J. Agr. Sc. Tech. (013) Vol. 15: 569-581 Numercal Smulaton and Expermental Study on a New Type of Varable-rate Fludc Sprnkler J. P. Lu 1, S. Q. Yuan 1, H. L 1, and X. Y. Zhu 1 ABSTRACT Due to the complex structure of the pressure-adustng devce used n most sprnklers for varable rrgaton, t s not possble to observe the flow behavor of the water passng through the flow feld. In ths paper, an ntegral three dmensonal (3D) numercal model based on the structural characterstcs of the fludc sprnkler was constructed to smulate the flow feld dstrbuton usng computatonal flud dynamcs (CFD). A new type of flud sprnkler (BPXH) was used n the experments. The man stream regon and the varable velocty regons were clearly dstngushed, and the detals of the varatons n pressure are dscussed. The results ndcated that the smulaton methodology generated suffcent data to analyze the sprnkler pressure and outlet velocty changes. The mnmum error of the dfference between the smulaton and the test pressure values was 0.049, wth a maxmum of 0.14. The turbulence model could accurately predct the relatonshp between the outlet velocty and the wetted radus. The outlet velocty ranged from 1.6 to 17.9 m s -1 durng the smulaton under the varable nlet boundary condtons of the sprnkler. Both the smulaton and test values of the wetted radus ncreased gradually wth the sprnkler rotatng angle. The absolute error of the smulaton and the test ranged from 0.07 to 0.16. Computatonal flud dynamcs provdes a promsng tool to help n the desgn of pressure-adustng devces usng a new type of varable-rate fludc sprnkler. Keywords: Fludc sprnkler, Inner flow feld, Numercal smulaton. INTRODUCTION As water supples become lmted, agrcultural water use needs to become more effcent to ncrease water productvty levels. Tso (004) ponted out that the three most mportant resources -people, land, and water- must be effectvely used to mprove agrcultural productvty and take advantage of new ntatves. Wth the rapd development of water-savng agrculture (Ahmad et al., 009), sprnkler rrgaton has been wdely appled due to ts hgh effcency and economcs (Keller and Blesner, 1990). Sprnkler s the key component n a sprnkler rrgaton system. The performance and water losses. Most studes about sprnkler rrgaton have focused on hydraulc performance (Sourell et al., 003; Hendaw et al., 005). An analyss of the flow behavor of the water flow n the sprnkler nner feld s also mportant to understand the mcro-characterstcs of the sprnkler. Researchers have used numercal smulaton to solve water flow modelng problems. Wang (006) analyzed the flow characterstcs n the emtter used n drp rrgaton nner feld usng computatonal flud dynamcs (CFD) technques and adopted the problem-solvng methods used n CFD technques to rrgaton equpment. It can smulate the flow behavors usng CFD to obtan pressure and velocty dstrbuton results (Anderson, 004). Some of the sprnkler drectly affects crop yeld 1 Research Center of Flud Machnery Engneerng and Technology, Jangsu Unversty, 301 Xuefu Road, Zhenang, Jangsu, People's Republc of Chna. Correspondng author; e-mal: luunpng401@163.com 569
Lu et al. basc studes have been performed on the nner flow characterstcs of sprnklers. In 1933, the desgner at the company Ranbrd (L et al., 1995) developed an mpact sprnkler for the frst tme. Experments were performed to evaluate the nner flow characterstcs of the mpact sprnkler compartment, and pressure losses were analyzed usng ANSYS software (Yan and Jn, 004; Yan et al., 007). Yan et al. (009) performed a 3D turbulent smulaton to analyze the flow behavor n an mpact sprnkler usng CFD technques and compared the flow rate, statc pressure dstrbuton and knetc energy values of dfferent current stablzers. In 005, researchers at Jangsu Unversty n Chna developed a new type of fludc sprnkler. The new sprnkler s shown n Fgure 