- Email: [email protected]
Impact of high-speed steam-droplet spray on solid surface
Fluid Dynamics Research 40 (2008) 627 – 636
Impact of high-speed steam-droplet spray on solid surface Toshiyuki Sanada∗ , Masao Watanabe, Minori Shirota, Masao Yamase, Takayuki Saito Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Nakaku, Hamamatsu 432-8561, Japan Received 3 November 2007; received in revised form 3 December 2007; accepted 3 December 2007 Available online 18 April 2008 Communicated by S. Fujikawa
Abstract A novel technique for the generation of impact by a high-speed steam-droplet spray is proposed. Relatively lowpressure super-purified steam (0.1–0.2 MPa) is mixed with super-purified water in a nozzle, and then sprayed on a solid surface, which is located at approximately 10 mm from the nozzle. This spray is found to cause harsh erosion. The most striking result of this experiment is that the degree of erosion is strongly dependent on temperature; this dependence is hardly explained by the classical droplet impact theory. We recognize the occurrence of a strong focused rarefaction wave in the middle of the droplet; this rarefaction wave may cause cavitation. The existence of cavitation may be supported by the temperature susceptibility of erosion. We experimentally measure both the droplet velocity and diameter distributions by a Phase-Doppler Anemometer. We also numerically study the dynamics of a high-speed liquid droplet impact on a solid surface by solving the Euler equation using the conditions obtained by the experiments. We discuss the possibility of the formation of cavitation bubbles as the primary cause of the experimentally observed harsh erosion on a solid surface. © 2008 The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved. Keywords: Droplet impact; Spray; Erosion; Cavitation; Cavitation nuclei
1. Introduction It is well-known that the liquid droplet impact on a rigid surface causes significant damages to the solid surface in various areas of industrial applications such as steam turbine blade operation and rain drop collision on a hypersonic plane. On the other hand, the liquid droplet impact is also applied for cleaning ∗ Corresponding author. Tel./fax: +81 53 478 1605.
E-mail address: [email protected] (T. Sanada). 0169-5983/$32.00 © 2008 The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved. doi:10.1016/j.fluiddyn.2007.12.014
628
T. Sanada et al. / Fluid Dynamics Research 40 (2008) 627 – 636
surfaces during the manufacturing of semiconductor. In this study, a novel technique for the generation of impact by a high-speed steam-droplet spray is proposed. Relatively low-pressure super-purified steam (from 0.1 to 0.2 MPa) is mixed with super-purified water in a nozzle and sprayed on a solid surface, which is located at approximately 10 mm from the nozzle. When the mixture is sprayed on the solid metal surface, the surface is severely damaged and harsh erosion is observed. The most striking result of this experiment is that the degree of erosion is strongly dependent on temperature; this dependence is hardly explained by the classical droplet impact theory. The pressure development process in the liquid–solid impact is well modeled mathematically, most frequently based on the one-dimensional “waterhammer” or elastic impact theory (Heymann, 1969). The typical expression of this model is written as P = 0 C0 V0 ,
(1)
where 0 and C0 are the density and sound velocity of the undisturbed liquid and V0 is the impact velocity. Although various modifications have been introduced to this formula, neither the liquid droplet temperature nor the surrounding thermodynamic environment has gained recognition as the prime factor for pressure development. On the other hand, our experiments strongly indicate that the surface erosion caused by the liquid droplet impact is highly susceptible to temperature. In other words, the droplet temperature and thermodynamic environment are extremely significant factors in the surface erosion or pressure development in the liquid–solid impact. Based on this experiments that the solid surface erosion is highly susceptible to temperature, we propose a hypothesis that cavitation bubbles are the dominant factor of this erosion. In this study, we examine the possibility of the formation of cavitation bubbles using a numerical approach. 2. Experimental apparatus and procedure In this study, steam and water are mixed in a nozzle. The mixture is accelerated in a converging–diverging nozzle and sprayed on a solid surface. The steam is generated by an electrical heating of super-purified water and stored in a pressure tank. The steam pressure p and water flow rate q range from 0.05 to 0.2 MPa and from 100 to 500 mL/min, respectively. The distance between the nozzle and the solid surface, h, is set as 10 mm. A schematic diagram of the experimental apparatus is shown in Fig. 1. The distribution of droplet diameters and velocities in the steam-droplet spray was measured by a PDA (Phase-Doppler Steam Pressure meter Water
Steam Traverse
Filter Purified water Nitrogen gas
Nozzle Water flow meter
Heater
Metal Pump
Fig. 1. Experimental apparatus.
