J Shanghai Univ (Engl Ed), 2011, 15(3): 201 206 Digital Object Identifier(DOI): 10.1007/s11741-011-0721-2 Simulation investigation on fluid characteristics of jet pipe water hydraulic servo valve based on CFD LI Ru-ping (ox ) 1, NIE Song-lin (mt ) 2, YI Meng-lin ( ) 1, RUAN Jun (_ d) 1 1. School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, P. R. China 2. College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100124, P. R. China Shanghai University and Springer-Verlag Berlin Heidelberg 2011 Abstract Simulation investigation on fluid characteristics of the water hydraulic jet pipe servo valve (WHJPSV) is conducted through a commercial computational fluid dynamics (CFD) software package FLUENT. In particular, the factors to fluid characteristics of WHJPSV are addressed, which include diameter combination of jet pipe and receiver pipe, jet pipe nozzle clearance, angle between two jet receiver pipes and deflection angle of the jet pipe. It is concluded from the results that: (i) Structural parameters have great influences on fluid characteristics of WHJPSV, when d 1 = d 2 = 0.3 mm, α= 45, b = 0.5 mm, and the simulation exhibits better fluid characteristics; (ii) The magnitude of the recovery pressure and flow velocity increase almost linearly with the deflection angle of jet pipe. The research work in this paper is important for determining and optimizing the structural parameters of the jet pipe and jet receiver. The relevant conclusions could be extended to the study of other water hydraulic servo control components. Keywords computional fluid dynamics (CFD), fluid characteristics, jet pipe, servo valve, water hydraulics Introduction Water hydraulic system is operated with raw water (seawater and fresh water) substituting for mineral oil. Many water hydraulic components have been successfully applied in many raw water hydraulic systems in some countries, such as USA, Germany, Japan and Denmark. Compared with the conventional mineral oil, raw water that acts as hydraulic fluid has several inherent advantages, including quick response, compact structure, low operation cost, sound environmental compatibility, and low pollution potential to products [1 4]. It is becoming more and more popular, especially in many fields such as steel industry, glass production, nuclear power generation, coal and gold mining, food and medicine processing, ocean exploration and underwater robotics. Water hydraulic jet pipe servo valve (WHJPSV) is one of the important components in water hydraulic system. However, owing to the higher vaporization pressure and lower viscosity than mineral oil, fluid characteristics are more different in water hydraulic components compared with hydraulic one, especially in WHJPSV. Generally, there are two main types of servo valves, which are JPSV and nozzle flapper servo valve. JPSV has many advantages over nozzle flapper one. Several studies have already focused on the flow and pressure field characteristics of the jet pipe and jet pipe hydraulic servo valve. Yang [5] investigated the flow field of prestage of one type servo valve using simulation and experiment methods. Simulations were carried out including the effects of pressure, velocity and cavitation, meanwhile visualization of the jet flow field were completed. Ji, et al. [6] reported the internal flow of the jet pipe amplifier using FLUENT code. The recovery pressure and flow in the jet pipe amplifier were obtained under different deflection angles of the jet, and thus the mathematical models of the recovery pressure and flow were established by using polynomial fitting method. However, in their theoretical and experimental study, the Received Nov.25, 2009; Revised Apr.27, 2010 Project supported by the National Natural Science Foundation of China (Grant Nos.50375056, 50775081, 51075007), the National High-Technology Research and Development Program of China (Grant No.2006AA09Z238), the New Century Excellent Talents in University of State Education Ministry (Grant No.NCET-07-0330), and the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (Grant No.20090203) Corresponding author NIE Song-lin, Ph D, Prof, E-mail: niesonglin@bjut.edu.cn