1. The pressure dfference can be modeled dscretely as arsng from the sgnal tube, and the drecton of the flow can be modfed, whch provdes the force to run the sprnkler. Compared to the sprnklers studed prevously, the structure of the new fludc sprnkler s smpler, and the hydraulc performance s excellent (L et al., 010). Studes of the new fludc sprnkler have focused on the nozzle. In these studes, the nner flow feld of the nozzle was smulated, and the pressure dstrbuton was obtaned (Yuan et al., 005; L et al., 004). However, on the bass of these successful studes, few other nvestgatons have been conducted on the full flow feld, and studes on complete smulatons of the sprnkler have been lmted. The mcro-characterstcs of the sprnkler reman to be evaluated. Wth the development of Low Energy Precson Applcaton (LEPA), the workng pressure can be changed whle the sprnkler s runnng (Frasse et al., 1995; Perry et al., 004). Implementng LEPA wth the new fludc sprnkler nvolves the addton of a pressure-adustng devce at the nlet that can change the workng pressure whle the sprnkler s runnng and also change the wetted radus. The structure of the new fludc sprnkler (BPXH: Marked by the frst letter of Chnese pronuncaton) wth the pressure adustng devce s shown n Fgures and 3. The pressure adustng devce ncluded swvel connecton, connectng sleeve, statc nsert, movement nsert, and hollow shaft. When the sprnkler s operatng, the nlet secton area can be changed, thus, changng the workng pressure and the wetted radus. As can be seen n Fgures and 3, n the varable-rate fludc sprnkler, one of the movng nserts s statonary and s referred to as the statc nsert. The statc nsert s fxed on a swvel connecton that does not rotate wth the sprnkler. The movement nsert s ftted on a hollow shaft that rotates wth the sprnkler. The statc nsert and the movement nsert move relatve to each other to change the nlet secton area, thus, changng the workng pressure of the sprnkler. Therefore, the wetted radus changes, and an rregularly shaped spray area can be covered. (a) The new type of fludc sprnkler Fgure 1. The new type of fludc sprnkler. (b) Nozzle 570
Numercal Smulaton of Varable-rate Sprnkler Fgure. The structure of the new fludc sprnkler wth a pressure-adustng devce. (1) Swvel connecton; () Connectng sleeve; (3) Statc nsert; (4) Movement nsert; (5) Hollow shaft; (6) Locaton lmt devce; (7) Reversng devce; (8) Sprayng body; (9) Sprayng ppe; (10) Plastc tube, (11) Nozzle. Because of the pressure-adustng devce n the sprnkler, an rregular boundary spray area s obtaned. As shown n Fgure 4, the sprnklers are set at the locaton of O pont. The R 0 s the wetted radus of a crcle sprnkler, and R s the maxmum wetted radus of the new fludc sprnkler for square spray area. R(t) s the wetted radus, whch changes wth tme, and b s the mnmum wetted radus of the new fludc sprnkler. Therefore, when the sprnkler rotates for a round, the wetted square area wth secton lnes s obtaned. The range and the adustng devce are mportant parameters of the performance. Therefore, the key compartment of the sprnkler needs to be studed usng CFD technques. The obectve of ths study was to model the structure of the new sprnkler features, to conduct a numercal smulaton of the flow characterstcs of the water feld usng the commercal CFD program FLUENT software, and to perform experments to verfy the smulaton results. MATERIALS AND METHODS Numercal Smulaton Physcal Model and Grd Generaton In ths study, the BPXH0 fludc sprnkler was chosen as the research obect for a more (a) Movement nsert (b) Statc nsert Fgure 3. The structural chart of the movng nserts. Fgure 4. Schematc dagram of sprayng shape 571
