J. Cent. South Univ. (2015) 22: 3712−3721 DOI: 10.1007/s11771-015-2914-y
Impingement capability of high-pressure submerged water jet: Numerical prediction and experimental verification
LIU Hai-xia(刘海霞)1, SHAO Qi-ming(邵启明)1, KANG Can(康灿)2, GONG Chen(龚辰)2
1. School of Material Science and Engineering, Jiangsu University, Zhenjiang 212013, China; 2. School of Energy and Power Engineering, Jiangsu University, Zhenjiang 212013, China
© Central South University Press and Springer-Verlag Berlin Heidelberg 2015
Abstract: At jet pressures ranging from 80 to 120 MPa, submerged water jets are investigated by numerical simulation and experiment. Numerical simulation enables a systematic analysis of major flow parameters such as jet velocity, turbulent kinetic energy as well as void fraction of cavitation. Experiments facilitate an objective assessment of surface morphology, micro hardness and surface roughness of the impinged samples. A comparison is implemented between submerged and non-submerged water jets. The results show that submerged water jet is characterized by low velocity magnitudes relative to non-submerged water jet at the same jet pressure. Shear effect serves as a key factor underlying the inception of cavitation in submerged water jet stream. Predicted annular shape of cavity zone is substantiated by local height distributions associated with experimentally obtained footprints. As jet pressure increases, joint contribution of jet kinetic energy and cavitation is demonstrated. While for non-submerged water jet, impingement force stems exclusively from flow velocity.
Key words: submerged water jet; cavitation; shear effect; impingement test; micro hardness; surface morphology
[2]. In this context, cavitating water jet is of great interest 1 Introduction in the investigation of jet impingement, but relevant studies have rarely been reported, particularly as jet Many industrial applications have benefited pressure exceeds 80 MPa [3]. In contrast, the considerably from the utilization of high-pressure water impingement mechanism of non-submerged water jet is jet, a promising material processing tool [1]. The straightforward, and two parameters, namely jet kinetic versatility of high-pressure water jet is being recognized energy and nozzle outlet diameter, are usually and one of the most impressive merits of water jet lies in underlined. the avoidance of excessive heat generation as water jet An in-depth understanding of submerged water jet stream impinges the target work piece. There are two is inseparable from its fluid dynamics features. Typical primary types of water jets, namely water jet and phenomena such as jet breakup, the formation and abrasive water jet (AWJ). For the latter, impingement development of vortices at jet rim, and cavitation have capability of the jet is largely ascribed to abrasive been widely recognized [4]. Weakness of generally used particles with diverse shapes. In comparison, water jet is experimental techniques is evident in measurements of not that powerful. Nevertheless, the participation of these transient and small-scale flow phenomena at high cavitation in submerged water jet opens possibilities for jet pressure. As far as optical flow measurement remarkable impingement or even damage effects. At high technique is concerned, dispersedly distributed bubbles or even ultra-high jet pressures, dual factors of jet kinetic and bubble clusters around the water jet stream hinder energy and cavitation erosion might contribute to the the penetration of laser into the jet stream. In some cases, damage to the impinged work piece. it is even difficult to distinguish the water jet stream In general, with a given nozzle, high jet pressure from ambient fluid. Alternatively, optical profiling leads to high jet velocity and thereby high jet kinetic apparatus facilitates a close examination of surface energy. Jet kinetic energy serves as a key factor morphology features of the impinged solid surface which underlying jet impingement. As for submerged water jet, might reveal flow-rated information, but so far only collapse of cavitation bubbles in high-velocity jet stream some preliminary conclusions have been obtained [5]. In contributes significantly to resultant impingement effects addition, numerical simulation, a vigorous instrument
Foundation item: Projects(51205171, 51376081) supported by the National Natural Science Foundation of China; Project(1201026B) supported by the Postdoctoral Science Foundation of Jiangsu Province, China Received date: 2014−09−22; Accepted date: 2015−05−11 Corresponding author: LIU Hai-xia, Associate Professor, PhD; Tel: +86−511−88780072; E-mail: [email protected]
