LARGE-AMPLITUDE OSCILLATIONS IN CLOSED SURGE CHAMBER

The governing equations for surge oscillations in a closed surge chamber yield a second-order nonlinear differential equation for constant power. The surge stability is investigated by the direct method of Liapunov, which introduces the Liapunov function from the energy consideration. The nonlinear terms arising from large surges are included. The resulting stability criterion is demonstrated on a phase plane. For the equilibrium point of practical interest, the stability diagram specifies domains of asymptotic stability as a function of the safety factor of the surge-chamber. The diagram indicates that large-amplitude surges necessitate larger chamber size than that laid down by Svee for damping and the surge stability deteriorates with downward oscillations. By postulating sinusoidal surge motion, the critical chamber area is equal to the product of the critical area in case of small oscillations (Svee's formula) and a factor greater than 1.0. The factor is a function of surge amplitude and air cushion parameters for given turbine head. Stability criteria for open surge tanks can be obtained as special cases of those for closed ones.