Purified water
T. Sanada et al. / Fluid Dynamics Research 40 (2008) 627 – 636
629
Anemometer, TSI 1-component). For comparison, the droplet diameters and velocities of an air-droplet spray were also measured. Surface erosion was quantitatively measured by an Atomic Force Microscope (AFM, Keyence, VN8010). The experimental parameters selected in this study were p and q. 3. Experimental results and discussion 3.1. Droplet diameter and velocity Fig. 2 shows droplet diameters and droplet velocities observed in both the steam-droplet spray and air-droplet spray. The experimental parameters are p and q. All the measurements were repeated thrice, and the averaged mean values are shown in these graphs. The droplet velocities in both the air-droplet spray and steam-droplet spray increased with an increase in pressure and decreased with an increase in the water flow rate. The droplet diameters in both the air-droplet spray and steam-droplet spray monotonously increased with the water flow rate, and showed almost the same value regardless of the change in the pressure. It was found that the diameters were of the order of 10 m, and the velocities were observed in the range of 150–300 m/s. 3.2. Observation of the eroded surface The surface erosion of metal test pieces was quantitatively measured by AFM. The properties of the test piece materials, i.e., aluminum, steel, and brass, are listed in Table 1. The steam-droplet mixture was sprayed on the surface of each test piece for 10 min under the conditions of p of 0.2 MPa, q of 300 mL/min, and h of 10 mm. The distributions of the surface roughness before and after the spray
350
30
25
250
Droplet diameter [µm]
Droplet velocity [m/s]
300
200 150 0.05MPa air 0.1MPa air 0.05MPa steam 0.1MPa steam
100 50
20
15
10
0.05MPa air 0.1MPa air 0.05MPa steam
5
0.1MPa steam
0
0 0
100
200 300 400 Water flow rate q [mL/min]
500
600
0
100
200 300 400 Water flow rate q [mL/min]
Fig. 2. Droplet diameter and velocity: (a) droplet velocity, (b) diameter.
500
600
630
T. Sanada et al. / Fluid Dynamics Research 40 (2008) 627 – 636
Table 1 Erosion test condition
z [µm]
Case 1 Case 2 Case 3
Material
Material marks
Hardness
Aluminum Steel Brass
A5052 SUJ2 C2600P
HRB90 HRB40
Pre surface Steam Air
1.5 1 0.5 0 -0.5 -1 -1.5 0
20
40
60
80 x [µm]
100
120
140
160
0
20
40
60
80 x [µm]
100
120
140
160
0
20
40
60
80 x [µm]
100
120
140
160
0.1 z [µm]
0.05 0 -0.05
z [µm]
-0.1
0.15 0.1 0.05 0 -0.05 -0.1 -0.15
Fig. 3. Surface roughness: (a) aluminum, (b) steel, (c) brass.
are shown in Figs. 3(a)–(c), with the results of the air-droplet spray for comparison. Surprisingly, drastic increases in the surface roughness, which indicate harsh erosion, are observed for all the test pieces in the case of the steam-droplet spray. It should be emphasized that the characteristic depth of the surface roughness of aluminum, which is rather soft and consequently easy to be eroded, was approximately 1.2 m by the steam-droplet spray for only 10 min. These results show the significant magnitude of the impact caused by the steam-droplet spray on the solid surface.
T. Sanada et al. / Fluid Dynamics Research 40 (2008) 627 – 636
631
100 µm
Fig. 4. AFM image of surface erosion: (a) original surface, (b) water droplet in steam, (c) hot water droplet in hot air, (d) water droplet in hot air, (e) water droplet in air.
Next we investigate the thermodynamic effects on the solid surface erosion by the droplet mixture spray. The surface erosion of an aluminum test piece caused by the water droplets in a hot air spray (inlet air temperature 430 K) and the hot water droplets (inlet water temperature 363 K) in a hot air spray, in addition to the steam-droplet and air-droplet sprays, were measured. Figs. 4(a)–(e) show the surface differential images of the original surface and the surfaces eroded by the steam-droplet, hot air-hot water droplet, hot air-droplet, and air-droplet sprays, respectively. These images suggest that surface erosion caused by the spray is susceptible to the thermodynamic environment or temperature of the sprays. We further examine these effects in the next section. 4. Model and method 4.1. Model and earlier studies The most striking observation from our experiments of the steam-water droplet spray on a solid surface is that the degree of erosion on the solid surface is highly susceptible to temperature. Based on this, we regard the phase change as a significantly important factor; we propose a hypothesis: “Cavitation bubbles cause this erosion: An extremely high pressure is generated due to the collapse of cavitation bubbles caused by the propagation of both the compression and expansion waves inside the liquid droplet”. We examine the contribution of cavitation bubbles inside the liquid droplet to the pressure increase.
