Analysis of Cavitation Phenomena in Water and its Application to Prediction of Cavitation Erosion in Hydraulic Machinery

P R E P R I N T ICPWS XV Berlin, September 8 11, 2008 Analysis of Cavitation Phenomena in Water and its Application to Prediction of Cavitation Erosion in Hydraulic Machinery Milan Sedlář a), Patrik Zima b), Tomáš Němec b) and František Maršík b) a) SIGMA Research and Development Institute s.r.o. J. Sigmunda 79, 783 50 Lutín, Czech Republic b) Institute of Thermomechanics, Academy of Sciences of the Czech Republic, v.v.i. Dolejškova 5, 182 00 Prague 8, Czech Republic Email: milan.sedlar@sigma-vvu.cz The cavitating flow behaviour is very sensitive to nuclei content, which is undoubtedly dependent on the physical properties of the liquid. For water, it is believed that heterogenous nucleation initiators prevail over homogeneous nucleation and this is understood to be the reason why the classical nucleation theories are regarded as unreliable for the treatment of cavitation. As a result, the problem of nuclei content is typically treated either empirically or experimentally. In this paper we show how the empirical approach can be used to obtain a useful picture of the cavitation flow aggressiveness (erosion potential) using numerical modelling of the turbulent cavitating flow. In addition, we present the latest advances in the understanding of the bubble nucleation process under cavitating conditions based on the modified binary nucleation theory. In this article we also shortly describe the experimental research of the cavitating flow aimed at the validation of the erosion potential model, development of the nuclei-content measurement and the validation of the bubble nucleation model. As far as the practical application of our work is concerned, the paper concentrates on an evaluation of the cavitation erosion potential in the hydraulic machinery, mainly water pumps and turbines. Introduction In general, there are three major reasons for numerical modelling of cavitation in industrial applications. The first reason is to predict changes in the flow field caused by the cavitation phenomena, which result mainly in a degradation of machine performance. The second reason is to determine cavitation instabilities, which can generate unwanted noise and vibrations. The third reason is to assess the potential of material erosion due to cavitation and to determine the areas on the blade surface (for example in pumps), which are most endangered with erosion. In all the above cases cavitation depends on many factors, which can be divided into two categories: hydrodynamic factors (such as flow parameters or turbulence level) and factors associated with the liquid properties (such as surface tension, bubble content and liquid composition). Nevertheless cavitation is mainly treated as a solely hydrodynamic problem and the dependence on the physical properties of the liquid is typically neglected. Prediction of cavitation phenomena in hydraulic devices is usually based on the assumption that a given spectrum of cavitation nuclei flow through the regions with rapidly changing static pressure, which results in a very complicated dynamic behaviour of the cavitation bubbles. From the point of view of an engineer one of the important challenges of the cavitation research is the determination of the number and size of the cavitation nuclei. These quantities naturally depend on the liquid properties; however, they are usually predicted empirically or by rather expensive and complicated measurements on the case-to-case basis. The consequences are most obvious in the case of water when the experimental measurements of the cavitation events under exactly the same hydrodynamic conditions can give very different results. The main problem in the theoretical estimation of the cavitation nuclei spectrum in water is that the classical nucleation theory predicts only one (critical) bubble size and that the bubble nucleation rate is much higher than the experimentally observed rate. This is true mainly in the case of pure water. The situation is simplified when we consider that the water running trough the hydraulic machinery parts contains a known number of air-

filled or vapour-filled microbubbles of known size distribution. Cavitation erosion model The main contribution to material erosion caused by cavitation arises from the mechanical effects of the violent collapses of bubbles near the solid surface. These effects can be represented by the impact of a spherical shock wave propagated from the centre of the collapsing bubble or by a jet produced during an asymmetric bubble collapse. These two mechanisms act on the solid surface either directly or indirectly due to plastic deformations of the surface. Provided that the cavitation bubble flows through the regions with rapidly changing static pressure, its local radius is obtained as the solution of the Rayleigh-Plesset equation [1 3]: 2 D R R + 2 Dt l DR 4ν + R DR 2σ R0 + [1 ( ) Dt ρ R R 3 2 e 3κ ( ) 1 ] 2 Dt L pv p0 R0 3κ p0 p R D = [ 1 ( ) ] + + ( pg