Abstract:

Scientific background  

Cavitation is a physical phenomenon, which describes a phase change from liquid to gas and back to homogeneous liquid by approximately constant temperature. Cavitation can be described as small vapor bubbles formation within the liquid, due to local pressure drop [1]⁠. Cavitation most often occurs on turbine machinery, valves and some parts of fuel injection system by internal combustion engines and even in bearings. Cavitation is in most cases undesirable phenomenon, which engineers try to avoid or to prevent, because it has several negative effects like noise, vibrations, loss of efficiency and even material erosion, which can all bring to machinery damage.

In general cavitation can be divided between hydrodynamic and acoustic or ultrasonic cavitation. The difference is in the mechanism, which causes the local pressure drop. By hydrodynamic cavitation the geometry of the submerged body is the reason for local velocity increase, which causes the local pressure drop, while by the acoustic cavitation the areas of low pressure occur due to ultrasonic radiation, which causes an oscillating pressure field within a bulk liquid. The principles which govern the hydrodynamic bubble and the acoustic bubble are basically the same.

Scientists do not only research cavitation to prevent it and it's negative effects [2]⁠, but also to effectively use it in several industrial applications [3]⁠. Nowadays cavitation can be used as a tool by surface cleaning, in medicine, in food industry, for cleaning different types of water and elsewhere. Different applications demand the use of different types of cavitations or a combination of different types to gain maximum results. That is why fundamental researches of hydrodynamic and also acoustic cavitation are incredibly important [4]⁠. Regardless of whether cavitation is seen in a positive or negative aspect, one must always take into account the possibility of the cavitation erosion occurrence and other unwanted effects which are associated with the presence of cavitation. Finally, failure to control cavitation conditions can lead to a reduction of the impact of a particular process and thereby increase operating and service costs. For example, the annual cost of 100,000€ for a refit are a consequence of cavitation erosion on the runner of the hydro power plant Avče (Slovenia).

 

Problem identification  

Most scientific researches, where cavitation is investigated, are performed with clean water, in which cavitation's characteristics are well known. However, very few researches were performed with liquids other than clean water, such as oils, solutions, suspensions, colloids and others. This presents a huge gap between the basic knowledge of cavitation in clean water and cavitation in industrial applications, where one often deals with presented liquids.

Sea water, which has an average salinity of 3.1% and 3.8%, is particularly different from the fresh water due to higher density. This and other rheological properties of the seawater and fresh water lead to differences in the appearance and characteristics of cavitation. Cavitation in seawater was until recently mainly investigated due to a significant undesirable effects on the ship propellers.  Mainly due to cavitation noise it is extremely undesirable on the submarines, while the cargo and passenger ships devotes the most attention to prevent cavitation erosion. In addition to the cavitation erosion, noise on commercial ship propellers becomes an issue, as the more and more studies on the effects of cavitation noise on the marine life are being performed. Even bigger problem has become with the ship ballast water discharge due to increased ship transportation. The issue of ballast water has been known for a long time and ranks among the greatest threats to the marine environment as the non-native organisms with the uncontrolled discharged can cause intense changes in local marine ecosystems, with  negative ecological, economic and social consequences. The idea of “cleaning" ballast water by means of cavitation is not new, but because of the tolerant legislation on the field of the ballast water discharge, it has not experienced a breakthrough on the market. To develop a system to clean the ballast water with cavitation device, one need an extensive knowledge about the properties of cavitation in seawater. Due to reduction of the  development costs, the manufacturers of any kind of machines and  devices, increasingly use numerical simulations instead of experimental work. To increase the accuracy of the numerical calculations, which is extremely challenging for the cavitating flows, more extensive basic investigations of the cavitation in seawater are crucial.