Lu et al. effectve analyss. The physcal model was the nner flow channel of the sprnkler. Grd selecton s an mportant technque to mprove accuracy n the numercal smulaton method. In ths study, an unstructured mesh method was attempted as test/hybrd elements wth grd type. Fgure 5 shows a vew of the grds of the physcal model of the structure of the sprnkler used n the smulaton. The entre model was meshed nto 318,057 unts. The mesh sensblty was tested usng a smaller cell sze, but no nfluence on the fnal results was found. Mathematcal Model The nlet cross-secton area was modfed by two movng nserts n relatve moton, the rotatng velocty was ω = 0.06 rad s -1, the materal was water and the nlet pressure was hgher than 0. MPa. The Reynolds number was calculated to be approxmately 10 7. The results showed that the flow feld n the sprnkler was turbulent. Therefore, a turbulence model n FLUENT software was used to smulate the flow behavor under every operatng condton to ensure a comprehensve analyss, and a steady flow unt was set n the flow channel. There are some models n FLUENT Fgure 5. The computatonal grds of the numercal model. software ncludng standard k ε, RNG k ε, realzable k ε and so on. Due to the smallest computatonal devaton error from the measured results, the standard k ε model equatons were chosen n ths study. The standard k ε turbulent model, whch s generally used for most engneerng calculatons, was chosen to descrbe the flow n the sprnkler. The governng equatons for the standard k ε turbulent model n FLUENT software are gven as follows (John, 004): Contnuty equaton: ( u) = 0 ρ (1) Naver-Stokes equaton: p u ( ρ u ) + ( ρuu ) = + ( µ ) + S t () k equaton: ( ρk) ( ρku u ) u u + = µ t ( + ) t k + [( µ + µ t ) ] ρε ε equaton: ( ρε ) ( ρεu ) 1 u + = ρcε1ε ( t u + ) (3) ε ε + [( µ + µ t / σ ε ) ] ρcε k + vε (4) Where, k = Turbulent knetc energy; ε = Rate of dsspaton; ρ = Flud densty; u = Velocty of the flow at x component; x = Dsplacement vector; µ = Fludc vscosty; p= Pressure; S= Source term; v= Velocty of the flow at y component; t = Tme; and = Vectors, C ε1, Cε and σ ε = Correctng coeffcents. Values of temperature durng rrgaton are not very large, hence, the flow n sprnkler are ncompressble. These equatons are used for calculatng the movng flud element of flow n the sprnkler. After calculaton and solvng Equatons (1) to (4), 57
Numercal Smulaton of Varable-rate Sprnkler the velocty and pressure n the flow feld can be obtaned. Boundary Condtons and the Numercal Method Generally, sprnkle rrgaton s mplemented at a gven pressure. Ths sprnkler works under varable pressure because of the pressure-adustng devce, that s, the nlet of the sprnkler does not keep a fxed pressure. The pressure and flow rate values at the dfferent rotatng angles of the sprnkler were adusted. As shown n Fgure 6, the movement nsert and statc nsert were n the rotatng angle of 0 to 45 degrees and the black part was the flow cross secton. The movements nsert rotated deasl and the angle ncreased. For square sprayng shape, the vared flow cross secton from 0º to 45º s the same wth 45º to 90º, from 0º to 90º s the same wth 90º to 180º, from 0º to 180º s the same wth 180º to 360º. The flow can be calculated wth rotaton angle from 0º to 45º, and the values of other angles can be symmetrcal. The flow rates were verfed by test values. The velocty values were obtaned from the flow value and the nlet secton area. Next, the nlet boundary condton was set by the velocty, and the outlet boundary condton was set by the outflow. The nlet boundary condtons for the veloctes used are shown n Table 1. In near-wall treatment, three knds of methods are avalable as Standard wall Table 1. The nlet boundary condtons of the sprnkler. Rotaton angle ( o ) 0 15 30 45 Flow rate (m 3 h -1 ).08.34.95 3.47 Velocty (m s -1 ) 1.84.07.37.61 functons, Non-equlbrum wall functons, and Enhanced wall treatment. Wth the advantages of less computaton tme and teraton steps, Standard wall functons were mplemented. The