Keywords

1 Introduction

Electromagnetic pilot valve is one of the key components of mining electro-hydraulic control system. It is commonly used in hydraulic and pneumatic systems to control the internal fluid flow through electromagnetic force, thereby achieving pressure and flow control of the main valve. The performance of electromagnetic pilot valves directly affects the safety and reliability of hydraulic mining machinery. However, the internal structure of pilot valves is complicated, and complex flow paths such as sudden expansion, contraction and bending can occur, which in turn generate phenomena such as vortex, reflux, de-wallization and re-attachment to the wall [1]. Improper design can lead to excessive energy loss, cavitation, and thermal deformation, thereby reducing the service life and performance of pilot valve components and affecting the operation of the entire system. Therefore, it is necessary to study the working process of electromagnetic pilot valves for improvement and optimization.

Choi et al. [2] were numerically investigated the flow characteristics of butterfly valves with different sizes under different valve opening percentages. They determined that increasing turbulence effect could cause many discrepancies between turbulence models, especially in areas with large pressure drop and velocity increase. In addition, sensitivity analysis of flow properties was conducted to determine the effect of constants used in each turbulence model. Huovinen et al. [3] investigated a flow past a choke valve by experimental and numerical means. The flow profile after a choke valve with high Reynolds number of approximately 1,000,000 was measured using a LDV and computed using RANS simulations. Gabel et al. [4] studied constitutes a coupled computational and experimental methodology to analyse the complex flow within a choke valve under laminar inflow conditions. The studies reveal that, at low valve openings, when only the small ports are engaged, there forms a four-lobed vortical structure which is established upon collision of the incoming jets. The vortical structure of the flow is much more complex at higher valve openings when both the small and large ports are engaged. Xavier and Ortiz [5] investigated cavitation characteristics in Hollow-Jet valves and possible solutions. Three-dimensional numerical simulations—CFD (Computational Fluid Dynamics) were carried out in an unsteady state, considering homogenous multiphase flow, to identify the phenomenon in these components. The results confirmed the occurrence of cavities with a mixture of vapor and liquid at the valve tip. The cavities are followed by a vortex generation near the same region.

In summary, domestic and foreign scholars attach great importance to the study of the internal fluid characteristics of hydraulic valves. Energy consumption, cavitation and other problems need to be solved in-depth understanding of its internal flow characteristics. Therefore, the research in this paper provides an important support for the optimisation of the structure of this new foreign electromagnetic pilot valve in order to obtain better flow control performance and to achieve the prediction of the liquid flow characteristics required by the system. This is to improve the existing products and develop more new electromagnetic pilot valves in line with China's needs has an important role in promoting.

2 Principle of Pilot Valve Structure

The solenoid pilot valve is to effectively convert the pulse electrical signal from the electronic control system into a hydraulic signal to drive the corresponding main control valve spool in the main control unit, so as to realize the precise control of the actuator [6].

The structure schematic diagram of the electromagnetic pilot valve studied in this paper is shown in Fig. 1. Under the action of the return spring, the left ball valve remains normally closed and the right ball valve remains normally open, with an opening of 0.1 mm. After the solenoid valve is powered on, electromagnetic force will be generated. The electromagnetic force pushes lever 8, driving the top rod 7 to move to the left, thereby pushing the ceramic ball valve core 6 to move 0.1 mm to the left. At the same time, the right valve port is blocked and the left valve port opens. Port P and Port A are connected, and high-pressure hydraulic oil enters Port A through a flow channel. When the electromagnetic signal disappears, under the action of the reset spring, the left ceramic ball valve core is pushed to move to the right. The left valve port is blocked, and the opening of the right valve port is 0.1 mm. At this time, hydraulic oil flows into port T from port A, that is, hydraulic oil flows to the oil tank to achieve unloading.

Fig. 1
A schematic diagram of a specimen. It consists of 10 different parts clockwise from the top left. These are valve sleeve rear seats, spring seat, left ceramic ball valve core, stem, valve sleeve, ceramic ball valve core, rod, lever, and damping pin. These parts are joined together.

Schematic diagram of the structure. 1-Valve sleeve rear seat. 2-Spring seat. 3-Left ceramic ball valve core. 4-Stem. 5-Intermediate valve sleeve. 6-Right ceramic ball valve core. 7-Top rod. 8-Lever. 9-Damping pin. 10-Valve seat

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3 Mathematical Model for Flow Field Simulation

This paper quantitatively analyses the characteristics of the flow field and the distribution of flow parameters in the solenoid pilot valve through numerical simulation to provide theoretical support for design optimization.