Many research has been performed, where cavitation is used as a tool for treating a wide variety of liquids, whereby cavitation is often perceived as a “black box” for which researchers can only assure that cavitation is present. So it would make sense to explore the behavior of cavitation  in a variety of liquids and to determine which characteristics of the liquid have an impact on the development and course of cavitation, to improve and customized each process to the specific needs. Collapse of the cavitation bubble can cause extremely high pressure pulsations, even more than 100 bar, when the bubble collapses asymmetrically a so called micro yet is formed, which can reach speed well over 100 m/s and from indirect measurements it is also shown that the bubble collapse can release extremely high temperatures up to several 1000 K, which can cause the disintegration of water molecules on the OH and H radicals. These extreme conditions can be advantageously used for the destruction of various microorganisms (bacterias, viruses), or the removal of various chemical compounds.   

Fuel injection in diesel engines are now boasts extremely high pressures up to 1000 bar, resulting in the occurrence of cavitation in the system and on the nozzle itself. Due to the extremely high inlet pressure occurs, that the liquid velocity is increased, which could lead to local pressure drop and the occurrence of cavitation and that leads from reducing the fuel flow to the cavitation erosion, which threatens the optimal functioning of the system and its life expectancy. Due to the complexity of measurements on real systems (the size of the nozzle channels are of the order of μm), the developers of injection systems intensively use computational simulations. Despite the fact that the use of the numerical simulations is increased most of the numerical models are based on the experimental data of the cavitation in the water. In order to improve numerical forecasts in these systems, we need a number of basic experimental studies in real liquids in which we are trying to predict cavitation. Only with the help of experimental data one will be able to implement appropriate improvements to existing cavitation models and their validation.  

As an extremely complex example, important for industrial space technology is the behavior of cavitation and its properties in cryogenic liquids, because spacecraft propulsion systems uses liquid hydrogen and liquid oxygen as fuel and oxidizer. Huge quantities of the two fluids must be pumped from the tank to the combustion chamber in a very short time, for which special turbopumps are needed. These pumps operate at extreme conditions, where cavitation in inevitable. Due to the extremely complex measurements, most researchers carried out measurements in non-cryogenic liquids, and then only predict the behavior of the machine in cryogenic liquids, without knowing the precise characteristics of cavitation in real used liquids. To improve the performance of these turbopumps, a number of basic researches in cryogenic liquids are needed.  

This basic post-doctoral research will based on acoustic cavitation due to several reasons. Acoustic cavitation caused by an ultrasonic horn is for basic research very suitable due to easy use and extremely good repeatability of the cavitation conditions over a longer time span, which is extremely important as far as we want to accurately compare the cavitation conditions depending on the operating liquid. Cavitation in selected liquid at the constant frequency and geometrically identical sonotrode, depends only on the amplitude of the sonotrode and ambient pressure, which both of the parameters can be very precisely controlled. Unlike ultrasonic cavitation, the hydrodynamic cavitation depends on several parameters, which is why the repeatability of the cavitation conditions is more difficult to achieve. Because of the potential dangerous liquids (various oils, fuel, cryogenic liquids, etc.), a small volume of the sample is crucial, since smaller volume of potentially dangerous liquid represent a lower risk for the health and safety of the researchers. Compared to the hydrodynamic cavitation, in which you need a certain flowrate through the selected constriction, acoustic cavitation can be seen in the much smaller volume samples without some additional parts of cavitation station, such as pump and constriction in the case of hydrodynamic cavitation.  

If we want to described ultrasonic cavitation with basic overview, it is necessary to define the dimensionless parameter, which would cover the basic cavitation characteristics. In the field of hydrodynamic cavitation exists for a long time (around the year 1925, Thoma suggested dimensionless parameter) the so-called Cavitation number, which represents the basic dimensionless number for a basic description of the state of hydrodynamic cavitation. Despite the fact that the cavitation number can not fully survey cavitation condition, this parameter is very welcome for a relative comparison of the different states of the cavtation. If for the hydrodynamic cavitation exists a basic parameter, which describes the basic status of cavitation, there is no proper proposal for a similar dimensionless parameter for the acoustic cavitation, which could be compared to the state of cavitation caused by ultrasonic. Due to the widespread use of acoustic cavitation in a number of processes, it would make sense to explore all the possible variables that affect the status of acoustic cavitation and propose a dimensionless number which can be compared to the state of cavitation, like the number of cavitation in hydrodynamic cavitation. In hydrodynamic cavitation one distinguish different forms of cavitation [1]⁠ from the initial cavitation with individual bubbles, fixed cavitation, developed cavitation to the supecavitation, which can all be linked to the certain values of the cavitation number in similar geometry. As by the hydrodynamic cavitation, there can also appear different forms of cavitation by acoustic cavitation (Figure 1), which so far have not yet been linked with the similar parameter.  

