Experimental and Simulation Investigation on the Kinetic Energy Dissipation Rate of a Fixed Spray-Plate Sprinkler

water

Article Experimental and Simulation Investigation on the Kinetic Energy Dissipation Rate of a Fixed Spray-Plate Sprinkler

Yisheng Zhang 1, Bin Sun 1,*, Hongyuan Fang 1, Delan Zhu 2, Lingxia Yang 1 and Zhansong Li 1 1 School of Water Conservancy and Environment, Zhengzhou University, Zhengzhou 450001, China; [email protected] (Y.Z.); [email protected] (H.F.); [email protected] (L.Y.); [email protected] (Z.L.) 2 College of Water Resources and Architectural Engineering, Northwest A&F University, Yangling 712100, Shaanxi, China; [email protected] * Correspondence: [email protected]; Tel.: +86-135-0345-2166

Received: 2 September 2018; Accepted: 28 September 2018; Published: 30 September 2018

Abstract: Sprinkler irrigation is promoted due to its remarkable advantages in water conservation, but the high energy consumption limits its development in a situation of energy scarcity. In order to determine the energy consumption of a fixed spray-plate sprinkler (FSPS), its discharge and initial trajectory velocity were investigated using a particle image velocimetry (PIV) technique and computational fluid dynamics (CFD) analyses. A nozzle diameter of 4.76 mm was used under windless conditions. Overall, good agreement between simulation results and experimental values was obtained. On the premise that the simulation method produced high accuracy, a series of simulations was performed with different nozzle diameters. The water distribution pattern, stream trajectory velocity and kinetic energy dissipation were analyzed. The results show that the jet produced at the nozzle is split by grooves after it hits the plate, with separation occurring earlier with decreasing nozzle diameter. The area of the flow cross-section of the outlet is mainly influenced by nozzle diameter rather than working pressure. The initial trajectory velocity of the grooves increases logarithmically with increasing working pressure. A high working pressure may not cause large kinetic energy dissipation. The dissipation rate of the FSPS ranged from 28.01–50.97%, i.e., a large kinetic energy rate was observed. To reduce this energy dissipation and improve water use efficiency, the structure of the FSPS should be optimized in further research.

Keywords: ﬁxed spray-plate sprinkler; jet velocity; kinetic energy dissipation; simulation

1. Introduction Agricultural production consumes enormous amounts of water, which is a threat to water resources [1]. Sprinkler irrigation is characterized by high levels of water conservation [2–5]. Commonly, linear-move and center-pivot irrigation machines are widely used for their high degree of automation [6]. The earlier sprinklers equipped in these machines were high-pressure impact, and in recent years, increasing energy costs have shifted the focus to increasing the energy efficiency of agricultural sprinkler applications and led to the development of various low-pressure sprinklers. The two main low-pressure spray-plate sprinklers are the rotating spray-plate sprinkler (RSPS) and fixed spray-plate sprinkler (FSPS) [7]. Compared with RSPS, the fixed spray-plate sprinkler (FSPS) offers the advantages of a relatively low working pressure, high wind resistance and low cost [2,8–10]. The working principle of the FSPS is simple: a jet of water from a nozzle strikes a refraction cone and forms a series of nappe adherences in the spray-plate grooves. The water distribution pattern from a single FSPS resembles a wetted circular crown [11]. However, as the water strikes the refraction cone,

Water 2018, 10, 1365; doi:10.3390/w10101365 www.mdpi.com/journal/water Water 2018, 10, 1365 2 of 13 the energy lost at the plate is extremely large, creating uncertainty about the initial velocity of the drops [12]. The initial trajectory velocity across the grooves is less than the jet velocity from the nozzle. This results in a reduction in the wetted width and control area during the irrigation with a liner-move irrigation machine [13]. In order to evaluate energy utilization efficiency, research on kinetic energy dissipation is required. The kinetic energy is mainly influenced by the velocity and discharge of the liquid. In general, the outlet flux of each groove and nozzle can be obtained using a weighing method. The calculation of initial jet velocity from the nozzle requires a measurement of flux, which is then divided by the nozzle area. However, the FSPSs used in pivot and linear movement irrigation systems are different from impact sprinklers [6], i.e., the jet produced at the nozzle undergoes an inelastic shock after it hits the plate, causing a large reduction in trajectory velocity [12]. Therefore, the main problem in calculating kinetic energy dissipation is in obtaining the initial trajectory velocity. Considering the handicap in estimating the initial trajectory velocity of FSPS, an experimental measurement was performed by Sánchez-Burillo et al. [12] using the photographic method. The instantaneous drop velocity vector at a bounded region close to the sprinkler was measured. Furthermore, a large head loss at the spray-plate was attained. By using the technique of low speed photography, Ouazaa et al. [14] determined drop velocity at a measurement point just after the plate, and the results showed that kinetic energy losses decreased with nozzle diameter increments. It is important to note that photographic method is available to acquire the initial trajectory velocity of FSPS. Besides, as one of photographic methods, the technique of particle image velocimetry (PIV) [15–17] can also be used in the measurement of jet velocity. The fundamental PIV is simple: once the fluid motion is received by the CCD camera, the positions of the droplet can be recorded at two instances of time, i.e., the droplet displacement, so it is realizable to calculate the trajectory velocity [18,19]. However, the measurement of velocity using the photographic method is inconvenient due to the requirement of a suitable experimental apparatus; in addition, the analysis of a large amount of samples is time consuming. With the development of computer technology and computational fluid dynamics (CFD) in recent years, numerical simulation has been widely used, as it offers the advantage of high efficiency [20,21]. Research on the initial trajectory velocity of a water jet has mainly focused on the free surface between the air and water. The interface tracking method, volume of fluid (VOF), which was proposed by Hirt and Nichols [22], providing insight into the underlying processes critical for primary and secondary atomization, is suitable in this regard [23–25]. In recent years, a coupled VOF with the level set method (LS-VOF) proposed by Osher and Sethian [26] has been tested by comparison against a standard VOF solver and experimental observation [27], and the result indicated that the LS-VOF model can improve surface tension implementation and provide a smooth variation of the physical properties across the interface between two fluids. Moreover, Jiang et al. [17] and Meredith et al. [28] have shown that the multiphase LS-VOF model can be successfully applied to simulate the performance of sprinklers. Several articles have been published describing the kinetic energy losses of FSPS [12,14,29]; unfortunately, these data were collected using the experimental method. Considering that a limited number of studies have been carried out on the simulation of the initial trajectory velocity and kinetic energy dissipation rate of a FSPS, the objectives of this study are as follows: (1) use a PIV technique to determine the stream jet velocity from the grooves at different working pressures with a nozzle diameter of 4.76 mm; (2) investigate the flux and jet velocity of each groove using the numerical simulation method, and estimate the validity of numerical simulation results; (3) based on these simulation results of different nozzle diameters, analyze the water distribution pattern, jet velocity of the stream and kinetic energy dissipation of FSPS. Water 2018, 10, 1365 3 of 13

2. Experimental Setup The selected FSPS was a Nelson D3000 (Nelson Irrigation Co., Walla Walla, WA 99362-2271, Water 2018, 10, x FOR PEER REVIEW 3 of 13 WaterUSA). 2018 The, 10 FSPS, x FOR was PEER equipped REVIEW with a 4.76 mm diameter nozzle and a deflector plate with 36 grooves3 of 13 center.(Figure The1). nozzle The diameter was installed of the 12.5 spray-plate mm above was the 31 spray-plate. mm and had During a cone operation, with a height the water of 2.8 mmjet from at its thecenter. nozzle The hits nozzle the deflector, was installed dividing 12.5 the mm flow above into the 36 spray-plate. streams. During operation, the water jet from the nozzle hits the deflector, deflector, dividingdividing thethe flowflow intointo 3636 streams.streams.

