A Comparative Study of Cavitation Characteristics of Nano-Fluid And

micromachines

Article A Comparative Study of Cavitation Characteristics of Nano-ﬂuid and Deionized Water in Micro-channels

Tao Li 1,2, Bin Liu 1,*, Jinzhi Zhou 1, Wenxuan Xi 1, Xiulan Huai 1,* and Hang Zhang 1,*

1 Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China; [email protected] (T.L.); [email protected] (J.Z.); [email protected] (W.X.) 2 University of Chinese Academy of Sciences, Beijing 100190, China * Correspondence: [email protected] (B.L.); [email protected] (X.H.); [email protected] (H.Z.); Tel.: +86-10-82543034 (B.L. & X.H. & H.Z.) Received: 7 February 2020; Accepted: 12 March 2020; Published: 16 March 2020

Abstract: Hydrodynamic cavitation has been widely applied in micro-fluidic systems. Cavitating flow characteristics are closely related to the fluid properties. In this paper, the cavitation characteristics of Cu nano-fluid in micro-channels were numerically investigated and compared with those of the deionized (DI) water. The mathematical model was verified by comparing the numerical results with the experiment observation. The curved orifice (R = 0.3 mm) was found to have the highest efficiencies of cavitation for both fluids. With the increase of inlet pressure, cavitating jet lengths of the two fluids significantly increased. While, the cavitating jet length of the nano-fluid was shorter than that of the DI water at the same inlet pressure. The cavitation inception number of the DI water and nano-fluid were approximately 0.061 and 0.039, respectively. The results indicate that the nano-particles played negative effects on the cavitation inception. In addition, with the decrease of outlet pressure, the cavitation strength gradually increased and the mass flow rate remained nearly unchanged at the same time.

Keywords: cavitation; nano-ﬂuid; micro-channel; numerical analysis

1. Introduction Cavitation is a complex two-phase flow that is caused by a sudden decrease of pressure in the liquid. The growth and collapse of cavities generate an extremely high level of temperature and pressure impulse, which induces a series of complicated physical and chemical effects [1,2]. In recent years, it has been found that cavitation in the micro-fluidic system can be widely applied in many fields, such as heat transfer enhancement, chemical engineering, water treatment, and nano-materials dispersion [3–8]. The characteristic of liquid-gas phase transition in the micro-fluidic channel can be significantly different from which in a macro-scale channel because of the dimension limitation. From previous experimental and numerical studies, the characteristics of cavitating flow in the micro-fluidic system have been widely investigated [9]. Mishra et al. [10] experimentally investigated hydrodynamic cavitation in a silicon micro-channel. The results showed that the cavitation inception number was much smaller than that obtained from previous studies on larger orifices. However, choking cavitation was observed to be independent of any pressure or velocity scale effects. Ghorbani et al. [11] studied the cavitating flows between the micro- and macro-scale channels, and results showed that the pressure profile and vapor phase distribution exhibited different features. The static pressure dropped to negative values (tensile stress) in micro-channels, while the minimum static pressure in mini-channels was found to be equal to vapor saturation pressure. Additionally, the higher velocity magnitudes, especially at the outlet, were visible in the micro-channels. It can be seen that, in spite of the geometric similarity, the inception of cavitating flow did not meet the demand of the Newton criterion of dynamic similarity. It was believed

Micromachines 2020, 11, 310; doi:10.3390/mi11030310 www.mdpi.com/journal/micromachines Micromachines 2020, 11, 310 2 of 14 that the amount of nuclei in the low pressure zone was the critical factor, which results in the difference of cavitating flow between the micro- and macro-scale. The silicon based high pressure cavitation micro-fluidic system was investigated [12]. The results showed that cavitation could be decreased and eliminated at a sufficiently high backpressure, and it was restricted to the vena contracta in orifice micro-channels. Pennathur and Peles [13] studied cavitation in micro-scale devices that cascaded of micro-pump blades. With increasing mass flow, the size of the cavitation zone grew about 50% being more slowly than predicted by theory. Mishra and Peles investigated the cavitating flow of deionized water (DI water) through various micro-orifices and micro-channels [14]. Multifarious cavitating flow patterns, including incipient, choking, and super-cavitating, were detected. The results displayed that, in spite of several parameters, the trends were similar at both scales, and the flow patterns were different for micro- and conventional scale orifices. For the super-cavitating flow patterns, vapor cavity was encompassed by liquid in the micro-channel; however, it was found inside the vapor pocket in the conventional scale orifices. The computational fluid dynamics (CFD) method plays an important role in the investigation of cavitation. Thus far, the full cavitation model [15], Schner–Sauer model [16], and Zwart-Gerber-Belamri model [17] are commonly used to simulate the hydraulic cavitating flow. The full cavitation model has been employed to simulate the cavitating flows in pumps and inducers. The effects of turbulent fluctuations and non-condensable gases were also considered in the model. The numerical simulation results precisely predicted the cavitating flow trends and the size, location, and shape of the cavitation zone [18]. The cavitation flows over a two dimensional (2-D) hydrofoil and an axisymmetric ogive were simulated, and the nuclei density solutions that were obtained by the simulation showed good consistency with measurements [19]. By using Zwart-Gerber-Belamri model, the cavitating flow through a micro-orifice was investigated. The results showed that the vapor cavity region increased with the rise of pressure and the entire micro-orifice wall could be covered by vapor. Additionally, it was recommended that the maximum l/d of a micro-orifice is about 1 [20]. In recent years, nano-fluid has been more widely applied in micro-fluidic systems, which is a multiphase fluid that contains nanometer-sized solid particles [21–23]. Because of the existence of nano-paritcles, the physical properties of nano-fluid, such as the viscosity, density, surface tension, and thermal conductivity, are significantly different when compared with the base liquid [24–26]. Thus, cavitation would be affected by the addition of nano-particles. Gu et al. [27] applied the acoustic method to experimentally study the effects of SiO2 nano-particles on cavitation inception. The temperature and particle size were variables and the dimensionless free energy of the critical bubble was calculated in the experiments. The results showed that the SiO2 particles always promoted the cavitation inception. However, the increase of particle concentration further promoted the cavitation, while the particle size had little effect. Bidhendi et al. [28,29] examined the effects of SiO2 nano-particles on initiation of cavitation in a centrifugal water pump. In the research, the nano-particle concentration, size, and fluid temperature were changed. It was found that SiO2 nano-particles could decrease the rate of cavitation growth. However, until recently, there is relatively little study of nano-fluid cavitation in the micro-fluidic system. In this paper, the computational fluid dynamics (CFD) method was employed for simulating the cavitating flows of nano-fluid and deionized (DI) water in micro-channels. The results were validated by comparison with experimental observations. The differences of cavitation dynamics between the nano-fluid and DI water were discussed in detail. Additionally, the effects of the orifice shape, the inlet pressure, and outlet pressure on cavitation were analyzed. This work is aimed to provide useful insights for the application of nano-fluid cavitation in MEMS and other devices with micro-channels. Micromachines 2020, 11, 310 3 of 14