632
T. Sanada et al. / Fluid Dynamics Research 40 (2008) 627 – 636
The photographic evidence of the formation and growth of multiple bubbles inside the liquid droplet immediately after the impact was shown in the experimental studies conducted by Brunton and Rochester (1979) and Field et al. (1989) although neither explicit statements of cavitation nor detailed investigations of the mechanism was provided. Rein (1993) discussed the possibility of the existence of cavitation by introducing variety of mechanism proposed in his review paper, and also pointed out that “Besides the high impact pressure and shear stresses occurring during jetting, cavitation inside the drop may contribute to erosion due to a drop impact”. Haller et al. (2002) showed the existence of a low-pressure region inside the liquid droplet by numerical analysis using the front tracking method, and pointed out that the presence of a low pressure, indicating a strong rarefaction in the middle of the droplet, could cause cavitation. A pair of the most important parameters in this process is the impact velocity and droplet diameter. The characteristic droplet diameter and impact velocity are set as 10 m and 200 m/s, respectively, in the following calculation. We solve the flow field of a high-speed liquid droplet in gas impacting a solid surface using the finite difference method in order to calculate the time evolution of pressure distribution and development inside the liquid droplet, and then discuss the possibility of the existence of cavitation. 4.2. Droplet fluid field calculation We solve the flow field of a high-speed liquid droplet in gas impacting on a solid surface by solving the Euler equation for a two-phase compressible fluid in a two-dimensional Cartesian coordinate system (Haller et al., 2003; Harten, 1987). For both the liquid and gas phases, the stiffened-gas equation of state is used to close the system (Haller et al., 2003), P = ( − 1)[E − 21 q 2 ] − ,
(2)
where P , , q, and E are the pressure, density, velocity magnitude, and total energy, respectively. For the modeling of water, the parameters of of 5.0 and of 6.13 × 108 Pa are used (Haller et al., 2002); of 1.4 and of 0 Pa are used for the modeling of gas, which corresponds to the ideal gas equation of state. We solve this two-phase flow field using the level-set method combined with the ghost-fluid method (Fedkiw et al., 1999). For discretization of the system, the third-order ENO-LLF (Shu and Osher, 1989) is used; the third-order TVD Runge–Kutta scheme (Harten, 1987) is also used for time integration. Our computation is performed on uniform 256 × 256 grid points, whose size, x, is set as 0.126 m, with a Courant number of 0.5. It should be noted that the liquid droplet is treated as consisting of only the pure liquid, i.e., a single-phase flow. The physical properties of water, and pv for T of 300 and 350 K, used in this study are 3.534 kPa and 71.69 mN/m, and 41.64 kPa and 63.25 mN/m, respectively (JSME Data Book, 1988). 5. Numerical results and discussion 5.1. Pressure development inside the droplet We calculated the droplet flow field with droplet diameter d of 10 m and impact velocity V of 200 m/s. Time evolution of both the pressure field distribution and density inside droplet is shown in Fig. 5. It is observed that the compression wave generated during the impact propagated upward, and then is reflected at the free surface to become the expansion wave; this qualitatively agrees with results of Haller et al.
T. Sanada et al. / Fluid Dynamics Research 40 (2008) 627 – 636
633
density
-1.5 x 108
3 x 108 [Pa]
Fig. 5. Time evolution of pressure and density distribution inside the liquid droplet: (a) t = 20.0 ns, (b) t = 21.3 ns, (c) t = 22.6 ns, (d) t = 23.9 ns, (e) t = 25.1 ns, (f) t = 26.4 ns, (g) t = 27.7 ns, (h) t = 29.0 ns, (i) t = 30.2 ns, (j) t = 31.5 ns, (k) t = 32.8 ns, (l) t = 34.1 ns.
(2002). We strongly believe that the focusing of the expansion wave is the key factor on cavitation. The maximum pressure of the point closest to the solid surface reaches 0.352 GPa, which agrees well with the impact pressure calculated by using Eq. (1), 0.35 GPa, with C0 of 1.75 × 103 m/s by Eq. (2). It is observed that the minimum pressure or maximum tensile stress (approximately 0.15 GPa) occurs at
634
T. Sanada et al. / Fluid Dynamics Research 40 (2008) 627 – 636
approximately two-thirds of the height (6.6 m), which qualitatively agrees well with the experimental results of Brunton and Rochester (1979) of cavitation inception inside the droplet. As Haller et al. (2003) pointed out, the existence of strong tensile stress may cause cavitation and may also cause severe erosion. It should be emphasized here that for cavitation to occur, there should exist cavitation nuclei. Now, we have to address the most fundamental question: “where do bubbles or bubble nuclei come from?” We will discuss this in the next section from a thermodynamic point of view. 5.2. Cavitation nuclei In super-purified water, as used in our experiments, neither particles nor contaminants exist. In other words, the quality of the liquid seriously hinders cavitation inception. First we discuss the noncondensed gas bubbles in the liquid. The simplest form of the bubble surface pressure pB in the liquid, as in Eq. (3), is used for simplicity: pB = pg + pv − 2/R,
(3)
where pg , pv , and are the noncondensible gas partial pressure, vapor saturated pressure, and surface tension coefficient, respectively. The physical properties of water, , and pv for T of 300 and 350 K, used in this study are 3.534 kPa and 71.69 mN/m, and 41.64 kPa and 63.25 mN/m, respectively (JSME Data Book, 1988). We assume that the dissolved gas is saturated at atmospheric pressure; hence, the equilibrium radius Req of bubble which can exist in the liquid of atmospheric pressure is obtained by Req = 2/pv .
