proyecto

CRACOW UNIVERSITY OF TECHNOLOGY

Faculty of Mechanical Engineering

Institute of Thermal and Process Engineering

ERASMUS PROGRAMME

MASTER OF SCIENCE

Vctor Gimnez Bravo

ACCOUSTIC EFFECTS OF CAVITATION AND DEGRADATION OF

POLYMERS

Supervisor:

PhD Eng. Konrad Nering

Cracow, acad.. year: 2014/2015

v

ABSTRACT

The following project explores the possibility of detecting cavitation in water in

certain installations using a simple microphone. This task is generally targeted to a

hydrophone. Hydrophones are expensive devices that require specific installation

settings. Therefore, being able to identify and measure this phenomenon through a

commercial microphone, which does not constitute a big investment and is easy to

install, can make a great difference.

As a second objective, the project will show the cavitation spectrum and will

also study the influence of degradation of a polymer solution in this spectrum. This

polymer will be PEO (polyethylene oxide) diluted in water. The aim of this research is

to detect degradation in future solutions and quantify the amount of this degradation

and the duration of it, again just by a simple noise test.

vii

CONTENTS

Abstract ............................................................................................................................ v

List of figures ................................................................................................................... ix

List of tables .................................................................................................................... xi

Nomenclature ................................................................................................................. xii

1. Introduction ............................................................................................................... 1

2. Theoretical background ............................................................................................. 2

2.1 Cavitation ........................................................................................................... 2

2.2 Types of cavitation ............................................................................................. 4

2.2.1. Cavitation through a Venturi tube ............................................................. 5

2.3 Cavitation damage ............................................................................................. 6

2.4 Fluids involved. .................................................................................................. 7

2.4.1. Newtonian fluids ......................................................................................... 7

2.4.2. Non-Newtonian fluids ................................................................................. 7

2.5 Noise ................................................................................................................... 9

2.5.1. The Rayleigh-Plesset equation ................................................................... 9

2.5.2. Sound pressure .......................................................................................... 13

2.5.3. Measuring devices ..................................................................................... 17

3. Setup and equipment .............................................................................................. 19

3.1 Installation ....................................................................................................... 19

3.2 Microphone ....................................................................................................... 21

3.3 Software ............................................................................................................ 21

4. Procedure and measurements ................................................................................. 23

4.1 First test: Clean water under cavitation ......................................................... 23

4.2 Second test: Aqueous solution of peo under cavitation ................................... 30

5. Results ..................................................................................................................... 33

5.1 Results for water .............................................................................................. 33

5.2 Results for aqueous solution of Peo ................................................................. 36

viii

5.2.1 50 ppm of Peo ............................................................................................ 37

5.2.2 100 ppm of Peo .......................................................................................... 39

6. Analysis and Conclusions........................................................................................ 41

7. Appendix I: Technical specifications ....................................................................... 44

7.1 Microphone ....................................................................................................... 44

7.2 Pump ................................................................................................................ 45

8. Bibliography ............................................................................................................ 49

ix

LIST OF FIGURES Figure 1.- Cavitation through a Venturi tube ................................................................. 2

Figure 2.- Process of formation and collapse ................................................................... 3

Figure 3. - Micro jet focusing the energy into the surface of the solid ............................ 3

Figure 4.- Cavitating hydrofoil ........................................................................................ 4

Figure 5. - Flow through a Venturi tube .......................................................................... 5

Figure 6. - Two flat plates separated by a layer of fluid ................................................. 7

Figure 7. - Different fluids under shear stress and their behavior ................................. 8

Figure 8. - Results of equation 2 for water at 300K ..................................................... 10

Figure 9. - Individual bubble collapsing ........................................................................ 11

Figure 10. - Individual bubble noise spectrum .............................................................. 12

Figure 11. - Axial flow pump noise spectrum ................................................................ 13

Figure 12. - Sound pressure produced by an individual bubble .................................... 15

Figure 13. - Acoustic spectrum for cavitation in water ................................................. 16

Figure 14. - Section of a usual ceramic transducer ....................................................... 18

Figure 15. Setup sketch............................................................................................... 19

Figure 16. Manometers ............................................................................................... 20

Figure 17. - Isolation of the Venturi tube ...................................................................... 20

Figure 18. - Behringer C-1U .......................................................................................... 21

Figure 19. - Cool Edit Pro screenshot ............................................................................ 22

Figure 20. - First setup for test one ............................................................................... 24

Figure 21. - Full spectrum measured. Frequency of 27 Hz/769 rpm ............................ 26

Figure 22. - Second setup for test one ............................................................................ 26

Figure 23. - Spectrum of noise for 769 rpm ................................................................... 28

Figure 24. - Denoising Process for 769 rpm ................................................................... 28

Figure 25. - Noise reduction menu ................................................................................. 29

Figure 26. - Noise spectrum of water for 711 rpm ......................................................... 34

Figure 27. - Noise spectrums of 711 rpm and 1397 rpm ............................................... 35

Figure 28. - Noise full spectra ........................................................................................ 35

Figure 29. - Noise spectra seen from above ................................................................... 36

Figure 30. - comparison between the first minutes of experiment and the last ones for

50 ppm ............................................................................................................................ 37

Figure 31. - Evolution of spectra during the experiment for 50 ppm............................ 38

Figure 32. - full spectra for 50 ppm of solution ............................................................. 38

Figure 33. - comparison between the first minutes of experiment and the last ones for

100 ppm .......................................................................................................................... 39

Figure 34. - Full spectra for 100 ppm of solution .......................................................... 40

Figure 35. - Evolution of noise produced during degradation of polymer ..................... 42

Figure 36. - Comparison of clean water vs solution ...................................................... 42

Figure 37. - Strong degradation zone............................................................................. 43

x

Figure 38. -Frequency response and polar pattern of the microphone ......................... 44

Figure 39. - Technical specifications of the microphone ................................................ 45

Figure 40. - SKA3 Self-Priming Pump ........................................................................... 45

Figure 41. - Head/flow curve of the pump...................................................................... 47

Figure 42. - Power/flow curve of the pump .................................................................... 47

Figure 43. - Efficiency/flow curve of the pump .............................................................. 48

Figure 44. - NPSHr/flow of the pump ............................................................................ 48

xi

LIST OF TABLES Table 1. - Variables and their effect on cavitation .......................................................... 6

Table 2. - Progress of all parameters for the first setup ................................................ 25

Table 3. - Progress of all parameters for the first setup ................................................ 27

Table 4. -First solution, no cavitation. Control parameters .......................................... 31

Table 5. -First solution, cavitation. Control parameters ............................................... 31

Table 6. -Second solution, no cavitation. Control parameters ...................................... 31

Table 7. -Second solution, cavitation. Control parameters ........................................... 32

Table 8. - Cavitation number evolution for water ......................................................... 33

Table 9. - Cavitation number evolution for 50 ppm of Solution .................................... 37

Table 10. - Cavitation number evolution for 100 ppm of Solution ................................ 39

Table 11. - Technical specifications of the pump ........................................................... 46

xii

NOMENCLATURE

Pressure coefficient

Events per second Acoustic energy Non-dimensional impulse

External pressure Bubble pressure Reference pressure Sound pressure Vapor pressure Maximum radius Critical radius Kinematic viscosity of a liquid Resonance frequency

Dynamic viscosity Frequency Area

Efficiency Force Impulse Nuclei concentration Radius Surface tension Volume velocity Density Cavitation number

1 Introduction

1. INTRODUCTION

Cavitation is one of the most common problems in hydraulic installations. Its

effects and behavior are important when designing machines such as pumps and

turbines, and hydraulic circuits. If it is not controlled properly it can produce

substantial damage.

