect on the index. of refraction. of water is given

in

Figure 8. In the same figure

the index of efraction for an aqueous solution of todiUm.Chiokide is plotted, against its doncentratiob /56/.

E.

CHAPTER IV

EXPERIMENTAL PROCEDURE AND RESULTS

4.1. Procedure.

The tests carried out in the high speed water tunnel can be divided into three categories: flow visualization tests,

cavitation tests and cavitation inception measurements. Essen-tially, the flow visualization and cavitation tests consisted of making holograms at prescribed conditions. Prior to each

series of tests the model was cleaned and the tunnel refilled. To adjust the air content, the water was passed through the deaeration circuit for a period of 11/2 h at a constant pressure

in the deaeration tank. During all test runs the air content a was held fixed at a value of about 5 am3/1 (1 cm3 of air per liter of water at S.T.P. corresponds to 1.325 ppm by weight). For each test the temperature of the tunnel water was measured and its value was used to compute the dynamic viscosity and the vapour pressure. The average value of the water temperature was 20°C. The flow visualization tests covered a velocity range of 4 to 20 m/s. To visualize the boundary layer flow, a 2 percent NaCl solution was injected with the hypodermic syringe. The injection

--rate was such that di was between 2 and 4 um. For the cavitation tests, the velocity ranged from 10 to 20 m/s. Polymer injection was provided by the Hughes Centurion-100 pump unit. The holograms were made at the instant of maximum injection rate. The injection rate was such that the average value of di2 was 2.6 um. For the cavitation inception measurements, the velocity ranged from 10 to 24 m/s. Inception (or desinence) was observed visually.

4.2. Flow visualization studies.

4.2.1. Newtonian flow.

Plate 3 shows a photograph of the holographic reconstruction of injected particles in the boundary layer of the hemispherical

92°

.0

A co A o o 8

0 2 percent NaCI injection

5 percent NaCl injection

A heated water injection

vo

/ inflexion point

Figure 10. Observed shapes of laminar separation bubble on hemi-spherical nose (schematically) and definitions- of length and maximum height of bubble.

0.3 0.4 0.5 0.6 0.7 0.8 1.0 1.5 20

Reynolds Number x 10-5

Figure 9. Boundary layer separation angle, Ys, as a function of Reynolds number for hemispherical nose.

A maximum 71188° 4 0

I

)34° I. if >6 3 80° 0 co 76°

0.35 0.30 0.25 to 0.20 "6 % 005 -J

30

a a 0 2 percent Na CL injection 0 5 percent Na Cl injection

6 heated water injection

0.3 0.4 0.5 0.6 0.7 0.8 1.0 1.5 2.0 Reynolds Number x 10-5

Figure 11. Length of separated bubble to diameter, L/D, as a function of Reynolds nuMber for hemispherical nose.

nose.. The nominal diameter of the particles is 25.7 um. The flow is from left to right. The Reynolds, number is 0.50 x 105 (Vo = 4.86 m/s). In Plate 4 the flow is visualized by the injection of heated water. It shows the laminar boundary layer separation

bubble

on the hemispherical nose at a-Reynolds number of 0..45 x 105 (Vo'= 5.0 m/s). In Plate 5 the flow is visualized by the in-jection of a 2 percent sodium chloride solution. It shows the laminar boundary layer separation bubble and the subsequent

z

,

Plate I. Overall view of high speed cavitation tunnel with holographic equipment.

YF 90°

- - - . . - . . , _

Plate 3. Photograph of holographic teconstrudtion-shoWirig:injeCted particles '01On-final .diameter. ., , .. . , _ .

25.7 fan) in boundary layer flow aboUt hemispherical nose. ThelloW is fica left:to fight

Re =0.50 x 105 (V. = 4:86 m/s).

. "

trnm.

.y=90°

--Plate 4. Photograph of holographic reconstruction showing laminar separation bubble on hemis. pherical nose. The flow is visualized by the injection of heated Water: The flo-WiS. from left to

right Re =045 x 105 (V.

5.0 m/s).

r

Plate 5. Photograph of holographic reconstruction showing larhinar sepaiation-:blibble:and. sub-sequent transition to turbulence on hemispherical nose. The flow is visualiied-.:by:the.

in-jection of a 2 percent NaC1 solution. The flow is from left to right. Re. =.-0:465 x .105

(V. = 5.07 m/s).

-Plate 6. Photograph of holographic reconstruction showing:.outflow -of heated water at nose Of hemispherical model. Se" = 4.4 gm. Re = 4.5 x 105.(V0, = 5.0 in/s).

.1mrn

Plate 7. Photograph of holographic reconstruction showing outflow of a 2 percent:NaC1 500-.

