# Analysis of the Internal Characteristics of a Deflector Jet Servo Valve

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## Abstract

In current research on deflector jet servo valves, the receiver pressure estimated using traditional two-dimensional simulation and theoretical calculation is always lower than the experimental data; therefore, credible information about the flow field in the prestage part of the valve can hardly be obtained. To investigate this issue and understand the internal characteristics of the deflector jet valve, a realistic numerical model is constructed and a three-dimensional simulation carried out that displays a complex flow pattern in the deflector jet structure. Then six phases of the flow pattern are presented, and the defects of the two-dimensional simulation are revealed. Based on the simulation results, it is found that the jet in the deflector has a longer core area and the fluid near the shunt wedge cannot resist the impact of the high-speed fluid. Therefore, two assumptions about the flow distribution are presented by which to construct a more complete theoretical model. The receiver pressure and prestage pressure gain are significantly enhanced in the calculations. Finally, special experiments on the prestage of the servo valve are performed, and the pressure performance of the numerical simulation and the theoretical calculation agree well with the experimental data. Finally, the internal mechanism described by the theoretical and numerical models is verified. From this research, more accurate numerical and theoretical models are proposed by which to figure out the internal characteristics of the deflector jet valve.

## Keywords

Deflector jet Servo valve Computational fluid dynamics (CFD) Numerical simulation## 1 Introduction

An electro-hydraulic servo valve plays an important role in energy conversion and control of hydraulic equipment. However, this type of valve is characterized by strong coupling of fluid, complex structures, electromagnetic activity, and temperature distribution. Due to its complexity, researchers have been concentrating on a variety of servo valves for years [1, 2]. Compared with more traditional nozzle flapper or jet-pipe servo valves, a deflector jet servo valve (DJV) was designed with consideration of both pollution resistance and dynamic performance, and has become a new crucial focus of activity.

It is generally accepted that the research on DJVs is derived from the jet pipe valves. Somashekhar et al. [3] established a numerical model including a jet pipe valve’s hydrostatic pressure cavities and armature components, and the effect of the fluid structure interaction on the equilibrium was analyzed. How the wall surface roughness acts on the jet flow pattern was analyzed by Pham [4]. Then other scholars built numerical models of the jet pipe valve [5, 6], and the effect of various factors on the jet characteristics was studied by RANS simulation [7, 8].

By comparison, the hydraulic amplifier of a DJV is more complex because of a V-shaped tapered slit in the deflector and the particular shape of the receiving port. Applying the standard *k*-*ε* turbulence model, Dhinesh [9] confirmed that the pressure difference of the two control chambers in the numerical simulation was lower than the experimental value, which was not explained. Then other scholars also carried out RANS simulations [10, 11, 12] and tried to explore the influence of the structural parameters, machining technologies, and external conditions on the flow pattern [13, 14]. In 2015, Yin et al. [15] built a simplified 3D model, using an RNG k-ε turbulence model to analyze the factors affecting cavitation. Then Jiang et al. [16] constructed a 3D model using tetrahedral meshes and obtained more detailed simulation results. However, for these 3D models, the flow field was assumed to have a uniform thickness and the same outflow location as the 2D model, which is not quite consistent with the actual structure. In terms of theoretical exploration, Dhinesh [9] and other scholars [17, 18, 19, 20] built flow and pressure analytical equations based on throttling theory, which were different from the phenomenon of simulation. Assuming that the jet was submerged and that the flow in the receiver was a piston, Li [5] made progress in the theoretical description of the receiver flow pattern. On the basis of the jet wall attachment theory, Yan et al. [21] modelled the flow distribution in the deflector analytically. Then Yan et al. [22, 23] applied the impact jet theory to the description of the DJV’s two jets and proposed an integrated theoretical model. With regard to experimental research, Li [24] established a visualized DJV jet prototype.

To sum up, the method for theoretical exploration of the DJV is shifting from throttling theory to jet theory, and the 2D numerical model is being replaced by a 3D one. However, the experimental results hardly conform to theoretical calculations and simulations. Specifically, the receiver pressure from simulation and theoretical calculation is always lower than the experimental values. Therefore, for the prestage pressure gain, it is very difficult to obtain consistent results in calculations, simulations, and experiments. To solve these issues and attain a better description of the DJV internal flow characteristics, a 3D numerical model with consideration of the return flow along the force feedback rod was built. Meanwhile, two essential assumptions were presented for modification of the theoretical model. Finally, an experiment on the receiver pressure was performed to verify the above theoretical and simulated analyses.

## 2 Theoretical Description of DJV

### 2.1 DJV Prestage Jet Process

### 2.2 Velocity Distribution of the First Jet

*u*

_{0}= 178.2 m/s.