Thus, being able to measure and quantify the amount of cavitation of a certain

installation will allow preventing the appearance of this phenomenon, or at least to

control it and keep it under safe values, where the damage can be negligible.

One of the main characteristics of cavitation is that it produces noise. In many

practical circumstances, the noise is important not only because of the vibration

caused, since it can also advertise the presence of cavitation and, therefore, the

likelihood of damage. Studying this noise and trying to extrapolate results in order to

be able to detect cavitation in future situations can be of great interest. As the project

scope, noise under cavitation is going to be measured and then this noise will be

processed and studied to get some conclusions about the spectrum of frequencies

generated.

The structure followed by the project will be, first of all, to get a brief summary

of all topics treated in it. Then afterwards, a close look will be taken at the installation

under consideration. Subsequently, several measurements of cavitation noise will be

made and they will be analyzed. Finally, the feasibility of the proposition is going to be

checked.

2 Theoretical background

2. THEORETICAL BACKGROUN D

2.1 CAVITATION

The formation of a vapor phase from a liquid phase of a fluid can be achieved

by different ways. The most well-known method is through heat addiction, but it is not

the only one. When this vapor phase is produced by a pressure drop the process is

called cavitation. Its name comes from the word cavity, which is precisely the effect

that causes in surfaces of solid boundaries. These solid boundaries are commonly pipes

(and its fittings), hydrofoils, pumps and propellers. In fact, this phenomenon was first

seen on the surface of a propeller of a British warship in 1893. Nonetheless it was

explained by Lord Rayleigh a few years later.

Cavitation damage is produced by the vapor bubbles. The behavior of these

bubbles and its formation are quite complex, but nowadays they are well understood,

as cavitation has been fully researched and there is a wealth of data on causes and

effects.

The best way to study cavitation is through a glass Venturi tube, where the

cavitating flow1 can be seen and heard as water flows. Most of the experimental data

included in this work will be measured on a workbench that has its own glass Venturi

tube, as will be outlined below. The following picture describes the pressure drop and

the two-phased region produced by the phenomenon.

FIGURE 1.- CAVITATION THROUGH A VENTURI TUBE

This experiment was first exhibited by Osborne Reynolds in 1894. Increasing

velocity produces a pressure drop that eventually makes the water boil, and the first

1 The two-phased flow composed of both liquid and vapor.


small bubbles are formed. These bubbles grow for a while and then collapse. This

cyclic process can occur thousands of times over a very short distance of travel. It is

important to realize that this collapse or implosion is completely different from a burst

of a vapor bubble that can occur on a heating pot. The implosion of a cavitation bubble

releases a large amount of energy, and this is the main difference between these two

ways of boiling water, and why cavitation is so dangerous. This energy can also be

directed in a single direction because of the so called micro jet2.

FIGURE 2.- PROCESS OF FORMATION AND COLLAPSE

As it can be seen in figure 3, the micro jet focuses all the energy against the

surface of the solid. A large number of micro jets are necessary before any significant

damage results.

FIGURE 3. - MICRO JET FOCUSING THE ENERGY INTO THE SURFACE OF THE SOLID

Now there is a basis of the process studied. These implosions and shock waves

produced will generate noise, and this noise will be the sign of the appearance of

cavitation. This sound will be measured in order to be able to detect cavitation and its

harmful effects on hydraulic machines. After measuring and creating spectrums of it,

some common patterns should appear.

2 The re-entrant micro jet forms at the bottom of the bubble, and directs the high amount of

energy per unit of volume concentrated during the formation and grow of the bubble.


Before going into the subject in depth, it will be necessary to study a few topics.

The first subject to be analyzed is cavitation types, and a brief look will be taken at the

main kinds of cavitation, but focusing on the ones more interesting for the research.

2.2 TYPES OF CAVITATION

The kinds of cavitation are usually classified depending on the hydraulic

machine that suffers from it.

Hydrofoils with a sharp leading edge usually suffer from cavitation, and it

begins at this edge. Cavitation will grow as the angle of attack is increased or the

ambient pressure is reduced. If it grows and extends beyond the trailing edge of the

hydrofoil, the flow is called super-cavitating. Cavitation in hydrofoils is a matter of

study for many articles and books, because of its importance in marine engineering.

However, it will not be analyzed in this work.

FIGURE 4.- CAVITATING HYDROFOIL

Another important type of cavitation occurs in marine propellers. There is also

a lot of bibliography about this problem. For instance, Marine Propellers and

Propulsion (Carlton, J. S.) fully defines this topic. Cavitating bubbles appear on each

blade and in the cores of the tip vortices (low pressure zones). There is a similarity of

the cavity on each blade to the one that occurs on the hydrofoil with the sharp leading

edge.

Other machines where cavitation can appear are pumps, turbines, Venturi

tubes. In fact, it also occurs simply because of fluid effects (when a solid body enters


water at high speed, in turbulent shear flows, bubble chambers, etc.).However, the

focus will be on the cavitation that occurs in the installation under study, and it will

be produced through a Venturi tube.

2.2.1. CAVI TATION T HRO UGH A VENT URI TUBE

When studying cavitation in Venturi tubes, it is necessary to describe the

Venturi effect or Bernoullis principle, which is the phenomenon that causes the

pressure change (a sequence of high-low-high pressure). The Venturi effect is similar

to a jet effect, when the area crossed by the flow is decreased, due to conservation of

mass, there is an increase of the velocity and therefore in the kinetic energy that

results in a pressure decrease. The following picture describes this effect, where point

2 is called the throat of the tube. So the high fluid velocity in the throat drops the

pressure of the liquid.

FIGURE 5. - FLOW THROUGH A VENTURI TUBE

As far as is known, cavitation requires a big pressure drop, but it is also

important to note that the damage usually occurs with high pressure differentials.

Therefore the components most subject to damage will be Venturi tubes, pumps and

valves, where the transition of pressure is sudden.


2.3 CAVITATION DAMAGE

There are numerous variables that affect this damage. Some of them are

mechanical factors of the system, while others will be liquid properties. The object of

this work will be to control some of these variables in order to measure the amount of

cavitation the installation is experiencing, and then relate this value to the sound

spectrums of each measurement. After that, it will be possible to tell if cavitation is

happening or not just depending on the presence of noise.

Here there are a few of these variables:

Factors of the system: suction pressure, velocity, temperature, surface roughness.

Liquid properties: vapor pressure, viscosity, density.

