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To solve problems of leakage, vibration, and noise caused by disorders of flow field distribution and working pulsation in the rotating-sleeve distributing-flow system, governing equations of plunger and rotating sleeve and computational fluid dynamics (CFD) model are developed through sliding mesh and dynamic mesh technology to simulate flow field and working pulsation. Simulation results show that the following issues exist: obviously periodic fluctuation and sharp corner in flow pulsation, backward flow when fluid is transformed between discharge and suction, and serious turbulence and large loss in kinetic energy around the damping groove in transitional movements. Pressure in the pump chamber rapidly rises to 2.2 MPa involving over 10% more than nominal pressure when the plunger is at the Top Dead Center (TDC) considering changes about damping groove’s position and flow area in two transitional movements. Shortly pressure overshoot gradually decreases to a normal condition with increasing flow area. Similarly, pressure in the pump chamber instantaneously drops to a saturated vapor pressure −98.9 KPa when the plunger is at the Bottom Dead Center (BDC). With increasing flow area the overshoot gradually increases to the normal condition. This research provides foundations for investigating flow field characteristic and structure optimization of rotating-sleeve distributing-flow system.

A distributing-flow system, the most important component of hydraulic system, is widely used in the fluid power industry because of robustness, controllability, and wide operating range. However, the distributing-flow system controlled flow by valves has many disadvantages including bulk mass, large pressure loss, noise, and going against high frequency, which can easily cause noise and vibration on account of flow pulsation [

Flow ripple, a significant characteristic of piston pump, is closely relevant with the pressure fluctuation, backward flow, and noise of inner fluid. Noises in pump can be effectively reduced by taking factors influencing the flow ripple into account and focusing on flow ripple in the process through structure optimization [

Recently, various analytic and simulative methods have been extensively studied on distribution of flow field and working pulsation. Particularly, the CFD simulation is generally utilized in many fluid field and hydraulic researches. Luo et al. [

The slide mesh and dynamics grid technology have been continually employed in CFD model to improve its simulation functions and apply varied motions into the model flexibly. Wang [

Fortunately, some researchers have found effective ways to reduce working pulsation to decrease noise. Lee et al. [

This paper aims to reduce vibration and noise by developing a novel rotating-sleeve distributing-flow system and analyzing the relationship between turbulence energy, velocity, and working pulsation through CFD simulation. In addition, the influences with respect to backward flow, flow pulsation, and pressure fluctuation are investigated. A complete simulation model with relevant parameters have been established and flow characteristics can be explicitly described. Furthermore, this work provides theoretical foundation for structure optimization of distributing-flow system and performance improvement.

In this section, a novel rotating-sleeve distributing-flow system is developed and analyzed. The plunger pulled by the crank-link mechanism achieves coupled reciprocating movement and then uses drive pin to transmit force into rotating sleeve along the cam groove pathway in unidirectional rotating movement. The drive pin moves while rolling with the cam groove molded line obtained by fitting linear equation through quadratic differential, rotating angle of rotating sleeve, and crank angle. Figure

Structure principle of rotating-sleeve distributing-flow system.

In this system, there are two major movements: axial reciprocating movement of the plunger and unidirectional rotating movement of rotating sleeve. The plunger finishes reciprocating movements powered by the crankshaft and connecting rod mechanism via a connector cross slider. The displacement of plunger in reciprocating motion is formulated as follows:

Due to

Angular velocity and acceleration of rotating sleeve have no obvious phase step and inflection point when sine molded line is selected for cam groove. Therefore, the relationship between the cam groove’s axial displacement and rotating-sleeve angle is given as follows:

Substituting (

The angular velocity of rotating sleeve by taking the derivative of

In light of structure and operating principle of rotating-sleeve distributing-flow system, the fluid model is established as shown in Figure

Fluid model of rotating-sleeve distributing-flow system.

In this paper, the fluid model is simulated and analyzed by fluid simulation software Fluent®. The motions of plunger and rotating sleeve are defined in fluid model using Users Defined Function. Standard

The parameters of distributing-flow system.