(4)
For example, Req is calculated as 40.6 and 3.04 m at T of 300 and 350 K, respectively. Reminding that the droplet diameter d is 10 m, the equilibrium diameter of the bubble, 81.2 m at T of 300 K is approximately one order larger than d, while that at T of 350 K, 6.08 m is approximately half of d. Hence, from the statistical point of view, we may assume that noncondensible gas bubbles at T of 350 K are possible to be taken inside the droplet, probably accompanied by a complicated break-up action, while those at T of 300 K are not. If this assumption holds, it is also reasonable to state that the difference in the equilibrium bubble diameters at the different temperatures plays a significant role in the generation of a high pressure during the drop impact on a solid surface. Further, it should be noted that it is possible for the bubbles to be absorbed into the liquid droplet by entrapment during the impact on a solid surface or during the droplet generation, or by other mechanisms (Rein, 1993). Here, we face another question: “whether smaller bubbles can exist as a result of break-up”. If the characteristic time for noncondensable gas dissolution into the liquid is significantly longer than that for the vapor, the bubbles with radii smaller than Req , which are generated as a result of the break-up, can exist during the droplet generation and droplet impact. In order to justify this assumption, we have to investigate the bubble dynamics and transport phenomena inside the bubble although not in this paper. Detailed modeling, particularly of the vaporization/condensation process, noncondensable gas dissolution process, spatial distribution of the vapor and gas, etc., are required for further investigation. If these smaller noncondensible gas bubbles exist during the droplet impact, it is possible that bubbles considerably smaller than Req exist during the impacting time due to the series of break-up action in the liquid droplet. The second possible theory is with regard to the molecular defects. Molecular defects in the liquid are also considered to be the candidate of cavitation nuclei (Kato, 1990), which causes erosion. A critical vacancy or bubble size, RC is to be calculated as the intermolecular distance of 10−10 m, and hence, the
T. Sanada et al. / Fluid Dynamics Research 40 (2008) 627 – 636
635
critical tensile strength pC is calculated by pC = 2/RC .
(5)
pC in Eq. (5) at T of 350 K is calculated approximately as the order of 109 Pa. As shown in Fig. 5,
the maximum tensile stress obtained by our calculation is approximately 1.5 × 108 Pa, which is an order smaller than the above calculated value. However, it should be noted that the present calculation is performed in a two-dimensional Cartesian coordinate system. In a three-dimensional coordinate system, it is possible that the magnitude of tensile pressure is considerably greater than that obtained in the two-dimensional coordinate system since the strong tensile stress region is formed as a result of the focus of the expansion pressure wave in the inner region of droplet. The focusing effect is, in general, more significant in the axisymmetric geometry than in the plane geometry. Unfortunately, we do not have sufficient knowledge to discuss how temperature affects these molecular defects, particularly distributions of the size and number densities. For further pursuit of the possibility of molecular defects, an approach totally different from this paper, for example, molecular dynamics simulation, will be required. 6. Conclusion We have developed a new technique for the generation of impact using a high-speed mixture of steam and purified water droplets, in which the droplet diameters are of the order of 10 m, and the droplet velocities are of the order of 100 m/s. Microscope analysis of several metal surfaces after spraying of the mixture revealed the presence of numerous pits due to erosion. In addition, the degree of erosion is strongly dependent on temperature. We numerically studied the cause of the generation of a significantly large pressure during a liquid droplet impact on a solid surface. As a result, it was observed that the compression wave generated on the impact propagated upward, and then reflected at the free surface to become an expansion wave, subsequently, the expansion wave was focused. The maximum pressure at the point closest to the solid surface reached 0.352 GPa, and the minimum pressure or maximum tensile stress of approximately 0.15 GPa occurred at the position of focusing the expansion wave. The existence of strong tensile stress may cause cavitation inside the liquid droplet and may cause the solid surface erosion. Acknowledgments The authors express their gratitude to Mr. Hiroshi Tsubouchi at the Intellectual Property Management Center of Kyushu University for giving the authors an opportunity to work on this project. The authors also wish to express their appreciation to Mr. Y. Nihino, Mr. M. Yamaguchi, and Mr. M. Ooe, members of Kyoritsu Gokin Co. Ltd. (EVERLOY) for their cooperation in the experiment on PDA measurements. This study was supported by an Industrial Technology Research Grant Program in 2006 from the New Energy and Industrial Technology Development Organization (NEDO) of Japan. References Brunton, J.H., Rochester, M.C., 1979. Erosion of solid surfaces by the impact of liquid drops. In: Preece, C.M. (Ed.), Erosion, Treatise on Materials Science and Technology, vol. 16. Academic Press, New York, pp. 186–248.
636
T. Sanada et al. / Fluid Dynamics Research 40 (2008) 627 – 636
Fedkiw, R., Aslam, T., Merriman, B., Osher, S., 1999. A non-oscillatory Eulerian approach to interfaces in multimaterial flows (The Ghost Fluid Method). J. Comput. Phys. 152, 457–492. Field, J.E., Dear, J.P., Ogren, J.E., 1989. The effects of target compliance on liquid drop impact. J. Appl. Phys. 65 (2), 533–540. Haller, K.K., Ventikos, Y., Poulikakos, D., 2002. Computational study of high-speed liquid droplet impact. J. Appl. Phys. 92 (5), 2821–2828. Haller, K.K., Ventikos, Y., Poulikakos, D., 2003. Wave structure in the contact line region during high speed droplet impact on a surface: solution of the Riemann problem for the stiffened gas equation of state. J. Appl. Phys. 93 (5), 3090–3097. Harten, A., 1987. Uniformly high order accurate essentially non-oscillatory schemes, III. J. Comput. Phys. 71, 231–303. Heymann, F.J., 1969. High-speed impact between a liquid drop and a solid surface. J. Appl. Phys. 40 (13), 5113–5122. JSME Data Book, 1988. Thermophysical Properties of Fluids, third ed., JSME, Tokyo Kato, H., 1990. Cavitation. second ed.. Maki-Shoten, Tokyo. (in Japanese). Rein, M., 1993. Phenomena of liquid drop impact on solid and liquid surface. Fluid Dyn. Res. 12, 61–93. Shu, C.W., Osher, S., 1989. Efficient implementation of essentially non-oscillatory shock-capturing schemes, II. J. Comput. Phys. 83, 32–78.