202 J Shanghai Univ (Engl Ed), 2011, 15(3): 201 206 working media was mineral oil. Neither pure tap water nor sea water, particularly the relations between the fluid characteristics and the structural parameters of the jet pipe amplifier were not investigated. In order to have full understanding on water hydraulic jet pipe servo apparatus and to design WHJPSV effectively, it is essential to investigate the fluid characteristics of WHJPSV. The objectives of this research are detailed as follows: (i) Based on CFD software, three dimensional model and grid divisions are performed to explore the fluid characteristics of WHJPSV; (ii) The effects of the structural dimensions of the jet pipe and receiver pipe on the fluid characteristics of WHJPSV are investigated; (iii) Comparison analyses are conducted on the simulation results. 1 Profile and working principle WHJPSV mainly consists of torque motor, jet pipe amplifier, slide valve, spring feedback pole and filter. A simplified model of WHJPSV is illustrated in Fig.1, in which N and S are two magnetic poles of torque motor, respectively, P s the inlet pressure, P t the outlet pressure, P a and P b the load pressures, α the angle between two jet receiver pipes, and b the clearance between jet pipe and receiver. The developed WHJPSV is shown in Fig.2. firstly. Then it transforms the kinetic energy to pressure energy through jet receiver. When control current is added to the current coil which twists on the armature of WHJPSV, the torque motor outputs corresponding torque to armature, which leads the armature and spring pipe groupware to roll a deflection angle around their rotating centre. Then the jet pipe deflects an angle, and it will result in a recovery pressure difference between two chambers of the receiver pipes. The recovery pressure difference moves the spool in sleeve of slide valve, which leads to servo control water hydraulic load. Meanwhile, the spool pulls the jet pipe and spring pipe groupware back to their original position through the spring feedback pole, which will reduce the deflection angle of jet pipe and decrease the recovery pressure difference. When the moment of spring feedback pole equals to the torque motor moment, the spool will keep stationary in the sleeve. Hence, the spool displacement is basically proportional to the control current, and the output flow of JPWHSV is also proportional to control current too. 2 Mathematical model and grid generation The fluid inside the WHJPSV chamber is threedimensional flow. 3D unstructured tetrahedral grids are generated through software GAMBIT, and the total number of the elements is over about 800 000 1 000 000 (see Fig.3). The boundary conditions are inlet pressure, outlet pressure, and the walls. Generally, the walls are supposed to be adiabatic, and there are no heat exchange between the walls and fluid. The working medium is water with ρ = 998.2 kg/m 3, μ = 0.001 003 Pa s. In addition, the density and viscosity are assumed to be independent of temperature. Fig.1 Structure schematic diagram of WHJPSV Fig.3 Grid of the fluid domain of WHJPSV Fig.2 Picture of the developed WHJPSV The jet amplifier formed by jet pipe and jet receiver is the pre-stage of WHJPSV, which transforms the pressure energy to kinetic energy through jet pipe nozzle Under the conditions of different pressure and flow velocity, the water jet flow through the jet pipe nozzle maybearapidstrainflowwithreynoldsnumbers(re) ranging from 10 3 to 10 6, the renormalization group theory (RNG) k-ε turbulence model and the multi-phase
J Shanghai Univ (Engl Ed), 2011, 15(3): 201 206 203 model combined with the wall functions are utilized to simulate the fluid field in this research. Boussinesq hypothesis is employed to relate Reynolds stresses to the mean velocity gradients, and it can be obtained that ρu i u j = μ (U i t + U j ) 2 x j x i 3 ρkδ ij. (1) The turbulence kinetic energy k and its rate of dissipation ε can be obtained from the following equations: t (ρk)+ x i (ρku i )= x j ( αk μ eff k ) x j + G k ρε, (2) t (ρε)+ (ρεu i )= ( ε ) αε μ x i x eff j x j ε + C 1ε k G k C2ερ ε2 k. (3) In this research, the multiphase model concerns liquid and gas phases that are treated as interpenetrating continua. The law of conservation of mass and momentum is satisfied by each phase. The derivation of the conservation equations can be done by ensemble averaging the local instantaneous balance for each phase. Phasic volume fractions α p represents the space occupied by gas phase. The continuity equation for gas phase can be expressed as t α p + (α p U i )= 3α p x i R 2(p v p) 3ρ q, (4) where k = 1 2 u i u i, ε = ν u i u i k x jx j, μ t = ρc 2 μ ε, C2ε C 2ε + Cμρη3 (1 η η ) 0 1+βη, η = Sk 3 ε, R =(3αp 4πn ) 1 3, { G k = ρu i u u j 1, i = j, j x i, δ ij = 0, i j. In these equations, G k represents the generation of turbulence kinetic energy due to the mean velocity gradient, and σ k and σ ε are the inverse effective turbulent Prandtl numbers for k and ε, respectively. In the high- Reynolds-number limit μ mol μ eff 1, σ k = σ ε 1.393. C 1ε, C 2ε, η 0 and β are model constants set as C 1ε = 1.42, C 2ε = 1.68, η 0 = 4.38, β = 0.012. C μ = 0.085 4 is derived from RNG theory, which is very close to the empirically-determined value of 0.09 used in the standard k-ε model. 