2. Numerical Models

2.1. Governing Equations The Reynolds Averaged Navier-Stokes (RANS) approach was used to analyze the cavitation ﬂow ﬁeld in the micro-channel. The mass conservation equation is expressed as:

∂ (ρui) = 0 (1) ∂xi

Here, ρ and ui are the ﬂuid density and average velocity component, respectively. The Reynolds-averaged momentum conservation equation can be expressed as:

∂ ∂p ∂ ∂ui (ρuiuj) = + [µ + Rij] (2) ∂xj −∂xi ∂xj ∂xj

Here, µ stands for the kinematic viscosity and Rij is the Reynolds stress tensor. In this study, the volume of ﬂuid (VOF) model tracks the volume fraction of the each ﬂuid throughout the domain. The tracking of interface between phases is accomplished by the solution of a continuity equation for the volume fraction of one (or more) of the liquid phases, and this equation has the following form:

1 (αqUq) = (mpq mqp) (3) ∇ · ρq −

Here, mqp is the mass transfer rate of the liquid phase q to the vapor phase p, and mpq is the mass transfer rate of the vapor phase p to the liquid phase q. Uq is the mean velocity of the q phase. The liquid phase volume fraction is computed, based on the following equation:

αq + αp = 1 (4)

2.2. Turbulence Modeling So far, little study has been conducted on the eﬀects of turbulence models on cavitating ﬂow in the micro-channels. In this study, the Standard k-ω model, k-ω Shear-Stress Transport (SST) model, Standard k-ε model, and Realizable k-ε model are selected. The transport equations of Standard k-ω model are shown, as follows

∂ ∂ ∂k (ρkui) = (Γk ) + Gk Yk + Sk (5) ∂xi ∂xj ∂xj −

Additionally ∂ ∂ ∂ω (ρωui) = (Γω ) + Gw Yω + Sω (6) ∂xi ∂xj ∂xj − The turbulence kinetic energy k and the specific dissipation rate ω are obtained from these two transport equations. In these equations, Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients. Gω represents the generation of specified dissipation rate. Yk and Yω represent the dissipation of k and ω due to turbulence. Sk and Sω are user-defined source terms. Γk and Γω represent the effective diffusivity of k and ω, respectively, which are expressed as:

µt Γk = µ + (7) σk

µt Γω = µ + (8) σω Micromachines 2020, 11, 310 4 of 14

The k-ω Shear-Stress Transport (SST) model is based on the standard k-ω model and the turbulent viscosity µt is amended.

MicromachinesThe transport 2020, 11, equationsx of standard k-ε model are shown, as follows: 4 of 14 " # ∂ ∂ µt ∂k (ρ ku ) = (µ + ) + G + G ρ ε Y + S (9) ∂∂m i m μ ∂εεk b m M ε2 k ∂xi ∂xj t σk ∂xj − − ()ρεuCGCGCS=+++−+ ( μ )εεεε ( ) ρ ∂∂mi mσ ∂112 k b (10) xxijε xk j k " # 2 ∂ ∂ µt ∂ε ε ε (ρmεui) = (µm + ) + C1ε (Gk + C1εGb) C2ερ + Sε (10) Here, Gb is∂ thexi generation∂x ofj turbulenceσε ∂ kineticxj energyk due to buoyancy− kand YM represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate. Here, Gb is the generation of turbulence kinetic energy due to buoyancy and YM represents the contributionThe model of of Realizable the ﬂuctuating k-ε model dilatation is based in compressible on the standard turbulence k-ε tomodel the overalland the dissipation mathematical rate. Theconstraint model ofis used Realizable to improvek-ε model the performance is based on the of standardthe model.k-ε model and the mathematical constraint is used to improve the performance of the model. 2.3. Cavitation Model 2.3. CavitationIn the study, Model the Schner-Sauer model was employed. The mass transfer source terms connected to theIn growth the study, and the collapse Schner-Sauer of the vapor model bubbles, was employed. which are The based mass transferon the Rayleigh-Plesset source terms connected equations to theand growth defined and as: collapse of the vapor bubbles, which are based on the Rayleigh-Plesset equations and deﬁned as: ρρ − pq32s ()PP p mqp =−αα(1 ) (P P) , when P ≤ Pv ρpρρρq pp3 2 p (11) mqp = αp(1 αp) RBq3 − , when P Pv (11) ρ − RB 3 ρq ≤ ρρ s − qp32()PP p mpq =−ρqρp αα(1 ) (P Pp) , when Pv ≤ P ρρpp3 2 (12) mqp = αp(1 αp) RBq3 − , when Pv P (12) ρ − RB 3 ρq ≤

Here,Here, RRBB means thethe bubblebubble radius.radius.

3.3. ResultsResults andand DiscussionDiscussion

3.1.3.1. ModelModel ValidationValidation InIn thisthis section,section, thethe numericalnumerical resultsresults werewere firstfirst comparedcompared withwith experimentalexperimental datadata [[30]30] toto proveprove thethe accuracyaccuracy andand reliabilityreliability ofof thethe model.model. InIn thethe previousprevious experiment,experiment, aa copper-basedcopper-based plateplate withwith rectangularrectangular micro-channelsmicro-channels waswas fabricated,fabricated, whichwhich consistedconsisted ofof sevenseven parallelparallel channels.channels. EachEach ofof thethe channelschannels waswas 26 mm long, long, 0.5 0.5 mm mm wide, wide, and and 0.2 0.2 mm mm deep. deep. At At 2 mm 2 mm downstream downstream of the of theentrance, entrance, the therectangle rectangle orifice orifice with with the the width width of of0.1mm 0.1mm and and length length of of 0.2mm 0.2mm was was designed, designed, as as shown shown in in Figure Figure 11.. TheThe DIDI waterwater flowedflowed through through channels channels that that were were driven driven by by the the pump pump and and cavitation cavitation was was induced induced by by a suddena sudden drop drop of of liquid liquid pressure pressure at at the the orifice. orifice.