p) ρ R ρ ρ c Dt l l l = (1) Here p 0 is the liquid ambient pressure at undisturbed initial condition, p v is the equilibrium vapour pressure, p g is the pressure of gas mixture inside the bubble, ρ l is the liquid density, c l is the sound velocity of the liquid, σ is the surface tension of the liquid and κ is the polytropic index for the gas mixture inside the bubble. ν e represents the effective viscosity [4]. In the following calculations the isothermal behaviour of the gas mixture is supposed, which corresponds to the value κ = 1. It is assumed that the bubble interior is formed by a mixture of non-condensable gases obeying the polytropic law p g R 3κ 3κ = p g0 R 0, (2) and the initial gas pressure holds p g0 = p 0 - p v + 2σ/R 0. (3) This assumption is very important because only bubbles with gas content can oscillate with their natural frequency and reach more collapses. The mass of gas inside the bubble is assumed to be constant with no phase change. A new model of the cavitation erosion potential is presented in this article. It is based on the estimation of the energy dissipated by the collapses of the cavitating bubbles. In this model, the Runge- Kutta fourth-order scheme is applied to integrate the Rayleigh-Plesset equation along the flow streamlines obtained from the 3D Reynoldsaveraged Navier-Stokes equations. The adaptive step-size algorithm is employed to provide sufficiently small time steps for marching through violent bubble collapses, especially the first one. The numerical algorithm is fully described in previous works [1 3] as well as in the proceedings of ICPWS XIV [5]. By neglecting the energy portion emitted as an acoustic energy or used to evaporate/condense the vapour and heat up the non-condensable gas inside the bubble we can assume that all the energy dissipated during the bubble collapse is used to form the shock wave propagating from the bubble centre. One half of the shock wave energy (emitted towards the solid surface) is supposed to represent the erosion potential ΔE EP : ΔE EP = CΔE i, C = 1/2, (4) ΔE i denotes the energy dissipated during the i-the collapse of the bubble. ΔE i is obtained as the difference between the work done by the pressure inside the bubble p b against the ambient liquid pressure p to expand the bubble from the minimum radius R min,i to the maximum radius R max,i during the i-the growth and the same work done during the (i+1)-th bubble growth [6] : ΔE i+1 = W growth W growth R max, i R min, i R R - W growth R max, i+ 1 R min, i+ 1, R max max 2 R min = 4π R ( p pb) dr. (5) min The effect of liquid viscosity, compressibility and surface tension is neglected in the present model. The values of ΔEEP must be calculated for each bubble in the ensemble of bubbles of different initial sizes and for each individual collapse of a bubble of the given size along the streamlines nearest to the solid surface. Initial spectrum of cavitation nuclei In our numerical model we take into account a finite number of nuclei sizes in water with a given discrete spectrum. Typically, we prescribe 10 initial nuclei radii in the range from 10-5 m to 2.10-4 m (Fig. 1). The initial bubble size distribution is assumed empirically according to measurements. The spectrum of cavitation nuclei can be measured in the test facility used for the pump tests or, more frequently, it is taken from the literature. There is a 2

lot of data measured in cavitation tunnels with various configurations (e.g., measurements [7] used in the cavitation analysis presented in this paper), but unfortunately there is a lack of measurements for industrial applications. The reason is that monitoring the bubble distribution during the industrial tests of hydraulic machinery is very expensive and time consuming. Further problems arise from scaling the cavitation events (from the test pump to the real-size pump) and from the fact that during the design of a hydraulic machine little information is available about the physical properties of water; the spectrum of cavitation nuclei is typically missing. The situation would be less complicated if there was a correct physical model able to predict the nuclei distribution based on the basic properties of water (like temperature, ambient pressure, surface tension etc.). maintaining constant volume flow rate. The transit time of one fluid particle resulting simply from a complete tunnel loop capacity is 72s for the maximum flow rate. The currently tested hydrofoils are prismatic with a typical chord length of 100 mm and a maximum span of 150 mm (corresponding to the width of the test section). The profile incidence angle can vary between 0 and ± 180. The test section is made of organic glass to facilitate visualization (Fig. 3). To enable monitoring of the cavitation nuclei in the inlet flow to the test section a bypass section is installed allowing to measure nuclei content using the acoustic spectrometer. Before the nuclei-content measurement is put into operation we assume for the inlet flow in our present numerical simulations the