Water hammer mitigation via PDE-constrained optimization
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This paper considers an optimal boundary control problem for ?uid pipelines with terminal valve control. The goal is to minimize pressure ?uctuation during valve closure, thus mitigating water hammer effects. We model the ?uid ?ow by two coupled hyperbolic PDEs with given initial conditions and a boundary control governing valve actuation. To solve the optimal boundary control problem, we apply the control parameterization method to approximate the time-varying boundary control by a linear combination of basis functions, each of which depends on a set of decision parameters. Then, by using variational principles, we derive formulas for the gradient of the objective function (which measures pressure ?uctuation) with respect to the decision parameters. Based on the gradient formulas obtained, we propose a gradient-based optimization method for solving the optimal boundary control problem. Nu- merical results demonstrate the capability of optimal boundary control to signi?cantly reduce pressure ?uctuation.
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Chen, T.; Xu, C.; Lin, Qun; Loxton, Ryan; Teo, Kok Lay (2015)This paper considers an optimal boundary control problem for fluid pipelines with terminal valve control. The goal is to minimize pressure fluctuation during valve closure, thus mitigating water hammer effects. We model ...
Chen, T.; Ren, Z.; Xu, C.; Loxton, Ryan (2015)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 ...
Ren, Z.; Xu, C.; Lin, Qun; Loxton, Ryan (2015)This paper proposes a new control synthesis approach for the stabilization of boundary-controlled parabolic partial differential equations (PDEs). In the proposed approach, the optimal boundary control is expressed in ...