And now the effect of these variables on cavitation can be explained, as it can

be seen on the following chart:

Variable Cavitation

Increase suction pressure Reduced3

Increasing velocity Increased

Increased temperature Increased4

Increased surface roughness Increased

Lower vapor pressure Reduced

Higher viscosity Reduced

Higher density Increased TABLE 1. - VARIABLES AND THEIR EFFECT ON CAVITATION

It is important to remark that a reduction in the amount of cavitation does not

necessary have to be for the best of the installation. In fact, it can increase the

cavitation damage. This is produced because the reduction of the amount of cavitation

is usually generated by reducing the formation and growth of bubbles, but it increases

the number of collapses and as a result, the quantity of energy released. There will be

fewer bubbles, but they will be smaller, and therefore the effect of concentrating the

energy into a smaller area will eventually cause more damage.

3 Most of these changes on cavitation can be explained by studying the cavitation number,

which is the most important indicator of the level of cavitation: =2()

2

Where:

is the reference pressure is the vapor pressure is the density of the fluid is the velocity So a higher cavitation number means that cavitation is less likely to happen. 4 An increase of temperature means an increase on vapor pressure.


Some other contributing factors that influence the cavitation damage are the

presence of gases dissolved in the liquid5 and a high ratio between vapor and liquid

specific volume, which increases the volume of the bubble

2.4 FLUIDS INVOLVED .

The main fluid used during the measurements will be distilled water;

nevertheless two additional fluids will be studied, composed of the same water and

different solutions of Polyethylene oxide, which will result in a non-Newtonian fluid.

Non-Newtonian fluids behave differently than Newtonian ones, and this is going to be

explained on the following point.

2.4.1. NEWTONI AN FLUI DS

It is a fluid in which the velocity gradient is directly proportional to the shear

stress. If two flat plates of area A are separated by a layer of fluid of thickness d and

move relative to each other at a velocity , then the rate of shear is /d and the shear

stress is F/A where F is the force applied to each. For a Newtonian fluid:

=

( 1 )

Where is the Newtonian viscosity. Many liquids are Newtonian over a wide

range of temperatures and pressures.

FIGURE 6. - TWO FLAT PLATES SEPARATED BY A LAYER OF FLUID

2.4.2. NON-Newtonian fluids

Some fluids show a different behavior under shear stress; these ones are called

Non-Newtonian fluids. For instance, in some liquids the viscosity increases as the

velocity gradient increases, so the faster the liquid moves, the more viscous it becomes.

Such liquids are called dilatant. Dilatant fluids usually are pastes and suspensions. In

5 When the bubble is formed, the gas occupies part of the bubble volume. Then the vapor inside

condenses almost instantaneously during the collapse, but the gas is unable to go back in

solution as fast, and it acts as a shock absorber.


other cases, not only the velocity gradient, but also the time will have an effect on

viscosity. This is called thixotropy. For these liquids, the faster they move, the less

viscous it becomes. This is what happens to most lubricating oils and nondrip paints.

Another example is the non-Newtonian flow of macromolecules in solution or in

polymer melts. In this case the shearing force F is not parallel to the shear planes and

the linear relationship does not apply. In general, the many types of non-Newtonian

fluid are somewhat complicated and no theory has been developed to accommodate

them fully.

The following figure shows different behaviors for different fluids:

FIGURE 7. - DIFFERENT FLUIDS UNDER SHEAR STRESS AND THEIR BEHAVIOR

2.4.2.1 POLY ETHY LEN E O XI DE

It is a polymeric product which is either a viscous liquid or a wax-like

substance, depending on the degree of polymerization. It is somewhat soluble in water,

and it has no outstanding mechanical properties. The monomeric ethylene oxide is

polymerized in the presence of acidic or alkaline catalyst, such as boron trifluoride, tin

tetrachloride or calcium oxide. The technological applications of polyethylene oxide are

limited by its partial water solubility. It is used almost exclusively as a softener,

textile conditioner, wood protection, water-soluble lubricant, stabilizer for lubricating

oils, emulsifier, additive to cellulose nitrate paints and in the production of plastic

foils.


2.5 NOISE

Cavitation is the most intense source of noise in fluid machinery and

underwater acoustics. Cavitation inception, the development that follows and the

sound emitted by the intense, interactive processes that take place during this

development are extremely complex. A theoretical analysis would be restricted to

isolated spherical bubbles containing varying amounts of non-condensable gas. This

theoretical analysis was, at first, approached from the behavior of this single

cavitation bubble such that the bubble dynamics were considered into a variable

pressure field.

These analyses make up a valuable contribution to the understanding of

cavitation noise, but it remains largely unsolved, given its complexity. For example, if

it is based on measurements of noise radiated by scale models in a water tunnel, a

large number of hydrodynamic and hydroacustic conditions must be accomplished in

order to achieve a good extrapolation. To get this extrapolation it is interesting to

perform several measurements to have full-scale data of the sound, what is called a set

of canonical experiments in the environment in which the machine operates. This is

exactly what it is going to be performed in this work.

Just prior to visible cavitation inception, it has been observed that the

measured noise increase in a narrow frequency range. When the collapse state is

reached, shock waves are produced and they produce in turn noise. This noise is

essentially white noise, covering a frequency band up to around 1 MHz.

2.5.1. THE RAYLEI GH-PLESS ET EQ UATION

Before any discussion of cavitation noise, it is useful to identify the natural

frequency with which individual bubbles will oscillate into a quiescent liquid. This

natural frequency can be obtained from the Rayleigh-Plesset equation. This equation

governs the dynamics of a spherical bubble in an infinite body of liquid.

()()

=

2

2+

3

2(

)

2+

4

+

2

( 2 )

Where () is the pressure within the bubble, assumed to be uniform, () is

the external pressure infinitely far from the bubble, is the density of the

surrounding liquid, assumed constant, R(t) is the radius of the bubble, is the

kinematic viscosity of the surrounding liquid, assumed to be constant and S is the

surface tension of the bubble.


In order to calculate the natural frequency of oscillation of an individual

bubble, R(t) will be substituted for an expression consisting of a constant, , plus a

small sinusoidal perturbation of amplitude, , at a general frequency, . Steady state

oscillations like these ones, need a pressure to be preserved. This pressure will consist

of another constant , plus a sinusoidal perturbation of amplitude , and frequency, .

Obtaining the relation between the linear perturbations, and , from the Rayleigh-

Plesset equation, it is found that the ratio, / , has a maximun at a resonant

frequency, , given by:

= (()

+

)

( 3 )

The results of this equation for bubbles in water at a temperature of 27 C for

various levels of pressure are:

FIGURE 8. - RESULTS OF EQUATION 2 FOR WATER AT 300K

Note that the bubbles below about 0.03 m are damped, and have no resonant

frequency. Even though the nuclei are excited in a highly nonlinear way by the

cavitation, one might expect that the spectrum of the noise should have a wide

maximum at the peak frequency corresponding to the size of the most numerous nuclei

participating in the cavitation, since this frequency would be the resonance frequency.