3 Simulation results and analysis In FLUENT6.1 software, some boundary conditions are assumed that: the residual value is 10 5 ;thetemperature is 300 K; the working medium is tap water; and the system inlet and outlet pressure are 10 MPa and 0.5 MPa, respectively. 3.1 Effects of diameter combination of jet pipe and receiver pipe on the fluid characteristics In order to research the effects of diameter parameter combination of jet pipe and receiver pipe on the fluid characteristics, the paper makes simulation investigation on 5 models, which are shown in Table 1. In addition, the angle α is 45, the clearance b 0.5 mm, the jet pipe deflection angle ϕ 0.4, d 1 the diameter of jet pipe, and d 2 the diameter of jet receiver pipe. The contours of the recovery pressure under different d 1 levels are shown in Fig.4 when d 2 is 0.3 mm. The effects of diameter parameter combination on the fluid characteristics are illustrated in Fig.5. From Fig.5, it can be seen that the recovery pressure (P r ) and recovery flow velocity magnitude (V r ) will vary with the different diameter parameter combination. When the diameter of jet pipe d 1 is 0.3 mm, the magnitude of the recovery pressure and the recovery flow velocity will gradually decrease with the increasing of diameter of jet receiver pipe d 2.When d 2 is 0.3 mm, the magnitude of the recovery pressure and the recovery flow velocity will gradually decrease with the increasing of diameter of jet pipe d 1 too. It is because the jet flow becomes slowly with the increasing of jet pipe and jet receiver pipe diameters, which will lead more flow pressure energy becoming turbulent kinetic energy. Considering the antipollution capability of WHJPSV [7], the simulation result indicates that scenario 3 (d 1 = d 2 = 0.3 mm) is acceptable. Table 1 Diameter parameter combination of jet pipe and jet receiver pipe Scenario d 1 /mm d 2 /mm 1 0.2 0.3 2 0.3 0.2 3 0.3 0.3 4 0.3 0.4 5 0.4 0.3 Notes: The angle α is 45. The clearance b is 0.5 mm and the jet pipe deflection angle ϕ is 0.3. 3.2 Effects of jet pipe clearance on the fluid characteristics In order to research the effects of jet pipe nozzle clearance on the fluid characteristics, simulation on four scenarios are conducted, in which the clearance b is set as 0.2, 0.3, 0.4, 0.5 mm, respectively. In addition, the other assumption parameters include that both of d 1 and d 2 are 0.3 mm, the angle α 45,andthe deflection angle ϕ 0.4. The contours of turbulent kinetic energy under different b levels are shown in Fig.6 when other parameters are the same. From Fig.6, it can be seen that the turbulent kinetic energy becomes smaller when clearance level decreases. The effects of
204 J Shanghai Univ (Engl Ed), 2011, 15(3): 201 206 Fig.4 Contours of recovery pressure under different d 1 levels (d 2=0.3 mm) Fig.5 Effects of diameter combination of jet nozzle and receiver pipe on the fluid characteristics Fig.6 Contours of turbulent kinetic energy under different b levels clearance b on the fluid characteristics are illustrated in Fig.7. From Fig.7, it can be seen that the magnitude of the recovery pressure will decrease with increasing of jet pipe nozzle clearance b obviously. That is because when b becomes little, jet pipe nozzle will be near the jet receiver, which leads more flow pressure energy becoming turbulent kinetic energy, and the reaction caused by jet receiver will also consume more jet flow pressure
J Shanghai Univ (Engl Ed), 2011, 15(3): 201 206 205 energy. From Fig.7, it can also be seen that the magnitude of recovery flow velocity will increase with increasing of b synchronously. That is because when b becomes big, jet pipe nozzle will be far away from the jet receiver, which leads more flow pressure energy becoming kinetic energy, and the reaction caused by jet receiver will also consume less jet flow pressure energy. Considering the compact structure of WHJPSV, the simulation result indicates that model jet pipe nozzle clearance b = 0.5 mm is acceptable. Fig.7 Effects of jet nozzle clearance on the fluid characteristics 3.3 Effects of angle between two jet receiver pipes on the fluid characteristics In order to investigate the effects of angle between two jet receiver pipes on the fluid characteristics, simulation