Impact of high-speed steam-droplet spray on solid surface Toshiyuki Sanada∗ , Masao Watanabe, Minori Shirota, Masao Yamase, Takayuki Saito Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Nakaku, Hamamatsu 432-8561, Japan Received 3 November 2007; received in revised form 3 December 2007; accepted 3 December 2007 Available online 18 April 2008 Communicated by S. Fujikawa
Abstract A novel technique for the generation of impact by a high-speed steam-droplet spray is proposed. Relatively lowpressure super-purified steam (0.1–0.2 MPa) is mixed with super-purified water in a nozzle, and then sprayed on a solid surface, which is located at approximately 10 mm from the nozzle. This spray is found to cause harsh erosion. The most striking result of this experiment is that the degree of erosion is strongly dependent on temperature; this dependence is hardly explained by the classical droplet impact theory. We recognize the occurrence of a strong focused rarefaction wave in the middle of the droplet; this rarefaction wave may cause cavitation. The existence of cavitation may be supported by the temperature susceptibility of erosion. We experimentally measure both the droplet velocity and diameter distributions by a Phase-Doppler Anemometer. We also numerically study the dynamics of a high-speed liquid droplet impact on a solid surface by solving the Euler equation using the conditions obtained by the experiments. We discuss the possibility of the formation of cavitation bubbles as the primary cause of the experimentally observed harsh erosion on a solid surface. © 2008 The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved. Keywords: Droplet impact; Spray; Erosion; Cavitation; Cavitation nuclei
1. Introduction It is well-known that the liquid droplet impact on a rigid surface causes significant damages to the solid surface in various areas of industrial applications such as steam turbine blade operation and rain drop collision on a hypersonic plane. On the other hand, the liquid droplet impact is also applied for cleaning ∗ Corresponding author. Tel./fax: +81 53 478 1605.
E-mail address: [email protected] (T. Sanada). 0169-5983/$32.00 © 2008 The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved. doi:10.1016/j.fluiddyn.2007.12.014
628
T. Sanada et al. / Fluid Dynamics Research 40 (2008) 627 – 636
surfaces during the manufacturing of semiconductor. In this study, a novel technique for the generation of impact by a high-speed steam-droplet spray is proposed. Relatively low-pressure super-purified steam (from 0.1 to 0.2 MPa) is mixed with super-purified water in a nozzle and sprayed on a solid surface, which is located at approximately 10 mm from the nozzle. When the mixture is sprayed on the solid metal surface, the surface is severely damaged and harsh erosion is observed. The most striking result of this experiment is that the degree of erosion is strongly dependent on temperature; this dependence is hardly explained by the classical droplet impact theory. The pressure development process in the liquid–solid impact is well modeled mathematically, most frequently based on the one-dimensional “waterhammer” or elastic impact theory (Heymann, 1969). The typical expression of this model is written as P = 0 C0 V0 ,
(1)
where 0 and C0 are the density and sound velocity of the undisturbed liquid and V0 is the impact velocity. Although various modifications have been introduced to this formula, neither the liquid droplet temperature nor the surrounding thermodynamic environment has gained recognition as the prime factor for pressure development. On the other hand, our experiments strongly indicate that the surface erosion caused by the liquid droplet impact is highly susceptible to temperature. In other words, the droplet temperature and thermodynamic environment are extremely significant factors in the surface erosion or pressure development in the liquid–solid impact. Based on this experiments that the solid surface erosion is highly susceptible to temperature, we propose a hypothesis that cavitation bubbles are the dominant factor of this erosion. In this study, we examine the possibility of the formation of cavitation bubbles using a numerical approach. 2. Experimental apparatus and procedure In this study, steam and water are mixed in a nozzle. The mixture is accelerated in a converging–diverging nozzle and sprayed on a solid surface. The steam is generated by an electrical heating of super-purified water and stored in a pressure tank. The steam pressure p and water flow rate q range from 0.05 to 0.2 MPa and from 100 to 500 mL/min, respectively. The distance between the nozzle and the solid surface, h, is set as 10 mm. A schematic diagram of the experimental apparatus is shown in Fig. 1. The distribution of droplet diameters and velocities in the steam-droplet spray was measured by a PDA (Phase-Doppler Steam Pressure meter Water
Steam Traverse
Filter Purified water Nitrogen gas
Nozzle Water flow meter
Heater
Metal Pump
Fig. 1. Experimental apparatus.