Typically, this would correspond to the radius of the critical nucleus6. The typical

range of frequencies produced by cavitation is between 10-100 kHz, which is correlated

with a nuclei size between 10-100 m. This problem of predicting noise from cavitation

using the Rayleigh-Plesset equation was first used by Fitzpatrick and Strasberg

(1956); focusing on individual collapses and the spectra that such process would

produce. The noise from an individual cavitation bubble is shown in the figure below.

FIGURE 9. - INDIVIDUAL BUBBLE COLLAPSING

In the figure, it can be seen a large positive peak of pressure, which is of course

the first collapse; however it can also be noted a second collapse after a few

oscillations. The radiated acoustic pressure is related to the second derivative of the

volume of the bubble, V(t).

=

( 4 )

Where l is the distance of the measurement from the center of the bubble. The

pressure peak corresponds to the point where the bubble is close to the minimum size

during the collapse. Then the impulse, I, is defined as the area under the pressure

curve. Afterwards, 1 and 2 are selected to cover the pulse, from = 0.

=

( 5 )

6 This critical nucleus can be obtained from the equation:

~/2( )

Cpmin is the minimum pressure coefficient


Now that the behavior of an individual bubble is familiar, a full spectrum of

this specific perform can be achieved. Besides, it can be assumed that random

cavitation would also follow that same spectrum.

FIGURE 10. - INDIVIDUAL BUBBLE NOISE SPECTRUM

This figure will be of great importance for the research, because it is a very

characteristic frequency pattern from 1 kHz to 50 kHz. The drop about 80 kHz

corresponds the limit of the measuring instrument, in this case a hydrophone, which is

the most used device for measuring noise in water.


For an axial flow pump, the spectrum is shown below.

FIGURE 11. - AXIAL FLOW PUMP NOISE SPECTRUM

In this figure, it can be noted the shaft or blade passage7 frequencies that occur

in the absence of cavitation, but may be amplified or attenuated by cavitation.

2.5.2. SOUN D PR ESS UR E

The level of the sound produced by a cavitating flow is the result of two factors,

namely the impulse I, produced by each event of collapse (equation 5) and the event

rate or number of events per second, , which is somewhat like a density of collapses.

= ( 6 )

The development of cavitation noise can be understood by studying the scaling

of these two components. Nevertheless, it is required an omission of some factors of

proportionality, since it will be a qualitative analysis.-

7 A blade passage causes the flow an internal loss of heat, due to the difference between the

actual enthalpy of the working fluid at the exit of this passage and the enthalpy for isentropic

flow. The reason is friction of the working fluid.


On the one hand, there is the non-dimensional impulse from a single cavitation

event, defined by:

= / ( 7 )

Where U and D are reference velocity and length in the flow. This impulse is

strongly correlated with the maximum volume of the cavitation bubble, and appears

virtually independent of the other flow parameters.

~

=

/ ( 8 )

The evaluation of the impulse is completed by some estimate of the maximum

bubble size, RM. This size is independent of U for a given cavitation number, so I will

be linear in U. Modeling is complicated. Given a streamtube with a cross sectional

area A in the upstream reference flow, the result would be:

= ( 9 )

Where N is the nuclei concentration per volume. Therefore, the sound pressure

level will result in:

( )

/ ( 10 )

Nonetheless some constants have been omitted. Thus, scales with 2 and 4,

since A~f (D2). This scaling with velocity does correspond to the often observed in

simple traveling bubble flows. However, only those nuclei larger than a critical size

will grow to become cavitation bubbles. This critical radius is a function of the

cavitation number and U. This means N will be a function of and U. In the end, the

pressure of sound will be function of (n>2).


It has been studied how the acoustic pressure depends on the size of the bubble.

In the following figure, this relation is shown:

FIGURE 12. - SOUND PRESSURE PRODUCED BY AN INDIVIDUAL BUBBLE

Note that there is a little delay {

} which appears due to the fact that the

sound travels through the water at a velocity c, equal to 1450m/s. Therefore, it just

takes the instantaneous radius and its derivatives to fully get the acoustic energy

produced by a bubble. In the picture, it can be observed the first collapse, which is the

principal, and then successive collapses8 after rebounds.

Finally, it can be obtained the acoustic energy emitted by the bubble; it will be

determined by the following expression:

=

()

( 11 )

8 There is more than just one collapse (see figure 9 in page 19).


During the expansion of the bubble, it should be assumed that the pressure

applied is constant and the inequilibrium of pressure is equal to p. in this case it is

known that the radial velocity of the bubble is almost constant. A good approximation

of the acoustic energy radiated is given by the following equation:

=

(

)

= .

( 12 )

Which is, in fact, proportional to the maximum volume attained by the bubble.

The spectrum of the radiation caused by acoustic cavitation follows singles

lines rising above a noise base. These lines position themselves according to

harmonics, subharmonics and ultrasubharmonics of the excitation frequency. The

following figure shows an example of this effect for a cavitation region in water. The

measurement was taken by a piezoceramic transducer at a fundamental resonance

frequency of 10 kHz.

FIGURE 13. - ACOUSTIC SPECTRUM FOR CAVITATION IN WATER

The presence of these single lines in the measurement is related to nonlinear

dynamics of single gas bubbles that occur in the field of an intense acoustic wave and

experience a series of bifurcations of period doubling or even a transition to dynamic

chaos.

So far, the nature of these spectral lines of a finite width has been poorly

understood.


2.5.3. MEAS URIN G DEVICES

Measuring sound underwater is quite different from measuring airborne sound.

Nonetheless, it is also measured in decibels, due to the advantages that using a

logarithmic scale can carry9. Thus, the decibel provides a convenient way of handling

large numbers and large changes in variables. It also permits quantities to be

multiplied simply by adding their decibel equivalents.

The differences between underwater sound and airborne sound include: a

different reference pressure (1 Pa instead of 20 Pa), different hearing sensitivity

and differences in interpretation.

Something has already been pointed about these measuring devices. Commonly

it is used a transducer. A modern transducer is based on piezoelectric ceramic

properties. This device changes physical shape under an electrical current. This

change in shape causes a pressure wave and then it converts this wave into an

electrical current. Thus, it can be said that the transducer is both source and receiver

of the sound.

When a transducer converts electrical energy to sound energy, there is a loss in

friction and dielectric effects. Usually, a ceramic transducer has an efficiency of 50

percent. This efficiency is defined by the ratio of power:

= /

Usually a transducer is resonant. Therefore they will perform the best

measurements at the frequency they are designed for, and the further from this value,

the more the sensitivity drops. It is interesting to utilize a control parameter to

indicate us the bandwidth. The typical Q-value10 is between 5 and 10.

Another useful tool to control how sensitive the value is measured is the beam

pattern, which indicates the sensitivity for different directions (being the maximum

value usually at a perpendicular direction to the transducer face).

9 It is known that many processes in nature have a great dynamic range. Using a logarithmic

scale allows us to work with smaller numbers, and the measurement will be approximately

linear to the perceived sensation of sound. Therefore is easier and clearer to employ decibels to

quantify noise. 10 = /


FIGURE 14. - SECTION OF A USUAL CERAMIC TRANSDUCER

The typical transducer used to measure underwater noise is a hydrophone.

