Analytical Approaches To Modeling Transient Vaporous Cavitation in Multi-Pipe Fluid Systems
AFT Impulse™ Technical Paper
Authors: Trey Walters, P.E., Applied Flow Technology, USA
Published in Chemical Engineering, January 2000
ABSTRACT
The formation of vapor cavities in piping systems experiencing column separation during liquid transient flow is of engineering interest because of the very high transient pressures that can occur when the vapor cavities collapse. Several approaches have been proposed for modeling vaporous cavitation in single-pipe fluid systems.
One approach for modeling this phenomenon is the Vaporous Cavitation Model (VCM). The VCM method for a single-pipe system is described by Streeter (1972) and amplified by Wylie and Streeter (1983). In order to model vaporous cavitation in a complex multi-pipe system, analytical expressions are required for the fluid connecting elements that join the pipes together. Although the VCM method has been used for many years, it is difficult to find descriptions in the open literature of how the VCM method is applied to common fluid system connecting elements.
This paper describes how the VCM method was applied at General Dynamics Space Systems Division.
CONCLUSION
The Vaporous Cavitation Model can be applied to a number of fluid
system connecting elements often found in multi-pipe systems. The same limitations that have been identified for single-pipe applications also affect models of multi-pipe systems. However, reasonable agreement can be demonstrated with available data, even though some cavities grow much larger than considered permissible. Peak pressure predictions are shown to agree well with the data, and the major features of the flow are predicted by the model.
Additional experiments for complicated fluid systems with vaporous cavitation are required to explicitly verify the models developed in this paper. However, the basic approach of the VCM method is well understood, and the consistent application of the VCM method to multi-pipe fluid elements is a relatively straightforward extension of the method.
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Introduction
The formation of vapor cavities in piping systems experiencing column separation during liquid transient flow is of engineering interest because of the very high transient pressures that can occur when the vapor cavities collapse. Several approaches have been proposed for modeling vaporous cavitation in single-pipe fluid systems. One approach for modeling this phenomenon is the Vaporous Cavitation Model (VCM).
The VCM method for a single-pipe system is described by Streeter (1972) and amplified by Wylie and Streeter (1983). In order to model vaporous cavitation in a complex multi-pipe system, analytical expressions are required for the fluid connecting elements that join the pipes together.
Although the VCM method has been used for many years, it is difficult to find descriptions in the open literature of how the VCM method is applied to common fluid system connecting elements. This paper describes how the VCM method was applied at General Dynamics Space Systems Division.
SINGLE-PIPE VCM METHOD
The starting point for any investigation of column separation begins
with the basic equations of waterhammer (Wylie, 1984a). These equations consist of two partial differential equations that are derived from the continuity and one-dimensional momentum equation. When applied to a stiff liquid-filled pipe, the equations are expressed as shown in the paper.
The method of characteristics is then used to reduce the equations to
a series of four ordinary differential equations (Streeter, 1972, and Wylie and Streeter, 1983). Finite difference techniques reduce the equations further to algebraic form, which allows solution by digital computer. When written in difference equation form, two unknowns are left to be determined after selection of the distance and time computation steps. The two unknowns, piezometric head and volumetric flowrate are determined for pipe section i at time P from the equation as shown in the paper.