Wave-Plan Analysis of Unsteady Flow

An analytical method for computing unsteady flow conditions in liquid-filled flow systems is developed. The method which is called the wave plan incorporates distributed parameter and nonlinear effects including the effects of viscous resistance. The wave plan is essentially a solution synthesized from the effects of incremental step pressure pulses. The pressure pulses are generated because of incremental flow-rate changes that originate in a hydraulic system from a variety of sources, including the mechanical motion of the system structure. The pressure pulses propagate throughout the system at sonic velocity and are partially transmitted and reflected at each discontinuity. The velocity change caused by each pressure pulse is obtained from the Joukowski relation. Pressure and velocity time histories at any point in the system are obtained by a timewise summation of the contributions of the incremental pressure pulses passing that point. The analysis is presented in a form general enough to be applied to a variety of hydraulic systems. To illustrate the application of the method to a specific system, the response of a straight hydraulic line to a sinusoidal orifice-area variation of an upstream valve is computed. Both a constant-cross- section line and a tapered line are analyzed in the examples, and various nonlinear effects evaluated. Comparisons are carried out with experimental data obtained for the constant-diameter line and good agreement is shown to exist.