Nevertheless it can also be used a microphone with a correct isolation in some cases

where using a hydrophone can be difficult or problematic due to vibration.

19 Setup and equipment

3. SETUP AND EQUIPMENT

3.1 INSTALLATION

The installation used to measure noise is shown in the picture below.

FIGURE 15. SETUP SKETCH

As it can be seen, it is mainly composed of the following elements:

Venturi tube

Tank

Pump

Inverter

Measuring devices (thermometer, flow meter, tachometer, manometers, etc.)

It is important to mention that there is an additional pipeline which is not

going to be used.


FIGURE 16. MANOMETERS

Cavitation is going to be measured through the Venturi tube, so it should be

properly isolated. To that end, it is going to be used Styrofoam (extruded polystyrene

foam) because of its great isolating properties. The picture below will show this

isolation:

FIGURE 17. - ISOLATION OF THE VENTURI TUBE

More information about the pump used can be found in Appendix I.


3.2 MICROPHONE

As it was said earlier, it is viable to use a microphone to measure cavitation

noise as long as using a hydrophone is complicated or requires a vibration isolator.

This is the case of installation studied, where a hydrophone would necessitate a

difficult setting up in the pipeline for each measure, and the problem generated by the

vibration and resonance in the pipeline would require employing a vibration isolator.

For these reasons, it will be interesting to use a microphone, since the setup

will be easier. On the one hand it will not be necessary to worry about a Q-value, so

the measurements will be more accurate; however the range of frequencies measured

will be from 1 Hz to 20 kHz. Nevertheless, this range will be adequate to catch the

main noise spectrum of cavitation.

The microphone used is a Behringer C-1U, which is an electrostatic microphone

shown in the picture below. Its main characteristics are also exposed in Appendix I.

FIGURE 18. - BEHRINGER C-1U

The microphone includes a USB port which will allow us to connect it to the

computer.

3.3 SOFTWARE

It is required an audio software application to process the signal obtained by

the microphone. For this purpose it is going to be used Cool Edit Pro, developed by

Syntrillium Software Corporation, nowadays property of Adobe. It is an advanced

multi track sound editing program for windows. Its main capabilities are: sound filters


via digital signal processing effect, multi track function, plug-ins capability and batch

process files. The version will be 2.1.

The following picture shows a typical screenshot of the program:

FIGURE 19. - COOL EDIT PRO SCREENSHOT

After all measurements are completed, and the signal is processed (it will be

exposed in the next section) the results will be exported to Excel and Matlab. Then

these programs will be used to classify all data and plot the outcomes.

23 Procedure and measurements

4. PROCEDURE AND MEASUREMENTS

The procedure to be followed will be to take measurements of cavitation in

clean water. Afterwards, the water will be changed and replaced by a solution of 50

ppm of PEO in water. The last measurement will be made in a 100 ppm solution of

PEO. Once these stages are finished, all recorded audio files will be analyzed and

processed.

During the following chapters, the procedure will be fully explained and

described. For these tests, some parameters are going to be measured in order to

control the correct progress of the experiment. These parameters will be:

Temperature. It will affect vapor pressure and density of the fluid.

Inverter frequency. Changing the frequency will modify the speed of the pump.

Rotational speed of the pump.

Torque. It will indicate the performance of the pump.

Flow rate. It is necessary to calculate the velocity of the flow.

Pump pressure.

Pressure before the Venturi tube. It is needed to estimate the cavitation number.

4.1 FIRST TEST : CLEAN WATER UNDER CAV ITATION

For this test, it is going to be used water, and there will be two scenarios: one of

them will present cavitation and the other will not.


For this experiment, the installation will have the following setup:

FIGURE 20. - FIRST SETUP FOR TEST ONE

The fluid goes through one pipeline. Then the pump starts driving fluid

through the circuit. Initially, the inverter is set to 25 Hz. In this situation, there will

be cavitation through the Venturi tube.

The procedure will be to start raising the frequency of the inverter and

measure noise of flow through the Venturi tube. The objective of this first

measurement is to get the noise from cavitation. Unfortunately, even though the

Venturi is correctly isolated with Styrofoam, there are several interferences. The most

important interference is the noise from the pump, but it also has to be taken into

account noise produced by the flow through pipelines. That is the reason why it will be

required another measurement.


The following table shows the development of all control parameters.

Inverter setting

Rotational speed

Torque Flow rate Pump pressure

Venturi pressure

drop

Pressure before Venturi

T

Hz rpm Nm l/min bar mbar [mbar] C

25 711 1.32 23 0.384 297 232 25.9

26 739 1.42 23.2 0.435 344 275 25.9

27 769 1.44 23.7 0.489 400 326 26

28 797 1.49 24.1 0.546 452 376 26

29 827 1.56 24.5 0.605 508 433 26.1

30 853 1.62 24.9 0.661 563 483 26.2

31 881 1.69 25.3 0.724 621 542 26.2

32 909 1.76 25.9 0.786 683 600 26.3

33 939 1.84 26.4 0.856 744 673 26.3

34 967 1.9 26.9 0.923 809 739 26.4

35 995 1.98 27.4 0.992 875 803 26.5

36 1023 2.05 28.1 1.066 939 868 26.5

37 1051 2.13 28.3 1.136 1009 938 26.6

38 1077 2.21 28.9 1.211 1073 1002 26.7

39 1105 2.29 29.6 1.286 1145 1080 26.7

40 1131 2.38 29.8 1.361 1212 1145 26.8

41 1159 2.48 30.5 1.441 1283 1221 26.8

42 1158 2.57 30.8 1.521 1356 1295 26.9

43 1213 2.65 31.5 1.601 1433 1375 27

44 1239 2.75 31.7 1.686 1505 1445 27.1

45 1265 2.85 32.4 1.766 1582 1520 27.1

46 1293 2.96 33 1.856 1653 1603 27.2

47 1321 3.05 33.5 1.946 1730 1682 27.3

48 1347 3.15 33.9 2.036 1810 1763 27.4

49 1371 3.26 34.5 2.125 1869 1827 27.5

50 1397 3.38 34.9 2.216 1870 1854 27.6

TABLE 2. - PROGRESS OF ALL PARAMETERS FOR THE FIRST SETUP

As it can be seen in the table, the inverter controls the rotational speed of the

pump increasing it, and the flow rate also goes up. Therefore there will be an audio file

for each measurement, 25 audio files in total. These recordings have an average

duration of about 30 seconds. The following picture shows the spectrum of one audio

file.


FIGURE 21. - FULL SPECTRUM MEASURED. FREQUENCY OF 27 HZ/769 RPM

Note that the frequency scale is logarithmic, the reason if it is going to be

explained below. Pump noise belongs to low frequencies, less than 1 kHz, therefore

using a logarithmic scale will show undoubtedly the difference between this spectrum

and the one denoised, which will be achieved as soon as all interferences are cut and

the clean spectrum of cavitation is obtained. Using a logarithmic scale is simply a

matter of clearness in this case.