Purified water
T. Sanada et al. / Fluid Dynamics Research 40 (2008) 627 – 636
629
Anemometer, TSI 1-component). For comparison, the droplet diameters and velocities of an air-droplet spray were also measured. Surface erosion was quantitatively measured by an Atomic Force Microscope (AFM, Keyence, VN8010). The experimental parameters selected in this study were p and q. 3. Experimental results and discussion 3.1. Droplet diameter and velocity Fig. 2 shows droplet diameters and droplet velocities observed in both the steam-droplet spray and air-droplet spray. The experimental parameters are p and q. All the measurements were repeated thrice, and the averaged mean values are shown in these graphs. The droplet velocities in both the air-droplet spray and steam-droplet spray increased with an increase in pressure and decreased with an increase in the water flow rate. The droplet diameters in both the air-droplet spray and steam-droplet spray monotonously increased with the water flow rate, and showed almost the same value regardless of the change in the pressure. It was found that the diameters were of the order of 10 m, and the velocities were observed in the range of 150–300 m/s. 3.2. Observation of the eroded surface The surface erosion of metal test pieces was quantitatively measured by AFM. The properties of the test piece materials, i.e., aluminum, steel, and brass, are listed in Table 1. The steam-droplet mixture was sprayed on the surface of each test piece for 10 min under the conditions of p of 0.2 MPa, q of 300 mL/min, and h of 10 mm. The distributions of the surface roughness before and after the spray
350
30
25
250
Droplet diameter [µm]
Droplet velocity [m/s]
300
200 150 0.05MPa air 0.1MPa air 0.05MPa steam 0.1MPa steam
100 50
20
15
10
0.05MPa air 0.1MPa air 0.05MPa steam
5
0.1MPa steam
0
0 0
100
200 300 400 Water flow rate q [mL/min]
500
600
0
100
200 300 400 Water flow rate q [mL/min]
Fig. 2. Droplet diameter and velocity: (a) droplet velocity, (b) diameter.
500
600
630
T. Sanada et al. / Fluid Dynamics Research 40 (2008) 627 – 636
Table 1 Erosion test condition
z [µm]
Case 1 Case 2 Case 3
Material
Material marks
Hardness
Aluminum Steel Brass
A5052 SUJ2 C2600P
HRB90 HRB40
Pre surface Steam Air
1.5 1 0.5 0 -0.5 -1 -1.5 0
20
40
60
80 x [µm]
100
120
140
160
0
20
40
60
80 x [µm]
100
120
140
160
0
20
40
60
80 x [µm]
100
120
140
160
0.1 z [µm]
0.05 0 -0.05
z [µm]
-0.1
0.15 0.1 0.05 0 -0.05 -0.1 -0.15
Fig. 3. Surface roughness: (a) aluminum, (b) steel, (c) brass.
are shown in Figs. 3(a)–(c), with the results of the air-droplet spray for comparison. Surprisingly, drastic increases in the surface roughness, which indicate harsh erosion, are observed for all the test pieces in the case of the steam-droplet spray. It should be emphasized that the characteristic depth of the surface roughness of aluminum, which is rather soft and consequently easy to be eroded, was approximately 1.2 m by the steam-droplet spray for only 10 min. These results show the significant magnitude of the impact caused by the steam-droplet spray on the solid surface.
T. Sanada et al. / Fluid Dynamics Research 40 (2008) 627 – 636
631
100 µm
Fig. 4. AFM image of surface erosion: (a) original surface, (b) water droplet in steam, (c) hot water droplet in hot air, (d) water droplet in hot air, (e) water droplet in air.
Next we investigate the thermodynamic effects on the solid surface erosion by the droplet mixture spray. The surface erosion of an aluminum test piece caused by the water droplets in a hot air spray (inlet air temperature 430 K) and the hot water droplets (inlet water temperature 363 K) in a hot air spray, in addition to the steam-droplet and air-droplet sprays, were measured. Figs. 4(a)–(e) show the surface differential images of the original surface and the surfaces eroded by the steam-droplet, hot air-hot water droplet, hot air-droplet, and air-droplet sprays, respectively. These images suggest that surface erosion caused by the spray is susceptible to the thermodynamic environment or temperature of the sprays. We further examine these effects in the next section. 4. Model and method 4.1. Model and earlier studies The most striking observation from our experiments of the steam-water droplet spray on a solid surface is that the degree of erosion on the solid surface is highly susceptible to temperature. Based on this, we regard the phase change as a significantly important factor; we propose a hypothesis: “Cavitation bubbles cause this erosion: An extremely high pressure is generated due to the collapse of cavitation bubbles caused by the propagation of both the compression and expansion waves inside the liquid droplet”. We examine the contribution of cavitation bubbles inside the liquid droplet to the pressure increase.