 

Figure 1: Different shapes of cavitation on the tip of the sonotrode [5]⁠.  

 

Objectives  

As stated, most studies of cavitation deals with pure water, where cavitation is relatively well known, but nevertheless still not fully nonetheless very phenomenon has not yet been fully explained, especially the mechanisms of the cavitation erosion. The postdoctoral project will deals with the understanding of cavitation and its undesirable effects (especially cavitation erosion) in various liquids with integration of experimental and theoretical methods in the field of fluid mechanics. Emphasis will be placed on finding links between cavitation in pure water and cavitation in various liquids. Within the project we want to determine the importance of individual rheological properties of fluids, their interactions and influence on the process of erosion. We are interested in the local volume of the cavitation, velocity fields of liquid and gaseous phase with turbulent fluctuations. Expected result of this postdoctoral project is also a physical model that takes into account the main rheological properties of different liquids, unsteady, non-isothermal, and turbulent two phase nature of the flow and ultimately enables prediction of the properties of cavitation and erosion in the desired liquid on the basis of experimental data in the acoustic cavitation.  

An important result of the project will also be a development of the dimensionless parameter for identifying the acoustic cavitation, which will described the basic forms of cavitation caused by an acoustic radiation in the stationary liquids. With the experimental modeling of different cavitation conditions by means of acoustic cavitation in a variety of liquids and taking into account as many variables which affect the cavitation state, we will propose a dimensionless parameter, which will be used to described a cavitation state of acoustic cavitation.  Hitherto known basic variables that affect the size and strength of the cavity are the amplitude and the frequency of the sound wave, but on the cavity affect also many other variables such as the properties and quality of the liquid, geometry of the space where cavitation is formed and others.    

 

State-of-the-art in the proposed field of research and survey of the relevant literature  

Postdoctoral project covers the area of acoustic cavitation in various liquids. Acoustic cavitation [6]⁠ generally involves the formation of vapor bubbles due to the ultrasonic waves through the liquid, which can be caused by standing waves within the ultrasonic bath [7]⁠ or due to high-frequency oscillation of the body (horn) in the liquid [5]⁠. Most studies with acoustic cavitation have been made for the research of individual cavitation bubbles in an ultrasonic bath [8]–[10]⁠, interaction between  more cavitation bubbles with each other [8]⁠, [11]–[14]⁠ and interaction between cavitation bubbles and the solid surface [15]–[17]⁠. Studies have done relatively good research work on the properties of cavitation on the sonotrode [18]–[21]⁠, also because of a standard erosion test G32 [22]⁠, which is used for testing the resistance of various materials to the cavitation erosion [23]–[26]⁠. Standard cavitation erosion test is based on cavitation on the ultrasonic sonotrode with the defined operating parameters. Samples of standard sizes and different materials are exposed to cavitation generated at the tip of the sonotrode, which damage to material.  

As it has been mentioned in the postdoctoral project application, most previous research conducted experiments with water. Comparing the properties of cavitation in a various liquids has been done by only few researchers. Among the latest was Tzanakis et al. [27]⁠ who observed the properties of cavitation on the sonotrode in the water, glycerol and ethanol. He noted that cavitation in the selected three liquids varies considerably. Also Žnidarčič et al. [28]⁠ observed cavitation at the tip of the sonotrode in the water, glycerol and ethylene glycol, and cataloged how the rheological properties of the liquids affect the properties of cavitation.  