The second test will be performed, where it is going to be used a different setup,

as it can be seen in the following image.

FIGURE 22. - SECOND SETUP FOR TEST ONE


Now the flow crosses both pipelines, and there will be no cavitation, since the

flow is shared by both pipelines, and the Reynolds number of the flow through the

Venturi will be lesser.

It has to be noted that the objective of this second measurement is mainly to

record the noise produced by the pump while pumping water, in order to denoise the

initial measurements recorded. Therefore, 25 additional measurements will be made,

each one for each rotational speed of the pump, since an individual speed will produce

a certain sound.

The evolution of all parameters during this second experiment will be as

follows:

Inverter setting

Rotational speed

Torque Flow rate Pump pressure

T

Hz rpm Nm l/min bar C

24.8 711 1.18 29.9 0.146 28.5

25.8 739 1.23 31.5 0.161 28.6

26.8 769 1.25 32.8 0.171 28.7

27.8 797 1.28 33.8 0.185 28.7

28.8 827 1.32 35.1 0.196 28.7

29.7 853 1.36 36.5 0.206 28.7

30.69 881 1.38 37.5 0.216 28.8

31.63 909 1.41 38.7 0.246 28.8

32.63 939 1.46 39.8 0.245 28.8

33.63 967 1.5 41.4 0.26 28.9

34.6 995 1.54 42.7 0.276 28.9

35.57 1023 1.57 43.7 0.286 29

36.54 1051 1.6 44.7 0.301 29

37.43 1077 1.64 45.8 0.316 29

38.43 1105 1.7 47.2 0.331 29.1

39.33 1131 1.77 48.4 0.341 29.1

40.33 1159 1.87 49.5 0.356 29.2

41.26 1158 1.91 50.8 0.376 29.3

42.19 1213 1.93 51.8 0.386 29.3

43.15 1239 2 52.6 0.406 29.4

44.12 1265 2.09 54.1 0.426 29.5

45.09 1293 2.15 55.3 0.441 29.5

46.05 1321 2.18 56.4 0.461 29.6

47.02 1347 2.3 57.5 0.474 29.7

47.92 1371 2.43 58.9 0.495 29.8

48.93 1397 2.49 59.6 0.51 30

TABLE 3. - PROGRESS OF ALL PARAMETERS FOR THE FIRST SETUP


As it can be seen, the inverter frequency is slightly lower, and there are no

measurements of pressure in the Venturi tube, since they are no longer of interest.

Now it is going to be shown the spectrum of sound for 769 rpm of rotational

speed, which is going to be the file used for denoising the spectrum shown above in

picture 21.

FIGURE 23. - SPECTRUM OF NOISE FOR 769 RPM

It can be seen in the spectrum a higher level of noise at lower frequencies, from

20 Hz to 1 kHz. Thereafter higher frequencies show several peaks of lower values.

After the measuring stage, the denoising phase is performed. This phase will be

carried out by the program Cool Edit Pro. Before explaining the procedure to be

followed, the picture below shows the result of a completed denoising operation,

specifically the one for 769 rpm, so it can be seen the effect of it.

FIGURE 24. - DENOISING PROCESS FOR 769 RPM


It can be seen in the picture that first it is obtained the full spectrum of noise

for a single rotating speed, and then it is measured sound for the same speed in a non-

cavitating scenario. Finally, the definitive cavitation spectrum is achieved by

subtracting both spectrums obtained. Note the great impact at low frequencies.

In order to begin the denoising process it is just required to have both audio

files, one from the first test and another from the second. It is relevant to add that

non-cavitating audio files last about 30 seconds, just as the cavitating ones. The

sequence is as follows:

a) Open the non-cavitation file and select a short section of the record. It should

be of about 10 seconds. For this selection it is important to avoid possible

glitches.

b) Once a good section is selected, it is time to get the sound profile of the

selection. This can be found in the Effects menu, by clicking on Noise

reduction.

FIGURE 25. - NOISE REDUCTION MENU

c) On the Noise reduction window, click on get profile from selection. A FFT size

of 16384 points should be appropriate. This profile has to be saved to use it

later.

d) Now the cavitation file has to be opened. After all audio is selected, click again

on Noise reduction. Then, the profile saved before has to be loaded. Click ok

and scan the file. The result of this scan should be a clean sound of cavitation.

The best way to check if the procedure is correctly completed is to listen to the

file.


Once the process is finished, it is obtained the correct spectrum of cavitation.

Nevertheless, the microphone uses a 16-bit analog-digital converter, which means that

the noise levels are stored in digital format from 96 dB to 0 dB. Therefore it is needed

to adapt this signal to a more clear scale, so the results can be plotted and visualized

properly.

4.2 SECOND TEST : AQUEOUS SOLUTION OF P EO UNDER CAVITATION

The second experiment involves two different solutions of polyethylene oxide.

This PEO will have a molecular weight approximate of 8.000.000, and it is inhibited

with 200-500 ppm of BHT. Again, there will be two sets of measurements. The

objective of this experiment will be to measure noise of cavitation of water with a

solution of polymer to check possible differences between the results obtained in clean

water and these new measurements. During the testing the polymer chains will break

and there will be degradation of them, so this effect can also influence the results. It is

important to clarify that these tests will be performed at a constant rotational speed of

the pump of 1000 rpm.

Every experiment will last 60 minutes; therefore the order will be as follows:

First experiment First solution of PEO without cavitation

Second experiment First solution of PEO with cavitation

Third experiment Second solution of PEO without cavitation

Fourth experiment Second solution of PEO with cavitation

For each experiment, sound will be measured 5 times during the test, in order

to look for any evolutions of noise, due to the polymer degradation process exposed

before.

The first solution will have a concentration of 50 ppm of PEO in water. Just as

it was performed on the clean water test, for no cavitation the solution will flow

through both pipelines, and for cavitation just through the one that incorporates the

Venturi nozzle. It is important to add that, since polymer chains break during the

experiment, it is necessary to change all fluid between both experiments.


In this case, the parameters are presented in the next tables:

No Cavitation

Time T Flow Rate Pump Pressure

Torque

min C l/min bar Nm

8 23.9 45.3 0.285 1.51

16 24.1 44.5 0.285 1.48

31 24.6 44.3 0.285 1.5

61 26 44.3 0.285 1.66

TABLE 4. -FIRST SOLUTION, NO CAVITATION. CONTROL PARAMETERS

Cavitation


Torque Venturi pressure

drop


min C l/min bar Nm mbar mbar

7 25 28 1.065 1.96 924 850

16 25.5 27.8 1.03 1.82 909 840

31 25.7 28 1.02 1.78 895 825

47 26.5 28 1.015 1.76 890 815

63 27.2 28.8 1.015 1.78 885 815

TABLE 5. -FIRST SOLUTION, CAVITATION. CONTROL PARAMETERS

As it can be observed, there are no important variations on the control

parameters. After all measurements solution was changed from the installation and a

new solution of 100 ppm of PEO is incorporated.