Figure 1. Fixed spray-plate sprinkler (FSPS) used in the investigation. Figure 1. Fixed spray-plate sprinkler (FSPS) used in the investigation.

AnAn experimental experimental test test (Figure (Figure 2)2 )to to evaluate evaluate the the ve velocitylocity of of the the stream stream was was set set up up at at the the Irrigation Irrigation HydraulicsAn experimental Experiment testStation (Figure at Northwest 2) to evaluate Agriculture the velocity and of Forestry the stream University, was set upYangling, at the Irrigation China. Hydraulics Experiment Station Station at at Northwest Northwest Agriculture Agriculture and and Forestry Forestry University, University, Yangling, Yangling, China. China. It Itconsisted consisted of ofa water a water jet jet system system and and PIV PIV system. system. The The water water jet jet system system was was comprised comprised of: of: (1) (1) a booster a booster pumpIt consisted of 2.2 kW, of a waterwhich jet was system controlled and PIV by system. a frequenc The ywater conversion jet system cabinet; was comprised (2) a water of: tank (1) awith booster a pump of 2.2 kW, which was controlled by a frequencyfrequency conversion cabinet; (2) a water tank with a capacity of 0.5 m3; 3(3) a Nelson D3000 sprinkler coupled with a deflector plate with 36 grooves; and capacity of 0.5 m3 ; (3) a Nelson D3000 sprinkler coupled with a deflector plate with 36 grooves; and (4)capacity a 32 mm of diameter 0.5 m ; (3) flow a Nelson pipe and D3000 pressure sprinkler sensor coupled. The PIVwith system a deflector used plateto obtain with the 36 grooves;jet velocity and (4) a 32 mm diameter flowflow pipe and pressure sensor.sensor. The PIV system used to obtain the jet velocity consistedconsisted of: of: (1) (1) a digital a digital high-speed high-speed video video camera camera (h (hotshototshot 512 512 sc); sc); (2) (2) a computer a computer to tocollect collect data; data; and and (3)consisted analysis of:display (1) a digital software high-speed (MOVIAS video Pro) camera for image (hotshot processing. 512 sc); The(2) a experiment computer to was collect performed data; and (3) analysis display software (MOVIAS Pro) forfor imageimage processing.processing. The experiment was performed usingusing PIV PIV visualization visualization technology, technology, i.e., i.e., PIV PIV techno technologylogy based based on on high-speed high-speed photography. photography. As As such, such, whenusing the PIV water visualization stream technology,jetted from i.e.,the PIVgroove, techno thelogy CCD based camera on high-speed recorded photography. the scattered As light such, when thethe water water stream stream jetted jetted from from the groove, the groove, the CCD the camera CCD recordedcamera therecorded scattered the light scattered distribution light distributionof the droplets of the at droplets short intervals. at short intervals. The travel The length travel over length a fixed over time a fixed was time then was processed then processed using the usingdistribution the MOVIAS of the Pro droplets software at short and theintervals. velocity The of travelthe water length jet overcalculated. a fixed time was then processed usingMOVIAS the MOVIAS Pro software Pro andsoftware the velocity and the of velocity the water of jetthe calculated. water jet calculated.

Figure 2. Experimental setup for velocity observation using particle image velocimetry (PIV). Figure 2. Experimental setup for velocity observation using particle image velocimetry (PIV). Figure 2. Experimental setup for velocity observation using particle image velocimetry (PIV). In general, the operating pressure could be adjusted between 34 and 413 kPa; accordingly, the workingIn pressuresgeneral, the were operating set to 50, pressure 100, 150, could 200 and be adju250 stedkPa. betweenAs the deflector 34 and 413plate kPa; had accordingly, a tri-sectional the structureworking and pressures the grooves were setin toeach 50, tri-section100, 150, 200 zone and were 250 kPa.symmetrical, As the deflector the number plate hadof experimental a tri-sectional groovesstructure could and be the reduced grooves to in six. each All tri-sectionexperiment zoneal measurements were symmetrical, were performedthe number under of experimental windless conditions.grooves could As each be reducedstream jetting to six. from All experiment a groove waal smeasurements relatively independent were performed [30], each under coherent windless jet conditions. As each stream jetting from a groove was relatively independent [30], each coherent jet Water 2018, 10, 1365 4 of 13

In general, the operating pressure could be adjusted between 34 and 413 kPa; accordingly, the working pressures were set to 50, 100, 150, 200 and 250 kPa. As the deflector plate had a tri-sectional structureWater 2018, and 10, x theFOR groovesPEER REVIEW in each tri-section zone were symmetrical, the number of experimental4 of 13 grooves could be reduced to six. All experimental measurements were performed under windless conditions.emitted by Asthe each groove stream could jetting be measured. from a groove In order was to relatively achieve independenthigh resolution [30 ],images, each coherent the area jet of emittedinterest bywas the set groove to 1280 could × 800 bepixels measured. and the Inframes order per to achievesecond to high 1000. resolution Each measurement images, the lasted area offor interest2 min, and was more set to than 1280 20× 800drops pixels for every and the combination frames per were second analyzed. to 1000. Each measurement lasted for 2 min, and more than 20 drops for every combination were analyzed. 3. Numerical Simulation 3. Numerical Simulation 3.1. Description of the Model 3.1. Description of the Model According to the actual size of the sprinkler, a three-dimensional flow region model was developedAccording using to thethe actual software size ofPro/Engineer. the sprinkler, Cons a three-dimensionalidering the geometric flow region symmetry modelwas of the developed FSPS, a usingsymmetrical the software boundary Pro/Engineer. condition Consideringwas applied along the geometric a symmetry symmetry plane, ofi.e., the only FSPS, half a of symmetrical the domain boundarywas modeled. condition An unstructured was applied along mesh a was symmetry used for plane, thei.e., simulation only half domain of the domain using wasANSYS modeled. ICEM Ansoftware. unstructured Based on mesh the wasexperimental used for the model, simulation the boun domaindaries usingof the ANSYSnumerical ICEM model software. were set Based as (i) onthe thewalls, experimental (ii) the water model, inlet, the (iii) boundaries the outlet, of (iv) the the numerical air inlet modeland (v) were symmetry set as (i) (Figure the walls, 3). The (ii) theNumber water 1 inlet,groove (iii) is the located outlet, in (iv)the thebeginning air inlet of and the (v)tri-section; symmetry the (Figure Number3). 6 The groove Number is near 1 groovethe symmetry is located axis inof the the beginning trisection. ofA theno-slip tri-section; condition the was Number applied 6 groove to the walls; is near a thevelocity symmetry inlet condition axis of the was trisection. applied Ato no-slip the water condition and air was inlets, applied and to a the pressure walls; aoutlet velocity condition inlet condition was applied was applied to the tooutlet. the water For mesh and airroughness inlets, and to ahave pressure a significant outlet conditioninfluence wason the applied sharpness to the of outlet. the interface For mesh between roughness air and to water, have a a significantgrid refinement influence of the on thegroove sharpness outlet ofwas the performed. interface between The calculation air and water, of initial a grid jet refinement velocity requires of the groovedischarge outlet to be was measured, performed. which The is calculation then divided of initial by the jet nozzle velocity area. requires The initial discharge velocities to be for measured, the water whichinlet at is different then divided working by the pressu nozzleres area. are presented The initial in velocities Table 1. for the water inlet at different working pressures are presented in Table1.