J. Cent. South Univ. (2015) 22: 3712−3721 3713 highlighted recently, has been attempted to treat submerged water jet [6]. With respect to averaged flow parameters, numerical results are fairly reliable. Nevertheless, unsteady numerical results still endure debates owing to inevitable uncertainties. Finite element method (FEM), another important numerical strategy, has been utilized to simulate stress wave propagation in impacted solid samples, but for submerged water jet, transient energy release due to bubble collapse cannot be Fig. 1 Image (a) and cross-sectional diagram (b) of nozzle embodied with current FEM models [7]. (Unit: mm) Under high pressure conditions, flow characteristics and impingement capability of submerged water jet are cylindrical subdomain is sufficiently spacious to two aspects that call for an in-depth investigation. In line accommodate the development of the water jet in both with this acknowledged viewpoint, the present work streamwise and lateral directions. In particular, the focuses on submerged water jet subjected to jet pressures dimension in streamwise direction exceeds 33d, where d varying from 80 to 120 MPa. Computational fluid is the diameter of the nozzle outlet section, which dynamics (CFD) technique is utilized to virtually ensures a fully developed turbulent water jet. Structured visualize distributions of flow velocity, turbulent kinetic grids were used to discretize the entire computational energy, as well as void fraction of cavitation. A further domain and grid refinement was executed for near-wall step is unfolded as impingement experiment is flow regions. With a grid independence examination, the undertaken to examine the effects of submerged water jet total grid number devoted to the numerical simulation is through impinged solid samples. Ti−6Al−4V samples are 3376780. used as target samples in this respect. Micro hardness and surface morphology are measured for the impinged samples. For comparison, non-submerged water jets are studied under similar jet pressure conditions. It is anticipated to trace flow-related factors underlying the impingement capability of high-pressure submerged water jet and to render support to the design and optimization of water jet devices.
2 Numerical model and procedure
2.1 Geometrical models Fig. 2 Geometrical model of computational domain As shown in Fig. 1, the geometrical model of a nozzle parallel to practical applications is used in the 2.2 Turbulence model present numerical simulation. This nozzle differs from The renormalization group (RNG) k-ε turbulence commonly used convergent nozzles in that the outlet part model, firstly proposed by YAKHOT and ORSZAG [8] is conically divergent rather than a straight pipe. With in 1986, represents an improvement relative to the this nozzle, a tiny water jet stream is entailed. Meanwhile, standard k-ε turbulence model. This model is established the coherent segment of the water jet stream is based upon fuzzy mathematics principles, and the lengthened due to alleviated air disturbance immediately parameters incorporated in this model are deduced from downstream of the nozzle. Therefore, the advantage of related formulae rather than empiricism or experiments. this nozzle in the presence of high and ultra-high jet Along this line, the resultant equation of turbulent kinetic pressures is salient. Nevertheless, small jet stream energy dissipation rate ε differs from its counterpart in diameter elevates the difficulty degree in both the standard k-ε turbulence model. The transport measurement and simulation of the jet stream. equations of turbulent kinetic energy k and ε are: A combination of computational subdomains is illustrated in Fig. 2 where a straight subdomain upstream Dk k t G (1) of the nozzle is not shown for clarity. At initial stage, k Dt xi k xi pure water discharged from the nozzle enters into a cylindrical subdomain filled with water and the D 2 t * streamwise direction is +Z direction. The plane of Z= C1 Gk C 2 (2) Dt xi xi k k 0 mm overlaps with the nozzle outlet section. This
3714 J. Cent. South Univ. (2015) 22: 3712−3721 And the variable C* in Eq. (2) is defined as flow parameters can lend their support to illustrating 2 such a discrepancy, therefore no theoretical exploration C 31 of submerged water jet is incorporated in the present C* C 0 (3) work [11]. 2 2 3 1 0.012 where non-dimensional strain-rate parameter η is 3.1 Velocity distributions obtained from η=Sk/ε, and S denotes mean strain rate. In general, velocity magnitude acts as an indicator of the impingement capability of water jet; thus a high In addition, μ and μt are viscosity and turbulent priority is often granted to cross-sectional velocity viscosity, respectively. Gk is a turbulent kinetic energy production term related to viscous force. distributions in water jet stream. For the three jet Predefined values of the constants in Eqs. (1) to (3) pressures considered, cross-sectional velocity distributions at Z=5, 10 and 15 mm are extracted from are: Cμ=0.0845, Cε1=1.42, Cε2=1.68, k 0.72, numerically obtained results. These three standoff 0.75, η0=4.38. distances are commonly used in jet impingement practice. In flow regions with low strain rates, η<η0, the eddy viscosity calculated with the RNG k-ε model is higher Given that