A Numerically Validated Approach to Modeling Water Hammer Phenomena Using Partial Differential Equations and Switched Differential-Algebraic Equations

Abstract

Water distribution networks are susceptible to abrupt pressure fluctuations and spikes due to rapid adjustments in valve and pump settings. A common occurrence resulting from the sudden closure of a valve, known as water hammer, can potentially cause damage to various components within the network if not adequately addressed. Traditionally, water hammer phenomena have been modeled using a set of hyperbolic partial differential equations (PDEs). This study introduces a simplified model that employs switched differential-algebraic equations (DAEs). Recognized for their capacity to generate infinite peaks in response to sudden structural changes, switched DAEs provide mathematical representations of infinite peaks, manifested as Dirac impulses. This modeling approach offers the potential for more straightforward analyses of complex water networks in future research. To validate the proposed technique, a numerical comparison was conducted between the PDEand DAE-based models, using a basic configuration consisting of two reservoirs, a pipe, and a valve.