The studies of cavitation in seawater was particularly important in the past due to erosion on the propellers, but recently has become increasingly popular due to issues of ballast water [29]⁠. One promising solution for cleaning ballast water is  cavitation [30]–[33]⁠ and because of this, basic knowledge of cavitation in seawater is crucial for the design of machinery and equipment by means of which one can treat ballast water. From the standpoint of erosion, it was found that the cavitation in seawater is more aggressive than cavitation in deionized water [34]⁠ but no exact reasons, why there are differences in the occurrence of damage to the material, were identified yet.  

By fuel injection in internal combustion engines comes in channels of the nozzle to intense cavitation, which is almost impossible to avoid. In most cases, researchers and developers of such kind systems use numerical methods to predicting cavitation [35], [36]⁠. There are only a few experimental studies with actual geometries in actual fuel. One of the few experimental studies in microchannel nozzles in various fuels was carried out by Jiang et al. [37]⁠. Similar research has been conducted by Payr et al. [38], [39]⁠, who has also observed cavitation in the microchannel by means of visualization.   The research of cavitation in cryogenic liquids is particularly important because of the so-called thermodynamic effect, which becomes significant in cases when working temperature gets close to the critical temperature of the liquid. Such liquids are called thermosensitive liquids and cryogenics are typical examples. Most of experimental studies about cavitation in cryogenic liquids were performed by Hord [40]–[42]⁠ in the 60s and 70s and most numerical models [43]–[45]⁠ (which take into account the thermodynamic effects) are still based on the experimental data of that time. For the development and validation of advanced numerical models is therefore crucial to implement new experimental studies [46], [47]⁠.  

In the field of hydrodynamic cavitation exists a long time the so-called Cavitation number, which describes the basic state of the cavitating flow. Despite the fact that it can not capture all of the characteristics of the cavitating flow [48]⁠, it often helps in comparing similar geometries. In the field of acoustic cavitation it has not been a proposal for a similar non-dimensional parameter.  

 

Detailed description of the work programme  

Research in the framework of the postdoctoral project will be based on the use of acoustic cavitation caused by ultrasonic horn in various liquids. Analytical comparison of cavitation characteristics between clean water and other liquids will lead to a better fundamental understanding of cavitation, but will also have a very strong applicative value. With the help of the fundamental knowledge one will be able to develop and improve numerical models for the prediction of cavitation in the various liquids, which will lead to the improvement of various technological processes.  

All activities within the postdoctoral project will be held at the University of Ljubljana, Faculty of Mechanical Engineering, where is available research equipment needed for the successful completion of the project.  

Postdoctoral project will be divided into four work packages (WP), which will follow the time course of the project. The content of work packages is divided into:

WP1: Design and construction of the test rig.

WP2: Characterization of cavitation in water.

WP3: Scaling cavitation in various liquids.

WP4: Analysis of the results and definition of the dimensionless parameter for acoustic cavitation description.  

 

WP1: Design and construction of the test rig.

Within the DS1 we will design and construct a test rig (Figure 2), which will be used for all further experimental work in the postdoctoral project. Conceptual design of the test rig is based on a closed container (tank) volume to 1L, into which is inserted the ultrasonic horn. The container is made of stainless steel, which will be resistant to the possible oxidation of the selected working fluids. The horn will be partially submerged into the working fluid, in which we will study the properties of cavitation. Cavitation forms due to high-frequency probe oscillations on the tip of the horn. Test rig must allow to set the ambient pressure in the container, as well as the temperature of the working liquid. With the help of the compressor and the vacuum pump the ambient pressure in the vessel will be controlled, while the temperature of liquid will be controlled with an electric heater installed on the outer side of the bottom of the container. The cooling system will be installed inside the container. Cavitation at the tip of the horn will be characterized by the visualization and pressure pulsations measurements in the vicinity of the horn tip. Since the container is made of stainless steel, for the purpose of visualization it will be necessary to make observation windows for the camera and illumination. Visualization will be performed with two high-speed cameras simultaneously, so that we will have better spatial description of the cavity. Pressure measurements will be performed simultaneously with the visualization. In addition to the visualization and pressure pulsation measurements must the test rig also allowed measurements of the gas phase (void fraction) in the region of the tip of the horn.  