Plmn Polyoz WSR-301 solution at nose of hemispherical model. Si* --- 3.1 gm: Re = 0.54 x 105 (V. = 6.0 m/s).

y=so° Plate 8. Photographs of h sequent transition

Re = 0.55 x

Re = 0.75 x

Re = 0.91 x

Re = 1.12 x

Re = 1.35 x

--TirrAr e7e', ' ,,, c 0.-**Tt' '4-rWE, r" _

olographic reconstructions showing laminar separation bubble and sub-to turbulence on hemispherical nose. The flow is from left sub-to right.

105 (V. = 6.0 m/s); 105 (V. = 8.1 m/s); 105 (V. = 9.95 m/s); 105 (V. = 12.1 m/s); 105 (V. = 14.5 m/s). (d) 44. t ' w w 410 fr

,

I Y

= 90°

"r"

-- irnm

Plate 9. Photograph of holographic reconstruction showing laminar separation bubble

and subsequent transition to turbulence on

hemis-pherical nose. The flow is visualized by the injection of a 2 percent NaCI solution. The flow

is from left to right. At the position of

separa-tion the interference pattern shows a "V". Re = 0.36 x 10 (V. = 4.0 m/s).

1)0=90°

Plate 10. Photograph of holographic reconstruction showing boundary layer flow about

hemispherical nose. Injection of a 2 percent NaCI +

- Ahlik401r411--14.1010{ 444 :;4, 4614,13,, .".j"t;" t

;

' ..s.a.r...04.4,..47,,r otat, All4 r.

r-41,.-,et ..+' , . e p,..*t4ik, A , !At Attet#1,t: ' 41=4, - 44 $'Q

-Plate 13. Photograph of holographic reconstruction showing development of 'boundary layerflow along nose and cylindrical part of

hemis-pherical. model. Injection of a 2,percent Naa, +.500 ppm Polyox WSR-301 solution. The flow is from left to right. Re = 0.37 x 10' (Vo

D =1.68 e-1 . .-S,, 'T ''' ' . ' 14"041/4? X° ill' ,,!' - ._ ° '14-;,* - -._,AL s t' I 't f l ' ,

plate 14. Photograph of holographic reconstruction showing transition frorn laminar to turbulent boundary layer flow oii bhint'nosC(S'1-/fY =

1.68). The flow is visualized by the injeetion of a 2 percent NaC1 solution. The flow is from left to right. Ile = OA) x 105(V. = 7.95

Plate 15.:" Photograph of holographic reconstruction showing trans tion feorklaM'inai

0.74 5).',Injection,of:a".2,percent NaCIK-14 500-;ppin-POlyois. vystz;'301 solution The flow is froin'leftiO right. Re

-31

;3.

5m m

( e )

Y=90°

Plate 16. Photographs of holographic reconstructions showing progressive development of cavita-tion on hemispherical noSe. The flow is from left to right.

c = 0.604, Re = 1.25 x .405 (V. = 13.1 m/s); o- = 0.593, Re = 1.25 x 10' (V. = 13.1 rn/s);

.0.559, Re = 1.27 x lO (V. = 13.2 m/s);

o- -= 0.469, Re = 1.26 x 10'(V=13.2 m/s);

= 0.387, Re = 1.27 x 10' (V. = 13.2 rn/s).

-t ^ (b) ( a) (d) 5mm _,fy.go°, I lmm.

Plate 17. Photographs of holographic reconstructions showing progressive development of cavita-tion on hemispherical nose, when a 500 ppm Polyox WSR-301 solucavita-tion is injected. Details of the cavity noses are given in insets. The flow is from left to right:

a = 0.405, Re = 1.20 x 105 (V. = 12.9 m/s);

a= 0.374, Re = 121 x 105 (V.

12.9 m/s);

a= 0.338, Re = 1.22 x 105 (V. = 12.9 m/s); a = 0.313, Re = 1.21 x 105 (V. = 12.8 m/s).

- from left to right.

a = 0.332, Re = 1.23 x 105 (V. = 12.9 ii/s); cr = 0.281, Re = 1.22 x 105 (V. = 12.8 m/s).

r6.

Plate 19. Photographs of holographic reconstructions showing cavitation on blunt nose, when a

500 ppm Polyox WSR-301 solution is injected. The flow is from left to right.

a = 0.284, Re = 1.21 x 105 (V. = 12.8 m/s); a = 0.296, Re = 1.41 x 105 (V. = 13.1 m/s); o = 0.284, Re = 1.35 x 105 (V. = 12.9 m/s).

'0x/0.014-3

'f:4; "

_

4

trarti

"

, r .24

.-- '- .

