Numerical–experimental research on the influence of inclined angle on the flow characteristics of angle seat valve

The influence of inclined angle on the flow characteristics of angle seat valve is investigated by the numerical and experimental study. The accuracy of numerical modelling and calculation is verified by comparing the flow coefficients obtained from numerical simulation and experiments under the different pressure difference at the inclined angle of 45° and 60°. The experiment results showed that the highest flow velocity, the maximum flow coefficient, and the minimum flow resistance exist as the inclined angle is 45°. The flow coefficient increases as the increase of inclined angle when it ranges from 45° to 60°, and the flow resistance decreases correspondingly. The observed result is discussed and explained by the computational fluid dynamics (CFD) method. The calculation results indicated that the flow coefficient mainly depends on the maximum flow velocity in the angle seat valve. Moreover, the flow capacity is also affected by the flow direction near the sealing surface, and the number, locations and intensities of flow vortex.


Introduction
The angle seat valve belongs to the industrial-process control valve. For the characteristics of sensitive action and quick response, the valve is commonly used to open or close the passage of pipeline [1]. In order to obtain the better flow capacity, the angle between the valve stem and the horizontal pipeline (called the inclined angle) is designed to lower than 90°. The inclined angle ranges from 40° to 60° in the commercial products, but the design principle has not been formed.
The flow capacity is regarded as an important parameter to evaluate the valve performance. To achieve the better the flow capacity in the limited internal space of valve, many attempts and efforts have been made by the engineers and researchers. Ye et al. [2] found that the groove shape has an important influence on the flow characteristics of the hydraulic pipeline valve. By the combination of numerical simulation and experiments, the relationship between the flow coefficient, groove structure, flowing condition, fitting coefficient, and stable value was derived. By using the computational fluid dynamics (CFD), T. Asim et al. [3] analysed the flow capacity of control valve at the high-pressure differential condition. The flow coefficients with different valve components are determined, and the correlation between the valve inner structure and flow capacity is established. In the flow tests of ball valve, X.F. He found the flow coefficient ranges from 0.9 to 1.0 when the half conical angle is 45° and the length of chamfering angle is small than Rcos/4. Z.J. Zheng et al [4] found the decrease of chamfering angle of valve spool will significantly alter the local flow field, reduce the ranges and intensities of reflux flow, and finally enhance the flow capacity. From the above research, it is known that the valve inner structure has a direct influence on the local flow field and flow coefficient. Therefore, the flow stability and capacity can be improved by using the optimised structure. However, the influence of inclined angle on the flow capacity of angle seat valve has not been cleared and the structure of flow field inside the valve should have been analysed.
In this paper, the numerical simulation and experimental research are combined to study the influence of inclined angle on the flow characteristics of angle seat valve. The accuracy of numerical modelling and calculation is verified by comparing the flow coefficients and flow resistances at different pressure difference obtained from numerical calculation and experiments, respectively. Then, the flow fields and flow capacities under different inclined angles are analysed, and the influence of inclined angles on the flow coefficient and flow resistance is obtained.

Geometry model and meshing
The angle seat valve is mainly composed of pneumatic actuator, valve stem, spool, and seat. The geometric structure is shown in Fig. 1. The valve inlet and outlet are on the right and left side, respectively. The valve works in the full open or close state. The inner diameter (D) of inlet and outlet pipeline is 50 mm, the pressure difference Δp between valve inlet and outlet ranges from 35 to 100 kPa, and the stroke of valve stem L is 14 mm. The inclined angle α is set as a variable parameter, and it is usually designed in the range of 40° to 60°. Therefore, the influence of inclined angle on the flow characteristics of angle seat valve is studied in this range.
In order to ensure the full development of flow as it passes through the valve, the length of inlet and outlet pipeline is set as 10D.The meshing of computational domain is conducted by using ICEM CFD software. The hexahedral structured grid is adopted in the meshing of straight pipeline, and the tetrahedral unstructured grid is adopted in the meshing of valve body. The verification of grid independence is conducted to avoid the influence of grid number on the calculation results. The numerical calculation is conducted with the gird numbers of 1.5, 3.0, and 4.5 million, respectively, when the Δp is 35 kPa, L is 14 mm, and α is 45°. The results showed that the volume flow rates are 18.20, 18.55, and 18.59 m 3 /h, and the corresponding maximum flow velocities are 10.7, 11.1, and 11.2 m/s in the cases with these three grid numbers. It is observed that when the grid number increases from 3.0 to 4.5 million, the relative error of volume flow rate and max flow velocity are 2.2 and 0.2%, respectively. Therefore, the independence of grid number can be confirmed. In consideration of

Numerical method
In the numerical simulation, the RNG k − ε model is used to describe the characteristics of turbulence flow in the angle seat valve, and the finite volume method is used to discretise the governing equations. The roughness of the inner surface inside the valve and connecting pipeline is set as 0.02 and 0.04 mm, respectively, according to the data provided by the manufacturers. The energy loss in the flow process is neglected in the calculation because the valve is operated in the normal temperature. The boundary conditions of pressure inlet and pressure outlet are imposed on the import and export of valve. The solid wall surface is regarded as adiabatic and no-slip. The SIMPLEC method is chosen to couple the calculation of velocity and pressure, and the two-order upwind scheme is used to discretise the terms of pressure, momentum, turbulent kinetic energy, and turbulent dissipation rate. When the difference of mass flow rate between the valve inlet and outlet is <1 × 10 −3 kg/s and the pressure variation of the monitoring point at the valve outlet is lower than 3%, the calculation result is regarded as convergence.