nucleus population shown in Fig. 1. Figure 1: Nuclei density distribution The modified theory of homogenous nucleation shown later in this article has already shown some promise and could become useful in determining the initial bubble spectrum. Experimental research in a cavitation tunnel In 2007, a new cavitation tunnel was built and put into operation in the SIGMA R&D Institute. The tunnel was designed to study the development of cavitation in hydraulic machines, and especially the erosion process triggered by cavitation. The facility is a closed, variable pressure, horizontal plane water tunnel (Fig. 2) for isolated 2-D and 3-D hydrofoils. The rectangular test section has inner dimensions 150 x 150 x 500 mm, which correspond to the tunnel inlet velocity 25 m/s for the maximum flow rate of the variable-speed driven axial-flow pump. The capacity of the main tank equipped with two sets of honeycombs is 35m 3. The closed loop is equipped with both compressor and vacuum pumps capable of creating different pressure levels while Figure 2: Cavitation tunnel An extensive tunnel testing has been performed to verify the tunnel functionality for a wide range of flow regimes and to compare observations with the preliminary numerical analysis. Figure 4 shows a typical pattern of attached cavitation starting behind the leading edge at about 8% of the chord length and disappearing at about 37% of the cord length. Supercavitation regime with the bubbles collapsing far behind the blade trailing edge can be seen in Fig. 5. 3

Figure 3: Tunnel test section Figure 4: Attached cavitation regime Figure 5: Supercavitation regime As was already stated, the design of the tunnel is oriented especially for a study of the cavitation erosion. This phenomenon exhibits a rather complicated time evolution of the mass-loss rate. Many different types of dependencies can be obtained experimentally depending on the material used and the erosion process typically undergoes four basic modes [7]: Incubation, during which no mass loss is observed. During this period the material undergoes plastic deformation in the form of rather small pits, which do not overlap. Acceleration, during which the rate of mass loss of eroded material grows linearly with time. Steady state, during which the mass loss rate is constant in time. Attenuation, during which the mass loss rate decreases with time. The decrease may be a consequence of weaker collapses due to decreased adverse pressure gradient. As a result, the actual erosion pattern on the blade surface is a function of time and the development of the erosion pattern has to be recorded during the experiment. In addition, the nuclei content has to be known and controlled accurately during the experiment. The first hydrodynamic tests in the tunnel are aimed to quantify the erosion potential by pitting tests during the incubation period. The erosion pits in the metal surface are usually circular with a diameter ranging from a few micrometers to one millimeter. The larger the initial cavitation nuclei, the larger the resulting pits. From a typical nuclei distribution (Fig. 1) we can conclude that the number of small pits is much higher than the number of the large ones. While the dependence of the number of events on the pit diameter has no inflexion point [8], the contribution to the eroded area has its maximum depending on the initial nuclei density distribution. Usually the nuclei in the range from 10 μm to 200 μm give the highest contribution to the material erosion [8]. Figure 6 shows the region on the hydrofoil where the material suffered from the plastic deformation. In Fig. 7 detail of the pits of different size is shown. When first signs of cavitation erosion are observed on the hydrofoil the pits are scanned using the optical profilometer FRT. The scan of the surface is recorded and the cavitation experiment is resumed with the same operating conditions. The procedure is repeated several times during the initial stages of erosion pattern development. An example image of the profilometric measurement of the eroded surface is shown in Fig. 8. The size of the scanned area shown in the figure is 3x3 mm. Figure 6: Incubation mode of cavitation 4

Figure 7: Pits of different sizes on the blade surface 13 times. Generally, the larger the nuclei, the lower the relative growth. Smaller bubbles collapse sooner than the larger ones. All first collapses are located between 34% and 36.5% of the chord length. In reality, the bubbles typically survive only the first few rebounds before they fission. As a result the most important collapses can be found in the region 34-40% of the chord length, which agrees well with the experimental observation (Fig. 4). Figure 11 shows the cumulative erosion potential of all bubbles of the same size along the streamline. The erosion potential of the first collapses is several orders higher than for the successive rebounds. In the detail picture of Fig. 11 the location of the first collapses can be seen for bubbles originating from different nuclei sizes. The