The flow field simulation analysis in this paper is based on the Realizable K–ε model in the Fluent model library. This model mainly aims to modify the normal stress of the standard model under conditions of extremely high strain rates, in order to avoid the generation of negative stresses and make the computed results reasonable. The expression is as follows: where \({C}_{1}={\text{max}}\left[0.43,\frac{\eta }{\eta +5}\right]\); \(\eta =\frac{Sk}{\varepsilon }\); the involved constant parameters are: C1ε = 1.44; C2 = 1.9; σk = 1.0; σε = 1.2 [7, 11].

$$\rho \frac{DK}{Dt}=\rho \left(\frac{\partial K}{\partial t}+{\overline{\mu }}_{j}\frac{\partial K}{\partial {x}_{j}}\right)=\frac{\partial }{\partial {x}_{j}}\left[\left(\mu +\frac{{\mu }_{t}}{{\sigma }_{\varepsilon }}\right)\frac{\partial K}{\partial {x}_{j}}\right]+{G}_{k}+{G}_{b}-\rho \varepsilon -{Y}_{M}$$
(1)
$$\begin{aligned} \rho \frac{D\varepsilon }{Dt} = & \rho \left(\frac{\partial \varepsilon }{\partial t}+{\overline{\mu }}_{j}\frac{\partial \varepsilon }{\partial {x}_{j}}\right)=\frac{\partial }{\partial {x}_{j}}\left[\left(\mu +\frac{{\mu }_{t}}{{\sigma }_{\varepsilon }}\right)\frac{\partial \varepsilon }{\partial {x}_{j}}\right] \\ & +\rho {C}_{1}S\varepsilon -\rho {C}_{2}\frac{{\varepsilon }^{2}}{k+{\left(v\varepsilon \right)}^{1/2}}+{C}_{1\varepsilon }\frac{\varepsilon }{k}{G}_{3\varepsilon }{G}_{b} \end{aligned}$$
(2)

Compared to the standard K–ε model, this model no longer utilizes the original turbulence viscosity formula. Instead, it derives a new viscosity formula by considering the rotational flow and jet curvature generated during fluid motion, achieving a closer approximation to the actual flow state of the fluid and more accurate computation results [12].

4 Model Preprocessing

4.1 Flow Domain and Grid Partitioning

As the solenoid pilot valve possesses a symmetrical structure, the fluid flow within the valve cavity also exhibits symmetry. Leveraging the principle of symmetry, it is possible to simulate only half of the structure, thereby enhancing the computational speed of numerical calculations and conserving computational time and memory [8]. Fig. 2 illustrates the utilization of SpaceClaim, a pre-processing software within the Workbench, to generate the Fluent flow field domain model. Subsequently, the mesh generation is performed using the confined geometry workflow provided by the software, followed by transferring it to Fluent for the solution setup. During the meshing process in Fig. 3, the local mesh encryption is executed due to the significant variation in pressure and velocity gradient at the inlet and outlet of the valve port, as well as the presence of a complex vortex field. Additionally, a relatively larger mesh is employed in regions where the gradient is minimal, thereby reducing the computation time [9, 10].

Fig. 2
Two schematic diagrams. A, fully open flow field model. B, partially open flow field model. It is a horizontal tube like model and the front circular part is joined to the lower tube.

Flow field domain model

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Fig. 3
Two mesh diagrams. A, fully open mesh model. The whole body is covered with hexagonal mesh. B, partially open mesh model. The whole body is covered with hexagonal mesh.

Mesh division

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4.2 Simulation Boundary Condition Setting

The pressure at port A of the pilot valve needs to be calculated first based on the force required to move the main valve. The main valve incorporates a spring with a stiffness of k = 6.48 N/mm, which is compressed from 46.50 mm to 31.91 mm. The effective area on the main valve is A = 314.16 mm2, while the area at the P port is A0 = 144.60 mm2. Frictional forces are neglected in the analysis. Using Eq. (3), the pressure for actuating the main valve is derived as P = 14.8 MPa.

$$P=\frac{F}{A}=\frac{k\Delta x+{P}_{0}\times {A}_{0}}{A}$$
(3)

The boundary conditions for the fully open valve are defined as follows: the fluid model is selected as Realizable K–ε turbulence model, while the wall adjacent to the fluid is considered stationary. The fluid medium, in this case, is an emulsion with a density of 997.7 kg/m3 and a viscosity of 0.00149 kg/(m·s). The inlet pressure is set to 31.5 MPa. The outlet pressure is varied as 0 MPa, 5 MPa, 10 MPa, and 15 MPa, with a valve opening of 0.1 mm. The right valve port is blocked.

