Analysis of pressure characteristics under laminar and turbulent flow states inside the pilot stage of a deflection flapper servo-valve: Mathematical modeling with CFD study and experimental validation

Electro-hydraulic servo-valves are widely used components in the mechanical industry, aerospace and aerodynamic devices which precisely control the airplane or missile wings. Due to the small size and complex structure in the pilot stage of deflection flapper servo-valves, accurate mathematical models for the flow and pressure characteristics have always been very difficult to be built. In this paper, mathematical models for the pilot stage of deflection flapper servo-valve are investigated to overcome some gaps between the theoretical formulation and overall performance of the valve by considering different flow states. Here, a mathematical model of the velocity distribution at the flapper groove exit is established by using Schlichting velocity equations for in-compressible laminar fluid flow. Moreover, when the flow becomes turbulent, a mathematical model of pressure characteristics in the receiving ports is built on the basis of the assumption of the collision between the liquid and the jet as the impact of the jet on a moving block of fluid particles. To verify the analytical models for both laminar and turbulent flows, the pressure characteristics of the deflection flapper pilot stage are calculated and tested by using numerical simulation and experiment. Experimental verification of the theory is also presented. The computed numerical and analytical results show a good agreement with experimental data.