Optimal Boundary Control for Water Hammer Suppression in Fluid Transmission Pipelines

TL;DR

This paper develops an optimal boundary control approach using nonlinear PDE modeling and numerical optimization to effectively suppress water hammer phenomena in pipeline systems, reducing pressure fluctuations.

Contribution

It introduces a novel boundary control framework for water hammer mitigation based on PDE modeling, control parameterization, and nonlinear optimization techniques.

Findings

Optimal boundary control significantly reduces pressure fluctuations.

Simulation results validate the effectiveness of the control method.

The approach can be implemented with standard nonlinear optimization tools.

Abstract

When fluid flow in a pipeline is suddenly halted, a pressure surge or wave is created within the pipeline. This phenomenon, called water hammer, can cause major damage to pipelines, including pipeline ruptures. In this paper, we model the problem of mitigating water hammer during valve closure by an optimal boundary control problem involving a nonlinear hyperbolic PDE system that describes the fluid flow along the pipeline. The control variable in this system represents the valve boundary actuation implemented at the pipeline terminus. To solve the boundary control problem, we first use {the method of lines} to obtain a finite-dimensional ODE model based on the original PDE system. Then, for the boundary control design, we apply the control parameterization method to obtain an approximate optimal parameter selection problem that can be solved using nonlinear optimization techniques such as Sequential Quadratic Programming (SQP). We conclude the paper with simulation results demonstrating the capability of optimal boundary control to significantly reduce flow fluctuation.