contnuty and Naver- Stokes equatons were solved by usng a SIMPLE Consstent (SIMPLEC) algorthm (embedded n FLUENT) proposed by Van Doormal and Rathby (1984). Compared to the mpact of the water pressure, the effect of gravty was consdered low and, therefore, the gravty of water was neglected. The convergence precson of the calculaton was set at 0.0001. Wetted Radus Calculaton We can also calculate the wetted radus by the formula developed by Tuo et al. (006): 1 1 K R = ln{ 1+ KV0 cosθ[( + arctan ) V 0 snθ K Kg g + h + 1 ( 1 + arctan Kg K g )( V 0 snθ ) g K Where, R= Wetted radus of the sprnkler (m); V 0 = (m s -1 ); θ = Angle of the sprnkler ]} (5) (a) 0º (b) 15º (c) 30º (d) 45º Fgure 6. The flow cross secton of the movement nsert and statc nsert 573
Lu et al. (30º); g = Acceleraton due to gravty (m s - ), h = Installaton heght (1. m). In Equaton (5), the coeffcent K s calculated as follows: 3 Cd ρ a K = ( )( ) (6) 4 d ρ w Where, C d = The frctonal resstance coeffcent determned by the Reynolds number. In ths paper, the Reynolds number s greater than 30, and the value of the frctonal resstance coeffcent s 0.44. ρ = Ar densty (1.9 kg m -3 ); d = Dameter of the sprnkler nozzle (8 mm), ρ w = Water densty (1 10 3 kg m -3 ). Therefore, the coeffcent K can be calculated, and Equaton (5) can be smplfed as follows: R = 18.79ln{1 + 0.006V 0 + 0.0007V 0} (7) In Equaton (7), when the V 0 value s obtaned, the wetted radus can be calculated. Expermental Procedure The expermental platform was set up n the ndoor laboratory of the Research Center of Flud Machnery Engneerng and Technology at Jangsu Unversty n Chna. There were no obstacles n the laboratory, and wnd nterference was elmnated. The experments were conducted accordng to the standards of the Amercan Socety of Agrcultural and Bologcal Engneers (ASABE) S436.1 and S398.1. The equpment for the experment a Fgure 7. The wetted areas of square shape for the sprnkler. ncluded the fludc sprnkler (model BPXH0, Shangha Watex Water-economzer Technology Co, Ltd.), ppelne, pump system, and water collectors. The values of the pressure and flow rates for each sample were recorded, the experment was performed three tmes, and the wetted radus was calculated ten tmes and then averaged. The wetted area of square shape for the sprnkler s shown n Fgure 7. The sprnkler was set n the center of the wetted area and, when the sprnkler rotated for a round, the pressure-adusted devce worked and produced a square wetted shape. Although the wetted radus and unformty experments can be used to obtan the hydraulc performance of the sprnkler, they cannot be used to evaluate the small flow felds nsde the channels. Consequently, an experment was conducted usng the test apparatus depcted schematcally n Fgure 8. As shown n Fgure 8, water was pumped Fgure 8. The schematc dagram of the expermental setup used to measure the flow felds of the sprnkler. 574
Numercal Smulaton of Varable-rate Sprnkler from the reservor by a centrfugal pump (model IS80-50-50), and the volume of the water flowng through the sprnkler channels was measured usng a flow meter (model MF/E500161100EH11). To measure pressure dfference between ponts A and B, pressure sensors A and B (model WT1151GP) were set at the ponts A and B, respectvely. As shown n Fgure 9, the flow characterstc through the pressure adustng devce and to the outlet, a dstance of 50 mm, s stable. Impact of dfferent dstances (40, 50, 60, 70 mm) from the nlet were compared and lttle varatons were found for the nfluence of pressure at 50, 60, and 70 mm dstances. But, at the dstance of 40 mm, the flow characterstc was unstable. Therefore, 50mm of pont A from the nlet was chosen. The measurement range was 0 to 1 MPa, and the precson was ±%. When the sprnkler was rotated, the pressure sensors detected a change n the pressure value n the