Wall Water inlet (velocity inlet)

Air inlet (velocity inlet)

Symmetry Outlet (pressure outlet)

Outlet (pressure outlet) (6) (5) Wall (3) (4) (1) (2)

FigureFigure 3. 3.3D 3D modeling modeling of of FSPS. FSPS.

Table 1. Inlet velocities (m/s) of four nozzle diameters for the simulations. Table 1. Inlet velocities (m/s) of four nozzle diameters for the simulations. Nozzle Diameter (mm) Working Pressure (kPa) Nozzle Diameter (mm) Working Pressure (kPa) 2.982.98 3.97 3.97 4.764.76 7.14 7.14 5050 9.80 9.80 9.95 9.95 9.879.87 9.92 9.92 100 13.43 13.87 13.69 13.76 100 13.43 13.87 13.69 13.76 150 16.39 17.03 16.75 16.88 200150 18.54 16.39 19.23 17.03 19.4216.75 16.88 19.40 250200 21.22 18.54 21.38 19.23 21.6519.42 19.40 21.51 250 21.22 21.38 21.65 21.51

3.2. Governing Equations The numerical simulations were carried out using the CFD software ANSYS FLUENT 17.0. The mass conservation equation and Navier–Stokes equations for incompressible, viscous flow are given by Equations (1) and (2) [31,32]: ∂ρ + div(ρu) = 0 (1) ∂t ∂(ρu) ∂p + div(ρuu) = − + div(µ grad u) + F (2a) ∂t ∂x x ∂(ρv) ∂p + div(ρvu) = − + div(µ grad v) + F (2b) ∂t ∂y y ∂(ρw) ∂p + div(ρwu) = − + div(µ grad w) + F (2c) ∂t ∂z z where ρ is fluid density (kg/m3); t is time; u is the flow velocity vector (m/s); p is pressure; u, v, w are averaged flow velocity components in the Cartesian coordinates x, y, and z, respectively (m/s); Fx, 2 Fy, Fz are body forces, Fx = 0, Fy = 0, Fz = −ρg(N); and µ is dynamic viscosity (N s/m ). The concepts of div (divergence) and grad (gradient) are introduced as: div(u) = ∂ux/∂x + ∂uy/∂y + ∂uz/∂z grad() = ∂()/∂x + ∂()/∂y + ∂()/∂z. In order to close the Navier–Stokes equations, the standard k-ε turbulence model was chosen to solve the unsteady calculation. The standard k-ε three-dimensional turbulence model is obtained from the following transport equations: " # ∂ ∂ ∂ui ∂uj ∂ui ∂ ∂k (ρk) + (ρkui) = µt( + ) + (µ + µt) − ρε (3) ∂t ∂xi ∂xi ∂xj ∂xj ∂xj ∂xj

" # 2 ∂ ∂ 1 ∂ui ∂uj ∂ ∂ε ε (ρε) + (ρεui) = ρCε1ε( + ) + (µ + µt/σε) − ρCε2 √ (4) ∂t ∂xi 2 ∂xj ∂xi ∂xj ∂xj k + vε where k is turbulence kinetic energy (m2/s2); ε is turbulence dissipation (kg·m2/s3); i and j are vectors; and Cε1, Cε1 and σε are correcting coefﬁcients. The multiphase LS-VOF model was adopted for this study, offering the advantages of fewer iterative steps and lower computation time. Standard wall functions were applied as the near-wall treatment. The SIMPLE algorithm (semi-implicit method for the pressure-linked equations) was chosen to solve mass conservation and the Navier–Stokes equations. A second-order upwind scheme for the discretization of momentum, turbulent kinetic energy and turbulent dissipation rate was selected. The gravity and operating air pressure were set to 9.81 m/s2 and 101,325 Pa, respectively. The time step size (t) was set to 0.001 s, and the convergence precision was set to 0.0001 for all equations.

4. Results Experimental data for flow rates and jet velocities were collected to compare with the simulation results. In general, the average velocities of water jetting from the grooves could not be obtained directly through the simulations; however, they could be calculated since the parameters of flow cross-section and mass flow rate were obtained. In order to obtain the cross-sectional area, the outlet flow pattern of each groove was observed through simulation with a 4.76 mm nozzle at the working pressure of 200 kPa, and Auto-CAD software was used to analyze the cross-sectional area. Cooperating with the simulation results of flux, the velocity with different volume fractions of water could be calculated. Figure4 illustrates the calculated velocity of each groove with different water volume fractions. The velocity showed a large range of variation as the volume fraction changed from 0.3–0.8. The measured velocities, which ranged from 14.51 m/s–16.02 m/s, were used to calibrate the flow cross-section. In Figure4, almost all the calculate velocities with a volume fraction of 0.5 and 0.6 were Water 2018, 10, x FOR PEER REVIEW 6 of 13 Water 2018, 10, 1365 6 of 13 were embraced in that region. Consequently, the shape of the free surface was determined from the water volume fraction using the ratio 0.55:1. embraced in that region. Consequently, the shape of the free surface was determined from the water volume fraction using the ratio 0.55:1.

20 Volume Fraction of Water 0.3 0.4 0.5 0.6 18 0.7 0.8

12 Initial trajectory velocity of grooves (m/s) grooves of velocity trajectory Initial 10 123456 Number of groove

Figure 4. Calculated velocity with different volume fractions of water. Figure 4. Calculated velocity with different volume fractions of water. 4.1. Comparison of Experimental Results and Simulated Values 4.1.Figure Comparison5 illustrates of Experimental the discharge Results of and the Simulated 1st–6th groove, Values showing numerical simulation values (SVs) and experimental values (EVs). As shown, for the EVs at different working pressures, the flow Figure 5 illustrates the discharge of the 1st–6th groove, showing numerical simulation values rates increased when the groove number was increased from 1–6. The SVs showed a tendency to (SVs) and experimental values (EVs). As shown, for the EVs at different working pressures, the flow decrease slightly at the second groove and then increase, i.e., the minimum flow rate appeared at rates increased when the groove number was increased from 1–6. The SVs showed a tendency to the second groove. Figure5 also shows the phenomenon that all the SVs for the first groove were decrease slightly at the second groove and then increase, i.e., the minimum flow rate appeared at the larger than the EVs, with relative errors of 2.60, 2.30, 3.15, 3.91 and 3.40%, respectively, for working second groove. Figure 5 also shows the phenomenon that all the SVs for the first groove were larger pressures from 50–250 kPa. Conversely, the SVs were smaller than the EVs in the second groove, with a than the EVs, with relative errors of 2.60, 2.30, 3.15, 3.91 and 3.40%, respectively, for working maximum relative error smaller than 1.94%. The primary reason for this was that a symmetry boundary pressures from 50–250 kPa. Conversely, the SVs were smaller than the EVs in the second groove, with condition was applied, meaning that scalar flux across this boundary was zero, and circumferential a maximum relative error smaller than 1.94%. The primary reason for this was that a symmetry water movement to the boundary was ignored. The maximum relative error was no larger than 3.91% boundary condition was applied, meaning that scalar flux across this boundary was zero, and for all working conditions, implying that the SVs were close to the experimental results. In addition, circumferential water movement to the boundary was ignored. The maximum relative error was no when the working pressure was fixed, the maximum and minimum EVs for the six grooves showed a larger than 3.91% for all working conditions, implying that the SVs were close to the experimental large difference (the same was true for the SVs). For example, when the working pressure was 50 kPa, results. In addition, when the working pressure was fixed, the maximum and minimum EVs for the the maximum and minimum flow rate EVs were 0.0165 m3/h and 0.0202 m3/h, respectively, i.e., a 20% six grooves showed a large difference (the same was true for the SVs). For example, when the working difference (under the same conditions, the difference in the SVs was about 19.22%). pressure was 50 kPa, the maximum and minimum flow rate EVs were 0.0165 m3/h and 0.0202 m3/h, respectively, i.e., a 20% difference (under the same conditions, the difference in the SVs was about 19.22%). Velocity is an important parameter for evaluating the difference between the simulated and experimental results. The reported velocity of each stream was the average velocity calculated from flow rate divided by flow cross-section, as mentioned above. The free surface of the water outlet profile was determined in the calibration process. Numerical jet velocity results for the different working pressures were compared with the experimental results. Table 2 presents the data for six grooves at five working pressures. It shows that the relative deviation (RD) of each working pressure was smaller than 10%. When the working pressure was increased from 50–250 kPa, the maximum Water 2018, 10, x FOR PEER REVIEW 7 of 13

