The flow model of the overlap spool valve considering the transition between laminar and turbulent flow

It remains uncertain whether the flow state at the spool valve is laminar or turbulent under small openings. The annular slit flow and the damping hole flow are proposed to be equated to model the spool valve flow. The mutual transition criterion between laminar and turbulent flows is developed. The results indicate that the flow turns from transitional flow to turbulence as the valve opening increases to 5.2 μm. The flow coefficient increases linearly in transitional flow and remains constant in turbulence. Laminar flow may occur when the annular gap's length exceeds 9.45 μm. The effect of structural parameters including overlap, radial clearance, wear fillet, and temperature on flow transition is discussed. Wear on the valve port counteracts the positive overlap. Flow gain continues to rise, pressure gain increases and then falls, reaching a maximum of 5 × 10¹² Pa/m. Valve performance exhibits a brief ramp-up time. The theoretical model and analysis aim to elucidate the flow characteristics and performance evolution of the spool valve.