on three models are conducted, in which the angle α is set as 40,45 and 50, respectively. In addition, the other assumption parameters include that both of d 1 and d 2 are 0.3 mm, the clearance b 0.5 mm, and the jet pipe deflection angle ϕ 0.4. The contours of dynamic pressure under different angle α levels are shown in Fig.8, while other parameters are the same. From Fig.8, it can be seen that negative pressure appears in jet flow chamber when angle α are 40 and 50, respectively, and the minimum pressure are 0.06 MPa and 0.6 MPa. It is easy to form vapour when chamber pressure is lower than the vapour pressure of water, which is 12 kpa at 323 K. Particularly, the maximal pressure in jet flow domain is 6.8 MPa in Fig.8(a). It will lead ablation and erode the joint of two receiver pipes, which will be adverse to static and dynamic characteristics of WHJPSV. This indicates that scenario 2 is acceptable. 3.4 Effects of deflection angle of the jet pipe on the fluid characteristics In order to research the effects of deflection angle of the jet pipe on the fluid characteristics, simulation on six models are conducted, in which the deflection angles ϕ are set as 0,0.1,0.2,0.3,0.4 and 0.5 respectively. In addition, the other assumption parameters include that both of d 1 and d 2 are 0.3 mm, the angle α 45, and the clearance b 0.5 mm. The effects of deflection angle ϕ on the fluid characteristics are illustrated in Fig.9. From Fig.9, it can be seen that the magnitude of the recovery pressure and recovery flow velocity increase almost linearly with the increasing of jet pipe deflection angle ϕ obviously. It is because that the bigger the deflection angle ϕ is, the more pressure energy the jet receiver accepts. Therefore, the magnitude of recovery pressure and flow velocity will increase almost linearly, which agrees perfectly with the working principle and requirement of WHJPSV. Fig.8 Contours of dynamic pressure under different α levels
206 J Shanghai Univ (Engl Ed), 2011, 15(3): 201 206 Fig.9 Effects of deflection angle of the jet pipe on fluid characteristics The simulations in this research focus on the structural parameters which influence the fluid characteristics of WHJPSV. However, it is a more complex fluid issue, which is effected by several factors besides the geometrical dimensions, such as the material characteristic, friction force, system back pressure, working medium temperature, Reynolds number. The most attention should be paid to the experimental investigation, especially the static and dynamic characteristics study, which can prove and explain the simulation results. It is significant to be addressed in future research. 4 Conclusions Simulations on the effects of structural parameters on the fluid characteristics of WHJPSV are performed while the raw water is used as the working media. Research results show that structural parameters influence the magnitude of the recovery pressure and flow velocity greatly. The relevant conclusions can be obtained: (i) In this research, when d 1 = d 2 = 0.3 mm, α = 45, b = 0.5 mm, the simulation model exhibits better fluid characteristics. (ii) The magnitude of recovery pressure and flow velocity increase almost linearly with the deflection angle of jet pipe. (iii) The simulation results on the fluid characteristics have reference meanings to the design of water hydraulic servo valve and other water hydraulic control components. References [1] Trostmann E. Hydraulic components using tap water as pressure medium [C]// Proceedings of the 4th Scandinavian International Conference on Fluid Power, Finland. 1995: 942 954. [2] Nie SL,Huang GH,Li YP,Yang YS,Zhu YQ. Research on low cavitation in water hydraulic two-stage throttle poppet valve [J]. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 2006, 220(3): 167 179. [3] Nie SL, Huang GH, Li Y P. Tribological study on hydrostatic slipper bearing with annular orifice damper for water hydraulic axial piston motor [J]. Tribology International, 2006, 39(11): 1342 1354. [4] Urata E, Miyakawa S, Yamashina C. Development of a water hydraulic servo valve [J]. JSME International Journal, Series B, 1998, 41(2): 286 294. [5] Yang Yue-hua. Analysis and experimental research of pre-stage jet flow field in hydraulic servo valve [D]. M. S. dissertation, Harbin: Harbin Institute of Technology, 2006, 8 9 (in Chinese). [6] Ji Hong, Wei Lie-jiang, Fang Qun, Qiang Yan, Jin Yao-lan. Investigation to the flow of the jet pipe amplifier in a servo valve [J]. Machine Tool and Hydraulics, 2008, 36(10): 119 121 (in Chinese). (Editor HONG Ou)