RD was 3.28, −4.07, 3.71%, 5.81 and 9.44% respectively, i.e., a generally increasing trend. The reason for this is that a higher working pressure yields a higher jet velocity as a large measurement error exists when the experimental jet velocity is high, and the simulation process neglected this factor. However, a good agreement between the simulation results and experimental values was obtained, which indicates that both PIV measurement and CFD simulation with the LS-VOF method could be used to analyze the jet velocity and discharge of the stream. Water 2018, 10, 1365 7 of 13

0.045 50kPa- SV 50kPa- EV 100kPa- SV 100kPa- EV 150kPa- SV 150kPa- EV 200kPa- SV 200kPa- EV

) 0.040 250kPa- SV 250kPa- EV -1 ·h 3 0.035

0.030

0.025

0.020 Dischargegroove of the (m

0.015 123456 Number of groove

Figure 5. Jet flow rates for various numbers of grooves. SV, simulation value; EV, experimental value. Figure 5. Jet flow rates for various numbers of grooves. SV, simulation value; EV, experimental value. Velocity is an important parameter for evaluating the difference between the simulated and experimental results.Table 2. Initial The reportedtrajectory velocity velocity (m/s) of with each variou streams numbers was of thegrooves average corresponding velocity to a calculated 4.98-mm from nozzle at different working pressures. flow rate divided by flow cross-section, as mentioned above. The free surface of the water outlet profile was determined in the calibration process. NumericalWorking jet Pressure velocity (kPa) results for the different working Groove 50 100 150 200 250 pressures wereNumber compared EV SV with RD the experimentalEV SV RD results.EV SV Table RD2 presentsEV SV the dataRD forEV sixSV grooves RD at five working pressures.m s−1 Itm shows s−1 100% that m thes−1 relativem s−1 100% deviation m s−1 m s (RD)−1 100% of eachm s−1 workingm s−1 100% pressure m s−1 m wass−1 100% smaller Groove 1 7.90 7.84 −0.71 11.40 11.22 −1.66 13.02 13.25 1.72 14.51 15.18 4.41 15.78 16.47 4.17 than 10%. WhenGroove 2 the 7.71 working 7.48 − pressure3.10 11.21 was10.78 increased−4.07 12.75 from12.58 50–250−1.33 15.30 kPa, 14.56 the maximum−5.08 14.55 15.73 RD was 7.50 3.28, Groove 3 7.69 7.79 1.28 11.61 11.29 −2.83 13.42 13.10 −2.42 15.25 15.06 −1.25 15.72 16.35 3.84 −4.07, 3.71%,Groove 5.81 4 and7.67 9.44%7.93 respectively, 3.28 11.28 11.37 i.e., a0.75 generally 12.92 13.38 increasing 3.41 16.02 trend. 15.36 The−4.32 reason 16.79 for16.65 this −0.81 is that Groove 5 7.90 7.98 1.07 11.52 11.43 −0.82 12.89 13.39 3.71 16.32 15.50 −5.28 15.19 16.77 9.44 a higher workingGroove 6 pressure7.75 7.78 yields 0.31 a10.92 higher 11.13 jet velocity1.86 12.84 as13.08 alarge 1.87 measurement15.99 15.11 −5.81 error 15.53 exists 16.40 when 5.32 the experimental jet velocity isEV: high, experimental and the value; simulation SV: simulation process value; neglected RD: relative this deviation. factor. However, a good agreement between the simulation results and experimental values was obtained, which indicates that both PIV measurement4.2. Fluid-Phase and Nephogram CFD simulation and Initial Trajectory with the Velocity LS-VOF method could be used to analyze the jet velocity and dischargeGiven the of satisfactory the stream. agreement between the experimental and simulation results, the simulation method was used to evaluate the water surface profile and jet velocity with different Table 2.nozzleInitial types. trajectory Table velocity3 presents (m/s) the contours with various of the numbers water fraction of grooves at a pressure corresponding of 200 kPa to aand 4.98-mm nozzle nozzlediameters at different of working2.98, 3.97, pressures. 4.76, and 7.12 mm. In this table, the contours of the water distribution pattern of the FSPS show that when the nozzle diameter is 2.98 mm, the stream is split by the grooves as soon as the water jetting from the nozzle strikesWorking the cone Pressure in the (kPa) center of the plate. However, separation of Groove the stream50 along the groove 100was not obvious at 150increased nozzle diameters, 200 e.g., when the 250 nozzle Number EV SV RD EV SV RD EV SV RD EV SV RD EV SV RD m s−1 m s−1 100% m s−1 m s−1 100% m s−1 m s−1 100% m s−1 m s−1 100% m s−1 m s−1 100% Groove 1 7.90 7.84 −0.71 11.40 11.22 −1.66 13.02 13.25 1.72 14.51 15.18 4.41 15.78 16.47 4.17 Groove 2 7.71 7.48 −3.10 11.21 10.78 −4.07 12.75 12.58 −1.33 15.30 14.56 −5.08 14.55 15.73 7.50 Groove 3 7.69 7.79 1.28 11.61 11.29 −2.83 13.42 13.10 −2.42 15.25 15.06 −1.25 15.72 16.35 3.84 Groove 4 7.67 7.93 3.28 11.28 11.37 0.75 12.92 13.38 3.41 16.02 15.36 −4.32 16.79 16.65 −0.81 Groove 5 7.90 7.98 1.07 11.52 11.43 −0.82 12.89 13.39 3.71 16.32 15.50 −5.28 15.19 16.77 9.44 Groove 6 7.75 7.78 0.31 10.92 11.13 1.86 12.84 13.08 1.87 15.99 15.11 −5.81 15.53 16.40 5.32 EV: experimental value; SV: simulation value; RD: relative deviation.