Plate 20. Photograph of reconstruction of multiple exposure hologram showing three stages of cavity growth near nose of blunt model. The time separation Ati = 50 /am and At2

--100 Azsec. Theflow isfrom right to left.

a = 0.314, Re = 0.925 x 105 (V. = 10.0 m/s).

r.

x/ID =0.543 mm

Plate 21. Photograph of reconstruction of multiple exposure hologram showing three stages of travelling bubble along blunt nose. The time separation Ati = 50 psec and At2 = 100

psec. The flow is from left to right.

= 0.314, Re = 0.925 x 105 (V. = 10.0 m/s).

Cavity

Plate 22. Photograph of holographic reconstruction showing bubble cavitation on hemispherical

nose. Theflow isvisualized by the injection of a 4 percent NaC1 solution. The approximate

shape of the cavity is indicated on the lower figure Theflow isfrom right to left.

0.035-Q030 0 0 .025 I. a 2. Q020 0 a .o 0.015 a a m Q010 .-o cs

Q00 percent Naa injection

5 percent NaCl injection

A _{heated water injection}

03 0.4 05 0.6 0.7 0.8 1.0 1.5 20

Reynolds Number x10-5

Figure 12. Height of separated bubble to diameter, HID, as a function of Reynolds number for hemispherical nose.

transition to turbulence on :the hemispherical nose. The Reynolds number is 0.465 g 105 (V = 5.07 m/s). The position of separation is marked by "S".. For the hemispherical model, the outflow from the nose of the model took place quite symmetrically. This is illustrated

by

the photographs presented in Plates 6 and. 7, where heated water and water containing 2 percent NaC1 and 500 ppm Polyox WSR7301 are injected respectively. Plate 8 provides a sequence of photographs showing the laminar boundary layer sepa-ration bubble, and subsequent transition to turbulence on the

0 03 12 0 74 -1 CE 41 8 .o 2 .13.1 X 0 4 .0 a

00

CN 411) (2) 0 A 9

2 percent NaCI injection 5 percent NaCI injection heated water injection

0.4 0.5 0.6 0.7 0.8 1.0 1.5 20

Reynolds Number x 10-5 Figure 13. Length to height ratio of separated bubble, L/H, as a

function of Reynolds number for hemispherical nose.

hemispherical nose for a series of Reynolds numbers. The flow is visualized by the injection of a 2: percent IslaC1 solution. Another example of the detailed flow pattern on the hemispherical nose, obtained by the injection of a 2 percent NaC1 solution, is presen-ted in Plate 9. The Reynolds number is 0.36 .x 10.5 (Vo = 4.0 m/s).

In analyzing the holograms, it was easy to find the position of separation. At this location the interference pattern showed a distinct "V", as indicated on Plate 9. The position of separation for the hemispherical nose is given in Figure 9. In this figure

the angular position of laminar boundary layer flow separation, is plotted against the Reynolds number. It should be noted that each hologram provides information on the upper and lower side of the body and thus, in general, two data points are ob-tained from each hologram. The determination of the length and the maximum height of the laminar separation bubble from the holo-grams was somewhat more complicated. This is due to the fact that the height of the bubble may show a maximum, as illustrated by case A in Figure 10, or that the outer flow line shows an inflexion point, as illustrated by case: B in Figure 10. The interpretations, used in this study, of the length L and the maximum height H of

2.4

0 2 percent NaCL injection

2 percent NaCl +500ppm Polyox WSR-301 injection

.o

03 0.4 0.5 0.6 0.7 0.8 1.0

Reynolds Number x 10-5

Figure 14- Streamwise distance to boundary layer transition over diameter, sT/D, as a, function of Reynolds number for blunt nose. The open data points refer to

flow

visua-lization by the injection of a 2 percent NaC1 solution. The solid data points refer to the injection of a 2 percent NaC1 500 ppm Polyox WSR-301 solution.

the bubble are indicated. The results are given in Figures 11 and 12- Results of the length to height ratio of the separated bub-ble are given in Figure 13.

A series of holograms was made where the boundary layer flow on the blunt nose was visualized by the injection of a 2 percent NaC1 solution. For this model, the outflow from the nose of the model was not always symmetrical and in some cases even quite irregular. Laminar flow separation did not occur. Howevei-,

transition from laminar to turbulent boundary layer flow 'could be

located. Plate 14 shows an example of transition to turbulence on the blunt nose. The streamwise distance to transition over the diameter of the Model, ST/D, is 1.68, where is measured from the stagnation point. The Reynolds number is 0.81 x 105 (V0 =, 7.95 m/s). A plot of the transition data for the blunt nose is given in Figure 14. In some cases it was difficult to locate the precise position of transition from the holograms, but an upper or lower bound could still be found. In Figure 14 these data points are marked with an arrow. When the arrow is pointing up-ward the data point Is considered to be the lower bound;_ when

the arrow is pointing downward the data point is considered to be the upper bound.