632
T. Sanada et al. / Fluid Dynamics Research 40 (2008) 627 – 636
The photographic evidence of the formation and growth of multiple bubbles inside the liquid droplet immediately after the impact was shown in the experimental studies conducted by Brunton and Rochester (1979) and Field et al. (1989) although neither explicit statements of cavitation nor detailed investigations of the mechanism was provided. Rein (1993) discussed the possibility of the existence of cavitation by introducing variety of mechanism proposed in his review paper, and also pointed out that “Besides the high impact pressure and shear stresses occurring during jetting, cavitation inside the drop may contribute to erosion due to a drop impact”. Haller et al. (2002) showed the existence of a low-pressure region inside the liquid droplet by numerical analysis using the front tracking method, and pointed out that the presence of a low pressure, indicating a strong rarefaction in the middle of the droplet, could cause cavitation. A pair of the most important parameters in this process is the impact velocity and droplet diameter. The characteristic droplet diameter and impact velocity are set as 10 m and 200 m/s, respectively, in the following calculation. We solve the flow field of a high-speed liquid droplet in gas impacting a solid surface using the finite difference method in order to calculate the time evolution of pressure distribution and development inside the liquid droplet, and then discuss the possibility of the existence of cavitation. 4.2. Droplet fluid field calculation We solve the flow field of a high-speed liquid droplet in gas impacting on a solid surface by solving the Euler equation for a two-phase compressible fluid in a two-dimensional Cartesian coordinate system (Haller et al., 2003; Harten, 1987). For both the liquid and gas phases, the stiffened-gas equation of state is used to close the system (Haller et al., 2003), P = ( − 1)[E − 21 q 2 ] − ,
(2)
where P , , q, and E are the pressure, density, velocity magnitude, and total energy, respectively. For the modeling of water, the parameters of of 5.0 and of 6.13 × 108 Pa are used (Haller et al., 2002); of 1.4 and of 0 Pa are used for the modeling of gas, which corresponds to the ideal gas equation of state. We solve this two-phase flow field using the level-set method combined with the ghost-fluid method (Fedkiw et al., 1999). For discretization of the system, the third-order ENO-LLF (Shu and Osher, 1989) is used; the third-order TVD Runge–Kutta scheme (Harten, 1987) is also used for time integration. Our computation is performed on uniform 256 × 256 grid points, whose size, x, is set as 0.126 m, with a Courant number of 0.5. It should be noted that the liquid droplet is treated as consisting of only the pure liquid, i.e., a single-phase flow. The physical properties of water, and pv for T of 300 and 350 K, used in this study are 3.534 kPa and 71.69 mN/m, and 41.64 kPa and 63.25 mN/m, respectively (JSME Data Book, 1988). 5. Numerical results and discussion 5.1. Pressure development inside the droplet We calculated the droplet flow field with droplet diameter d of 10 m and impact velocity V of 200 m/s. Time evolution of both the pressure field distribution and density inside droplet is shown in Fig. 5. It is observed that the compression wave generated during the impact propagated upward, and then is reflected at the free surface to become the expansion wave; this qualitatively agrees with results of Haller et al.
T. Sanada et al. / Fluid Dynamics Research 40 (2008) 627 – 636
633
density
-1.5 x 108
3 x 108 [Pa]
Fig. 5. Time evolution of pressure and density distribution inside the liquid droplet: (a) t = 20.0 ns, (b) t = 21.3 ns, (c) t = 22.6 ns, (d) t = 23.9 ns, (e) t = 25.1 ns, (f) t = 26.4 ns, (g) t = 27.7 ns, (h) t = 29.0 ns, (i) t = 30.2 ns, (j) t = 31.5 ns, (k) t = 32.8 ns, (l) t = 34.1 ns.
(2002). We strongly believe that the focusing of the expansion wave is the key factor on cavitation. The maximum pressure of the point closest to the solid surface reaches 0.352 GPa, which agrees well with the impact pressure calculated by using Eq. (1), 0.35 GPa, with C0 of 1.75 × 103 m/s by Eq. (2). It is observed that the minimum pressure or maximum tensile stress (approximately 0.15 GPa) occurs at
634
T. Sanada et al. / Fluid Dynamics Research 40 (2008) 627 – 636
approximately two-thirds of the height (6.6 m), which qualitatively agrees well with the experimental results of Brunton and Rochester (1979) of cavitation inception inside the droplet. As Haller et al. (2003) pointed out, the existence of strong tensile stress may cause cavitation and may also cause severe erosion. It should be emphasized here that for cavitation to occur, there should exist cavitation nuclei. Now, we have to address the most fundamental question: “where do bubbles or bubble nuclei come from?” We will discuss this in the next section from a thermodynamic point of view. 5.2. Cavitation nuclei In super-purified water, as used in our experiments, neither particles nor contaminants exist. In other words, the quality of the liquid seriously hinders cavitation inception. First we discuss the noncondensed gas bubbles in the liquid. The simplest form of the bubble surface pressure pB in the liquid, as in Eq. (3), is used for simplicity: pB = pg + pv − 2/R,
(3)
where pg , pv , and are the noncondensible gas partial pressure, vapor saturated pressure, and surface tension coefficient, respectively. The physical properties of water, , and pv for T of 300 and 350 K, used in this study are 3.534 kPa and 71.69 mN/m, and 41.64 kPa and 63.25 mN/m, respectively (JSME Data Book, 1988). We assume that the dissolved gas is saturated at atmospheric pressure; hence, the equilibrium radius Req of bubble which can exist in the liquid of atmospheric pressure is obtained by Req = 2/pv .
(4)
For example, Req is calculated as 40.6 and 3.04 m at T of 300 and 350 K, respectively. Reminding that the droplet diameter d is 10 m, the equilibrium diameter of the bubble, 81.2 m at T of 300 K is approximately one order larger than d, while that at T of 350 K, 6.08 m is approximately half of d. Hence, from the statistical point of view, we may assume that noncondensible gas bubbles at T of 350 K are possible to be taken inside the droplet, probably accompanied by a complicated break-up action, while those at T of 300 K are not. If this assumption holds, it is also reasonable to state that the difference in the equilibrium bubble diameters at the different temperatures plays a significant role in the generation of a high pressure during the drop impact on a solid surface. Further, it should be noted that it is possible for the bubbles to be absorbed into the liquid droplet by entrapment during the impact on a solid surface or during the droplet generation, or by other mechanisms (Rein, 1993). Here, we face another question: “whether smaller bubbles can exist as a result of break-up”. If the characteristic time for noncondensable gas dissolution into the liquid is significantly longer than that for the vapor, the bubbles with radii smaller than Req , which are generated as a result of the break-up, can exist during the droplet generation and droplet impact. In order to justify this assumption, we have to investigate the bubble dynamics and transport phenomena inside the bubble although not in this paper. Detailed modeling, particularly of the vaporization/condensation process, noncondensable gas dissolution process, spatial distribution of the vapor and gas, etc., are required for further investigation. If these smaller noncondensible gas bubbles exist during the droplet impact, it is possible that bubbles considerably smaller than Req exist during the impacting time due to the series of break-up action in the liquid droplet. The second possible theory is with regard to the molecular defects. Molecular defects in the liquid are also considered to be the candidate of cavitation nuclei (Kato, 1990), which causes erosion. A critical vacancy or bubble size, RC is to be calculated as the intermolecular distance of 10−10 m, and hence, the
T. Sanada et al. / Fluid Dynamics Research 40 (2008) 627 – 636
635
critical tensile strength pC is calculated by pC = 2/RC .