Experimental platform
The flow coefficient and resistance are tested on the platform for the flow test of angle seat valve, as shown in Fig. 2. There are three test stations on this platform, corresponding to the different ranges of flow rates [5]. The differential pressure sensor is installed on the upstream and downstream of test section, the range of instrument is 10-100 kPa, and the precision is 0.5%FS. The electromagnetic flowmeter is located on the upstream of test section, the range is 0∼45 m 3 /h, and the precision grade is + 5%R.
The experimental process is conducted according to the standard of solenoid valves for industrial-process measurement and control systems (JB/T 7352-2010), and can be briefly described as follows [6]: (i) padlocked the angle seat valve and upstream and downstream cut-off valves in full open position; (ii) pumped the water to fill the whole test loop and flush the circulation loop for 3 min, and in this step, most of the impurities in the water are removed by the filtration system; and (iii) set the pressure difference between the valve inlet and outlet and test the volume flow rate. Then the flow coefficient and flow resistance can be calculated. In order to get the process parameters in a stable state, the flow rate and pressure difference are collected after 90 s from the start of test. Every test is repeated for 5 times, and the average value is regarded as the final result.

Reliability of numerical simulation
Numerical simulation and experimental test are conducted when L is 14 mm, and α are 45° and 60°. The comparison of calculated and experimental data is shown in Fig. 3. It is known that when α are 45° and 60°, the volume flow rate increases linearly with the pressure difference Δp . The volume flow rates at α of 45° are much higher than those at α of 60° under the same pressure difference. In addition, the roughness of inner surface in the valve and pipeline is considered in the numerical simulation, so the calculated data is close to the experimental value, and all the relative error is below 5%. Therefore, the reliability of numerical simulation can be verified.

Influence of inclined angle on flow performance
The calculated and experimental values of flow coefficient and flow resistance under different inclined angles when the pressure differences are 35 and 70 kPa are shown in Figs. 4 and 5, respectively. It indicates that as the inclined angle ranges from 40°t o 50°, the flow coefficient gradually increases but the flow resistance decreases accordingly with the increase of pressure difference. However, when the inclined angle is in the range of 50°t o 60°, the flow coefficient and flow resistance are not sensitive to the variation of pressure difference. The reason can be briefly explained as follows: as the inclined angle is below 50°, the flow capacity is greatly influenced by the flow velocity in the valve. Therefore, the increase of pressure difference will increase the flow velocity and finally enhance the flow performance. Conversely, the number and distribution of the flow vortex become the dominant factors affecting the flow performance. If the pressure difference increases, the moving area and intensities of flow vortex will be enhanced; thus, it will weaken the flow capability.
It also indicates that the highest flow coefficient and lowest flow resistance both exist when the inclined angle is 45° at the pressure difference of 35 and 70 kPa. When it ranges from 45° to 60°, the flow coefficient significantly decreases but the flow resistance rapidly increases with the increases of inclined angle. For example, the experimental values of flow coefficient are 32.49 and 27.33 at the inclined angles of 45° and 60°, respectively, and down 15.9%, when the pressure difference is 70 kPa.

Analysis on the internal flow field of valve
The flow coefficient is closely related to the flow characteristics in the angle seat valve [7]. Therefore, the internal flow fields with different inclined angle are analysed to determine the relationship between the flow performance, flow velocity, and streamlines. The contours of flow velocity at different inclined angles when the pressure difference is 70 kPa are shown in Fig. 6. It is known that the regions of high velocity mainly concentrate on the valve outlet and the downstream area (25 mm away from the valve outlet). In the range of 50-100 mm from the valve outlet, the flow velocity on the lower side of pipeline is higher than that on the upper side. The velocity difference between the lower and upper side ranges from 3 to 10 m/s. It also can be observed that the large pressure difference leads to the unstable internal flow field. The maximum flow velocity in the valve is 15.2 m/s at the inclined angle of 45°, higher than that at the other inclined angles (13.0 m/s). As the flow capability directly depends on the flow velocity, the flow coefficient is highest in this state.
The streamlines in the valve at different inclined angles (Δp = 70 kPa) are shown in Fig. 7. It is known that the flow vortex mainly concentrates on the bottom of valve spool and the area within 40 mm away from the valve outlet. The streamline becomes smooth once the flowing distance exceeds 60 mm away from the valve outlet.
There are two asymmetrical vortices located on the bottom of valve spool at the inclined angle of 45°. Besides, two large vortices can be observed in the upper and lower sides of the outlet pipeline. Therefore, the flow resistance will be enhanced because of this flow pattern. When the inclined angle is 50°, the numbers of vortices located on the bottom of valve spool and valve outlet increase obviously. The irregular distribution of vortices can be observed. Compared with the vortices at the inclined angle of 40°, the intensities and areas are obviously decreased. In addition, a vortex is formed on the left corner of valve spool. As the centre of vortex on the lower side of the outlet pipe locates near the valve throat, the streamlines in this section are narrowed. It finally results in the decrease of volume flow rate. As the inclined angle increases to 55°, the streamlines further narrow. Simultaneously, the directions of flow that passes through the valve throat change significantly. The fluid directly impacts on the bottom of the outlet pipe with high velocity and leads to the large loss in fluid kinetic energy. When the inclined angle is 60°, the distribution of vortices becomes more irregular, then the flow resistance further increases. Therefore, the lowest flow capacity can be observed. Combined with the analysis on the fields of flow velocity and streamlines, it is