4.2. Fluid-Phase Nephogram and Initial Trajectory Velocity Given the satisfactory agreement between the experimental and simulation results, the simulation method was used to evaluate the water surface profile and jet velocity with different nozzle types. Table3 presents the contours of the water fraction at a pressure of 200 kPa and nozzle diameters of 2.98, 3.97, 4.76, and 7.12 mm. In this table, the contours of the water distribution pattern of the FSPS Water 2018, 10, 1365 8 of 13 show that when the nozzle diameter is 2.98 mm, the stream is split by the grooves as soon as the water jetting from the nozzle strikes the cone in the center of the plate. However, separation of the stream along theWaterWater groove 2018 2018, 10, 10 was, x, xFOR FOR not PEER PEER obvious REVIEW REVIEW at increased nozzle diameters, e.g., when the nozzle diameter8 8of of 13 13 was WaterWater 20182018,, 1010,, xx FORFOR PEERPEER REVIEWREVIEW 88 ofof 1313 increased toWater 7.12 2018 mm,, 10, x FOR the PEER stream REVIEW was divided until the water flows out of the outlet. The8 water of 13 surface diameter was increased to 7.12 mm, the stream was divided until the water flows out of the outlet. profile indiameterdiameterdiameter TableWater3 2018 indicateswas waswas, 10 , increased increasedxincreased FOR PEER that REVIEWto thetoto 7.12 7.127.12 area mm, mm,mm, of the flowthethe stream streamstream cross-section wa wawass s divided divideddivided of the until untiluntil third the thethe groovewater waterwater flows flowsflows increased out outout of ofof the as8 the theof the13 outlet. outlet.outlet. nozzle The water surface profile in Table 3 indicates that the area of flow cross-section of the third groove diameterTheTheThe increased.diameter water waterwater surface surfacesurfacewas The increased profile freeprofileprofile surfaces to in inin 7.12 Table TableTable mm, present 3 33 indicatesthe indicatesindicates stream as athat thatwathat convexs the thedividedthe area areaarea line until of ofof when flow flowflow the watercross-section cross-sectioncross-section the diameterflows out of ofof of asthe the thethe2.98 third thirdthirdoutlet. or groove groovegroove 3.97 mm, increasedincreasedincreasedThediameter water asas as was surfacethethe the increasednozzlenozzle nozzle profile diameterdiameter diameterto in 7.12 Table mm, increased.increased. 3increased. indicates the stream thatTheThe The wa the freesfree freedivided area surfacessurfaces surfaces of untilflow presentpresent thecross-sectionpresent water asas asflows aa aof convexconvex convextheout thirdof thelineline line groove outlet. whenwhen when thethe the but presentincreasedWater a concave 2018 as, 10 the, x FOR line nozzle PEER when REVIEW diameter the diameter increased. was The 4.76 free or surfaces 7.12 mm. present as a convex line8 whenof 13 the diameterdiameterdiameterincreasedThe water asas as 2.982.98 as 2.98surface the oror or 3.97nozzle3.97 3.97profile mm,mm, mm, diameter in butbut Tablebut presentpresent present increased.3 indicates aa a concavconcav concav The that freee ethe e lineline line areasurfaces whenwhen when of flow thethepresent the cross-sectiondiameterdiameter diameter as a convex waswas was of 4.764.76the 4.76line third oror orwhen 7.127.12 7.12groove mm.mm.the mm. diameterincreased as 2.98as the or nozzle3.97 mm, diameter but present increased. a concav The freee line surfaces when thepresent diameter as a convex was 4.76 line or when 7.12 mm.the diameterdiameter aswas 2.98 increased or 3.97 mm, to 7.12 but mm, present the astream concav wae lines divided when theuntil diameter the water was flows 4.76 outor 7.12 of the mm. outlet. diameter as 2.98 or 3.97 mm, but present a concave line when the diameter was 4.76 or 7.12 mm. TableTable 3.TableContours 3. 3. Contours Contours of the of of the water the water water fraction fraction fraction at at 200at 200 200kPa kPa kPa of of working working pressure. pressure. The water surfaceTableTable profile 3.3. ContoursContours in Table ofof3 indicates thethe waterwater that fractionfraction the area atat 200200 of kPa kPaflow ofof cross-section workingworking pressure.pressure. of the third groove Table 3. Contours of the water fraction at 200 kPa of working pressure. increased as the nozzle diameter increased. The free surfaces present as a convex line when the NozzleNozzleNozzleNozzle Diameter DiameterDiameter Diameter Table 3. ContoursFigure:Figure:Figure:Figure: of Contourthe ContourwaterContour Contour fraction of Waterofof of WateratWater Water 200 kPa of workingSubfigure: pressure.Subfigure:Subfigure:Subfigure: Water Surface WW Wateraterater SurfaceSurface ProfileSurface NozzlediameterNozzle Diameter as Diameter 2.98 or 3.97 mm, but Figure:present Contour aContour concav ofe lineof Water Water when the diameterSubfigure: Subfigure:was 4.76 W orater 7.12 W Surfaceater mm. Surface (mm)(mm)(mm)(mm) DistributionDistributionDistributionDistribution Pattern PatternPattern Pattern ofProfileProfileProfile Third ofof of Groove ThirdThird Third GrooveGroove Groove Nozzle(mm)(mm) Diameter Figure:DistributionDistribution Contour Pattern ofPattern Water Subfigure:ProfileProfile of Third W ofater Third Groove Surface Groove (mm) Distribution Pattern ProfileArea:Area: Area:of Third 2.742.74 2.74 Groove ×× × 1010 10−−77− 7mm m22 2 Table 3. Contours of the water fraction at 200 kPa of workingArea: pressure.Area:Area: 2.74 2.74 × ×2.74 1010−7− ×m7 102m −27 m2 Area: 2.74 × 10−7 m2 WaterNozzle 2018, 10 Diameter, x FOR PEER REVIEW Figure: Contour of Water Subfigure: Water Surface8 of 13 (mm) Distribution Pattern Profile of Third Groove diameter was increased to 7.12 mm, the stream was divided until the waterArea: flows 2.74 out × 10of −the7 m 2outlet. The water2.98 surface profile in Table 3 indicates that the area of flow cross-section of the third groove 2.982.982.982.982.98 increased 2.98as the nozzle diameter increased. The free surfaces present as a convex line when the diameter as 2.98 or 3.97 mm, but present a concave line when the diameter was 4.76 or 7.12 mm. 2.98 Table 3. Contours of the water fraction at 200 kPa of working pressure.

Nozzle Diameter Figure: Contour of Water Subfigure: Water− 7Surface2 Area: 4.42 × 10 m −7 2 Area: 4.42 −×7 7102 −72− 7m 2 2 (mm) Distribution Pattern ProfileArea:Area:Area:Area: 4.42Area:of 4.42 Third× 4.42 4.42×4.42 10 Groove × × × m 10 1010m −7 m mm2 Area: 2.74 × 10−7 m2

Area: 4.42 × 10−7 m2 3.97 3.973.973.97 3.973.973.97 2.98 3.97

−7 2 Area: 6.32 × 10 m −7 2 Area: 6.32 × 10 m Area:Area: 6.32 6.32 × ×10 10−−77− m7 m22 2 Area:Area:Area: 4.42× 6.32×6.32 10− − 7×× 7m 10102 −27m m2 Area: 6.32 10 m Area: 6.32 × 10−7 m2 4.76 4.76 4.76 4.764.764.764.763.97 4.76

Area: 1.32 × 10−6 m2 −6 2 Area: 1.32 × 10 m

Area: 6.32 × 10−7 m2 Area:Area:Area: 1.321.32 1.32 ×× × 1010 10− −66− 6mm m22 2 Area: 1.32− × 10−6 m2 Area:Area: 1.32 1.32× × 10−6 6mm2 2 7.12 7.12 4.76 7.127.127.12 7.127.127.12

