# A Model-Based Investigation of the Performance Robustness of the Deflector Jet Servo Valve
###### Abstract
Current studies are focused on numerical research to explore the flow characteristics of DJV [8; 9]. Remarkably, with the standard k-\(\varepsilon\) model employed, a RANS-based simulation was performed by [PERSON], who discovered that the pressure difference between the two receivers in the simulation is significantly lower than the experimental data [10], which implied possible imperfection of this methodology. Still, the RANS simulation following two-dimensional modeling has become prevalent in investigating the effect of internal parameters, external conditions, and manufacturing techniques on the DJV [11; 12; 13]. In recent years, with the development of new three-dimensional numerical models, the flow distribution in the DJV was formulated in more detail [14] and the cavitation situation was analyzed [15]. In these studies, the RNG k-\(\varepsilon\) model was considered as a rational alternative to DJV simulation. Further, a three-dimensional simulation with consideration of the flow along the force feedback rod in actual scenarios was conducted, obtaining a higher receiver pressure but almost no cavitation, which represented stability beyond previous expectations [16]. However, according to two-phase flow simulations, some researchers still think that the cavitation phenomenon exists in the DJV [17]. Currently, the actual condition of the DJV cannot be well learned from experiments. To ultimately understand the internal mechanism of jet-type servo valves, people have attempted to establish theoretical models. Based on a throttling assumption, the flow rate and the pressure in the receivers of the jet pipe valve were first expressed theoretically [2; 18]. Additionally, then, this assumption was applied to the modeling of the DJV [19]. However, some researchers put forward a novel assumption; that is, the fluid in the receiver of the DJV was taken as a piston, deriving new pressure expressions [5; 20]. Moreover, as a two-stage servo valve, the first-stage flow of DJV was modeled while ignoring the pressure drop in the control stage [21]. In research conducted prior to this paper, a theoretical model based on the jet impact assumption was built [22] and the wall attachment effect in the DJV was discussed [23]. Then, a modification of the effective impact-sustaining length of the receiver was proposed to correct the calculation of the pressure gain [16]. In addition, the reflection pattern of the jet was also utilized for researching the pressure-generation mechanism in the receiver [24]. In summary, in comparison with emerging three-dimensional numerical simulations, relevant theoretical research still stays in the two-dimensional world on account of the complexity of the hydraulic amplifier. Using the two-dimensional free jet theory to describe the turbulent velocity distribution [25]. For a rectangular jet orifice of the DJV, the jet's extensive features in the direction of jet-pan thickness cannot be described. Furthermore, the velocity and pressure distribution differences in different regions of the pilot's hydraulic amplifier are ignored. It follows that the mathematical model cannot comprehensively explain the phenomena reflected in CFD simulation and cannot give a correct prediction of the performance. As a consequence of that, research on the performance robustness of DJVs is rather lacking. Hence, a theoretical model with consideration of the third dimension is established in this paper. With a series of assumptions presented and jet nonlinear expansion considered, the spatial distribution of the flow velocity and pressure is formulized to unveil the subtle operation mechanism so that the analytical expressions of the receiver pressure and the pressure gain can be acquired. Additionally, then, numerical simulations and experiments are carried out to verify the validity of the proposed model.