Values of the DJV parameters

Parameter | Value |
---|---|

First jet half-width | 7.498 × 10 |

Second jet half-width | 7.012 × 10 |

Inflow width | 1.147 × 10 |

Shunt wedge width | 1.09 × 10 |

Receiver width | 1.9 × 10 |

Inflow angle | 13 |

Sidewall’s inclination angle | 16.5 |

Hydraulic oil density | 847 |

Initial pressure | 21 |

Jet back pressure | 3.1 |

Gravity acceleration | 9.8 |

Deflector’s distance | 8.84 × 10 |

Second jet height | 1.95 × 10 |

In the simulation result, the velocity of the fluid rises with increase of its distance from the inner wall at the rate of 2.25 (m/s)/μm. To ensure that the average velocity is equal to the calculated value *u*_{0}, it is convenient to learn that the initial width of the core area 2*b*_{1} = 0.12 mm and that the velocity in the core area *u*_{1} = 195 m/s. Therefore, different from traditional opinion, the initial width of the core area is less than the jet’s width.

### 2.3 Stagnation Point in the Deflector

*x*

_{f}is the deflector displacement. Then, according to Eqs. (13)‒(18), we can obtain the stagnation point’s location with the result that

*x*

_{r}= 0.57 mm, when

*x*

_{f}is zero.

### 2.4 Stagnation Point in the Deflector

*p*

_{s}is the stagnation point’s pressure on the impact surface,

*b*

_{p}is the distribution pressure’s Eigen half width, and \(\lambda\) is the distribution coefficient.

*p*

_{s}can be described as

*p*

_{s}= 15.1 MPa. Meanwhile, referring to the simulation results, we can determine that

*b*

_{p}= 0.05 mm and \(\lambda = 0.833\). Then the pressure distribution on the impact surface can be computed using Eq. (23).

*x*

_{f}is the deflector displacement, and it is positive when the deflector moves to the right. The receiver pressures for different deflector displacements are listed in Table 2.

Receiver pressures for different deflector displacements

Displacement (mm) | Left receiver (MPa) | Right receiver (MPa) |
---|---|---|

0.04 | 2.8 | 8.6 |

0.03 | 3.0 | 7.0 |

0.02 | 3.3 | 5.8 |

0.01 | 3.7 | 4.9 |

0 | 4.2 | 4.2 |

− 0.01 | 4.9 | 3.7 |

− 0.02 | 5.8 | 3.3 |

− 0.03 | 7.0 | 3.0 |

− 0.04 | 8.6 | 2.8 |

If the deflector has no offset, the two receivers have the same pressure, which is referred to as the balance pressure \(p_{r}\), which will be an important parameter for evaluating the accuracy of the theoretical model. According to Eq. (26), we learn that *p*_{r} = 4.2 MPa.

Unfortunately, it is noticed that the balance pressure \(p_{r}\) is always much lower than the experimental data, which is a problem that has plagued researchers for a long time. Moreover, the prestage pressure gain is calculated based on the receiver pressure, so a large error is caused.

## 3 Three-dimensional Numerical Simulation

### 3.1 Flow Distribution of the 3D Simulation

Because the structure of the deflector valve is very small and complex, in order to explore the internal flow pattern, explain the inaccuracy of the theoretical model, and modify the theoretical model, the numerical simulation needs to show the detailed features of the flow field intuitively.

*k*-

*ε*turbulent model, the 3D flow field was simulated and it was ensured that all the residuals were less than 10

^{−5}. Boundary conditions are shown in Table 3, and the simulation parameters are given below. The hydraulic diameters of the inlet and the outlet are 1.15 mm and 1.03 mm, and the turbulence intensity is 10%. In order to improve the precision of calculation, the second-order upwind was selected in the simulation. Figure 13 displays the velocity vectors of the flow field and clearly describes the flow pattern of the first jet, the second jet, and the impact jet near the receivers.

Boundary conditions

Parameter | Value |
---|---|

Oil density (kg/m | 849 |

Viscosity (kg/(m·s)) | 0.01026 |

Inlet pressure (MPa) | 21 |

Outlet pressure (MPa) | 3.1 |

Comparison of the balance pressures

Parameter (MPa) | Value |
---|---|

Experimental result | 5.6 |

Theoretical calculation | 4.2 |

2D simulation calculation | 4.8 |

3D simulation calculation | 5.3 |

Therefore, compared with 2D numerical simulation and previous calculations, the new 3D numerical model has a more accurate result for the balance pressure, which can prove the validity of this numerical model to a certain extent.

### 3.2 Discussion on the Flow Pattern

Therefore, the flow in the deflector jet structure can be divided into the six phases shown in Figure 20. Phase 1 is the forward flow, which starts from the inlet and passes through the deflector. Phase 2 is the return flow after impacting the deflector, which means that the oil returns to back pressure zones on both sides after the second jet. Phase 3 is defined as entrainment flow. The first jet leads to the entrainment effect, causing the oil in the back pressure zone to flow to the inlet through the gap. Phase 4 is the spiral flow, by which the oil in the deflector finishes the spatial movement perpendicular to the central section. Phase 5 is the free flow in the back pressure zone, which has a random trajectory. Last, Phase 6 is departing flow, by which the oil leaves the structure and returns to the outflow interface. These six phases can be used to accurately describe the flow pattern in the deflector valve. However, with 2D simulation, only Phases 1 and 2 can be simulated properly. Remarkably, with regard to Phase 3, the 2D simulation shows the opposite flow direction. Therefore, the 3D simulation has much better credibility and the 2D simulation defects are identified.