maximum of the cumulative energy of the first collapses can be found for the bubbles with the initial radius 14 μm. Figure 8: Scan of the eroded surface with FRT optical profilometer. Size of scanned area 3x3 mm, resolution 10 μm Numerical analysis of cavitating flow in cavitation tunnel Detailed numerical analysis of the cavitating flow in the cavitation tunnel was carried out using the numerical method and cavitation erosion model described above. Various flow regimes were tested; however, to compare the results with those of experiments only one case of closed cavitation regime on the hydrofoil surface was considered. This regime corresponds to the flow conditions represented by the visualisation in Fig. 4. To avoid the influence of the side boundary layers the results were evaluated at mid-span of the hydrofoil. Figure 9 shows the typical streamline in the mid-span plane close to the blade surface and the corresponding static pressure distribution. The dynamics of two bubbles originating from the smallest (10 μm) and the largest (200 μm) cavitation nuclei (see nuclei distribution in Fig. 1) can be seen in Fig. 10. The relative growth of the two nuclei is quite different: the radius of the smallest nuclei increases 185 times before the first collapse while the largest one increases about Figure 9: Streamline at mid-span and the corresponding distribution of static pressure Figure 10: Dynamics of the smallest (fine line) and the largest (thick line) cavitation nucleus along the streamline in Fig. 9 5

the first collapses is slightly lower now, which corresponds to slightly lower bubble relative growth (the radius of the smallest nuclei increases 169 times while the largest one increases 11 times). Figure 11: Cumulative erosion potential of bubbles of different size along the streamline from Fig. 9 Numerical analysis of cavitating flow in pump impeller As stated above our aim is to study cavitation in hydraulic machines, and especially the erosion process associated with this phenomenon. Our test case for the theory and methodology used above is the blade damage of the cast-iron mixed-flow pump impeller. The 3D model as well as the picture of the cavitation damage on the real impeller can be seen in Fig. 12. Figure 13 shows several streamlines near the suction surface of the blade, along which the cavitation analysis was performed for 10 initial nuclei radii in the range from 10-5 m to 2.10-4 m with the nuclei-density distribution seen in Figure 1. As described in the previous paragraph, the erosion potential of the first collapses is several orders higher than the potential of other ones. As a result the region on the blade surface most endangered with the cavitation erosion should coincide with the location of the calculated first collapses of the cavitation bubbles. Figure 14 compares the location of the first calculated collapses with the real erosion pattern. The agreement is very good. The fact that the region on the blade damaged with cavitation erosion is quite wide can be related to the flow unsteadiness and to changes of the pump operating point. The erosion potential along the streamline passing through the centre of the erosion hole can be seen in Fig. 15. Comparing to the case of the tunnel hydrofoil (Fig. 11), the erosion potential of Figure 12: Impeller geometry and cavitation damage of the blades Figure 13: Computational streamlines close to the suction surface of impeller blade Advanced cavitation modelling using multicomponent classical nucleation theory In this section, an outlook of the future possibilities in cavitation modelling using the Classical Nucleation Theory (CNT) is presented. As shown earlier in this paper, the current state of cavitation modelling in the commercial CFD codes is restricted to the description of bubble dynamics using a severely reduced Rayleigh-Plesset equation, with the nuclei density distribution prescribed empirically. The reason for relying on empirical distributions lies in the fact that the existing 6

theoretical predictions of homogeneous nucleation rates for cavitation in water are rather inaccurate. The usual formulation of CNT [4, 9, 10, 12] predicts the nucleation process to occur at large negative pressures of hundreds of megapascals at room temperature rendering the homogeneous nucleation process highly improbable under the thermodynamic conditions of the water flow in hydrodynamic machines studied in this work. Figure 14: Location of the first calculated collapses compared with the erosion pattern Figure 15: Cumulative erosion potential of the first collapses of bubbles along the streamline passing through the centre of the hole in Fig. 14 Let us point out here that the deficiencies of the CNT predictions are caused by the oversimplifying assumptions made within the theory. In this work, we demonstrate the procedure required to increase the accuracy of CNT. Emphasis will be placed on the proper evaluation of the nucleation work whose extreme (saddle point) is critical for the evaluation of the nucleation rate. The nucleation