Figure 6 shows the water surface profile at different working pressures with a nozzle diameter Figure 6 shows the water surface profile at different working pressures with a nozzle diameter of 3.97 mm. The area of flow cross-section has a decreasing tendency withArea: increasing 1.32 × 10−6 workingm2

pressure,of 3.97 mm. although The areathe decline of flow in cross-sectionvalue is not st hasrong. a Thedecreasing maximum tendency and mini withmum increasing values of workingthe area werepressure, 4.71 ×although 10−7 m2 and the 4.42decline × 10 in−7 mvalue2, respectively. is not strong. Between The maximum the working and pressuresminimum of values 50 and of 200 the kPa, area FigureFigure 6 shows 6 shows−7 2the the water water surface surface−7 2 profileprofile atat diffdifferenterent working working pressures pressures with with a nozzle a nozzle diameter diameter wereFigureFigureFigure 4.71 6 6×6 shows shows10shows m theand thethe water 4.42waterwater × 10 surface surfacesurface m , respectively. profile profileprofile at atat diff diff diffBetweenerenterenterent workingthe workingworking working pressures pressurespressures pressures with withwith of 50 a a aand nozzle nozzlenozzle 200 kPa, diameter diameterdiameter theof 3.97maximum mm. The rate areaof change of flow was cross-section about 6.15%. has However, a decreasing the rates tendency of change with were increasing 38.01, 30.06 working and Figureofofof 3.97 3.97the63.97 shows maximummm. mm.mm. The theTheThe rate waterarea areaarea of of ofchange surfaceof flow flowflow was cross-section cross-sectioncross-section proﬁle about 6.15%. at different has has hasHowever, a a a decreasing decreasingdecreasing working the rates tendency pressurestendency tendencyof change with withwere with increasing 38.01,increasingincreasing a nozzle 30.06 and diameterworking workingworking of of 3.97pressure, mm. 7.12although The area the ofdecline flow in cross-section value is not st rong.has a The decreasing maximum tendencyand minimum with values increasing of the area working pressure,pressure,pressure, althoughalthough although thethe the declinedecline decline inin in valuevalue value isis is notnot not stst strong.rong.rong. TheThe The maximummaximum maximum andand and minimini minimummummum valuesvalues values ofof of thethe the areaarea area 3.97 mm.pressure, Thewere area 4.71 although of× 10 ﬂow−7 m the2 and cross-section decline 4.42 × 10 in−7 value m2 has, respectively. is a not decreasing strong. Between The tendency maximumthe working with and pressures increasingminimum of 50 valuesand working 200 of kPa, the pressure, area werewerewere 4.714.71 4.71 ×× × 1010 10−−77− m7m m22 and2and and 4.424.42 4.42 ×× × 1010 10−−77− m7m m22,, 2 respectively.,respectively. respectively. BetweenBetween Between thethe the workingworking working pressurespressures pressures ofof of 5050 50 andand and 200200 200 kPa,kPa, kPa, althoughwere thethe 4.71 declinemaximum × 10−7 inm rate2 valueand of change4.42 is × not 10 was−7strong. m about2, respectively. 6.15%. The However, maximum Between the the andrates working of minimum change pressures were values 38.01, of 50 30.06 of and the and 200 area kPa, were thethethe maximummaximum maximum raterate rate ofof of changechange change waswas was aboutabout about 6.15%.6.15%. 6.15%. However,However, However, thethe the ratesrates rates ofof of changechange change werewere were 38.01,38.01, 38.01, 30.0630.06 30.06 andand and 4.71 × 10the−7 maximumm2 and 4.42 rate ×of 10change−7 m 2was, respectively. about 6.15%. Between However, the the workingrates of change pressures were of38.01, 50 and30.06 200 and kPa,

Figure 6 shows the water surface profile at different working pressures with a nozzle diameter of 3.97 mm. The area of flow cross-section has a decreasing tendency with increasing working pressure, although the decline in value is not strong. The maximum and minimum values of the area were 4.71 × 10−7 m2 and 4.42 × 10−7 m2, respectively. Between the working pressures of 50 and 200 kPa, the maximum rate of change was about 6.15%. However, the rates of change were 38.01, 30.06 and Water 2018, 10, 1365 9 of 13

the maximumWater 2018 rate, 10 of, x FOR change PEER REVIEW was about 6.15%. However, the rates of change were 38.01,9 of 13 30.06 and 52.12% when the nozzle diameter was increased from 2.98–7.12 mm at 200 kPa of working pressure (Table3). This52.12% indicates when the that nozzle compared diameter was to the increased nozzle from diameter 2.98–7.12 parameter, mm at 200 kPa working of working pressure pressure had little (Table 3). This indicates that compared to the nozzle diameter parameter, working pressure had little impact on theimpact area on ofthe ﬂow area of cross-section. flow cross-section.

A: 50 kPa B: 100 kPa C: 150 kPa (Area: 4.71 × 10−7 m2) (Area: 4.70 × 10−7 m2) (Area: 4.61 × 10−7 m2)

D: 200 kPa E: 250 kPa (Area: 4.42 × 10−7 m2) (Area: 4.52 × 10−7 m2)

Figure 6.FigureWater 6.surface Water surface proﬁle profile ofthe of the third third groove groove with with a nozzle a nozzle diameter diameter of 3.97 ofmm. 3.97 mm.

The initialThe trajectory initial trajectory velocity velocity of eachof each groove groove was was calculated calculated from from the simulation the simulation results. results. ConsideringConsidering the negligible the negligible differences differences in in jet jet velocity velocity among among the the 36 grooves 36 grooves of the ofFSPS the (Table FSPS 2), (Table2), nozzle number average velocity was analyzed. As shown in Figure 7, the jet velocity curves present nozzle number average velocity was analyzed. As shown in Figure7, the jet velocity curves present logarithmic increases with increasing working pressure. The figure also shows that the jet velocity logarithmicincreased increases when with the nozzle increasing diameter working increased pressure.at a constant The working ﬁgure pressure. also shows that the jet velocity increased when the nozzle diameter increased at a constant working pressure.

4.3. Kinetic Energy Dissipation The kinetic energy dissipation is defined as the kinetic energy difference between the water inlet cross-section and the water outlet cross-section (Figure4). The kinetic energy dissipation under different working conditions was calculated. As shown in Figure8, dissipation decreased as the nozzle diameter increased at a constant working pressure. For example, when the sprinkler working pressure was 50 kPa, the energy dissipation was 50.97, 46.47, 37.57 and 28.01% for nozzle diameters of 2.97, 3.98, 4.76 and 7.12 mm respectively. When the working pressure was 200 kPa, the dissipation only very slightly decreased from 39.48 and 39.33% as the diameter increased from 3.98–4.76 mm. Calculation error may have caused this phenomenon. In addition, the level of kinetic energy dissipation fluctuated when the working pressure was changed with a fixed nozzle diameter, although regulation of the fluctuations affected by working pressure was not obvious. Water 2018, 10, 1365 10 of 13 Water 2018, 10, x FOR PEER REVIEW 10 of 13

18 2.98mm

） 3.97mm

m/s 4.76mm

（ 16 7.14mm

Initial trajectory velocity of grooves of velocity trajectory Initial 6 50 100 150 200 250 Woking pressure(kPa)

Water 2018, 10, x FOR PEER REVIEW 11 of 13 FigureFigure 7. 7. NumericalNumerical results results of of initial initial trajectory trajectory velocity velocity at different nozzle diameters.

