Design and analysis on the flow fluctuation of a new horizontal space multiphase crankshaft pump

: In civil aviation ground deicing system, the traditional reciprocating pump is often used as the power supply device to ensure the physical and chemical properties of high viscosity deicing fluid. The traditional reciprocating pump exist the problem of flow fluctuation. A new horizontal space multiphase crankshaft pump is proposed to suppress the flow fluctuation. The new type of pump adopts segmented crankshaft: each crank pin on the crankshaft drives two connecting rods simultaneously. The connecting rod drives the pistons distributed on both sides of the crankshaft to achieve linear reciprocating motion. Three sections of the crank pin are arranged by 120° phase space circular, and this kind of crankshaft implements multiple phase coupling of piston movement. The hydraulic cylinder adopts the horizontal layout, so the machine structure presents spatial symmetry. A mathematical model of two connecting rods driven by crankpin is established for the new type of pump. The kinematics equation of the piston is solved by the analytical method and then the flow rate of the pump is calculated. In contrast with the experimental data, the new pump can effectively reduce the flow fluctuation.


Introduction
In cold winter, the surface of the aircraft is prone to ice, which is a serious threat to flight safety. Therefore, deicing is very important and necessary. The deicing fluid is a high viscosity mixture with macromolecule. In order to ensure its chemical and physical properties, the reciprocating pump is used as a feeding device of deicing fluid.
Many investigators study the properties of high viscosity fluid. Boman et al. [1] study the effect of different viscosity fluids on the supply of single absorption pump. Kumar [2] analyzes the physical properties changes of fluid caused by the change of fluid viscosity in the channel. The axial velocity curve is changed due to the change of viscosity. The radial flow is caused by the continuity of flow. Elcioglu et al. [3] report the experimental results of the effect of fluid viscosity on nanoparticle fraction at different temperatures. The importance of fluid viscosity is ranked from low to high temperature, nanoparticle fraction, and nanoparticle diameter.
Many scholars analyse the flow pulsation of pump. Lu et al. [4] calculate the pulsation in the reciprocating pump through the periodic motion of the piston. Through the three-dimensional transient model, Marijonas et al. [5] propose a mathematical model of multi-stage centrifugal pump and pipeline system. The influence of impurities in fluid is evaluated, which shows that impurities increase the pulsation of centrifugal pump. Shim et al. [6] develop a new positive displacement rotary drum pump. The performance of the pump is analysed from the aspects of simulated flow, differential pressure, driving torque and efficiency. Compared with reciprocating pump, rotary drum pump produces relatively low pulsation and increases displacement with lower vibration and power loss. Diao et al. [7] investigate the pulsation of the whole pump by setting up the piston pump simulation model. Raush et al. [8] study the pulsation of positive displacement pump using timeresolved particle image technology. The flow pulsation at the outlet of wheel pump is measured by visualising the velocity distribution. Through sliding mesh, Zhang et al. [9] develop the control equations of the plunger. The dynamic grid technology studies the vibration problems caused by the flow field disturbance and pulsation in the rotating-sleeve flow system.
The crankshaft is studied for pump by several researchers. Lee et al. [10] analyse the kinematics and fluid dynamics of the pump in terms of piston displacement, flow, and piston pressure. The function equation of crankshaft is obtained for the analysis of three-cylinder high pressure reciprocating pump. Peng and Zhang [11] study dynamic characteristics of crankshaft through crankshaft modelling. The maximum principal stress, minimum principal stress and Mises stress are obtained under critical conditions of crankshaft. The dangerous position of crankshaft fracture is analysed in critical area. Iannetti [12] proposes the middle-chamber model of three-cylinder positive displacement reciprocating pump by transient numerical method, in order to evaluate the performance of the pump when crank rotates.
In the research of flow fluctuation of reciprocating pump, the flow pulsation can be reduced by the parallel connection of multiple reciprocating pumps [13,14]. Through numerical simulation, the flow pulsation of odd number piston pumps is smaller than that of even number piston pumps [15,16]. The flow pulsation is severe to traditional reciprocating pump. Aiming at this problem, a new horizontal space multiphase crankshaft pump is designed. Then, the mathematical model of the new pump is established. Based on the model, the kinematics simulation is carried out. The flow pulsation rate is calculated in contrast with the experimental data of traditional reciprocating pump.  connecting rods. This structural feature makes the mechanism compact and the crankshaft is easily disassembled. The large flow operation is achieved through the simultaneous operation of multiple sets of hydraulic cylinders.

Intensity check and dynamic balance analysis
When checking the strength of crankshaft, the crankshaft is analysed according to the maximum force of three sets of connecting rods.
where [σ −1b ] = 55 MPa. The resultant force of each crank pin is horizontal. The centrifugal force of crank pin is F 1 = 5.2N, the centrifugal force of crank pin is The dynamic equilibrium condition of the crankshaft is The study shows that the crankshaft conforms to the strength requirements and dynamic balance.

Motion equation.
The crankshaft pump converts the rotation of crankshaft into the linear reciprocating motion of piston, realising deicing fluid's suction and discharge. Fig. 4 shows the mathematical model of two connecting rods driven by crank pin.
Displacement equation of piston IV on the right side is where λ = r/l is the crank radius-connecting rod length ratio. According to the trigonometric function: cos β can be expanded to binomial series by using Taylor series, that is where λ ≤ 1/3, cos β can be written as The displacement equation of piston IV can be expressed as Velocity equation: Accelerated velocity equation In the same way, the equation of piston I on the left side is given by

Kinematics simulation.
The pistons on both sides of the same crank pin have 180° phase difference. The kinematic law of the left side's pistons (I, II, III) is shown in Figs. 5 and 6. The velocity superposition curve of six pistons is depicted in Fig. 7. In Fig. 6, the acceleration curve of each piston is continuous and smooth, so there is no abrupt change in velocity. From Fig. 7, the superposition velocity of the six pistons fluctuates is less and tends to be stable. Therefore, the new pump can effectively reduce the flow fluctuation.

Calculation result
Flow rate: Flow pulsation: where Q i is the flow rate of a hydraulic cylinder, l/min; A is the effective area of the piston, m 2 ; v i is the velocity of a hydraulic cylinder, m/s; Q max is maximum flow, l/min; Q min is minimum flow, l/min; Q aver is average flow, l/min. The instantaneous flow of each hydraulic cylinder is calculated by (16). Also then, Fig. 8

Experimental verification.
In the previous study, double acting aircraft deicing fluid pump is proposed in order to suppress the flow pulsation [17]. The flow pulsation variation of double acting pump is obtained through the experiment, as shown in Fig. 9. Flow pulsation rate:  The layout of the three crank pins is spatially arranged, and their phase difference is 120°. This layout realises the multiphase coupling of piston motion. The crankshaft pump adopts multi-cylinder symmetrical layout, which enables large flow operation. 2. The simulation results show that the new pump effectively reduces the flow fluctuation. In contrast with the experimental data, the rationality of the pump design is further explained. The research in this paper can provide a reliable theoretical basis for the development of ground deicing equipment for civil aviation aircraft.