work is the work necessary to create a bubble of a given volume V and composition (mole fractions) x g1,...x gn of the components 1,, N within a liquid mixture of temperature T, pressure p, and composition x l1,...,x ln. We will ascribe the prevailing component (water in this case) the subscript 1. The additional components of the liquid can be, such as in our case, the dissolved gases. The nucleation work is evaluated consistently as an increase of the grand thermodynamic potential Ω whose total differential follows dω= SdT pdv nd i μi + σda, (6) i where S is entropy, n i are numbers of molecules of the i-th component, μ i is the chemical potential of the i-th component, σ is the surface tension of water [13], and A is the surface area. The differential (6) has to be integrated over a reversible path between the thermodynamic state of the parent aqueous mixture and the thermodynamic state of a given bubble surrounded by the aqueous liquid mixture. As a result, the nucleation work W takes the form N W = Aσ + Vp+ niδμi, (7) i=1 where Δμi is the difference between the chemical potentials of the gaseous- and the liquid-phase thermodynamic states of component i. The general formula for nucleation work of an N-component bubble (7) has to be evaluated for the particular mixture of our interest. For our flow of ordinary water in a pump we choose to describe the flow medium as a mixture of water and dissolved air (constituted by nitrogen, oxygen, argon, and carbon dioxide). The concentrations of the respective gases in water are given by their equilibrium concentrations under the pressure of one atmosphere, which can be calculated using the Henry constant (shown in Table 1 for selected gases). k H p i x i [GPa] [Pa] [1] N 2 8.772 79118.6 9.02 10-6 O 2 4.492 21223.5 4.72 10-6 CO 2 0.174 38.8074 2.24 10-7 Table 1: Henry constant k H [11] at 300 K for nitrogen, oxygen, and carbon dioxide; their partial pressure pi in air at one atmosphere, and the corresponding equilibrium mole fractions in water x i To make the theoretical description and its numerical solution feasible, we will, however, simplify the water-air mixture to a binary system of 7

water and nitrogen as the first approximation. In such a case the nucleation work takes the form 2 4 3 W = 4πσ r + πpr + 3 xl1p xl2 p + ktn 1 ln + ktn2 ln, (8) p x k x sat g1 where r is the bubble radius, p sat is the saturation pressure of water [15], k H is the Henry constant [11] given by k H l 2 l2 H pg2 = lim. (9) x x 0 ni is the number of molecules of water (subscript 1), and nitrogen respectively (subscript 2), inside the bubble and it can be calculated as n x VN gi A i = N xg im i ρ i= 1 gi g2, (10) where ρ gi is the density of the (gas-phase) component i inside the bubble (under the pressure 2σ pg = p + ) and N A is the Avogadro constant. r The nucleation work is shown in Fig. 16 as a function of the bubble radius (in nanometers) and the mole fraction of nitrogen constant [11]) inside the bubble. A typical saddle-shaped surface of the nucleation work can be observed, forming an energy barrier to nucleation. The lowest maximum of this energy barrier W (i.e., the saddle point) is crucial for the evaluation of the nucleation rate whose general form is [14] * c = 0(1) λ W J exp kt. (11) 2π det D kt The evaluation of formula (11) involves, first of all, the determination of the saddle point W of Eq. (7). As the nucleation work is generally a function of N independent variables (bubble radius r, and mole fractions of admixtures x g2,...x gn ) the search for the saddle point might become computationally intensive. We, therefore, selected a simpler binary mixture of water-nitrogen for an exemplary calculation. On the other hand, as nitrogen is the main component of air, the nucleation characteristics of this binary system can be taken as a rough approximation for the description of bubble nucleation in the cavitating water-air system. In Figs. 17 21 the nucleation parameters of the water-nitrogen liquid mixture, calculated using the theory presented above, are shown as functions of temperature (0 80 C ) and pressure (1 15 kpa). The mole fraction of nitrogen in water was taken x l2 = 1.16 10-5, i.e., its equilibrium value at 300 K Figure 16: Nucleation work W of the waternitrogen binary bubble as a function of the bubble radius and nitrogen mole fraction (1 zeptojoule [zj] is 10-21 J). The saddle point of the nucleation work W is denoted by the black dot. The thermodynamic state of the parent liquid mixture is 300 K, 101325 Pa, x l2 = 1.16 10-5 (i.e., the equilibrium concentration of dissolved nitrogen under 1 atm according to the Henry Figure 17: The log 10 -scaled nucleation rate J [m 3 s 1 ] in the water-nitrogen liquid mixture calculated according to Eq. (11) as a function of pressure and temperature of the liquid. The mole fraction of the dissolved nitrogen is x l2 = 1.16 10-5. The dashed line shows the saturation pressure of water [15] 8