(5)
pC in Eq. (5) at T of 350 K is calculated approximately as the order of 109 Pa. As shown in Fig. 5,
the maximum tensile stress obtained by our calculation is approximately 1.5 × 108 Pa, which is an order smaller than the above calculated value. However, it should be noted that the present calculation is performed in a two-dimensional Cartesian coordinate system. In a three-dimensional coordinate system, it is possible that the magnitude of tensile pressure is considerably greater than that obtained in the two-dimensional coordinate system since the strong tensile stress region is formed as a result of the focus of the expansion pressure wave in the inner region of droplet. The focusing effect is, in general, more significant in the axisymmetric geometry than in the plane geometry. Unfortunately, we do not have sufficient knowledge to discuss how temperature affects these molecular defects, particularly distributions of the size and number densities. For further pursuit of the possibility of molecular defects, an approach totally different from this paper, for example, molecular dynamics simulation, will be required. 6. Conclusion We have developed a new technique for the generation of impact using a high-speed mixture of steam and purified water droplets, in which the droplet diameters are of the order of 10 m, and the droplet velocities are of the order of 100 m/s. Microscope analysis of several metal surfaces after spraying of the mixture revealed the presence of numerous pits due to erosion. In addition, the degree of erosion is strongly dependent on temperature. We numerically studied the cause of the generation of a significantly large pressure during a liquid droplet impact on a solid surface. As a result, it was observed that the compression wave generated on the impact propagated upward, and then reflected at the free surface to become an expansion wave, subsequently, the expansion wave was focused. The maximum pressure at the point closest to the solid surface reached 0.352 GPa, and the minimum pressure or maximum tensile stress of approximately 0.15 GPa occurred at the position of focusing the expansion wave. The existence of strong tensile stress may cause cavitation inside the liquid droplet and may cause the solid surface erosion. Acknowledgments The authors express their gratitude to Mr. Hiroshi Tsubouchi at the Intellectual Property Management Center of Kyushu University for giving the authors an opportunity to work on this project. The authors also wish to express their appreciation to Mr. Y. Nihino, Mr. M. Yamaguchi, and Mr. M. Ooe, members of Kyoritsu Gokin Co. Ltd. (EVERLOY) for their cooperation in the experiment on PDA measurements. This study was supported by an Industrial Technology Research Grant Program in 2006 from the New Energy and Industrial Technology Development Organization (NEDO) of Japan. References Brunton, J.H., Rochester, M.C., 1979. Erosion of solid surfaces by the impact of liquid drops. In: Preece, C.M. (Ed.), Erosion, Treatise on Materials Science and Technology, vol. 16. Academic Press, New York, pp. 186–248.
636
T. Sanada et al. / Fluid Dynamics Research 40 (2008) 627 – 636
Fedkiw, R., Aslam, T., Merriman, B., Osher, S., 1999. A non-oscillatory Eulerian approach to interfaces in multimaterial flows (The Ghost Fluid Method). J. Comput. Phys. 152, 457–492. Field, J.E., Dear, J.P., Ogren, J.E., 1989. The effects of target compliance on liquid drop impact. J. Appl. Phys. 65 (2), 533–540. Haller, K.K., Ventikos, Y., Poulikakos, D., 2002. Computational study of high-speed liquid droplet impact. J. Appl. Phys. 92 (5), 2821–2828. Haller, K.K., Ventikos, Y., Poulikakos, D., 2003. Wave structure in the contact line region during high speed droplet impact on a surface: solution of the Riemann problem for the stiffened gas equation of state. J. Appl. Phys. 93 (5), 3090–3097. Harten, A., 1987. Uniformly high order accurate essentially non-oscillatory schemes, III. J. Comput. Phys. 71, 231–303. Heymann, F.J., 1969. High-speed impact between a liquid drop and a solid surface. J. Appl. Phys. 40 (13), 5113–5122. JSME Data Book, 1988. Thermophysical Properties of Fluids, third ed., JSME, Tokyo Kato, H., 1990. Cavitation. second ed.. Maki-Shoten, Tokyo. (in Japanese). Rein, M., 1993. Phenomena of liquid drop impact on solid and liquid surface. Fluid Dyn. Res. 12, 61–93. Shu, C.W., Osher, S., 1989. Efficient implementation of essentially non-oscillatory shock-capturing schemes, II. J. Comput. Phys. 83, 32–78.