Finite Difference Methods for solving hydraulic behaviour equations of
the surge tanks
Abstract
In this paper, the hydraulic behaviour of different types of surge tanks
is modelled and solved using four different types of the Finite
Difference Method. Water hammer is one of the most important phenomena
in hydraulic systems. Surge tank is one of the most important devices
used to reduce damages of this phenomenon. Here, the equations of
hydraulic behaviour of simple, orifice and closed surge tank are derived
at with or without friction condition in both gradually and suddenly
valve closing. The Explicit Euler, Implicit Euler, Predictor-Corrector
Euler and forth order Rung-Kutta methods are used to solve these
hydraulic equations and the results are presented and compared.
Comparison of the results show that the value ranges of fluid level
oscillation at with friction condition is smaller than those at without
friction condition using all proposed methods at both suddenly and
gradually valve closing. Furthermore, for all types of surge tanks' at
all different considering conditions, the smallest ranges of fluid level
oscillation are obtained when the Implicit Euler is used. In addition,
by using Implicit Euler method the fluid level oscillation converges
faster than the other methods. Moreover, fluid level oscillations are
unsteady for simple and closed surge tank at without friction condition
in both gradually and suddenly valve closing using Explicit Euler and
Predictor-Corrector Euler. However, other obtained fluid level
oscillations are steady.