Figure 18: The critical nucleation work W [zj] corresponding to the nucleation rate shown in Fig. 17. The values are calculated numerically from the saddle point of Eq. (8) Figure 19: Critical radius r [nm] corresponding to Fig. 17 Figure 20: Number n g1 * of water molecules in the critical bubble corresponding to Fig. 17 Figure 21: Number n g2 of nitrogen molecules in the critical bubble corresponding to Fig. 17 (according to the Henry constant [11]). For clarity, the saturation curve p sat (T) [15] is shown in all the figures as a dashed line. We can see that we no longer need the large negative pressures required by the previous theoretical descriptions [10, 12] to achieve an observable homogeneous nucleation process; we just need to sufficiently lower the pressure under the saturation pressure of water. At 25 C, for example, the nucleation process is predicted to occur at a pressure of roughly 1 kpa, which is a small but positive pressure. The result of our theoretical treatment can be summarized as follows: if the thermodynamic state of water is around 20 C above its saturation curve at a given pressure, one can expect homogeneous nucleation of bubbles (see the temperature difference between the saturation curve and the curve of J = 10 10 m 3 s 1 in Fig. 17). Summary and Conclusion In this paper we have shortly described the numerical modelling as well as the experimental research of cavitation in hydraulic machines. The main interest was focused on the flow aggressiveness associated with cavitation. The presented numerical model predicts regions highly endangered by the bubble collapses as well as the energy of these collapses denoted as erosion potential. The first stage of experimental research in the cavitation tunnel was also presented. This stage is aimed at validation of the erosion potential model, visualisation of the cavitation bubbles, development of the nuclei content measurement and the validation of the bubble nucleation model. Though the nuclei content in the numerical model was still determined empirically, the agreement of 9

the theoretical results and the observations is encouraging. The measurements of the cavitation nuclei in water by light scattering and the acoustic spectrometry are being completed to provide accurate nuclei distribution. Finally, we have shown that the Classical Nucleation Theory can be improved to reliably predict the process of bubble nucleation under cavitation conditions. As far as the practical application of our work is concerned, the paper demonstrates the analysis of the cavitation erosion in the impeller of the mixedflow water pump. Acknowledgments This work has been supported by the Grant Agency of Czech Republic under grant 101/07/1612 The effect of physical properties of water on bubble nucleation and cavitation damage in pumps and by the Grant Agency of the Czech Academy of Sciences under grant KJB400760701 Classical multicomponent nucleation theory for cavitation and condensation. Literature [1] M. Sedlar: Calculation of Quasi-Three- Dimensional Incompressible Viscous Flows by the Finite Element Method. Int. J. Num. Meth. Fluids 16: 953-966 (1993). [2] M. Sedlar, F. Marsik, and P. Safarik: Modelling of Cavitated Flows in Hydraulic Machinery Using Viscous Flow Computation and Bubble Dynamics Model, Proc. Fluid Dynamics 2000, TU Prague (2000). [3] M. Sedlar, F. Marsik, and P. Safarik: Numerical Investigation of Blade and Tip Clearance Geometry Influence on Tip Clearence and Tip Vortex Cavitations. Proc. 5 th ISAIF, Vol.1, Gdansk: 237-245 (2001). [4] Ch. E. Brennen: Cavitation and Bubble Dynamics. Oxford University Press (1995). [5] P. Zima, M. Sedlar, and F. Marsik: Bubble Creation in Water with Dissolved Gas: Prediction of Regions Endangered by Cavitation Erosion. Water, Steam, and Aqueous Solutions for Electric Power. Kyoto, Maruzen Co., Ltd.: 232-235 (2005). [6] M. Müller: Dynamic behaviour of cavitation bubbles generated by laser. Ph. D. Dissertation, Faculty of Mech. Engineering, Technical University of Liberec (2007). [7] T.A. Waniewski, C. Hunter, and C.E. Brennen: Bubble Measurements Downstream of Hydraulic Jumps. Int. J. Multiphase Flow 27: 1271-1284 (2001). [8] J. P. Franc and J. M. Michel: Fundamentals of Cavitation, Kluwer Academic Publishers (2004). [9] M. Blander and J.L. Katz: Bubble Nucleation In Liquids. AIChE Journal, 21: 833-848 (1975). [10] F. Caupin and E. Herbert: Cavitation in Water: A Review. C. R. Phys. 7: 1000-1017 (2006). [11] R. Fernandez-Prini, J. L. Alvarez, and A. H. Harvey: Henry's Constants and Vapor-liquid Distribution Constants for Gaseous Solutes in H2O and D2O at High Temperatures. J. Phys. Chem. Ref. Data 32: 903-916 (2003). [12] S. F. Jones, G. M. Evans, and K. P. Galvin: Bubble Nucleation from Gas Cavities - A Review. Adv. Colloid Interface Sci. 80: 27-50 (1999). [13] IAPWS Release on Surface Tension of Ordinary Water Substance. IAPWS (1994). [14] T. Němec: Homogeneous Nucleation in Selected Aqueous Systems. Ph.D. thesis, Czech Technical University in Prague (2006). [15] W. Wagner and A. Pruß: The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. J. Phys. Chem. Ref. Data: 31:387 (2002). 10