4.2.2 Non-Newtonian flow.

The influence of polymer additives on the boundary layer flow about the models was investigated by the injection of a 500 ppm (parts per million by weight) Polyok WSR-301 solution from the nose of the models. The injection was made with the hypoder-mic syringe. To visualize the flow, sodium chloride was added to the solution. Polyox WSR-301 (manufactured by Union Carbide) is one of the grades of poly (ethylene oxide) which have a molecular weight of several millions. Each molecule of poly (ethylene oxide) consists of a long chain of carbon and oxygen atoms.

joined by primary valence bonds; to each carbon atom two hydrogen atoms are attached. Poly (ethylene oxide) is designated a linear polymer since there is no cross-linking between parts of the

same chain. The structural unit or mer is

H H

( - C - C - 0 - )n

H H

where n is the number of mers. Individual molecules of poly (ethylene oxide) in water are usually considered to be randomly coiled when at rest. The average diameter of a randomly coiled molecule of Polyox WSR7301 is about 0.5 um. If such a molecule were strung out in a straight line, its length would be approxi-mately 40 pm. Details on the preparation of stock solutions are

0.65 0.55 a a a 0.45 es SA AA a

00

A AA 0 0

00

.00

0.35 80° 82° 84° 86° 88° 90° 92°

Cavitation Separation Angle Xcs

94° 96°

Figure 15. Cavitation separation angle, cs, as a function of cavitation number and Reynolds number for hemispherical nose,

given in Ref. /45/.

Plate 10 shows a photograph of the holographic reconstruction of the boundary layer flow about the hemispherical nose, when

Polyox wSR-301 is injected. The Reynolds number, based on the viscosity of pure water., is 0.37 x 105 (Vo = 4.0 m/s). On this photograph laminar flow separation can not be observed. A similar Photograph is presented in Plate 11. In this case a solution con-sisting of 4 percent NaC1 and 500 ppm Polyox WSR-301 is injected. The Reynolds number is 0.55 x 105 (V0 = 6.1 m/s). Plate 12pro-vides a sequence of photographs showing the characteristics of

the boundary layer flow on the hemispherical nose for a series .of Reynolds numbers, when a solution consisting of 2 percent NaCl

and 500 ppm Polyox WSR-301 is injected. Plate 13 shows a photo-graph of the development of the boundary layer flow along the nose and the cylindrical part of the hemispherical model, when Polyox WSR-301 is injected. The Reynolds number is 0.37 x 105

0.943 x105

Pe= 1.267 x 105

a Re..1.538x105

0.65

b-a55

0

.3,a45

0.35 0 0.05 0.10 0.15 0.20 025 0.30

Length of Sheet Cavity Over Diameter, LsciD

Figure 16. Length of sheet cavity over diameter, 'LSC(D' as a function of cavitation number and .Reynolds number for hemispherical nose..

(V =4.0 mis). The occurrence of laminar- flaw separation

could

mot be, observed, on any-of the: hdlograms where Polyox WSR-301 was injected. It was not possible to precisely locate the position of'boundery-layer transition,

Plate '15 shows a. photograph

of

the' boundary)ayer flow Rout

the blunt nose, when Polyox WSR7301 is injected. The Reynolds number'i 0.83 x 105 (Vo = 8.0 m/s).: From the holographic recon-strUctiOn:the-approximate position of transition

to

turbulence

could be. This position is marked on. the photograph.

The etreamwise distance to transition over the diameter of the modeli'sT/D; is 0.715. Some more data are plotted in Figure 14.

It

should be noted that the values given, are approximate values

onlY.-Re =0.943 x105 Re -1:267x 105 Fie =1.538 x105

0.35

0

Figure 17. Length to height ratio of sheet cavity, LSC /RSC' as a function of cavitation number and Reynolds number for hemispherical nose.