4.3. Kinetic Energy 60Dissipation 2.98mm 3.97mm The kinetic energy dissipation is defined as the 4.76mm kinetic energy difference between the water inlet 7.14mm cross-section and 50the water outlet cross-section (Figure 4). The kinetic energy dissipation under different working conditions was calculated. As shown in Figure 8, dissipation decreased as the nozzle diameter increased at a constant working pressure. For example, when the sprinkler working 40 pressure was 50 kPa, the energy dissipation was 50.97, 46.47, 37.57 and 28.01% for nozzle diameters of 2.97, 3.98, 4.76 and 7.12 mm respectively. When the working pressure was 200 kPa, the dissipation only very slightly 30decreased from 39.48 and 39.33% as the diameter increased from 3.98–4.76 mm. Calculation error may have caused this phenomenon. In addition, the level of kinetic energy dissipation fluctuated when the working pressure was changed with a fixed nozzle diameter, although regulation20 of the fluctuations affected by working pressure was not obvious. Figure 8 also shows that the minimum dissipation of the FSPS was 28.01% at a nozzle diameter of 7.12 mm and working10 pressure of 50 kPa, i.e., a large kinetic energy rate was observed. This value was as large as 50.97% with a nozzle diameter of 2.98 mm. This indicates that more than half of the energy was converted FSPS(%) of dissipation energy Kinetic into heat; the low efficiency of the FSPS was a critical factor affecting energy consumption. To reduce0 energy dissipation, the structure of the FSPS should be optimized in further research. 50 100 150 200 250 Working pressure(kPa)

FigureFigure 8. 8. KineticKinetic energy energy dissipation dissipation of of FSPS. FSPS.

5. DiscussionFigure8 also shows that the minimum dissipation of the FSPS was 28.01% at a nozzle diameter of 7.12 mm and working pressure of 50 kPa, i.e., a large kinetic energy rate was observed. This valueThis was research as large contributes as 50.97% with to the a nozzle characterizati diameteron of of 2.98 the mm. energy This dissipation indicates that of moreFSPS thanwith halfan experimentalof the energy and was numerical converted simulation into heat; method. the low The efﬁciency discharge of the and FSPS velocity was results a critical indicated factor affecting that the experimentalenergy consumption. method led To reduceto a larger energy data dissipation, uncertainty the than structure the numerical of the FSPSsimulation should method, be optimized and the in instabilityfurther research. of working pressure may be the main source of error [12]. In addition, the accuracy of initial trajectory velocity with the numerical simulation method is mainly influenced by the shape of the free surface. In this research, the shape of the free surface was calibrated using the measured value. Despite the fact that PIV is close enough to the outlet of the sprinkler, a 5–10 cm spacing exists between the measurement point and outlet of the groove, and this may result in a calculation error in the determination of free surface. However, in our prior research [33], the jet velocity close to the sprinkler had no significant difference with small spacing, i.e., the calculation of initial trajectory velocity with numerical simulation method appeared valid. As the jet produced at the nozzle hit a plate, part of kinetic energy is transformed to heat energy. In addition, there is a discrepancy in elevation amounting to 12.5 mm between the nozzle and spray- plate, and part of the potential energy may likewise be transformed to heat energy while emitting. However, the gravity was taken into consideration in this research, and the calculation error caused by the minor change in potential energy can be ignored. The energy dissipation ranged from 28.01%– 50.97%, and a similar result was presented by Sánchez-Burillo et al. [12] with kinetic energy losses of 33–55%. According to Ouazaa et al. [14], the energy losses are 45% and 34.7% as the nozzle diameter are larger than 5.1 mm and 6.8 mm, respectively. In this paper, the largest energy dissipations are 40.59 and 30.14% with a nozzle diameter of 4.76 mm and 7.14 mm. All these results suggest that numerical simulation method can be applied to test jet velocity and the performance of FSPS.

5. Discussion This research contributes to the characterization of the energy dissipation of FSPS with an experimental and numerical simulation method. The discharge and velocity results indicated that the experimental method led to a larger data uncertainty than the numerical simulation method, and the instability of working pressure may be the main source of error [12]. In addition, the accuracy of initial trajectory velocity with the numerical simulation method is mainly inﬂuenced by the shape of the free surface. In this research, the shape of the free surface was calibrated using the measured value. Despite the fact that PIV is close enough to the outlet of the sprinkler, a 5–10 cm spacing exists between the measurement point and outlet of the groove, and this may result in a calculation error in the determination of free surface. However, in our prior research [33], the jet velocity close to the sprinkler had no signiﬁcant difference with small spacing, i.e., the calculation of initial trajectory velocity with numerical simulation method appeared valid. As the jet produced at the nozzle hit a plate, part of kinetic energy is transformed to heat energy. In addition, there is a discrepancy in elevation amounting to 12.5 mm between the nozzle and spray-plate, and part of the potential energy may likewise be transformed to heat energy while emitting. However, the gravity was taken into consideration in this research, and the calculation error caused by the minor change in potential energy can be ignored. The energy dissipation ranged from 28.01–50.97%, and a similar result was presented by Sánchez-Burillo et al. [12] with kinetic energy losses of 33–55%. According to Ouazaa et al. [14], the energy losses are 45% and 34.7% as the nozzle diameter are larger than 5.1 mm and 6.8 mm, respectively. In this paper, the largest energy dissipations are 40.59 and 30.14% with a nozzle diameter of 4.76 mm and 7.14 mm. All these results suggest that numerical simulation method can be applied to test jet velocity and the performance of FSPS.

6. Conclusions Water scarcity is a serious problem throughout the world, especially in agricultural production. Sprinkler irrigation is characterized by high levels of water conservation. However, the kinetic energy dissipation can be very high. In this study, the discharge and jet velocity of an FSPS were investigated using a PIV technique and CFD analyses. The comparison of experimental and simulated results shows that the maximum relative error of discharge is no larger than 3.91%; this means that numerical simulation with the LS-VOF method achieved reliable results at different working pressures. On the basis that high accuracy was obtained using the simulation method, a series of simulations were performed. A fluid-phase nephogram shows that the jet produced at the nozzle is split by the grooves after it hits the plate. However, the separation effect of each stream along the grooves decreases with increasing nozzle diameter. Comparing working pressures, the nozzle diameter has an appreciable impact on the area of flow cross-section of the outlet, with the area increasing as nozzle diameter increased. The initial trajectory velocity of the grooves presents a logarithmic increase with the increase in working pressure. Kinetic energy dissipation decreases as the nozzle diameter increases at a constant working pressure. A high working pressure may not cause large kinetic energy dissipation. In general, the dissipation rate of the FSPS ranged from 28.01–50.97%, i.e., a large kinetic energy rate was observed, and the same phenomenon was revealed by Sánchez-Burillo et al. [12]. In general, the shape, ridges and curvature of the deflecting plate determine the number of secondary jets, the vertical initial angle and initial velocity [12,34]; for the purpose of reducing energy dissipation, the structure of the deflecting plate could be optimized with a numerical simulation method in the future.