sprnkler nner flow feld. The data acquston and collecton were performed usng LabVIEW software ver. 8. (Natonal Instrument Corp., Austn, Texas). The data samplng frequency rate was set at 1,000 Hz. RESULTS AND DISCUSSION Analyss of the Flow Characterstcs Fgure 10 shows the velocty contours of the pressure-adustng devce and the velocty dstrbuton when the sprnkler Fgure 9. Schematc dagram of actual ponts A and B n the sprnkler. rotaton occurred at low pressure. The manstream regon and the varable velocty regons were clearly dstngushed. The water flows through the pressure-adustng devce and the recrculaton developed above the clearance can be seen n Fgure 10. The flow pattern s turbulent. Fgure 11 shows the velocty value n dfferent dstance from nlet cross secton n dfferent rotatng angles. It can be seen n Fgure 11 that the velocty value ncreased wth ncrease n the rotatng angle. Varaton of Pressure Fgure 1 shows the pressure dstrbuton of the sprnkler at dfferent angles. The pressure ncreased as the angle of rotaton of the sprnkler ncreased. The average pressure value at a 50 mm dstance from the Fgure 10. The contour of the velocty of the pressure-adustng devce at an angle of rotaton. 575
Lu et al. Fgure 11. The velocty value n dfferent dstances from nlet cross secton n dfferent rotatng angles. (a) 0 (b) 15 (c) 30 (d) 45 Fgure 1. The pressure dstrbuton of the sprnkler. nlet s shown n Fgure 13. As shown n Fgure 13, the pressure ncreased as the rotatng angle ncreased and the mnmum and maxmum pressure values were 0.18 and 0.65 MPa, respectvely. At a dstance of 50 mm from the nlet, the pressure changes wth the rotatng angle of the sprnkler. All statstcal analyses were 576
Numercal Smulaton of Varable-rate Sprnkler Fgure 13. The pressure value at a 50 mm dstance from the nlet of the sprnkler. conducted usng a 95% confdence nterval. A second-order polynomal regresson lne ( y = 0.00004x + 0.00138x + 0. 1859, where y s the pressure value at a locaton 50 mm from the sprnkler, x s the rotaton angle of the sprnkler, and r = 0.99988) was ftted to pressure and angle of rotaton to estmate the dfference between the test data and the smulaton data. Fgure 14 shows the pressure values for sectons A and B. In ths dagram, P B s the pressure at secton B, the nlet of the sprnkler, and P A s the pressure at secton A, 50 mm from the nlet of the sprnkler. Durng the sprnkler rotaton, pressure data were recorded for 8 seconds n ths experment. Fgure 14 depcts the whole pressure drop from the nlet to the outlet over fve perods. P s the workng B pressure, and the range of P B s larger than P A. As shown n Fgure 4, every quadrant s one perod, and there are four quadrants for a complete round. The wetted radus for the square sprayng area changed over four perods for a round when the sprnkler rotatng and the nlet and outlet pressure also changed over those four perods. Therefore, we selected half of the perods over whch the pressure fluctuated and transformed the pressure as a functon of the angle of rotaton nstead of tme. The smulaton and test values were compared, and the results are presented n Fgure 15. As seen n Fgure 15, the tendences of the pressure P A remaned farly constant. From 6.0 to 8.0 seconds, the pressure P B ncreased. The mnmum error of the dfference between the smulaton and the test pressure values was 0.049, whle the maxmum was 0.14. Ths ndcated a very good agreement between smulaton and test results. In contrast, the smulaton values were larger than the expermental values durng the perod from 6.75 to 8.0 seconds. Ths s because the physcal model s extremely clean, whle, n realty, the sprnkler cannot be expected to be as clean; thus, durng the sprnkler rotaton, the axal clearance of the movng nserts may not be n good agreement wth the physcal model n the smulaton. Therefore, the smulaton results overestmated the pressure n the system. Fgure 14. Pressure values for sectons A and B. Fgure 15. Comparson of the relatonshp between pressure and tme from the smulaton and the test. 577