For the partially open valve, the following boundary conditions are set: the fluid model is again selected as Realizable K–ε turbulence model, while the wall adjacent to the fluid is considered stationary. The fluid medium remains the same as the fully open valve scenario. The inlet pressure at the P port is maintained at 31.5 MPa, while the outlet pressures at the A and T ports are set to 14.8 MPa and 0 MPa, respectively. The left valve port opening sizes are set to 0.08 mm, 0.06 mm, and 0.04 mm.

5 Results and Discussion

Turbulent flow is a physical quantity that reflects the amplitude of fluid velocity fluctuations. The greater the kinetic energy of turbulence, the more intense the velocity fluctuations generated, and the greater the energy loss generated. Therefore, the reason for energy dissipation inside the valve can be evaluated based on the magnitude and distribution of turbulent kinetic energy.

5.1 Effect of Different Pressure Differences on Turbulent Kinetic Energy Dissipation

From the turbulent kinetic energy distribution plots in Fig. 4(a)–(d), it can be observed that significant energy dissipation occurs at the valve orifice. This is due to the rapid increase in flow velocity and turbulence intensity at the contracted area of the orifice, leading to an increase in turbulent kinetic energy. Significant energy dissipation also occurs at the corners of the flow passage inside the valve chamber. This is caused by the change in flow streamline and the generation of vortices, which increase the turbulent kinetic energy. However, under a constant inlet pressure and varying outlet pressures of 0 MPa, 5 MPa, 10 MPa, and 15 MPa, the maximum turbulent kinetic energy reaches 3349 m2/s2 at 0 MPa, and it decreases as the pressure difference decreases, indicating a reduction in turbulence intensity and energy dissipation.

Fig. 4
Four heat maps. These present the distribution of the turbulent kinetic energy. The lowest values of turbulent kinetic energy are distributed throughout the whole body. A, values lie between 3.349 e plus 02 and 5.122 e minus 10 units. B, values lie between 2.8 e plus 02 and 2.4 e minus 10 units.

Turbulent kinetic energy distribution for different differential pressure conditions. (a) 0 MPa. (b) 5 MPa. (c)10 MPa. (d) 15 MPa

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5.2 Effect of Different Ball Valve Openings on Turbulent Energy Dissipation

From the distribution of turbulent kinetic energy in Fig. 5(a)–(c), it can be concluded that significant energy dissipation occurs due to the contraction of the valve ports on both sides, leading to an increase in turbulent kinetic energy. Energy dissipation also occurs at the flow passage corners in the middle section of the valve chamber. Under constant pressure differential conditions, the valve aperture was set at 0.04 mm, 0.06 mm, and 0.08 mm. The turbulence kinetic energy reached a minimum of 2470 m2/s2 at 0.06 mm aperture. As the aperture gradually increased, the turbulence intensity of the pilot valve weakened and then strengthened, resulting in a decrease in turbulence kinetic energy, which in turn led to reduced energy dissipation.

Fig. 5
3 heat maps. These present distribution of turbulent kinetic energy. The lowest values of turbulent kinetic energy are distributed throughout whole body. Values lie between A, 3.76 e plus 02 and 1.02 e minus 11 units. B, 2.4 e plus 02 and 1.7 e minus 12 units. C, 2.8 e plus 02 and 1.3 e minus 11.

Distribution of turbulent kinetic energy for different openings. (a) 0.08 mm. (b) 0.06 mm. (c) 0.04 mm

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6 Conclusion

In this study, the internal flow field of the electromagnetic pilot valve during operation was simulated and analyzed using Fluent. The distribution map of turbulence kinetic energy and the internal flow state of the pilot valve were obtained. By analyzing and comparing different pressure differential conditions and valve aperture sizes, the variation patterns of turbulence kinetic energy and vortex intensity were determined. The results are as follows:

  1. (1)

    With unchanged valve aperture, only the outlet pressure was varied. As the outlet pressure increased from 0 to 15 MPa, turbulence kinetic energy gradually decreased, resulting in reduced impact on the valve core and 48.9% decrease in energy dissipation.

  2. (2)

    Under constant pressure differential conditions, only the valve aperture was changed. As the aperture increased from 0.04 mm to 0.08 mm, turbulence kinetic energy initially decreased and then increased. Increasing the valve aperture to a certain extent improved energy dissipation.