For this set of measurements the procedure is the same, and the table below

shows the development of all parameters:

No Cavitation


Torque

min C l/min bar Nm

6 25.2 44 0.285 1.25

16 25.3 44.3 0.285 1.28

33 25.7 44 0.285 1.28

47 26.2 44 0.285 1.31

60 26.6 44 0.285 1.42

TABLE 6. -SECOND SOLUTION, NO CAVITATION. CONTROL PARAMETERS


Cavitation


Torque Venturi pressure

drop


min C l/min bar Nm mbar mbar

6 25.3 27.8 1.085 1.93 955 890

16 25.4 28 1.055 1.88 930 865

31 25.9 28.2 1.03 1.9 906 840

46 26.5 28.4 1.025 1.81 900 835

61 27.2 28.7 1.02 1.77 895 830

TABLE 7. -SECOND SOLUTION, CAVITATION. CONTROL PARAMETERS

Using the cavitation number as indicator of the presence of cavitation can be

really useful, since it is easy to obtain it through the parameters shown previously.

Therefore, it is going to be calculated for each situation of cavitation. As explained

before, the equation employed is:

=()

( 13 )

Since is a dimensionless number, it can be calculated from any reference

values. In this case, the reference will be the pipe section before the Venturi. Where P1

is obtained by the expression:

= ( ) + ( 14 )

With Pa, atmospherical pressure, assumed constant and equal to 100,2 kPa.

33 Results

5. RESULTS

This chapter will display the results of all measurements and will point out the

most interesting ones, in order to be discussed below.

5.1 RESULTS FOR WATER

First of all, it is going to be studied the development of the cavitation number

during the experiment. Taking into account the variation of density and vapor

pressure due to the increase of temperature, several lineal interpolations must be

performed. The results are shown in the following table:

T Venturi pressure

Flow rate Velocity pv

C mbar l/min m/s [Pa] [kg/m3] []

25.9 232 23 1.35200875 3341.15 996.845 131.776369

25.9 275 23.2 1.36376535 3341.15 996.845 134.152804

26 326 23.7 1.39315684 3360 996.82 133.807893

26 376 24.1 1.41667004 3360 996.55 134.437983

26.1 433 24.5 1.44018323 3381 996.793 135.545949

26.2 483 24.9 1.46369643 3402 996.766 135.892716

26.2 542 25.3 1.48720963 3402 996.766 136.982031

26.3 600 25.9 1.52247942 3423 996.739 135.715057

26.3 673 26.4 1.55187091 3423 996.739 136.705209

26.4 739 26.9 1.58126241 3444 996.712 136.953766

26.5 803 27.4 1.6106539 3465 996.685 136.938873

26.5 868 28.1 1.65180199 3465 996.685 134.981732

26.6 938 28.3 1.66355859 3486 996.658 138.144796

26.7 1002 28.9 1.69882839 3507 996.631 136.907381

26.7 1080 29.6 1.73997648 3507 996.631 135.678752

26.8 1145 29.8 1.75173308 3528 996.604 138.104504

26.8 1221 30.5 1.79288117 3528 996.604 136.582826

26.9 1295 30.8 1.81051607 3549 996.577 138.456351

27 1375 31.5 1.85166416 3570 996.55 137.045105

27.1 1445 31.7 1.86342076 3591 996.522 139.358887

27.1 1520 32.4 1.90456885 3591 996.522 137.551901

27.2 1603 33 1.93983864 3612 996.494 137.014936

27.3 1682 33.5 1.96923014 3633 996.466 137.037182

27.4 1763 33.9 1.99274333 3654 996.438 137.909625

27.5 1827 34.5 2.02801313 3675 996.41 136.271393

27.6 1854 34.9 2.05152632 3696 996.382 134.447018

TABLE 8. - CAVITATION NUMBER EVOLUTION FOR WATER

34 Results

As cavitation number is just a dimensionless indicator of cavitation, it can be

observed that cavitation occurs during all measurements.

As it was mentioned when the microphone was described, the range of

frequencies for a good measurement goes from 1 Hz to 20 kHz, which means that

values close to these limits should be omitted, since they can be erroneous. Therefore,

results from 20 Hz to about 18 kHz will be assumed correct. The following figure

shows a spectrum of noise for water, specifically for 25 Hz and 711 rpm of rotational

speed:

FIGURE 26. - NOISE SPECTRUM OF WATER FOR 711 RPM

This spectrum for 711 rpm can be compared with other rotational speeds. It

can be observed in the following image, where it is compared with a rotational speed of

1397 rpm.

0

10

20

30

40

50

20 2020 4020 6020 8020 10020 12020 14020 16020 18020

No

ise

(d

B)

Frequency (Hz)

35 Results

FIGURE 27. - NOISE SPECTRUMS OF 711 RPM AND 1397 RPM

In view of this comparison, it can be observed a pattern of noise, followed by

both spectra. However, the best way to check the complete evolution of noise through

all rotational speeds will be a 3D surface where any change can be detected. For this

purpose it is going to be used MATLAB. The following surface shows these spectra.

FIGURE 28. - NOISE FULL SPECTRA

0

10

20

30

40

50

20 2020 4020 6020 8020 10020 12020 14020 16020 18020

No

ise

(d

B)

Frequency (Hz)

711 1397

36 Results

In the figure, it can be seen a slight raise in noise when the rotational speed is

increased. Nonetheless, seen from above it is easier to get a visual image of the effect.

FIGURE 29. - NOISE SPECTRA SEEN FROM ABOVE

In the figure it can be observed a raise of decibels especially at about 2 kHz and

10 kHz, although there is a general increase in all a frequencies. It is also important to

add that there is a zone at low rotational speeds (from 700 rpm to 800 rpm) where

some values are likely to be erroneous, probably due to the denoising process.

5.2 RESULTS FOR AQUEOUS S OLUTION OF PEO

For this experiment, as there will be a single rotational speed, the display and

analysis of the results will be quite different.

37 Results

5.2.1 50 P P M O F PEO

For this concentration of the solution, the following table will display the

evolution of the cavitation number during the process.

T Venturi pressure



25 850 28 1.6459237 3171.5 997.07 134.779655

25.5 840 27.8 1.6341671 3265.75 996.945 135.92103

25.7 825 28 1.6459237 3303.45 996.895 132.854194

26.5 815 28 1.6459237 3465 996.685 132.021806

27.2 815 28.8 1.69295009 3612 996.494 124.710108

TABLE 9. - CAVITATION NUMBER EVOLUTION FOR 50 PPM OF SOLUTION

Degradation occurs mainly in the pump, but can also occur in the Venturi,

maybe supported by cavitation itself. The next plot shows how noise spectrum changes

from the first eight minutes to the last ones.

FIGURE 30. - COMPARISON BETWEEN THE FIRST MINUTES OF EXPERIMENT AND THE LAST ONES FOR 50 PPM

It can be observed how the spectrum for 61 minutes is clearly quieter. If they

are plotted together with the 16 minutes measure it can be seen a progression.