FigureFigure 1.1. TheThe structurestructure ofof thethe micro-channels.micro-channels.

In the simulation, one channel was selected, so that the amount of calculation can be effectively reduced, and only a half of the channel geometry was modeled due to the presence of symmetry planes. We employed structured quadrilateral meshes to capture the vapor phase, as the micro-channel was not geometrically complex, as shown in Figure 2. The mesh was generated with ICEM CFD software. In order to evaluate the grid dependency of the studied geometry, three different cell numbers were compared: 158,730, 335,223, and 484,290, respectively.

Micromachines 2020, 11, 310 5 of 14

In the simulation, one channel was selected, so that the amount of calculation can be eﬀectively reduced, and only a half of the channel geometry was modeled due to the presence of symmetry planes. We employed structured quadrilateral meshes to capture the vapor phase, as the micro-channel was not geometrically complex, as shown in Figure2. The mesh was generated with ICEM CFD software. Micromachines 2020, 11, x 5 of 14 InMicromachines order to evaluate2020, 11, x the grid dependency of the studied geometry, three diﬀerent cell numbers were5 of 14 compared:Micromachines 158,730,2020, 11, x335,223, and 484,290, respectively. 5 of 14

Figure 2. The micro-channel geometry in the simulation. Figure 2. The micro-channel geometry in the simulation. Figure 2. The micro-channel geometry in the simulation. The boundary conditions of the inlet and outlet pressure were set to be 355 and 8.5 kPa in The boundary conditions of the inlet and outlet pressure were set to be 355 and 8.5 kPa in accordance with the experimental parameters [30]. The cavitation flow field was obtained while accordanceThe boundary with the conditions experimental of the parameters inlet and [30] outlet. The pressure cavitation were flow set fi toeld be was 355 andobtained 8.5 kPa while in using the commercial CFD software ANSYS CFX release 14.0. The finite volume method was accordanceusing the commercial withwith thethe experimental experimental CFD software parameters parameters ANSYS [30 [30]CFX]. The. Therelease cavitation cavitation 14.0. flow The flow field finite fi waseld volume obtainedwas obtained method while while using was utilized to perform a discrete solution for the governing equations. The second order upwind theusingutilized commercial the to commercialperform CFD a software discreteCFD software ANSYS solution CFXANSYS for release th eCFX governing 14.0. release The equations.14.0. finite The volume finiteThe method secondvolume wasorder method utilized upwind was to scheme was used to discretize the mass, momentum, turbulent quantities and vapor transport performutilizedscheme awasto discrete perform used solutionto a discretizediscrete for the solution the governing mass, for mome equations.the governingntum, Theturbulent secondequations. quantities order The upwind second and schemevapor order wastransport upwind used equations. The pressure corrections were computed using the body force weighted Pressure toschemeequations. discretize was The theused mass,pressure to momentum,discretize corrections the turbulent mass, were mome quantitiescompntum,uted and usingturbulent vapor the transport quantitiesbody force equations. and weighted vapor The transport pressurePressure Staggering Option (PRESTO!) scheme. For pressure-velocity coupling, the semi-implicit method for correctionsequations.Staggering OptionThe were pressure computed (PRESTO!) corrections using scheme. the bodywereFor pressure-velocity forcecomp weighteduted using Pressure coupling, the body Staggering the force semi-implicit weighted Option method (PRESTO!) Pressure for pressure linked equations (SIMPLE) algorithm was employed. The micro-channel walls were scheme.Staggeringpressure Forlinked Option pressure-velocity equations (PRESTO!) (SIM scheme. coupling,PLE) Foralgorithm thepressure-velocity semi-implicit was employed. methodcoupling, The for the micro-channel pressure semi-implicit linked wallsmethod equations were for treated as non-slip boundaries with standard wall functions. In the simulation, convergence was (SIMPLE)pressuretreated as linked algorithm non-slip equations wasboundaries employed. (SIM withPLE) The standard algorithm micro-channel wa wasll functions. walls employed. were In treated theThe simulation, asmicro-channel non-slip convergence boundaries walls were withwas assumed when the residuals dropped below a value of 10−4. Figure 3 depicts the calculated vapor standardtreatedassumed as wallwhen non-slip functions. the boundariesresiduals In the dropped simulation,with standard below convergence awa valuell functions. of was10−4. assumed FigureIn the 3simulation, whendepicts the the residuals convergence calculated dropped vapor was fractions at the cross-section4 z = 0.1 mm of the micro-channel. It can be observed that the difference belowassumedfractions a value atwhen the of cross-sectionthe 10− residuals. Figure3 z droppeddepicts = 0.1 mm the below of calculated the a micro-channel. value vapor of 10 fractions−4. FigureIt can at be the3 depictsobserved cross-section the that calculated thez = difference0.1 mmvapor of between the vapor fractions became negligible as the number of cells more than 335,223. Thus, the thefractionsbetween micro-channel. theat the vapor cross-section It fractions can be observed zbecame = 0.1 mm thatnegligible of the the di ffmicro-channel. aserence the number between It of the can cells vapor be more observed fractions than that335,223. became the difference negligibleThus, the grid was applied for all cases in this paper. asbetweengrid the was number theapplied vapor of cellsfor fractions all more cases than became in this 335,223. paper.negligible Thus, theas the grid number was applied of cells for more all cases than in 335,223. this paper. Thus, the grid was applied for all cases in this paper.