Parameters | Value | Symbol/unit |
---|---|---|

The radius of bent axle | 0.03 | m |

The ratio of crank and connecting link | 0.25 | / |

Crankshaft speed | 150 | n/(r/min) |

Water density | 998 | kg/m^{3} |

Water viscosity | 0.001003 | Pa/s^{−1} |

Inlet pressure | 0.1 | MPa |

Outlet pressure | 2 | MPa |

Saturated vapor pressure | 2339 | Pa |

Time step | 0.001 | S |

The cavitation model is based on the flow equation Navier-Stokes with variable density and standard viscosity in hydromechanics. In this paper, taking the viscidity and turbulence into consideration and gas-liquid two-phase flow as the object of study, the transmission equation considering the content of gaseous mass is given as follows [

Based on the bubble dynamic equation of Rayleigh-Plesset, the bubble dynamics can be described by the variation of bubble radius under the surface tension term and the second derivative term in the equation neglected as follows:

Combining transmission equation of mass with the equation of continuity, the relationship of density in mixture and volume fraction is described as follows:

If the bubble numbers are

Substituting (

According to the above equations, the velocity of bubble in generation and disappearance can be described, respectively, as follows:

The gas volume fraction is proportional to average velocity and average velocity can be denoted by turbulence energy. When the surface tension coefficient of bubble is introduced, the velocity of bubble in generation and disappearance also can be described, respectively, as follows:

Turbulence energy represents turbulent fluctuation and directly reflects dissipation and stability of fluid flow. If turbulence energy is larger in some areas, these areas will have more loss of kinetic energy and become more unstable [

The distribution of turbulence energy for one working cycle is shown in Figure

Distribution of turbulence energy for one working cycle.

The velocity distribution in

Velocity distribution in

Figure

Local velocity vector distribution with rotating-sleeve angle of 180°.

Figure

Local velocity vector distribution with rotating-sleeve angle of 360°.

Figure

Fluid model grid of distributing-flow system.

Flow pulsation is the source of noise, pressure pulsation, and vibration of plunger pump. It can have adverse impacts towards working parts, especially some precise hydraulic system. Hence it should be emphasized that the characteristic of fluid is most meaningful with respect to the flow pulsation of the distributing-flow system. Figure ^{−4 }m^{3}/s and backward flow appears at the end of processes, that is, suction and discharge. It can be illustrated that these analyses are consistent with findings in Figures ^{−4 }m^{3}/s according to the left zoom in plot corresponding to the TDC in Figure ^{−4 }m^{3}/s according to the right zoom in plot corresponding to the BDC in Figure

The characteristic of outlet flow pulsation.

The characteristic of local outlet flow pulsation.

The phenomena incorporating backward flow, local cavitation, and erosion can easily cause pressure pulsation with regard to inner flow. And once pressure pulsation happens, it can lead to intensive vibration of pump and cavitation and even resonance. Figure ^{6} Pa involving over 10% more than nominal pressure when the plunger is at the TDC on account of throttling action in the damping groove. However, pressure overshoot gradually reduces to normal condition followed by increasing flow area. Because of throttling action in the damping groove, pressure in the pump chamber abruptly drops to the saturated vapor pressure about −98.9 KPa of fluid when the plunger is at the BDC; however, the overshoot gradually increases to the normal condition with increasing flow area.

The characteristic of pressure in the pump chamber.

The characteristic of local pressure in the pump chamber.

According to characteristic of the novel rotating-sleeve distributing-flow system, the governing equations between the plunger and rotating sleeve are established to obtain the dynamic model of distributing-sleeve system. By utilizing sliding mesh and dynamic mesh technology, the improved CFD model taking the cavitation and turbulence into consideration is employed to simulate flow field and working pulsation.

Simulations of rotating-sleeve distributing-flow system have been conducted based on the governing equations and the improved CFD model. Primary performance parameters such as turbulence energy distribution, velocity distribution, and working pulsation have been investigated. In addition, the relationship between performance parameters is studied for the distributing-flow system.

Periodic fluctuation and sharp corner exist in flow pulsation in addition to the backward flow issue between discharge and suction. Serious turbulence and large loss in kinetic energy around the damping groove exist. Moreover the noticeable periodic fluctuation and sharp corner appear in the pressure pulsation, and pressure in the pump chamber rapidly rises to 2.2 MPa involving over 10% more than nominal pressure when the plunger is at the TDC. On the other hand, pressure in the pump chamber instantaneously reduces to the saturated vapor pressure −98.9 KPa when the plunger is at the BDC. For the rest time period, the pressure overshoot gradually reaches stability until it closes to the normal condition with increasing flow area. Fluid field and working pulsation simulation could provide foundations for structure optimization.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

The research work was supported by National Natural Science Foundation of China (Grant no. 51575286) and Shandong Province Science Foundation of China (no. 2014ZRB01503).