The subject of this monograph is the fluid dynamics of liquid turbomachines, particularly pumps. Rather than attempt a general treatise on turbomachines, we shall focus attention on those special problems and design issues associated with the flow of liquid through a rotating machine. There are two characteristics of a liquid that lead to these special problems, and cause a significantly different set of concerns than would occur in, say, a gas turbine. These are the potential for cavitation and the high density of liquids that enhances the possibility of damaging unsteady flows and forces.

/pdf/hydrodynamics-of-pumps-10hab8zdsk.pdf

Hydrodynamics of Pumps

http://link.springer.com/content/pdf/10.1007/978-3-642-81528-7_1.pdf

Flow-Induced Vibrations in Nuclear Reactors and Heat Exchangers

An analytical method for computing unsteady flow conditions in liquid-filled fluid systems is developed. The method, termed 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 partly transmitted and reflected at each discontinuity. The velocity change caused by each pressure pulse is obtained from the Joukowsky relationship. 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.

Closure of "Wave-Plan Analysis of Unsteady Flow in Closed Conduits"

Surge wave characteristics for hydropower station with upstream series double surge tanks in load rejection transient

Modeling and validation of pressure propagation in drilling fluids pumped into a closed well

When the velocity of flow in a steady-state system is altered at any cross section, an hydraulic transient is initiated. The alteration of velocity requires that an un­ balanced pressure impulse be applied, which is· transmitted through the system at the acoustic speed a of the liquid in the system. The magnitude of the pressure pulse may be attenuated due to the action of fluid friction, or it may be changed due to changes in cross-sectional area of the conduit. For a frictionless liquid in a horizontal, prismatic, elastic tube, the application of a pressure differential Ap would result in a change in liquid velocity Av given by Ap = pa Av. in which p is the density. This Av and Ap would be transmitted unchanged throughout the length of the tube at speed a. This relation is a consequence of the impulse-momentum principle. The acoustic speed is determined by the bulk modulus of the liquid, Young's modulus for the pipe wall material, pipe wall thickness, pipe diameter, and method of supporting the pipe. An additional complication is that the bulk modulus of the liquid changes greatly with very small amounts of entrained gases or air. In the simple case of a reservoir, a pipe of length L. and a downstream valve, we can see how pressure waves are transmitted and reflected through the system. If the frictional effects are neglected and the valve is suddenly closed during a steady uniform flow of velocity Vo. the pressure suddenly jumps by Ap = paVo' This wave travels upstream, bringing the velocity to zero and raising the pressure by Ap. At instant L/a. the liquid in the pipe is at rest, the pipe diameter is enlarged, and the liquid is compressed. An unbalanced force exists on the segment of liquid at the upstream end of the pipe, causing it to be set in motion with speed Vo upstream and causing the pressure to drop to reservoir pressure. This wave arrives at the valve at 2L/a sec, at which time all the liquid is moving upstream at speed Vo. with pressure throughout at reservoir pressure. An un­ balanced condition exists at the closed valve, however, as the liquid cannot move away from the valve without causing a drop in pressure. In fact (if the transient isn't too strong and vapor pressure is not attained), the layer of liquid at the gate is held at zero velocity by a drop in pressure at the gate. This pressure drop

E. B. Wylie

Papers

Waterhammer and Surge Control