Figure 3. The vapor fraction at the cross-section z = 0.1 mm of the micro-channel, (a) Grid 158,730 FigureFigure 3.3. TheThe vaporvapor fraction fraction at at the the cross-section cross-sectionz = z0.1 = 0.1 mm mm of theof micro-channel,the micro-channel, (a) Grid (a) Grid 158,730 158,730 cells; cells; (b) Grid 335,223 cells; and, (c) Grid 484,290 cells. (Figurecells;b) Grid (b 3.) 335,223 GridThe 335,223vapor cells; fraction and,cells; ( cand,) at Grid the(c) 484,290 Gridcross-section 484,290 cells. cells. z = 0.1 mm of the micro-channel, (a) Grid 158,730 cells; (b) Grid 335,223 cells; and, (c) Grid 484,290 cells. When fluid flowed through the micro-orifice, some specific features, including cavitation WhenWhen fluidfluid flowed flowed through through the the micro-orifice, micro-orifice, some some specific specific features, features, including including cavitation cavitation clouds clouds and high speed vapor-liquid jet, would occur. Therefore, a critical task of suitable turbulence andclouds highWhen and speed highfluid vapor-liquid speedflowed vapor-liquid through jet, would the jet, micro-orifice, occur.would Therefore,occur. Therefore,some a critical specific a taskcritical features, of suitabletask ofincluding suitable turbulence turbulencecavitation model model was to capture the dynamics of cavitation growth and collapse correctly in a very small scale. wascloudsmodel to capturewasand highto capture the speed dynamics the vapor-liquid dynamics of cavitation jet,of cavitation would growth occur. andgrow Therefore, collapseth and collapse correctly a critical correctly in task a very of in suitable small a very scale. turbulencesmall Table scale.1 Table 1 provides the calculated mass flow rate with different turbulence models. As observed, the providesmodelTable 1was provides the to calculated capture the calculatedthe mass dynamics flow ma rate ssof flowcavitation with rate diff erentwith grow different turbulenceth and collapse turb models.ulence correctly Asmodels. observed, in a As very observed, the small solution scale. the solution of the standard k-ɷ model was quite close to the experimental data, with a maximum of 1.5% ofTablesolution the standard1 provides of the standard themodel calculated k-ɷ was model quitema sswas closeflow quite torate close the with experimental to differentthe experimental turb data,ulence with data, models. a maximum with aAs maximum observed, of 1.5% of error. the1.5% error. By comparison, for the Standard k-ε and Realizable k-ε model, the errors of mass flow rate Bysolutionerror. comparison, By of comparison, the standard for the Standardfor k- ɷthe model Standardk-ε wasand Realizable quitek-ε and close Realizablek to-ε model,the experimental k the-ε model, errors ofdata,the mass errors with flow aof maximum rate mass increased flow of rate 1.5% to increased to about 7.1% and 7.3%, respectively. abouterror.increased 7.1%By comparison,to and about 7.3%, 7.1% respectively. for and the 7.3%, Standard respectively. k-ε and Realizable k-ε model, the errors of mass flow rate increased to about 7.1% and 7.3%, respectively. Table 1. Mass flow rate calculated by different turbulence models. Table 1. Mass flow rate calculated by different turbulence models. TableItems 1. Mass flow Massrate calculated flow rate by(L/h) different Error turbulence (%) models. Items Mass flow rate (L/h) Error (%) Experiment 9.6 － ExperimentItems Mass flow9.6 rate (L/h) Error－ (%) Standard k-ε model 8.92 7.1% StandardExperiment k-ε model 8.929.6 7.1%－ Realizable k-ε model 8.90 7.3% RealizableStandard k k-ε-ε model model 8.92 8.90 7.1%7.3% k-ω SST model 9.07 5.5% Realizablek-ω SST k model-ε model 8.9 9.070 7. 5.5%3% Standard k-ω model 9.45 1.5% Standardk-ω SST k -modelω model 9.07 9.45 5.5% 1.5% Standard k-ω model 9.45 1.5%

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Table 1. Mass ﬂow rate calculated by diﬀerent turbulence models.

Items Mass Flow Rate (L/h) Error (%) Experiment 9.6 — Standard k-ε model 8.92 7.1% Realizable k-ε model 8.90 7.3% k-ω SST model 9.07 5.5% Standard k-ω model 9.45 1.5% Micromachines 2020, 11, x 6 of 14

TheThe simulatedsimulated vapor-liquidvapor-liquid distributionsdistributions atat thethe cross-sectioncross-section zz == 0.1 mmmm byby variousvarious turbulenceturbulence modelsmodels werewere comparedcompared withwith thethe experimentalexperimental result,result, asas displayeddisplayed inin FigureFigure4 .4. The The calculated calculated vapor-liquidvapor-liquid distributiondistribution byby StandardStandard kk--ωω modelmodel showedshowed betterbetter agreementagreement withwith thethe experimentalexperimental result.result. ForFor cavitationcavitation thatthat occurredoccurred inin aa confined confined space, space, a a shear shear flow flow boundary boundary layer layer that that formed formed by by a largea large velocity velocity gradient gradient existed existed between between the vapor the va andpor liquid and phase.liquid phase. Meanwhile, Meanwhile, the Reynolds the Reynolds number wasnumber relatively was relatively low downstream low downstream of the orifice. of the The orifice. Standard The kStandard-ω model k considers-ω model theconsiders low Reynolds the low numberReynolds e ffnumberects and effects shear and flow shear diffusion. flow diffusion. Thus, it is Thus, more it suitable is more for suitable the wall-bound for the wall-bound and jet flows and calculationjet flows calculation as the cavitating as the cavitating flow in the flow micro-channel. in the micro-channel.

FigureFigure 4.4. The comparison of vapor-liquid distribution between the experimental data [[30]30] andand simulationsimulation results,results, (a ()a experimental) experimental result; result; (b) standard(b) standardk-ε model; k-ε model; (c) realizable (c) realizablek-ε model; k-ε ( dmodel;) standard (d) kstandard-ω model; k- andω model; (e) k- ωandShear-Stress (e) k-ω Shear-Stress Transport Transport (SST) model. (SST) model.

Additionally,Additionally, thethe calculation calculation result result was was compared compared with thewith experimental the experimental result that result was that obtained was byobtained Rooze etby al. Rooze [31], aset shownal. [31], in as Figure shown5. Itin could Figure be 5. seen It could that a cavitatingbe seen that jet a formed cavitating when jet the formed fluid flowedwhen the through fluid theflowed micro-orifice. through Thethe liquidmicro-orifice. jet was surrounded The liquidby jet twin was vapor surrounded bubbles by near twin the orifice.vapor Thebubbles liquid–gas near the two orifice. phase The mixtures liquid–gas were observedtwo phase at mixtures downstream were of observed the liquid at jet. downstream With the recovery of the ofliquid pressure, jet. With those the cavitation recovery bubblesof pressure, collapsed those andcavitation turned bubbles into liquid. collapsed The comparison and turned between into liquid. the presentThe comparison results and between the experimental the present data results from literatureand the furtherexperimental verified data the validityfrom literature of the proposed further numericalverified the method. validity of the proposed numerical method. 3.2. Cavitating Flow Characteristics of Nano-fluid and DI Wwater In the work, the Cu nano-fluid with 3% volume fraction and particle size of 100 nm was selected. The density and viscosity of the nano-fluid were 1250 kg/m3 and 1.18 10 3 kg/m s, respectively. × − · The inlet and outlet pressure were set to be 355 and 8.5 kPa, respectively. Figure6 shows the cavitating flow fields of the nano-fluid and DI water near the rectangle orifice. It can be observed that the cavitation jets for both nano-fluid and DI water were quite similar. However, the cavitating jet length

Figure 5. The comparison of vapor-liquid distribution with the experimental observation [31].

