Reaction thrust of water jet for conical nozzles

J Shanghai Univ (Eng] Ed), 2009, 13(4): 305 -310Digital Object Identifer(DOI): 10.1007/s11741-009-0411-1Reaction thrust of water jet for conical nozzlesHUANG Guo-qin (黃国勤)，YANG You-sheng (杨有胜)，LI Xiao-hui (李晓晖)，ZHU Yu-quan (朱玉泉)School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, P. R. ChinaAbstract Clear knowledge on the reaction thrust of water jet is valuable for better design of water jet propulsion system. Inthis paper, theoretical, numerical and experimental studies were carried out to investigate the effects of the nozzle geometryag well as the inlet conditions on the reaction thrust of water jet. Comparison analyses reveal that the reaction thrust has adirect proportional relationship with the product of the inlet presure, the square of flow rate and two-thirds power exponentof the input power. The results also indicate that the diamneter of the cylinder column for the conical nozzle has great influenceon the reaction thrust characteristics. In addition, the best values of the half cone angle and the cylinder column length existto make the reaction thrust reach its maximum under the same inlet conditions.Keywords conical nozzle, reaction thrust, thrust coefficient, wate jetNomenclaturelarge vessels, it is currently employed in some high-speedcraft and autonomous underwater vehicles (AUV) andF: reaction thrust (N)remains the quietest of the thrusters availablel5l. Inp: density of fuid (kg/m*)comparison with other means of propulsion, it offers: flow rate (m*/h)unique advantages, such as high acceleration, no risk ofv: mean velocity of flow through nozzle (m/s)engine overload, good maneuverability and high speedd: diameter of cylinder column (mm)0: half angle of cone (°)efficiencyl6.l: length of cylinder column (mm)However, in water jet propulsion systems, water isCq: fAow coefficientinducted at the forward end of the vehicles, passedCp: thrust coeficientthrough high-pressure pumps, and then exhausted atOp: pressure drop (MPa)the stern through one or more nozzles that produce highpo: environmental pressure (MPa)speed water jets and reaction thrust. That is to say, theinlet pressure (MPa)geomnetries of the nozzle have significant efects on theP: input power (kW)reaction thrust. In the past, several scholars have inves-n: unit vector normal to the area element dAtigated the flow and pressure fields of water jets. Basedr: viscous pressure (MPa)on Plandtl's mixing-layer concept, Schlichtingh7] studiedr: unit vector tangent to the area elemnent dAthe free jet flow theoretically and provided its analyticalAo: outlet area of cylindrical nozzle (mm2)solution. Looney, et al.s numerically studied the lam-Ab: back area of high pressure chamber (mm2 )inar free jet and fully developed turbulent free jet andAq: front area of high pressure chamber (mm2 )the impinging jet. Their numerical solution was consis-R: radius of inlet column (mm)tent with the experimental results perfectly. Begenirslr: radius of cylinder column (mm)reported the effect of the nozzle geometry on the characμ: water viscosity (Pa.s)teristics of hydrogen tangling water jets, whose researchIntroductionresults were in excellent agreement with the other ex-perimental and computational results. Soyamal10) obWater jet is a rapidly growing- up technology, whichserved the characteristics and structures of high-speedhas been widely used in many areas, such as water jetsubmerged water jets with cavitation. Yang, et al.1cleaning and cutting[n), water mist fire suppression!2)discussed the reaction thrust of the submerged waterand oceanic engineering3). In addition, due to the reac-ets. However, it is from the cylinder nozzles, due totion principle, water jets can work as thrusters, whichthe sudden contraction, the conversion eficiency of thiscreate jets of water for propulsion4. Although waterkind of nozzles is very low. Most of researches have paidjet propulsion has not been proved to be successful for中国煤化工Received Sept.7, 2008; Revised Feb.13, 2009Project supported by the National Natural Science Foundation ofMHC N M H Gd the National High.Technology Research and Development Program of China (Grant No.2006AA09Z238)Corresponding author ZHU Yu-quan, Prof, E mail: zhuyuquan@hust.edu.cn306J Shanghai Univ (Engl Ed), 2009, 13(4): 305 310more attention to the pressure and flow field of water jetIn (6), the thrust cofficient is the gain of the reac-systems. In order to design a nozzle with high eficiency,tion thrust including the efects of the nozzle. Obviously,further studies need to be carried out to investigate thethe contribution of the nozzle increases with increasingreaction thrust of water jets.Cp. Essentially, Cp represents an energy conversion ef-The objectives of this research are as follows: (i)ficiency of the pressure energy converting to the kineticTheoretical models and physical models of the reactionenergy including the effect of the nozzle, and it is one ofthrust as well as thrust cofficients are established; (i)the main performance parameters for a water jet unit.Computation fuid dynamics (CFD) simulations are con-1.2 Physical modelducted to describe the static pressure and mean velocityObviously, the theoretical model is not consistentvectors inside conical nozzles, then the reaction thrustwith the physical one. In order to improve its accu-can be calculated; (ii) A bench test is conducted toracy, it is essential to investigate the reaction thrust ofinvestigate the reaction thrust of water jets from coni-water jets in more detail by emulation. The simplifiedcal nozzles; (iv) Comparison analyses are performed onmodel is shown in Fig.1. It consists of a high-pressurethe results of theoretical models, CFD simulation andchamber and a nozle. The high-pressure water entersexperiments.the high- pressure chamber through the inlet, and thenjets out from the nozzle. The reaction thrust of the wa-1 Modelingter jet is the integration of the diferential force on all1.1 Theoretical modelsurfaces of the high-pressure chamber and the nozzle. ItTypically, elementary momentum theory is used tocan be obtained from the following equation:determine the reaction thrust of water jets, which canbe expressed as(7)F= pqv=(1)In order to simplify the calculation, several assump-tions are made: (i) The high -pressure chamber is ax-The direction of F is the negative direction of theisymmetric. The flow in the chamber is one dimensional,water jet. The fow characteristics of conical nozzlessteady and incompressible. (i) The high-pressure cham-can be written asber is in an unchanged environment and has no motionin the jet direction. (ii) The effects of fuid weight and(2)shear stresses on the reaction thrust are negligible.q=CaV警Inlerwhere Cq is the flow cofficient and Cq≈0.60 -0.82|12- 14 under the condition of no back pressure. In年A。Aothis research, Cq is set as a constant (Cq=0.71) at thea[~ 4 OutletAxisaverage of its interval value. For the submerged waterjet, the outlet pressure is the environmental pressure, soFig.1 Physical model of the deviceAp= Pin- Po≈Pin.According to (1) and (2), the reaction thrust modelTherefore, (7) can be simplified asF≈.. pmdA.(8)F = Cq√2pOp = 2C2AoPin.(3)J J Ab+At+AoAccording to (1) and (3), the reaction thrust modelThe pressure distribution on the walls Ab, Ap andA。should be acquired. The pressure on A。equals en-vironmental pressure Po and the pressure on Ab equalsF = (4pA.C)(Opg)善= (4pAoCq)tpf.the inlet pressure PinThe energy equation on the walls Ap can be writtenIn order to get a better understanding of the influ-asences of the nozzle on the reaction thrust, a thrust co-efficient Cp is defined as匹+坚(9)f2pf2P隆F唔Cp=p-Dng(5)中国煤化工conical wall surfaceby the surface area,According to (1) and (3), the thrust coficient modelequeYHCN M H G be expressed ascan be described as(6)Pt= Pin +pq_ pqr