4.3. Cavitation studies.

4.3.1. Newtonian flow.

Plate 16 provides a sequence of photographs showing the pro-gressive development of cavitation on the hemispherical nose by gradually lowering the cavitation number. The mean value of the Reynolds number is 1.26 x 105 (Vo = 13.2 m/s). The flow is from left to right. Bubble cavitation, sheet cavitation and developed cavitation are all shown. Plate 22 shows a photograph of bubble cavitation on the hemispherical nose. The flow is visualized by the injection of a 4 percent NaC1 solution. The flow is from right to left. The Reynolds number is 0.91 x 105 (Vo = 9.95 m/s)

0.65 055 3 0.45 ea 4 0 0 A 0 0 0

00

A 0 Pe-0.843x105 Re=1.267x105 Re=1.538x105 Re=2.030x105 2 4 6 8 10 12 14

Length to Height Ratio of Sheet Cavity. Lsc/Hsc

L 3 0.65

b

0.55 co 3 0'45

38

se Re=0.943xhiD5 Re=t267x10

§e=t538x105

Re =z0304(105 0 0 0.35 0 02 0.4 0.6 0.8 1.0 1.2

Cavity Length over Diameter, Lc/13

1.4

Figure 18. Total length of .cavity over diameter, Lc/D, as a function of cavitation number and Reynolds number for hemispherical nose.

and'the cavitation number a is 0.561. The approximate shape of the cavity is indicated on the same plate..

The main information on the shape and dimensions of the cavities on the hemispherical nose was obtained from holograms taken at the following mean values of the Reynolds number: Re = 0.943. x 105, 1.267 x 105, 1.538 x 105 and 2.03 x 105. It should be noted that "mean value" means that the maximum deviations occurring in one set of measurements are within 1 percent. The cavitation separation angle as a function of the cavitation number is plotted in Figure 15. Values of the length and length over maximum height ratio of the sheet cavities are given in Figures 16 and 17. Values of the total length and total length over maximum height ratio of the cavities are given in Figures

0.65 b 0'55 0 3 0.45 0.350 Pe=0.943x105 Pe.1.267x105 a Re =1.538x105 Pe =2.030 x105

.0

0 0 2 4 6 8 10 12

Length to Height Ratio of Cavity . Lc/Hc

Figure 19. Total length to maximum height ratio of cavity, Lc/Hc, as a function of cavitation number and Reynolds num-ber for hemispherical nose.

Plate 18 shows two photographs of cavitation on the blunt nose. The mean value of the Reynolds number is 1.22 x 105 (170 =

12.85m/s) . The flow is from left to right. The top photograph shows "travelling bubble cavitation". The justification for this definition originates from the photographs presented in Plates 20 and 21. These photographs were taken from one hologram, where three pulses were generated by the ruby laser. The separation between the first and second pulse was 50 psec, the separation between the second and third pulse 100 psec. The Reynolds number is 0.925 x 105 (Vo = 10.0 m/s) and the cavitation number is 0.314. Plate 20 shows the growth of a cavity near the nose of the blunt model. The flow is from right to left. Plate 21 shows a travelling bubble further downstream on the blunt model. The flow is from left to right.

0.2 0 To. 0.3 6 6 aa a a 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 16

Streamwise Distance to Cavitation Separation

over Diameter. sciD

Figure 20. Streamwise distance to cavitation separation over dia-meter, s /D, as a function of cavitation number and Reynolds number for blunt nose. Also plotted are some data points Where no cavitation was observed on one or both sides of the model.

The main information on the shape and dimensions- of the cavi-ties on the blunt nose was obtained from holograms taken at the following mean values of the Reynolds number: Re = 0.942 x 105, 1.225 x 105, 1.555 x 105 and 2.08 x 105. The streamwise distance to cavitation separation over the diameter of the model, sc/D, as a function of the cavitation number is plotted in Figure 20. Also plotted are data points where no cavitation was observed on one or both sides of the model in the- hologram. Values of the total length and maximum height of the first cavities along the model contour are given in Figures 21 and 22.

0.5 -4=0.942 x105 Fte.1.225 x105 e=1.555 x105 Re=2080 x105 a.;

0.5 0.4 0.3 451-0.2 0 02 0.4 0.6 0.6 1.0 1.2 1.4

Cavity Length over

Diameter. Lc/13

1.6 1.8

Figure 21. Total length of first cavity along model contour over diameter, L /D, as a function of cavitation number and Reynolds number for blunt nose.

4.3.2. Non-Newtonian flow.

Plate 17 provides a sequence of photographs showing the progressive development of cavitation on the hemispherical nose, when a 500 ppm Polyox WSR-301 solution is injected. The mean value of the Reynolds number is 1.21 x 105 (T70 = 12.85 m/s). The flow is from left to right. Details of the cavity noses are given in insets. The main information on the shape and dimensions of the cavities on the hemispherical nose, when Polyox WSR-301 was injected, was obtained from holograms taken at the following mean values of the Reynolds number: Re = 1.209 x 105, 1.518 x 105 and

ae. 0.942 x105

Fte. 1.225x105

A B..e.1.555x105