3.2. Cavitating Flow Characteristics of Nano-fluid and DI Wwater In the work, the Cu nano-fluid with 3% volume fraction and particle size of 100 nm was selected. The density and viscosity of the nano-fluid were 1250 kg/m3 and 1.18 × 10−3 kg/m·s, respectively. The inlet and outlet pressure were set to be 355 and 8.5 kPa, respectively. Figure 6 shows the cavitating flow fields of the nano-fluid and DI water near the rectangle orifice. It can be

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The simulated vapor-liquid distributions at the cross-section z = 0.1 mm by various turbulence models were compared with the experimental result, as displayed in Figure 4. The calculated vapor-liquid distribution by Standard k-ω model showed better agreement with the experimental result. For cavitation that occurred in a confined space, a shear flow boundary layer that formed by a large velocity gradient existed between the vapor and liquid phase. Meanwhile, the Reynolds number was relatively low downstream of the orifice. The Standard k-ω model considers the low Reynolds number effects and shear flow diffusion. Thus, it is more suitable for the wall-bound and jet flows calculation as the cavitating flow in the micro-channel.

Figure 4. The comparison of vapor-liquid distribution between the experimental data [30] and simulation results, (a) experimental result; (b) standard k-ε model; (c) realizable k-ε model; (d) standard k-ω model; and (e) k-ω Shear-Stress Transport (SST) model.

Additionally, the calculation result was compared with the experimental result that was obtained by Rooze et al. [31], as shown in Figure 5. It could be seen that a cavitating jet formed when the fluid flowed through the micro-orifice. The liquid jet was surrounded by twin vapor Micromachines 2020, 11, 310 7 of 14 bubbles near the orifice. The liquid–gas two phase mixtures were observed at downstream of the liquid jet. With the recovery of pressure, those cavitation bubbles collapsed and turned into liquid. ofThe nano-ﬂuid comparison (2 mm) between was a the little present shorter results than the and length the ofexperimental the DI water, data which from is in literature agreement further with theverified experiment the validity that wasof the conducted proposed by numerical Medrano method. [32].

Micromachines 2020, 11, x 7 of 14 Micromachines 2020, 11, x 7 of 14 observedobserved thatthat thethe cavitationcavitation jetsjets forfor bothboth nano-flunano-fluidid andand DIDI waterwater werewere quitequite similar.similar. However,However, thethe cavitatingcavitating jetjet lengthlength ofof nano-fluidnano-fluid (2(2 mm)mm) waswas aa lilittlettle shortershorter thanthan thethe lengthlength ofof thethe DIDI water,water, whichwhich isis inin agreementagreement withwith thethe experimentexperiment thatthat waswas conductedconducted byby MedranoMedrano [32].[32]. FigureFigure 5.5. The comparison ofof vapor-liquidvapor-liquid distributiondistribution withwith thethe experimentalexperimental observationobservation [[31].31].

Figure 6. The vapor-liquid distribution of the fluids: (a) deionized (DI) water; and, (b) nano-fluid. FigureFigure 6.6. The vapor-liquid distributiondistribution ofof thethe ﬂuids:fluids: (a)) deionizeddeionized (DI)(DI) water;water; and,and, ((bb)) nano-ﬂuid.nano-fluid.

FigureFigure 7 77 displays displaysdisplays the thethe pressure pressurepressure profiles profilesprofiles of ofof nano-fluid nano-fluidnano-fluid and andand DI DIDI water waterwater along alongalong the thethe centerline centerlinecenterline on onon the thethe symmetrysymmetry plane. plane. WhenWhen When thethe the fluidsfluids fluids flowedflowed flowed throughthrough thethe orifice, orifice,orifice, a a sudden sudden pressure pressure drop drop belowbelow thethe saturatedsaturated vapor vapor pressure pressure (3540 (3540 Pa) Pa) was was observed, observed, which which caused caused the the vapor-liquid vapor-liquid phase transition. DownstreamDownstream ofofof the thethe orifice, orifice,orifice, the thethe pressure pressurepressure gradually graduagradua recoveredllylly recoveredrecovered to about toto 8.5aboutabout kPa. 8.58.5 The kPa.kPa. pressure TheThe recoverypressurepressure ofrecoveryrecovery the nano-fluid ofof thethe nano-fluidnano-fluid was a little waswas bit aa fasterlittlelittle bitbit when fasterfaster compared whwhenen comparedcompared with that withwith of the thatthat DI ofof water thethe DIDI due waterwater to aduedue higher toto aa surfacehigherhigher surfacesurface tension. tension.tension. Thus, theThus,Thus, length thethe lengthlength of nano-fluid ofof nano-fnano-f cavitatingluidluid cavitatingcavitating jet was jetjet shorter waswas shortershorter due to duedue an earlier toto anan earlierearlier vapor bubblevaporvapor bubblebubble collapse. collapse.collapse.

Figure 7. The pressure distributions along centerline on the symmetry plane. Figure 7. The pressure distributions along centerline on the symmetry plane.

FigureFigure 88 showsshows thethe velocitiesvelocities alongalong thethe centerlinecenterline onon thethe symmetrysymmetry plane.plane. ThereThere waswas aa significantsignificant increaseincrease inin flowflow velocityvelocity atat thethe orifice,orifice, duedue toto thethe suddensudden decreasedecrease ofof thethe flowflow areaarea andand thethe cavitationcavitation phasephase change.change. ThThee maximummaximum cavitatingcavitating jetjet velocivelocityty ofof thethe DIDI waterwater reachedreached approximatelyapproximately 22.922.9 m/s,m/s, whichwhich waswas aa littlelittle higherhigher thanthan thethe jetjet velocityvelocity ofof thethe nano-fluidnano-fluid (20.4(20.4 m/s).m/s). ItIt indicatedindicated thatthat thethe cavitationcavitation intensityintensity ofof nanonano-fluid-fluid couldcould bebe aboutabout 12%12% lower.lower. AfterAfter flowingflowing throughthrough thethe orifice,orifice, thethe velocitiesvelocities ofof bothboth fluidsfluids bebegangan toto decline.decline. AtAt thethe veryvery beginning,beginning, thethe velocityvelocity decreaseddecreased relativelyrelatively slowerslower inin thethe cavitationcavitation zonezone,, becausebecause ofof thethe presencepresence ofof thethe vaporvapor phase.phase. ByBy comparison,comparison, aa moremore significantsignificant declinedecline ofof thethe vevelocitylocity occurredoccurred afterafter thethe cavitationcavitation collapse.collapse.

