Optimal boundary control for water hammer suppression in fluid transmission pipelines

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.

Water hammer mitigation via PDE-constrained optimization

“…For numerical testing, we implemented three solution methods in MATLAB: the new CP-PDE approach described in Sections 2 and 3, the previous CP-ODE approach described in Chen et al (2015), and the particle swarm optimization (PSO) method described in Montalvo, Izquierdo, Pérez, and Tung (2008). These MATLAB implementations use ODE23 to solve the differential equations.…”

“…Our test scenario is based on a 200 m stainless steel pipeline connected to a reservoir of height 20 m (Chen et al, 2015;Zhao, Zhang, Zhao & Dong, 2009). The corresponding parameters in the PDE model (1) (7), since once the valve is fully closed, the pressure along the pipeline is the same as the pressure generated by the reservoir.…”

“…Mitigation strategies for water hammer are numerous and here we refer to just a few, such as those for oil pipelines (Xu, Dong, Ren, Jiang, & Yu, 2015), air compressor pipelines (Lee & Ngoh, 2002), spacecraft propulsion systems (Lecourt & Steelant, 2007), heat exchange systems in nuclear reactors (Erath, Nowotny, & Maetz, 1999;Tian, Su, Wang, Qiu, & Xiao, 2008) and even cardiovascular flow in human blood vessels (Pedley, 1980). This paper models water hammer mitigation by an optimal boundary control problem governed by hyperbolic PDEs (Chen, Ren, Xu, & Loxton, 2015). We consider the benchmark pipeline system shown in Fig.…”

“…In Chen et al (2015), we developed a discretize-then-optimize computational approach for solving Problem P 0 . This approach involves first using the finite-difference method to approximate the PDE model (1)-(3) by a system of ODEs, then applying control parameterization (Teo, Goh, & Wong, 1991) to approximate the boundary control by a piecewise-linear or piecewise-quadratic function.…”

Fail-safe design and analysis for the guide vane of a hydro turbine

“…Generally, waterhammer occurs when the fluid flowing through the penstock is forced to suddenly stop or change direction. 13 Specifically, it occurs when the guide vanes close as soon as possible to avoid a sudden increase in the rotation speed of the hydro turbine due to disconnection of electric power.…”