0

10

20

30

40

50

60

0 5000 10000 15000 20000

No

ise

(d

B)

Frequency (Hz)

8min 61min

38 Results

FIGURE 31. - EVOLUTION OF SPECTRA DURING THE EXPERIMENT FOR 50 PPM

On figure 32 it is shown the surface of the entire experiment seen from above,

where it can be seen the decrease of noise as the process progresses.

FIGURE 32. - FULL SPECTRA FOR 50 PPM OF SOLUTION

0

10

20

30

40

50

60

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

No

ise

(d

B)

Frequency (Hz)

8min 16min 61min

39 Results

5.2.2 100 PP M O F PEO

For this new concentration, the results follow the same pattern. Cavitation

numbers for each measurement are displayed in the table.

T Venturi pressure



25.3 890 27.8 1.6341671 3228.05 996.995 139.698433

25.4 865 28 1.6459237 3246.9 996.97 135.848099

25.9 840 28.2 1.65768029 3341.15 996.845 132.05066

26.5 835 28.4 1.66943689 3465 996.685 129.76907

27.2 830 28.7 1.68707179 3612 996.494 126.638423

TABLE 10. - CAVITATION NUMBER EVOLUTION FOR 100 PPM OF SOLUTION

The following plot compares the first measurement at 6 minutes of experiment,

and the last one, at 60 minutes.

FIGURE 33. - COMPARISON BETWEEN THE FIRST MINUTES OF EXPERIMENT AND THE LAST ONES FOR 100 PPM

This effect of decreasing noise happens again for this new solution, and now the

effect is greater. Taking a look at the full spectra, the entire development can be

observed.

0

10

20

30

40

50

60

0 5000 10000 15000 20000

No

ise

(d

B)

Frequency (Hz)

6 min 61 min

40 Results

FIGURE 34. - FULL SPECTRA FOR 100 PPM OF SOLUTION

41 Analysis and Conclusions

6. ANALYSIS AND CONCLUSIONS

The first and most important conclusion is that cavitation can be detected

using an ordinary electrostatic microphone, which presents a great advantage when

detecting cavitation in a lot of installations, taking into account the ease of use and

installation, without mentioning the lower costs compared to other methods, such as a

hydrophone.

It is also been showed how cavitation at higher speeds causes the general

amount of noise to increase. Another conclusion can be drawn from a simple look at

the charts shown in the results, and it is the typical spectrum of cavitation of the

installation, distinguished by a great influence of low frequencies, below 4 kHz, and

some peaks of sound around frequencies of 4 kHz, 11 kHz and 12 kHz.

However, something that must be pointed out is the presence of undesirable

noise at low speeds (from 700 rpm to 800 rpm) generated due to a non-perfect isolation

probably. Other possible causes are glitches and interferences that seem to disappear

at higher speeds.

Different conclusions can be obtained of the second experiment, involving

polymer degradation mixed with cavitation. Most of this degradation should occur

through the pump; nonetheless, it appears to affect the results a lot. This indicates

that the fluid may undergo degradation through the Venturi itself. Other possible

source of noise can be a redirection of polymer chains through the nozzle during the

lifetime of these chains, that is, while degradation is still happening. In any case, it

seems to appear a source of noise added to cavitation. Since the results of this

experiment are denoised using a profile of noise from a non-cavitating setup, this new

sound from the polymer is produced only during cavitation, and it is probably created

by cavitation itself. This effect is more intense for a higher amount of polymer in

water, which is the case of 100 ppm, and this is logical since the number of chains is

greater. This experiment offers clearer results.

The following picture shows the noise effect of chains in motion for 100 ppm of

solution. This image displays how the effect is mitigated and the spectrum tends to a

stable value. It can be also compared with a clean water spectrum of a similar

rotational speed. However, the experiment was made in a different room and a

different day, so there can be some differences between both test conditions.


FIGURE 35. - EVOLUTION OF NOISE PRODUCED DURING DEGRADATION OF POLYMER

FIGURE 36. - COMPARISON OF CLEAN WATER VS SOLUTION

Figure 36 shows the comparison of clean water and solution, where it can be

observed that, even though the spectra of water and 61 minutes of pumping with

solution of PEO have some differences, the amount of noise is similar, which means

that the polymer is fully degraded by 61 minutes of pumping.

0

10

20

30

40

50

60

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

No

sie

(d

B)

Frequency (Hz)

6 min 61 min 46 min

0

10

20

30

40

50

60

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

No

ise

(d

B)

Frequency (Hz)

water 6 min 61 min


In fact, it can be observed the process of degradation taking a closer look at the

surface of spectra obtained for 100 ppm of solution, where it can be approximated the

duration of degradation.

FIGURE 37. - STRONG DEGRADATION ZONE

In the picture above, it can be observed the zone where degradation is more

pronounced, and therefore additional noise is generated. This zone comprises the first

30 minutes of pumping.

44 Appendix I: Technical specifications

7. APPENDIX I: TECHNICAL SPECIFICATIONS

7.1 MICROPHONE

Behringer C-1U

FIGURE 38. -FREQUENCY RESPONSE AND POLAR PATTERN OF THE MICROPHONE


FIGURE 39. - TECHNICAL SPECIFICATIONS OF THE MICROPHONE

7.2 PUMP

The pump used is a SKA3 self-priming pump manufactured by Hydro Vacuum.

The exact pump model is: Hydro-Vacuum SKA 3 01 1 1010 5 101 1. The picture below

shows a similar pump.

FIGURE 40. - SKA3 SELF-PRIMING PUMP


The next picture is an exploded view of the pump:

The table below shows the main technical specifications of the pump:

Parameter Value

Capacity [m3/h] 1.0 3.0

Delivery head [m] 11.0224.0

Pumped liquid temperature Up to 110C

Liquid density Up to 1300 kg/m3

Liquid viscosity Up to 150 mm2/s

Mass 34.0409.0 kg

Motor Power 0.5530.0 kW TABLE 11. - TECHNICAL SPECIFICATIONS OF THE PUMP


Finally, the following charts display curves head/flow, power/flow,

efficiency/flow and NPSH/flow.

FIGURE 41. - HEAD/FLOW CURVE OF THE PUMP

FIGURE 42. - POWER/FLOW CURVE OF THE PUMP


FIGURE 43. - EFFICIENCY/FLOW CURVE OF THE PUMP

FIGURE 44. - NPSHR/FLOW OF THE PUMP

49 Bibliography

8. BIBLIOGRAPHY

[1] J. Daintith and E. Martin, Dictionary of Science (6th Edition), Oxford University Press,

2010.

[2] R. Chhabra and J. Richardson, Non-Newtonian flow and applied Rheology - Engineering

Applications (2nd Edition), Elsevier, 2008.

[3] M. Eagleson, Concise Encyclopedia Chemistry, De Gruyter, 1993.

[4] J. S. Carlton, Marine Propellers and Propulsion (2nd edition), Elsevier, 2007.

[5] C. E. Brennen, Hydrodynamics of pumps, Cambridge University Press, 2011.

[6] Y. Lecoffre, Cavitation: Bubble Trackers, CRC press, 1999.

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