Micromachines 2020, 11, 310 8 of 14

Figure8 shows the velocities along the centerline on the symmetry plane. There was a significant increase in flow velocity at the orifice, due to the sudden decrease of the flow area and the cavitation phase change. The maximum cavitating jet velocity of the DI water reached approximately 22.9 m/s, which was a little higher than the jet velocity of the nano-fluid (20.4 m/s). It indicated that the cavitation intensity of nano-fluid could be about 12% lower. After flowing through the orifice, the velocities of both fluids began to decline. At the very beginning, the velocity decreased relatively slower in the cavitation zone, because of the presence of the vapor phase. By comparison, a more significant decline Micromachines 2020, 11, x 8 of 14 ofMicromachines the velocity 2020 occurred, 11, x after the cavitation collapse. 8 of 14

Figure 8. The velocity distributions at centerline on the symmetry plane. FigureFigure 8.8. TheThe velocityvelocity distributionsdistributions atat centerlinecenterline onon thethe symmetrysymmetry plane.plane. 3.3. Effects of the Orifice Structure 3.3.3.3. EffectsEffects ofof thethe OrificeOrifice StructureStructure In this section, the effects of the orifice structures on cavitation characteristics were analyzed. InIn thisthis section,section, thethe effectseffects ofof thethe orificeorifice structstructuresures onon cavitationcavitation characteristicscharacteristics werewere analyzed.analyzed. Besides the rectangle orifice, four orifices as the converging-diverging orifice, the converging BesidesBesides thethe rectanglerectangle orifice,orifice, fourfour orificesorifices asas thethe coconverging-divergingnverging-diverging orifice,orifice, thethe convergingconverging orifice,orifice, orifice, and the curved orifices (R = 0.3 and 0.6 mm) were selected, in which are shown Figure9. andand thethe curvedcurved orificesorifices ((RR == 0.30.3 andand 0.60.6 mm)mm) werewere selected,selected, inin whichwhich areare shownshown FigureFigure 9.9. TheThe Themicro-channel micro-channel width width to tothe the or orificeifice minimum minimum width width ratio ratio was was WWc/W/Womin = =5.5. For For the the micro-channel width to the orifice minimum width ratio was Wc/cWominomin = 5. For the converging-divergingconverging-divergingconverging-diverging orifice, orifice,orifice, the thethe contraction contractioncontraction and andand divergence divergencedivergence angles anglesangles areareare both bothboth 303030 degrees,degrees,degrees, asas shownshown in Figureinin FigureFigure9a. Additionally, 9a.9a. Additionally,Additionally, the contraction thethe contractioncontraction angle angleangle of the ofof the convergingthe convergingconverging orifice orificeorifice is 30 isis 30 degrees30 degreesdegrees (see (see(see Figure FigureFigure9b). The9b).9b). micro-channels TheThe micro-channelsmicro-channels with withwith curved curvedcurved orifices orificesorifices are areare shown shownshown in inin Figure FigureFigure9c,d, 9c,d,9c,d, and andand the thethe radiiradiiradii are are 0.60.6 0.6 andand and 0.30.3 0.3 mm,mm,mm, respectively. respectively.respectively.

FigureFigureFigure 9. 9.9.The TheThe orifice orificeorifice structures, structures,structures, ( a((a)a)) converging-diverging converging-divergingconverging-diverging orifice,orifice, orifice, ((b (bb)) ) convergingconverging converging orifice,orifice, orifice, ((cc) () c curvedcurved) curved orificeorificeorifice (R ((=RR =0.6= 0.60.6 mm), mm),mm), and andand ( d ((dd))) curved curvedcurved orifice orificeorifice ((RR == 0.30.3 mm).mm).

TheThe inletinlet andand outletoutlet pressurepressure inin thethe calculationcalculation werewere 355355 kPakPa andand 8.58.5 kPa,kPa, respectively.respectively. TableTable 22 showsshows thethe massmass flowflow raterate ofof thethe DIDI waterwater andand nanano-fluidno-fluid underunder differentdifferent orifices.orifices. Generally,Generally, thethe massmass flowflow raterate ofof thethe nano-fluidnano-fluid waswas approximatelyapproximately 12%12% lowerlower thanthan thatthat ofof thethe DIDI waterwater forfor allall ofof thethe differentdifferent orifices.orifices. Meanwhile,Meanwhile, forfor bothboth fluids,fluids, thethe minimumminimum flowflow ratesrates werewere underunder thethe rectanglerectangle orificeorifice attributingattributing toto aa moremore significantsignificant locallocal reresistancesistance loss.loss. WhenWhen comparedcompared withwith thethe rectanglerectangle orifice,orifice, thethe highesthighest massmass flowflow ratesrates werewere underunder thethe curvedcurved orifices,orifices, beingbeing aboutabout 30%30% higher.higher. However,However, withwith thethe increaseincrease ofof thethe radius,radius, thethe mamassss flowflow raterate waswas almostalmost keptkept unchangedunchanged forfor thethe curvedcurved orifice.orifice.

Micromachines 2020, 11, 310 9 of 14

The inlet and outlet pressure in the calculation were 355 kPa and 8.5 kPa, respectively. Table2 shows the mass flow rate of the DI water and nano-fluid under different orifices. Generally, the mass flow rate of the nano-fluid was approximately 12% lower than that of the DI water for all of the different orifices. Meanwhile, for both fluids, the minimum flow rates were under the rectangle orifice attributing to a more significant local resistance loss. When compared with the rectangle orifice, the highest mass flow rates were under the curved orifices, being about 30% higher. However, with the

Micromachinesincrease of the2020 radius,, 11, x the mass ﬂow rate was almost kept unchanged for the curved oriﬁce. 9 of 14

TableTable 2. MassMass flow ﬂow rate under different diﬀerent structures.

