Modeling water hammers via PDEs and switched DAEs with numerical justification. Issue 1 (July 2017)

• Record Type: Journal Article
• Authors: Kall, Jochen; Kausar, Rukhsana; Trenn, Stephan
• Is Part Of: IFAC-PapersOnLine. Volume 50:Issue 1(2017)
• Page Start: 5349
• Page End: 5354
• Publication Date: 2017-07
• Subjects: water distribution networks -- water hammer -- compressible flow -- switched DAEs -- Dirac impulses; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2017.08.927
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: In water distribution networks instantaneous changes in valve and pump settings may introduces jumps and peaks in the pressure. In particular, a well known phenomenon in response to the sudden closing of a valve is the so called water hammer, which (if not taken into account properly may destroy parts of the water network. It is classically modeled as a system of hyperbolic partial differential equations (PDEs). After discussing this PDE model we propose a simplified model using switched differential-algebraic equations (DAEs). Switched DAEs are known to be able to produce infinite peaks in response to sudden structural changes. These peaks (in the mathematical form of Dirac impulses) can easily be predicted and may allow for a simpler analysis of complex water networks in the future. As a first step toward that goal, we verify the novel modeling approach by comparing these two modeling techniques numerically for a simple set up consisting of two reservoirs, a pipe and a valve.