Lu et al. Relatonshp of the Outlet Velocty and Wetted Radus Theoretcally, the outlet velocty plays an mportant role n determnng the performance of the sprnkler wetted radus. The relatonshp between the outlet velocty and the wetted radus has to be determned to ensure the accuracy of the smulaton model. When the sprnkler was rotatng, the outlet velocty changed wth the rotatng angle. In ths study, the lowest workng pressure was found at the lowest secton area and at an angle of zero degree. The sprnkler workng pressure was changed n four perods, and a square shaped sprayng area was obtaned. The outlet velocty dstrbutons of sprnkler nozzle areas are shown n Fgure 16. The sectonal average velocty of the outlet at dfferent angles was derved from the smulaton, the outlet velocty ranged from 1.6 to 17.9 m s -1 durng the smulaton under the varable nlet boundary condtons of the sprnkler. The changed curve of the outlet velocty at dfferent angles s presented n Fgure 17, whch shows that the outlet velocty ncreased gradually wth the angle of rotaton of the sprnkler. Ths occurs because the workng pressure gradually ncreased wth the sectonal area of the sprnkler nlet. Therefore, the outlet velocty and the workng pressure ncreased wth the rotatng angle. The outlet velocty can be determned from the wetted radus. From the relatonshp between the outlet velocty and the wetted radus, the V 0 value n Equaton (7) s derved by usng the smulated velocty at the outlet. The relatonshp between the angle and the wetted radus obtaned by smulaton and expermentally, respectvely, s shown n Fgure 18. The values from smulaton and expermentaton were compared under the same condtons. As seen n Fgure 18, both the smulaton Fgure 16. The outlet velocty dstrbutons of sprnkler nozzle areas. 578
Numercal Smulaton of Varable-rate Sprnkler and test values of the wetted radus ncrease gradually wth ncrease n the rotaton angle of sprnkler and the two curves are almost parallel to each other; but, the test value s lower than the smulaton value. The relatve error of the smulaton and test values ranged from 0.07 to 0.16. As well known, the bgger the pressure, the longer s the wetted radus. The reasons for the smulaton values beng larger than the test values of pressure apply to the wetted radus as well. CONCLUSIONS In ths study, we conducted numercal smulatons on the nternal flow of the new fludc sprnkler and performed experments on the flow felds n the channels and on the hydraulc performance. We obtaned the followng results: The turbulence model was appled n a smulaton and the results ndcated that the turbulence model can accurately predct the workng pressure and the relatonshp between the outlet velocty and the wetted radus. By comparng the flow felds of the pressure-adustng devce, obtaned by calculaton and experment, t s feasble to employ LabVIEW software to measure the flow characterstcs. The varaton n pressure was characterzed and the mnmum error of the dfference between the smulaton and test pressure values was 0.049, wth a maxmum value of 0.14. The average velocty value of the outlet at dfferent angles of rotaton was derved from the smulaton, and both the smulaton and test values for the wetted radus ncreased gradually wth ncrease n the sprnkler rotaton angle. The absolute error of the smulaton and test ranged from 0.07 to 0.16. Ths shows that the turbulence model for smulaton provdes accurate results for the new varable-rate fludc sprnkler. The manstream regon and the varable velocty regons were clearly dstngushed. Accordng to the flow felds, structural optmzaton schemes for the channels can mprove the performance of the sprnkler. ACKNOWLEDGEMENTS