Z/d>30, the impact pressure sensed by the than that determined through the standard k-ε model, and target sample will fluctuate [12]. This adverse situation is this trend is reversed in high-strain-rate flow regions prevented with current selection of standoff distance. For submerged water jets, resultant velocity signified by η<η0. For the water jet stream considered, strong shear is bound to happen between working distributions are described in Fig. 3 where the same velocity scale is used. It is seen that overall velocity medium and ambient fluid, so advantages of the RNG k-ε magnitude increases with jet pressure, which is model are apparent. The Rayleigh-Plesset equation based especially apparent as jet pressure increases from 80 to cavitation model, reflecting the essence of cavitation 100 MPa. Meanwhile, velocity magnitudes in jet core physics, was used in the treatment of cavitation [9]. regions are saliently high. For each jet pressure, global
velocity declines along the streamwise direction, and 2.3 Discretization strategy and definition of boundary meanwhile, velocity in the jet core region also decays conditions rapidly. The resistance and disturbance deriving from Numerical simulation was carried out with the ambient water clearly impair the integrity of the water jet commercial CFD code ANSYS-CFX, which is flexible stream. As Z increases, contour lines keep stable circular and effective in coping with complex turbulent flows. shape irrespective of the change of jet pressure. At the jet Central finite difference scheme was introduced to treat pressures and standoff distances considered, both the advection terms involved. Discretization of breakup and jet instability have no chance to develop momentum and turbulent kinetic energy equations is with the submerged water jet streams. accomplished using second-order upwind scheme. Velocity distributions in the non-submerged water Velocity inlet boundary condition is defined at the inlet jets are shown in Fig. 4 in the same fashion as adopted in of the whole computational domain. Velocity magnitude Fig. 3. As for the variation of overall velocity magnitude, was calculated through the empirical relationship the tendency indicated in Fig. 4 is identical with that between velocity, density and water jet pressure. Since implied in Fig. 3. However, radial diffusion of that the water jet flowed downwards, gravity effect was high-velocity area is less severe in Fig. 4. Another taken into account. Static pressure conditions were set at characteristic of Fig. 4 is that at the same jet pressure, the outlet of the whole computational domain. Non-slip from Z=5 to 10 mm, velocity decay along the jet condition was applied for all solid boundaries. Near-wall direction is considerably weak relative to that indicated flow regions were treated with scalable wall functions. in Fig. 3. Such a tendency well supports the suitability of this range of standoff distance in practical applications of 3 Discussion of numerical results jet impingement. In this connection, velocity will attenuate dramatically as standoff distance exceeds a Both submerged and non-submerged water jets were threshold value, which has been substantiated [13]. simulated with the same set of geometrical models but Furthermore, most velocity contour lines in Fig. 4 cannot different ambient fluids. Three jet pressures, namely 80, maintain circular shape, which differs clearly from those 100 and 120 MPa, were used for the two jet types. displayed in Fig. 3. For non-submerged water jet, the Essentially, submerged water jet and non-submerged large gap of density between working medium and water jets are considerably different in terms of the ambient fluid promotes significantly the disturbance environmental disturbance [10]. Numerically obtained occurring at jet stream edge [14].
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Fig. 3 Cross-sectional velocity distributions associated with submerged water jets: (a1−a3) 80 MPa; (b1−b3) 100 MPa;
(c1−c3) 120 MPa
3.2 Turbulent characteristics simulations. In Fig. 5, a comparison between submerged Apart from distributions of averaged flow and non-submerged water jets is illustrated with parameters, turbulent features incorporating fluctuations cross-sectional distributions of turbulent kinetic energy are of obvious importance in view of remarkably high jet at jet pressure of 100 MPa. velocities. Furthermore, velocity fluctuations are in As for the non-submerged water jet, the annular direct relation with impingement effects on target area of high turbulent kinetic energy remains stable as Z surfaces. It is reasonable to expect that violent velocity increases. It is observable that the highest magnitude of fluctuations result in irregular footprint profiles. turbulent kinetic energy arises at standoff distance of Turbulent kinetic energy is inherently a second-order 10 mm. And the jet core is consistently dominated by a momentum of fluctuating velocity and can be obtained rather low level of turbulent kinetic energy, as implies with the turbulence model employed in the present that turbulent intensity is also very low in the jet core
