Hydrodynamic self-excited vibrations in leaking spherical valves with annular seal

Abstract

In hydraulic systems with large diameter pipes, such as the penstocks of hydro power plants, ball or spherical valves are frequently used because they are robust and, in closed state, they allow to obtain watertight closures even under high pressure jumps. To preclude water leakage between the internal rotary sphere and the casing, these valves have a metallic annular seal that can be tightened axially onto the ball, thus blocking the clearance. However during the last decades there have been several cases of violent vibrations developed in hydraulic systems that use that type of spherical valves, such as the Salime hydro power plant in Asturias (Spain). These vibrations happen to take place when the valves are closed, and are associated to the successive tapping of the annular seal against its seat on the ball. At the same time, large pressure fluctuations are induced in the piping as well as periodic leakage flow through the gap between seal and sphere. Since plant security requirements make these vibrations unacceptable, at the Salime hydro plant the problem was finally solved by installing an external pneumatic drive to strengthen the tightness of the seals. However, the nature of the vibration excitation and the conditions that originated it were still not understood, and so that encouraged the research of the present doctoral thesis.

The general purpose of this research has been to establish a simplified theoretical model for the hydraulic-mechanical system of interest, so that the model can reproduce the vibration excitation mechanism, simulate the transient behavior of the system as a function of the most relevant physical and geometrical parameters and advise on the conditions needed for safe operation without vibrations.

As a starting hypothesis, it was assumed that the vibration excitation only takes place if, due to manufacturing or mounting defects, the seal closure is not perfect and so there exists some initial leak flow. On that hypothesis a simplified physical-geometrical model was proposed to represent the flow-structure system of interest, which includes the penstock of the hydro station, the annular seal of the valve as a mobile structural element and an auxiliary pilot conduit to govern the tightness of the seal. The seal was modeled as a second order mechanical system subject to fluid-dynamic pressure forces, whereas each duct in the system was represented by the basic equations of continuity and energy conservation for 1D viscous unsteady flow, with incompressible and compressible flow versions. All this results in a closed system of non-linear differential equations with time-dependent variables such as the flow rate at each pipe section, the head energy at the nodes of the system and the displacement of the annular seal.

To begin with, the flow in the ducts was considered to be incompressible. After linearizing the equation system under the assumption of small amplitude harmonic disturbances around an equilibrium state, an algorithm for iterative resolution was elaborated that ultimately allows determining the frequency and the net damping of the coupled flow-structure system. According to this model, the development of high amplitude vibrations takes place when the net damping is negative, i.e., vibrations are self-excited and the underlying mechanism is a damping-controlled dynamic instability. For the second model, the flow in the pipes was considered to be subject to compressibility and pipe wall elasticity and so it was modelled with the usual equations in water hammer studies. In this case, a frequency domain formulation was chosen based on transfer matrices between nodes along the system piping. Again, the model allows to estimate the fluid-dynamic forces on the annular seal and to analyze the stability conditions for the coupled flow-structure system.

A dimensional analysis based on these models led to establish the non-dimensional parameters relevant in the phenomenon under study, which include ratios between mechanical energy, head loss and inertia head terms, ratios between geometrical variables, parameters involving the seal structural variables and, in the case of the compressible flow model, ratios between acoustic and mechanical variables. For both incompressible and compressible flow models, iterative resolution algorithms were designed and special computation programs were developed by means of the Matlab software. Computations were performed to characterize the dynamic behavior of the system and determine the critical conditions for stability under different configurations of the physical and geometrical parameters. As a whole, the results so obtained are consistent with the previous observations at the Salime hydro power plant on the vibration phenomenon, including the suppression of the vibrations when strengthening the seal tightness by external means. Therefore, it follows that the self-excitation mechanism implicitly assumed in the theoretical models can be considered correct. Besides, the results show that the compressibility of the medium and acoustic transmission can have a decisive effect on the fluid-dynamic forces on the seal and on the system stability; in the case of the Salime hydro plant, consideration of flow compressibility is necessary. In all cases, the operating range of the system under stability conditions was enlarged when increasing the hydraulic resistance of the pilot line, e.g. by means of a partially closed valve.