The authors gratefully acknowledge that the work presented n ths paper has been supported by the Natonal Natural Scence Foundaton of Chna No. 51109098, the Chna Natonal Hgh-Tech (863) Program Grant No. 011AA100506, and the Natonal Agrcultural Technology Transformaton Program No. 011GBC100015. REFERENCES 1. Ahmad, M. M., Ayyoubazdeh, S. A., Montazer Namn, M. and Saman, M.V. A D Numercal Depth-averaged Model for Fgure 17. The changed curve of the outlet velocty at dfferent angles. Fgure 18. Comparson of the relatonshp between the angle and wetted radus obtaned by smulaton and experment. 579
Lu et al. Unsteady Flow n Open Channel Bends. 009. J. Agr. Sc. Tech., 11: 457-468.. John D., Anderson J. R. 004. Computatonal Flud Dynamcs: The Bascs wth Applcatons. Tsnghua Unversty Press, Beng, Chna. 3. ASABE Standards. R007. S398.1: Procedure for Sprnkler Testng and Performance Reportng. ASABE, St. Joseph, Mch. 4. ASABE Standards. R007. S436.1: Test Procedure for Determnng the Unformty of Water Dstrbuton of Center Pvot and Lateral Move Irrgaton Machnes Equpped wth Spray or Sprnkler Nozzles. ASABE, St. Joseph, Mch. 5. Chrstansen, J. E. 194. Irrgaton by Sprnklng. Calforna Agrcultural Experment Staton Bulletn 670, Unversty of Calforna, Berkeley, Calforna. 6. Frasse, C. W., Duke, H. R. and Heermann, D. F. 1995. Laboratory Evaluaton of Varable Water Applcaton wth Pulse Irrgaton. Trans. ASAE, 38(5): 1363-1369. 7. Hendaw, M., Molle, B., Folton, C. and Graner, J. 005. Measurement Accuracy Analyss of Sprnkler Irrgaton Ranfall n Relaton to Collector Shape. J. Irr. Dran. Eng., 131(5): 477-483. 8. Keller, J. and Blesner, R. D. 1990. Sprnkler and Trckle Irrgaton. Van Nostrand Renhold, New York, NY, 65 PP. 9. L, H., Yuan, S. Q., Xang, Q. J., Wang, C. 010. Theoretcal and Expermental Study on Water Offset Flow n Fludc Component of Fludc Sprnklers. J. Irrg. Dran. Eng., 137(4): 34-43. 10. L, H., Xe, F. Q., Lang, T., Tang, Y., Jn, S. D. 004. Research Status n Quo and Development Trend n Full-et-flow Sprnkler Head. Chna Rural Water Hydropower, (3): 90-9. 11. L, J., L, Y., Kawano, H. and Yoder, R. E. 1995. Effects of Double-rectangular-slot Desgn on Impact Sprnkler Nozzle. Trans. ASAE, 38(5): 1435-1441. 1. Perry, C. D., Dukes, M. D. and Harrson, K. A. 004. Effects of Varable-rate Sprnkler Cyclng on Irrgaton Unformty. ASAE Annual Internatonal Meetng, Ottawa, Canada. PP. 879-889. 13. Sourell, H., Fac, J. M. and Playán, E. 003. Performance of Rotatng Spray Plate Sprnklers n Indoor Experments. J. Irr. Dran. Eng., 19(5): 376-380. 14. Tuo, Y. F., Yang, L. H., Cha, C. L., Gao, H. Y. 006. Expermental Study and Theoretcal Formula of the Sprnkler Wetted Radus. Trans. CSAE, (1): 3-6. 15. Tso, T. C. 004. Agrculture of the Future. Nature, 48: 15-17. 16. Van Doormal, J. P. and Rathby, G. G. 1984. Enhancement of the SIMPLE Method for Predctng Incompressble Flud Flows. Numer Heat Transf, 7: 147 163. 17. Wang, F. J. and Wang, W. E. 006. Research Progress n Analyss of Flow Passage n Irrgaton Emtters Usng Computatonal Flud Dynamcs Technques. Trans. CSAE, (7):118-1. 18. Yan, H. J. and Jn, H. Z. 004. Study on the Dscharge Coeffcent of Non-rottable Sprays for Center-Pvot System. J. Irrg. Dran., 3(): 55-58. 19. Yan, H. J., Ou, Y. J., Kazuhro.Nakano, Xu, C. B. 009. Numercal and Expermental Investgatons on Internal Flow Characterstc n the Impact Sprnkler. Irr. Dran. Sys., 3: 11-3. 0. Yan, H. J., Lu, Z. Q., Wang, F. X., Yang, X. G., Wang, M. 007. Research and Development of Impact Sprnkler n Chna. J. Chna Agrcultural Unversty, 1(1):77-80. 1. Yuan, S. Q., Zhu, X. Y., L, H., Ren, Z. Y. 005. Numercal Smulaton of Inner Flow for Complete Fludc Sprnkler Usng Computatonal Flud Dynamcs. Trans. CSAM, 36(10): 46-49. 580
Numercal Smulaton of Varable-rate Sprnkler (Fludc)......... (CFD) (BPXH)... 0/140 /049.. 17/9 1/6. 0/16 0/07.. 581