WP2: Characterization of cavitation in water.

Within postdoctoral project in the WP2 we will carry out detailed research on cavitation characteristics in distilled water and pure tap water at various operating conditions (different ambient pressures, various horn powers and different horn geometries), which results will be used as reference data for the comparison of  cavitation properties in other liquids. With the help of non-invasive methods, we will try to determine the current volume fraction of the cavity, measure pressure fluctuations, calculate velocities of both gaseous and liquid phase, as well as evaluate the void fraction in the field of cavitation.  

Visualization will be performed with a high-speed camera Photron SA-Z, allowing  20,000 frames per second at full resolution (1024 x 1024 pixels) and up to 2,100,000 fps at reduced resolution. To complement the information on a cavity volume, the second high-speed camera Fastec HiSpec 4 will bee used, which makes 523 frames per second at full resolution (1696 × 1710 pixels) and goes up to 300,000 fps at reduced resolution. Based on the visualization from two angles we can roughly reconstruct the 3D shape of the cavity at various operating conditions. The latest and most successful optical flow and hybrid correlation-optical flow methods will be studied, to measure velocity fields [49]⁠. The basic physical background of the method will be represented by advection-diffusion equation, which connects the velocity field of the flow with concentration field of cavitation bubbles. Research in direction of 3D flow visualization will be carried out and new algorithms are expected to be developed.  

Pressure pulsations caused by cavitation will be measured by hydrophone Reson TC4013, which will be installed in the vicinity of the ultrasonic horn. Pressure measurements will be performed simultaneously with visualization. When dealing with measurements at extreme temperatures, we also posses a high-pressure sensor PCB 112A05. For both sensors we have all the necessary power supply, amplifier and software. In addition to conventional local pressure measurements by means of high frequency pressure transducers we intend to try to carry out measurements with a matrix pressure sensor with a PVDF membrane (polyvinildenfluorid, C2H2F2). With special  technique of electrode matrix, the measurement of temporal and spatial distribution of pressure will be performed [50]⁠. When mechanical normal stress deforms the membrane, the electric charges inside the material are displaced and a difference in electrical potential between the upper and lower side of the membrane arises. The electric voltage between these two potentials serves as a direct measure for the pressure difference.  

According to Van Slyke-method, the presence of dissolved gases in the liquid will be monitored, as it is known that the proportion of dissolved gases in the water affects the properties of cavitation.  

Using optical methods we will try to measure the void fraction of cavitation.  

On the basis of the standard erosion test G32-10 we will also carriy out tests of cavitation erosion in water at various operating conditions. The results of erosion tests will serve as a reference to compare them with erosion tests in other selected liquids (seawater, fuel, liquid nitrogen). Erosion will be observed in materials of low hardness, such as. aluminum and copper. On Figure 3 left, shows the highly polished aluminum sample and on Figure 3 right the recording with a microscope before and after exposure to cavitation for 1 minute is made. As a basic method to compare the results we will use the so called pit-count method [51], [52]⁠. Based on the erosion tests and microscope images we will be able to measure the proportion of damaged areas in time, the number of pits and ultimately assess the aggressiveness of cavitation erosion. For longer erosion tests, where already comes to the material loss, where pits counting is no longer an option, we will weigh samples with scales (0.1 mg accuracy and linearity 0,3mg).     

WP3: Scaling cavitation in various liquids.

As mentioned, there are many cases where one is dealing with various liquids in number of real processes and can not be equated with water. That is why this postdoctoral project deals within the WP3 with at least three rheologicaly different liquids in which cavitation characteristics will be defined. Experiments will be carried out with sea water, fuel and liquid nitrogen. Liquids were chosen based on the current enquiry in the field of cavitation, but also due to different rheological properties based on which we can identify which rheological properties have a significant impact on the cavitation characteristics. Basic physical properties of fluids are listed in the table 1. In addition to the hydrodynamic cavitation analysis, we will also evaluate the cavitation erosion in selected liquids and compared the results with the erosion results in water. Erosion tests will be based on the standard G32-10, where the exact   prescribed procedure for carrying out the tests and their evaluations are listed.  

