Author(s): B. Petry; R. K. Gupta
Linked Author(s): Bela Petry
Keywords: Pressure surges; Analysis; Control; Pipe network; Transient design; Slowtransients; Optimal valve operation
Abstract: The problem of analysis and control of surges in a pipe network is of considerable significance and finds many applications in engineering practice. Analysis of a system for prescribed transient behaviour of some components and design of other components to meet specifications can be termed transient synthesis. Mathematical formulation of such problems in a comprehensive and physically meaningful way is often neither apparent nor straightforward. The problem of solvability of resulting models is dependent on the manner in which design parameters and corresponding boundary specifications are distributed over the network. In this paper, a general treatment is given and the formulation is presented for an arbitrary network. Formulation of the problem is based on graph-theoretic concepts. Possible boundary conditions are considered by categorising these into five element types. Necessary and sufficient conditions for the existence and uniqueness of a solution, which are important for an effective modelling of these problems, are also stated. Among other advantages, the algorithm provides an automatic separation of dependent and independent variables and results in a minimum set of independent variables for the numerical solution of the problem. Moreover, valve operation rules are calculated explicitly as valve openings are treated as dependent variables. The principle behind the methodology developed in this paper is that transient behaviour in some components of the system is specified and some other components are kept undetermined and to be designed in order to meet the imposed specifications. Analysis of the system directly yields the transient behaviour of these components, which are then accordingly designed. Application of this methodology is illustrated by an example. Valve operations are determined from direct analysis to satisfy imposed specifications. In general, the algorithm is found to be useful for transient design of other components of hydraulic networks such as surge tanks, conveyance elements.
Year: 1999