Author Contributions: Established the theoretical basis, Y.Z. Writing, original draft preparation, Y.Z. Writing, review and editing, B.S. and H.F. Funding acquisition, B.S. Performed the experiments, Y.Z. Software: D.Z. and Z.L. Visualization, H.F. and L.Y. Funding: This research was funded by [the National Natural Science Foundation of China] grant number (51509224) and [the Scientiﬁc and Technological Research Program of Henan Province] grant number (162102310522). Water 2018, 10, 1365 12 of 13

Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Gan, L.; Rad, S.; Chen, X.; Fang, R.; Yan, L.; Su, S. Clock Hand Lateral, a New Layout for Semi-Permanent Sprinkler Irrigation System. Water 2018, 10, 767. [CrossRef] 2. Kincaid, D.C. Application rates from center pivot irrigation with current sprinkler types. Appl. Eng. Agric. 2005, 21, 605–610. [CrossRef] 3. Playán, E.; Zapata, N.; Faci, J.M.; Tolosa, D.; Lacueva, J.L.; Pelegrín, J.; Salvador, R.; Sánchez, I.; Lafita, A. Assessing sprinkler irrigation uniformity using a ballistic simulation model. Agric. Water Manag. 2006, 84, 89–100. [CrossRef] 4. Clemmens, A.J.; Dedrick, A.R. Irrigation Techniques and Evaluations Management of Water Use in Agriculture; Springer: Berlin/Heidelberg, Germany, 1994; pp. 64–103. 5. Wrachien, D.D.; Lorenzini, G. Modelling Jet Flow and Losses in Sprinkler Irrigation: Overview and Perspective of a New Approach. Biosyst. Eng. 2006, 94, 297–309. [CrossRef] 6. Faci, J.M.; Salvador, R.; Playán, E.; Sourell, H. Comparison of fixed and rotating spray plate sprinklers. J. Irrig. Drain. Eng. 2001, 127, 224–233. [CrossRef] 7. Hanson, B.R.; Orloff, S.B. Rotator nozzles more uniform than spray nozzles on center-pivot sprinklers. Calif. Agric. 1996, 50, 32–35. [CrossRef] 8. Playán, E.; Garrido, S.; Faci, J.M.; Galán, A. Characterizing pivot sprinklers using an experimental irrigation machine. Agric. Water Manag. 2004, 70, 177–193. [CrossRef] 9. Hills, D.J.; Barragan, J. Application uniformity for fixed and rotating spray plate sprinklers. Appl. Eng. Agric. 1998, 14, 33–36. [CrossRef] 10. Ouazaa, S.; Latorre, B.; Burguete, J.; Serreta, A.; Playán, E.; Salvador, R.; Paniagua, P.; Zapata, N. Effect of the start–stop cycle of center-pivot towers on irrigation performance: Experiments and simulations. Agric. Water Manag. 2015, 147, 163–174. [CrossRef] 11. Sayyadi, H.; Nazemi, A.H.; Sadraddini, A.A.; Delirhasannia, R. Characterising droplets and precipitation profiles of a fixed spray-plate sprinkler. Biosyst. Eng. 2014, 119, 13–24. [CrossRef] 12. Burillo, G.S.; Delirhasannia, R.; Playán, E.; Paniagua, P.; Latorre, B.; Burguete, J. Initial drop velocity in a fixed spray plate sprinkler. J. Irrig. Drain. Eng. 2013, 139, 521–531. [CrossRef] 13. Zhang, Y.; Zhu, D.; Lin, Z.; Gong, X.; Wen, Y. Spatial Variation of Application Rate and Droplet Kinetic Energy for Fixed Spray Plate Sprinkler. Trans. Chin. Soc. Agric. Mach. 2015, 46, 85–90. 14. Ouazaa, S.; Burguete, J.; Paniagua, M.P.; Salvador, R.; Zapata, N. Simulating water distribution patterns for fixed spray plate sprinkler using the ballistic theory. Span. J. Agric. Res. 2014, 12, 850–863. [CrossRef] 15. Law, W.K.; Wang, H. Measurement of mixing processes with combined digital particle image velocimetry and planar laser induced fluorescence. Exp. Therm. Fluid Sci. 2000, 22, 213–229. [CrossRef] 16. Kadem, N.; Tchiftchibachian, A.; Pascal, M. Investigation of the Influence of Sprinkler Fins and Dissolved Air on Jet Flow. J. Irrig. Drain. Eng. 2006, 132, 41–46. 17. Jiang, Y.; Li, H.; Xiang, Q.; Chen, C. Comparison of PIV experiment and numerical simulation on the velocity distribution of intermediate pressure jets with different nozzle parameters. Irrig. Drain. 2017, 66, 510–519. [CrossRef] 18. Westerweel, J. Fundamentals of digital particle image velocimetry. Exp. Fluids 1997, 23, 1379. [CrossRef] 19. Willert, C.E.; Gharib, M. Digital particle image velocimetry. Exp. Fluids 1991, 10, 181–193. [CrossRef] 20. Yan, H.; Ou, Y.; Nakano, K.; Xu, C. Numerical and experimental investigations on internal flow characteristic in the impact sprinkler. Irrig. Drain. Syst. 2009, 23, 11–23. [CrossRef] 21. Tang, P.; Li, H.; Issaka, Z.; Chen, C. Impact forces on the drive spoon of a large cannon irrigation sprinkler: Simple theory, CFD numerical simulation and validation. Biosyst. Eng. 2017, 159, 1–9. [CrossRef] 22. Hirt, C.W.; Nichols, B.D. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 1981, 39, 201–225. [CrossRef] 23. Ibrahim, A.A.; Jog, M.A. Nonlinear breakup model for a liquid sheet emanating from a pressure-swirl atomizer. J. Eng. Gas Turb. Power 2007, 129, 945–953. [CrossRef] Water 2018, 10, 1365 13 of 13

24. Liu, G.M.; Huang, L.; Zhang, W.P.; Gao, X.H.; Lin, H.E.; Miao, X.H. Simulation and experiment on the characteristics of exhaust cooling and noise reduction equipment for marine diesel engine. Ship Eng. 2007, 8355, 325–328. 25. Alhendal, Y.; Turan, A.; Aly, W.I.A. VOF simulation of marangoni flow of gas bubbles in 2D-axisymmetric column. Procedia Comput. Sci. 2010, 1, 673–680. [CrossRef] 26. Osher, S.; Sethian, J.A. Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 1988, 79, 12–49. [CrossRef] 27. Albadawi, A.; Donoghue, D.B.; Robinson, A.J.; Murray, D.B.; Delauré, Y.M.C. Influence of surface tension implementation in volume of fluid and coupled volume of fluid with level set methods for bubble growth and detachment. Int. J. Multiph. Flow 2013, 53, 11–28. [CrossRef] 28. Meredith, K.V.; Zhou, X.; Wang, Y. Towards Resolving the Atomization Process of an Idealized Fire Sprinkler with VOF Modeling. In Proceedings of the 28th European Conference on Liquid Atomization and Spray Systems, València, Spain, 6–8 September 2017; pp. 257–264. 29. Kincaid, D.C. Spraydrop kinetic energy from irrigation sprinklers. Trans. ASAE 1996, 39, 847–853. [CrossRef] 30. Clark, G.A.; Srinivas, K.; Rogers, D.H.; Martin, V.L. Measured and simulated uniformity of low drift nozzle sprinklers. Trans. ASAE 2003, 4, 1–18. 31. Ramamurthy, A.S.; Tadayon, R. Numerical simulation of flows in cut-throat flumes. J. Irrig. Drain. Eng. 2008, 134, 857–860. [CrossRef] 32. Aydin, M.C.; Emiroglu, M.E. Determination of capacity of labyrinth side weir by CFD. Flow Meas. Instrum. 2013, 29, 1–8. [CrossRef] 33. Zhang, Y.; Zhu, D.; Lin, Z.; Gong, X. Water distribution model of fixed spray plate sprinkler sased on ballistic trajectory equation. Trans. Chin. Soc. Agric. Mach. 2015, 46, 55–61. 34. Deboerm, D.W. Drop and Energy Characteristics of a Rotating Spray-Plate Sprinkler. J. Irrig. Drain. Eng. 2002, 128, 137–146. [CrossRef]

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