Analysis and Stability of Closed Surge Tanks

The stability of closed surge tanks (tanks with compressed air at the top) is investigated using the phase plane method, which allows inclusion of nonlinear effects in the analyses. All singularities are analyzed and stability criteria are developed. Phase portraits are plotted using the method of isoclines. Six numerical techniques for integrating the governing equations are compared. The effect of the value of the polytropic gas constant on the surge amplitudes is investigated. Several important conclusions are: (1) For the stability of large oscillations, it is neither necessary to provide more tank area than critical area, as is presently done, nor to satisfy the second stability condition presented earlier by the writers; (2) the damping rate of oscillations is higher if the limit on the maximum gate opening is included in the analysis; (3) presently used first‐order methods for numerically integrating the governing equations may yield incorrect and sometimes unstable results; (4) the second‐order modified Euler method yields results comparable to higher‐order methods, and is recommended for practical applications; and (5) the polytropic gas law exponent, n, equal to unity (isothermal behavior) produces a larger amplitude of water surface oscillation than n=1.4(adiabatic).