## 4 New Assumptions and Modification of the Theoretical Model

### 4.1 Assumption of the Jet Core Length

*x*

_{r}= 0.624 mm, which shows that the stagnation point has a downward shift after the modification. In the meantime, Eq. (19) is modified as

Then the modified deflector outlet velocity can be computed again, with the result that \(u^{\prime}_{0} = 164.9\;{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. \kern-0pt} {\text{s}}}\). Thus, the second jet’s velocity increases after the modification.

### 4.2 Assumption of Receivers Effective Working Length

### 4.3 Calculation after Modification

Receiver pressures after modification

Displacement (mm) | Left receiver (MPa) | Right receiver (MPa) |
---|---|---|

0.04 | 3.9 | 10.3 |

0.03 | 4.1 | 8.7 |

0.02 | 4.5 | 7.3 |

0.01 | 4.9 | 6.3 |

0 | 5.5 | 5.5 |

− 0.01 | 6.3 | 4.9 |

− 0.02 | 7.3 | 4.5 |

− 0.03 | 8.7 | 4.1 |

− 0.04 | 10.3 | 3.9 |

## 5 Experiment and Comparative Analysis

Experimental results

Displacement (mm) | Left receiver (MPa) | Right receiver (MPa) |
---|---|---|

0.04 | 3.5 | 9.8 |

0.03 | 3.8 | 8.5 |

0.02 | 4.2 | 7.0 |

0.01 | 5.0 | 6.4 |

0 | 5.6 | 5.6 |

− 0.01 | 6.4 | 5.1 |

− 0.02 | 7.0 | 4.3 |

− 0.03 | 8.5 | 3.9 |

− 0.04 | 9.8 | 3.4 |

The experimental results show that when the deflector is in the central position, the pressure of the receiver is 5.6 MPa, which is closer to the theoretical calculation result (5.5 MPa) and the 3D simulation result (5.3 MPa). Thus, it can be deduced that this 3D numerical simulation is credible and that the new assumptions based on the 3D simulation are reasonable.

The experimental results show that when the deflector is in the central position, the pressure of the receiver is 5.6 MPa, which is closer to the theoretical calculation result (5.5 MPa) and the 3D simulation result (5.3 MPa). Thus, it can be deduced that this 3D numerical simulation is credible and that the new assumptions based on the 3D simulation are reasonable.

By comparing the theoretical calculation with the experimental data, it was learned that the modified theoretical model matches the experimental data well, especially when the deflector works near zero position, as illustrated in Figure 25. Moreover, Figure 26 describes two receivers’ pressure difference characteristics. In fact, it seems that the modification of the theoretical model has little effect on the pressure difference characteristics, but the modified model greatly improves the computational accuracy of the pressure gain, as shown in Figure 27. Accordingly, the modification is of great significance for modeling the servo valve.

## 6 Conclusions

- (1)
The analysis revealed that the fluid near the shunt wedge cannot resist the impact of high-speed fluid, so the assumption of the effective working length is suitable for the theoretical calculations. Because the real spatial flow in the deflector is more open, a longer core area should be given in the theoretical model.

- (2)
The receiver’s pressure in the 3D simulation reaches 5.3 MPa, which is clearly higher than the 2D simulation result. This means that the actual energy loss from internal flow is much less than in the traditional view, because there is no significant reflux for the first jet.

- (3)
Different from the traditional simulated 2D flow, the 3D simulation shows that the actual flow in the deflector jet valve is a complex spatially and involves six flow phases. This discovery is favorable for understanding the complexity of the DJV’s flow pattern.

## Notes

### Authors’ Contributions

HY was in charge of the whole trial and wrote the manuscript; YR did the numerical simulation of the deflector valve’s flow field; LY built the mathematical model of the deflector valve; LD plotted graphs. All authors read and approved the final manuscript.

### Authors’ Information

Hao Yan, born in 1979, is currently an Associate Professor at *School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, China*. He received his PhD degree from *Harbin Institute of Technology, China*, in 2007. His research interests include mechatronics and hydraulic valves.

Yukai Ren, born in 1989, is currently a PhD candidate at *School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, China*. He received his master degree from *North University of China, China*, in 2015. His research interests include electro-hydraulic servo valve and fluid simulation and calculation.

Lei Yao, born in 1991, is currently a master candidate at *School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, China*. He received his bachelor degree from *Hebei Agricultural University, China*, in 2016. His research interests include electro-hydraulic servo valve.

Lijing Dong, born in 1988, is currently holding a postdoc position at *School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, China*. She received her Ph.D. degree from the *School of Automation, Beijing Institute of Technology, China*, in 2016. Her research interests include hydraulic control systems and distributed control systems.

### Competing Interests

The authors declare that they have no competing interests.

### Funding

Supported by National Natural Science Foundation of China (Grant No. 51775032) and Foundation of Key Laboratory of Vehicle Advanced Manufacturing, Measuring and Control Technology, Beijing Jiaotong University, Ministry of Education, China.

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