3716 J. Cent. South Univ. (2015) 22: 3712−3721
Fig. 4 Cross-sectional velocity distributions associated with non-submerged water jets: (a1−a3) 80 MPa; (b1−b3) 100 MPa; (c1−c3) 120 MPa area [15]. In contrast, along the streamwise direction, 3.3 Cavitation prediction for submerged water jet the core area in the submerged water jet stream is Although no consensus has been reached for the gradually invaded by high turbulent kinetic energy and mechanism of cavitation, the inception and evolution of cross-sectional distribution of turbulent kinetic energy cavitation in submerged water jet have been consistently tends to be uniform. Shear effect, fostered both between pursued [16]. A common viewpoint states that natural working fluid and ambient fluid and between adjacent cavitation happens as local static pressure is lowered layers residing in working fluid, serves as a primary down to corresponding vaporization pressure of the factor boosting the increase of turbulent kinetic energy. working medium. Such a rationale differs appreciably In addition, both water jets cannot evade from the from the process of bubble generation due to injecting air disturbance of ambient fluid and the disturbance exerted into ambient water [17]. In the present work, it is on the non-submerged water jet is apparently more unambiguous that cavitation is the most distinct drastic. difference between submerged and non-submerged water
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Fig. 5 Cross-sectional turbulent kinetic energy distributions: (a1−a3) Submerged water jet of 100 MPa; (b1−b3) Non-submerged water jet of 100 MPa jets. In submerged water jets, cavitation might result from vorticity-related pressure drop. And the production 4 Experimental setup of vorticity is associated with the shear effect between high-and low-velocity flow layers. Owing to cavitation, The experimental study was conducted with an the severity of pressure fluctuations might be enhanced ultra-high pressure water jet machine shown in Fig. 7. [18]. Here, the parameter of cavitation void fraction is And this machine could furnish jet pressures higher than used to express cavitation in submerged water jet, as 380 MPa. During the experiment, water jet flowed shown in Fig. 6. vertically downward, as was remained invariant. The Shear layer effect is the most predominant impetus distance between the target surface and the nozzle outlet underlying cavitation inception in submerged water jets. section was accurately modified through a controlling It is natural that void fraction distributions at the same system. The nozzle used in the experiment is identical standoff distance but with different jet pressures are with its counterpart devoted to the numerical simulation. fairly analogous. As Z increases, cavitation region tends Cylindrical Ti−6Al−4V samples, 40 mm in diameter and to be expanded, and meanwhile, cavitation degree is 2.5 mm in thickness, served as target samples. Three jet consistently improved. Such a tendency hinges upon the pressures, namely 80, 100, and 120 MPa, were adopted laterally diffused jet stream with adequate kinetic energy in the experiment. The present experiment work involves to sustain the shear effect. Further downstream, there not just submerged water jet but also non-submerged must exist a critical position where cavitation collapses water jet. For the former, Ti−6Al−4V samples were fixed ultimately. As far as cavitation erosion is concerned, it and submerged in a tank at the bottom of the test rig, as can be predicted from Fig. 6 that surface damage due to shown in Fig. 7. cavitation will exhibit an annular shape. Similar cavity shape is found in Soyama’s work in which cavitation was 5 Experimental results created through an annular nozzle which concurrently injected two liquid jet streams with different initial 5.1 Micro hardness velocities into ambient air [19−20]. With impingement time less than 30 s and standoff
3718 J. Cent. South Univ. (2015) 22: 3712−3721
Fig. 6 Void fraction of cavitation for submerged water jet: (a1−a3) 80 MPa; (b1−b3) 100 MPa; (c1−c3) 120 MPa
distances ranging from 10.0 to 20.0 mm, both submerged and non-submerged water jets with pressures lower than 120 MPa exerted no obvious damage on target samples. In this case, micro hardness was measured for the impinged samples since micro hardness reflects elasticity and plastic characteristics of the material. With a certain load of 1.96 N and constant load time of 20 s, the length of the indentation was examined. For each sample, the procedure was repeated for three times and then an arithmetically averaged value was calculated. Vickers micro hardness was obtained through its relationship with the length of the indentation. The results are plotted Fig. 7 Arrangement of components of experimental test-rig in Fig. 8.