StructureStructure of of the the Orifice Orifice DI DI Wate Waterr (L/h) (L/h) Nano-fluid Nano-Fluid (L/h) (L /h) rectanglerectangle orifice orifice 9.45 9.45 8.39 8.39 converging-divergingconverging-diverging orifice orifice 11.56 11.56 10.37 10.37 converging orifice 11.53 10.29 converging orifice 11.53 10.29 curved orifice (R = 0.6 mm) 12.23 10.90 curved orifice (R = 0.6 mm) 12.23 10.90 curved orifice (R = 0.3 mm) 12.36 10.95 curved orifice (R = 0.3 mm) 12.36 10.95 Figure 10 shows the vapor volume fraction of the DI water and nano-fluid under various orificeFigure structures. 10 shows For theboth vapor fluids, volume the longest fraction cavi oftating the DI jet water lengths and were nano-fluid observed under under various the curved orifice orificestructures. with ForR = both0.3 mm. fluids, On theone longest hand, the cavitating flow resistance jet lengths under were the observed curved underorifice the(R = curved 0.3 mm) orifice was muchwith R lower.= 0.3 mm. On the On oneother hand, hand, the the flow smooth resistance curve under of the the orifice curved led orifice to slow (R = 0.3pressure mm) was recovery much downstreamlower. On the of other the hand,channel. the smoothThus, the curve mass of theflow orifice rate ledand to the slow cavitation pressure recoveryvapor fraction downstream were obviouslyof the channel. higher. Thus, Additionally, the mass it flow was ratefound and that the the cavitation cavitating vapor jet length fraction of DI were water obviously was a little higher. bit longerAdditionally, than the it was length found of thatnano-fluid the cavitating at each jet or lengthifice structure. of DI water The was addition a littlebit of longernano-particles than the increasedlength of nano-fluidthe viscosity at eachand orificesurface structure. tension of The the addition base fluid, of nano-particles which is believed increased to have the viscositynegative effectsand surface on cavitation tensionof inception. the base fluid, which is believed to have negative effects on cavitation inception.

Figure 10. TheThe vapor vapor volume volume fraction fraction with various orifice orifice structures: ( aa)) DI DI water water and and ( (b)) nano-fluid. nano-fluid. 3.4. Effects of the Inlet Pressure 3.4. Effects of the Inlet Pressure In this section, the effects of the inlet pressure on the DI and nano-fluid cavitation were analyzed. In this section, the effects of the inlet pressure on the DI and nano-fluid cavitation were The structure of curved orifice (R = 0.3 mm) was selected because of the highest cavitation efficiency. analyzed. The structure of curved orifice (R = 0.3 mm) was selected because of the highest cavitation efficiency. The outlet pressure was set to be 8.5 kPa. Figure 11 displays the mass flow rates of the DI water and the nano-fluid with different inlet pressures. For both fluids, the mass flow rates grew almost linearly with the increase of inlet pressure. While, for the same inlet pressure, the mass flow rate of the nano-fluid was always found to be lower than that of the DI water. Furthermore, the mass flow rate difference between the two fluids got higher with the growth of inlet pressure.

Micromachines 2020, 11, 310 10 of 14

The outlet pressure was set to be 8.5 kPa. Figure 11 displays the mass flow rates of the DI water and the nano-fluid with different inlet pressures. For both fluids, the mass flow rates grew almost linearly with the increase of inlet pressure. While, for the same inlet pressure, the mass flow rate of the nano-fluid was always found to be lower than that of the DI water. Furthermore, the mass flow rate difference betweenMicromachines the 2020 two, 11 fluids, x got higher with the growth of inlet pressure. 10 of 14

FigureFigure 11.11. MassMass flowflow ratesrates ofof thethe nano-fluidnano-fluid andand DIDI waterwater underunder didifferentfferent inlet inlet pressures. pressures.

TheThe cavitationcavitation inceptioninception numbernumber isis anan importantimportant dimensionlessdimensionless parameter,parameter, whichwhich isis usedused toto characterizecharacterize thethe initialinitial and critical state state of of cavitation. cavitation. The The cavitation cavitation inception inception number number is isdefined, defined, as asfollows: follows: Pout Pv σ = − (13) PP1 ρU−2 σ = 2outo v 1 Here, Pout is the outlet pressure, Pv is the vapor pressure,ρ 2 and Uo is the mean velocity at the orifice.(13) Uo Figure 12 shows the vapor volume fractions of two2 fluids with different inlet pressure. The cavitation inception of nano-fluid could be observed at σ = 0.039 (inlet pressure of 200 kPa). In contrast, σ for the Here, Pout is the outlet pressure, Pv is the vapor pressure, and Uo is the mean velocity at the DIorifice. water Figure was approximately 12 shows the 0.064.vapor Thus, volume the fraction nano-fluids of wastwo morefluids di withfficult different to generate inlet cavitation pressure. than The thecavitation pure water. inception Additionally, of nano-fluid the length could of the be nano-fluid observed wasat σ found = 0.039 to be(inlet shorter pressure when comparedof 200 kPa). with In thecontrast, DI water σ for for the the sameDI water inlet was pressure. approximately With the increase 0.064. Thus, of inlet the pressure, nano-fluid the lengthwas more of cavitating difficult jetto increasedgenerate cavitation significantly. than When the pure the inlet water. pressure Additiona grewlly, to the 500 length kPa, cavitating of the nano-fluid jet lengths was of found both fluids to be increasedshorter when to about compared 8 mm upwith to 30%the DI of thewater total for channel the same length. inlet Thus, pressure. increasing With the inletincrease pressure of inlet is onepressure, of the etheffective length ways of cavitating to promote jet the increased cavitation si intensity.gnificantly. When the inlet pressure grew to 500 kPa, cavitating jet lengths of both fluids increased to about 8 mm up to 30% of the total channel 3.5. Effects of the Outlet Pressure length. Thus, increasing the inlet pressure is one of the effective ways to promote the cavitation intensity.The outlet pressure of 5, 8.5 and 12 kPa were selected in order to study their effects on cavitation inside the micro-channel with the curved orifice (R = 0.3 mm). The inlet pressure was 350 kPa in the calculation. Table3 shows the mass flow rates of the DI water and nano-fluid under different outlet pressures. For both of the fluids, the mass flow rate was found to be independent of the outlet pressure. When the outlet pressure increased from 5 to 12 kPa, the mass flow rates of the both fluids remained nearly unchanged. Figure 13 shows the vapor volume fraction of the DI water and nano-fluid under different outlet pressures. As the outlet pressure decreased from 12 kPa to 5 kPa, the cavitating jet length gradually increased. Meanwhile, for the same outlet pressure, the vapor volume fraction of the DI water was a little higher than that of the nano-fluid. The result indicates that, by decreasing the outlet pressure, the higher cavitation intensity can be acquired without the change of mass flow rate.

