# Modeling of Closing Functions for Gate Valves Fitted with V-Ports

Michał Kubrak

Hydraulic transient analysis through numerical simulations is a widely used tool for predicting and mitigating potential severe pressure oscillations due to abrupt changes in flow velocity. In practice, water hammer events typically are induced by valve operations used to control the flow rate. One of the methods to enhance the throttling capabilities of a gate valve is to install a V-shaped notch (V-port) in its opening. This provides a more linear relationship between the position of the gate and the flow rate discharging through the valve. The exact range of the flow control is determined by the V-port opening angle. Because valve-induced pressure oscillations depend on the valve characteristics, in order to accurately simulate the transient event, the specific valve closing function is required. The primary objective of this paper was to develop valve closing functions of V-port gates for all possible opening angles. Two cases were considered: the linear closure of a knife (rectangular) and a circular gate fitted with a V-port. For this purpose, the analytical formulas for calculating the relative opening area of V-shaped gate valves were derived. On this basis, valve closing functions, in the form of a power function with two variables, were developed. To analyze the influence of the V-port angle on a simulated transient event, a case study with a simple reservoir–pipeline–valve system was investigated. One-dimensional unsteady flow equations were solved using the method of characteristics. The numerical calculations conducted indicate that installing a V-notch port can result in a smoother reduction of the flow rate as the gate closes, which may dampen both maximum and minimum pressure peaks and attenuate valve-induced pressure head oscillations. The developed valve closing functions offer practical utility for practitioners engaged in hydraulic system design and operation, providing a tool for predicting hammer events induced by valve gates fitted with V-ports.

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