J. Cent. South Univ. (2015) 22: 3712−3721 3719 In Fig. 8, the initial micro hardness of the sample is water jet to the surface is not remarkable, but the annular HV370. For non-submerged water jet, at standoff polished area well indicates cavitation effect. In distance of 20.0 mm, the three micro hardness values are comparison, in Fig. 9(b), a clear hole on the impacted slightly larger than HV370, irrespective of the increase surface is seen, and the contribution of high jet velocity of jet pressure. Overall micro hardness decreases as plays the dominant role in this context. There is also a standoff distance increases. At standoff distance of polished annular area surrounding the hole due to 10.0 mm, micro hardness increases consistently with jet relatively low kinetic energy. Furthermore, the rim of the pressure. But for the other two standoff distances, the hole displayed in Fig. 9(b) is not strictly circular, which increase from 100 to 120 MPa results in a decline of is related to wavy flow structures between water jet micro hardness. The cause behind this phenomenon lies stream and ambient air. in that the increase of jet pressure, simultaneously leading to the increase of flow rate, reduces the extent of concentration with respect to the impinged area. The maximum micro hardness of HV405 occurs at jet pressure of 120 MPa and standoff distance of 10.0 mm. In comparison, the attainable micro hardness is HV425 with submerged water jet, which is associated with jet pressure of 100 MPa and standoff distance of 15.0 mm. In this context, for submerged water jet, variation of the strengthening effect with jet pressure, as well as with standoff distance, is not monotonous. Figure 6 also supports such a tendency and it is seen in Fig. 6 that cavitation severity is comparatively high at standoff distance of 15.0 mm. Meanwhile, between the numerical results obtained at 100 and 120 MPa, no apparent difference in void fraction distribution is perceptible.
Fig. 9 Local surfaces impinged by water jet at 120 MPa with duration period of 45 s: (a) Local area impinged by submerged water jet; (b) Local area impinged by non-submerged water jet
5.3 Local height examination At jet pressures of 100 and 120 MPa, the Fig. 8 Comparison of micro hardness between submerged and impingement time was specified as 3 min and standoff non-submerged water jets distance 10.0 mm, and the representative local height distributions along the line crossing resultant footprint 5.2 Cavitation effect are plotted in Fig. 10. The line covers approximately the At jet pressure of 120 MPa and standoff distance of center of the footprint. The case shown in Fig. 10(a) 5.0 mm, two samples were impinged by submerged and involves submerged water jet at jet pressure of 100 MPa. non-submerged water jets, respectively. The same It is deduced from Fig. 10(a) that the sunken part at the impingement time of 45 s was used in the two bottom of the pit is largely ascribed to cavitation effect. impingement tests. A close observation of impinged In this context, the bottom profile of the footprint proves surfaces was implemented using a Zeiss AxioCSM700 that cavitation effect is particularly remarkable in an confocal microscope. Surface morphology feature annular area, as differs considerably from the pure implies not only solid-related but also flow-related impingement effect due to jet kinetic energy. information [20]. Two impinged local surfaces are shown Additionally, the submerged water jet has evidently in Fig. 9. In Fig. 9(a), the damage of the submerged penetrated into the target sample. As jet pressure
3720 J. Cent. South Univ. (2015) 22: 3712−3721 increases to 120 MPa, as shown in Fig. 10(b), the depth Numerical simulation enables the exploration of flow of the resultant pit is improved obviously. Regarding the parameter and cavitation, which cannot be accomplished pit profile, the slightly swelling middle segment at the using available flow measurement techniques. And bottom, along with the steep side edge, testifies the joint experiments confirm numerical results through practical contribution of cavitation and jet kinetic energy. Under jet impingement effects. such a condition, it is difficult to determine which factor 2) For jet pressures considered, overall jet kinetic is more predominant. As for the impingement effect of energy attenuates rapidly in streamwise direction. And non-submerged water jet, the results indicated in concurrently, the influence of ambient water on jet core Fig. 10(c) are explicit. Relative to Fig. 10(a) including area is intensified. Cross-sectional distributions of submerged water jet at the same jet pressure of 100 MPa, cavitation void fraction indicate the annular shape of non-submerged water jet owns preferable capability of cavitation zone which complies with the formation damaging the target sample. Apart from the increased mechanism dominated by shear effect. penetration depth compared with Fig. 10(a), the pit is 3) Experiments of submerged water jet featured by a bottom valley without any large-size bulge. impingement with Ti−6Al−4V samples not just provide This implies that the impingement force of non- evidence for cavitation damage but also yield submerged water jet comes solely from flow velocity. quantitative information of surface morphology features. Variation of micro hardness with standoff distance is in agreement with numerical results of cavitation void fraction. The profiles of resultant footprints in impinged samples reflect the cavitation effect in submerged water jet as well as jet impingement mechanism. At high jet pressures, contributions of cavitation and jet pressure should be combinedly considered.
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