Cavitation in seawater is significantly different from cavitation in pure water. Which rheological properties have a significant influence on the course of cavitation will be examined by varying the concentration of saline solution and with the addition of solid particles of different sizes. By varying the concentration of the dissolved salts in the water, the impact of the density and viscosity of the liquid will be studied on the cavitation characteristics. By adding solid particles we will study how the number of nucleus in the liquid affect the cavitation. Detailed knowledge of cavitation in the seawater has a major contribution to the knowledge, which is needed for ship propeller designers, and also for cleaning ballast water by means of cavitation, which is becoming a huge problem on a global scale due to the transfer of non-indigenous organisms.

Studies that investigate the cavitation in fuels are rare, therefore, the proposed study will contribute to a better fundamental understanding of cavitation in fuel and at the same time it will also have a major contribution to the development and improvement of numerical models. For the study of cavitation in fuels we will use two most commonly used derivatives diesel and 95-octane gasoline. For the developers of the injection systems results of cavitation behavior in both two fuels are extremely important, since the injection pressures in gasoline engines rises and catching up with the diesel versions. With high injection pressure it is easier to monitor the strict environmental requirements on emissions of harmful gases.

Researches in cryogenic liquids are due to the difficulty often avoided, that is why there is a lack of experimental results in this area, which inhibits the further development of advanced numerical models and finally the development of applications where cryogenic liquid used. Within postdoctoral project in WP3 we will also carried out experiments with liquid nitrogen, where we will observe the behavior and properties of cavitation and compared them with the results from other liquids.

Experimental measurements in all selected liquids within the WP3 will be conducted the same way as the experimental measurements in the WP2 with water. In all of the selected liquids we will be carried out visualization, pressure measurements, we will calculate the velocities, monitor the percentage of dissolved gas in the liquid and estimate the void fraction as it is described in the WP2 for the reference liquid, water. In addition to the hydrodynamic analysis, we will monitor the cavitation erosion in all liquids and compare the results with the cavitation erosion in the reference liquid, water.

WP4: Analysis of the results and definition of the dimensionless parameter for acoustic cavitation description. 

In the last part of postdoctoral project, which will be held in parallel with the WP3 we will carry out a thorough analysis of the experimental results obtained from all selected liquids. The results from WP3 will be compared with the reference results obtained in water, in WP2. Already during the WP3 with the help of Taguchi method and / or Box-Behnken experiment planning, we will try to optimize the operating conditions in which we will observed cavitation, to get a reliable model that will include the influence of some physical properties of tested liquids on the cavitation properties and characteristics.

Taguchi experiment planning method is generally applicable for the analysis and design of experiments. The aim of the Taguchi method is to identify the main parameters that have the greatest contribution to the variability of the experiment.
Like the Taguchi method, a Box-Behnken experiment design identify the most influential parameters and optimizes the number of individual tests to ensure that the  result.

Based on the analysis of the results we will determine which physical properties of fluids have significant impact on the development and progress of cavitation. The analysis will also show how cavitation in various liquids causes damages to the material and whether it is possible under certain rheological properties of the liquid to predict the intensity of cavitation erosion.

The proposed postdoctoral project is entirely feasible. Despite the fact that in large part is based on the known methods is innovative and it will offer new experimental data on the properties of cavitation in the various liquids, enabling development teams to improve both numerical models for the prediction of cavitation in such liquids and also improvements to various processes where cavitation is present. We have available the majority of necessary equipment for the execution of all phases of the project and the project leader is well acquainted with the topics of research.

Dissemination of the results from postdoctoral project will be implemented in the following ways:
- Publication of the results in internationally recognized scientific journals.
- Publication of the results at international conferences.
- Bachelor and master's thesis.
- Setting up an open database that will enable the progress of science and technology.

Dissemination activities will take place in parallel with the research activities from the start of the WP2 on.

 

 

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