Micromachines 2020, 11, 310 11 of 14 Micromachines 2020, 11, x 11 of 14

Figure 12. The vapor volume fraction with various inlet pressures: (a) DI water and (b) nano-fluid. Figure 12. The vaporTable volume 3. Mass fraction flow with rate various under diinletfferent pressures: outlet pressures. (a) DI water and (b) nano-fluid.

3.5. Effects of the OutletOutlet Pressure Pressure (kPa) DI Water (L/h) Nano-Fluid (L/h) 5 12.36 10.95 The outlet pressure of 8.55, 8.5 and 12 kPa 12.32were selected in order 10.93 to study their effects on Micromachinescavitation inside 2020, 11 the, x micro-channel12 with the curved 12.34 orifice (R = 0.3 mm). 10.94 The inlet pressure was12 of 350 14 kPa in the calculation. Table 3 shows the mass flow rates of the DI water and nano-fluid under different outlet pressures. For both of the fluids, the mass flow rate was found to be independent of the outlet pressure. When the outlet pressure increased from 5 to 12 kPa, the mass flow rates of the both fluids remained nearly unchanged.

Table 3. Mass flow rate under different outlet pressures.

Outlet Pressure (kPa) DI Water (L/h) Nano-fluid (L/h) 5 12.36 10.95 8.5 12.32 10.93 12 12.34 10.94

Figure 13 shows the vapor volume fraction of the DI water and nano-fluid under different outlet pressures. As the outlet pressure decreased from 12 kPa to 5 kPa, the cavitating jet length gradually increased. Meanwhile, for the same outlet pressure, the vapor volume fraction of the DI water was a little higher than that of the nano-fluid. The result indicates that, by decreasing the outlet pressure, the higher cavitation intensity can be acquired without the change of mass flow rate.

Figure 13. The vapor volume fraction with various outlet pressure: (a) DI water and (b) nano-ﬂuid. Figure 13. The vapor volume fraction with various outlet pressure: (a) DI water and (b) nano-fluid.

4. Conclusions

In this paper, the cavitation characteristics of the DI water and nano-fluid inside micro-channels with orifices were numerically investigated. The calculated results were compared with the experimental data, which proved the stability and reliability of the present model. The standard k-ω model is more suitable for micro-channel cavitation flow simulation. As to the rectangle orifice, the cavitating jet length and the maximum jet velocity of the nano-fluid were approximately 12% lower than those of the DI water when the Pin and Pout were 350 and 8.5 kPa, respectively. It proves that nano-particles played a negative effect on the cavitation inception. Subsequently, the effects of the orifice structure, inlet, and outlet pressure were discussed in detail. For both fluids, the curved orifice (R = 0.3 mm) had the highest cavitation efficiency and mass flow rate. With the increase of inlet pressure, the cavitating jet length and mass flow rate of two fluids increased significantly. Meanwhile, the mass flow rate difference between the two fluids became higher as the inlet pressure grows. In addition, the cavitaion inception number of the DI water and nano-fluid were about 0.061 and 0.039, respectively. With the decrease of outlet pressure, the cavitation intensity became stronger without the change of mass flow rate. The present research only considers the case of Cu nano-fluid with 3% volume fraction and a particle size of 100 nm. In the future, the effects of nano-particle type, size, and nano-fluid concentration on cavitation in the micro-channels would be further studied.

Author Contributions: conceptualization, B.L. and X.H.; methodology, B.L.; software, T.L.; validation, B.L., J.Z. and W.X.; formal analysis, B.L. and J.Z.; investigation, B.L. and W.X.; resources, B.L.; data curation, B.L.; writing—original draft preparation, T.L.; writing—review and editing, B.L.; visualization, H.Z.; supervision, X.H.; project administration, X.H.; funding acquisition, B.L.

Funding: This research was funded by National Natural Science Foundation of China through, grant number 51606190.

Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

References

1. Kumar, P.S.; Kumar, M.S.; Pandit, A. Experimental quantification of chemical effects of hydrodynamic cavitation. Chem. Eng. Sci. 2000, 55, 1633–1639.

Micromachines 2020, 11, 310 12 of 14

4. Conclusions In this paper, the cavitation characteristics of the DI water and nano-fluid inside micro-channels with orifices were numerically investigated. The calculated results were compared with the experimental data, which proved the stability and reliability of the present model. The standard k-ω model is more suitable for micro-channel cavitation flow simulation. As to the rectangle orifice, the cavitating jet length and the maximum jet velocity of the nano-fluid were approximately 12% lower than those of the DI water when the Pin and Pout were 350 and 8.5 kPa, respectively. It proves that nano-particles played a negative effect on the cavitation inception. Subsequently, the effects of the orifice structure, inlet, and outlet pressure were discussed in detail. For both fluids, the curved orifice (R = 0.3 mm) had the highest cavitation efficiency and mass flow rate. With the increase of inlet pressure, the cavitating jet length and mass flow rate of two fluids increased significantly. Meanwhile, the mass flow rate difference between the two fluids became higher as the inlet pressure grows. In addition, the cavitaion inception number of the DI water and nano-fluid were about 0.061 and 0.039, respectively. With the decrease of outlet pressure, the cavitation intensity became stronger without the change of mass flow rate. The present research only considers the case of Cu nano-fluid with 3% volume fraction and a particle size of 100 nm. In the future, the effects of nano-particle type, size, and nano-fluid concentration on cavitation in the micro-channels would be further studied.

Author Contributions: Conceptualization, B.L. and X.H.; methodology, B.L.; software, T.L.; validation, B.L., J.Z. and W.X.; formal analysis, B.L. and J.Z.; investigation, B.L. and W.X.; resources, B.L.; data curation, B.L.; writing—Original draft preparation, T.L.; writing—Review and editing, B.L.; visualization, H.Z.; supervision, X.H.; project administration, X.H.; funding acquisition, B.L. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by National Natural Science Foundation of China through, grant number 51606190. Conﬂicts of Interest: The authors declare no conﬂict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

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