On delay-partial-differential and delay-differential thermal models for variable pipe flow

TL;DR

This paper introduces a novel thermal model for variable pipe flow that combines delay systems and PDEs, offering a more accurate representation of heat transfer with practical approximation methods.

Contribution

It develops a delay-partial-differential equation model for pipe thermal dynamics, linking delay systems with PDEs, and demonstrates its effectiveness through simulations and experiments.

Findings

The model accurately captures thermal behavior in variable pipe flow.

Finite-dimensional approximation yields a generalized delay-differential equation.

The proposed approach outperforms traditional models in simulations and experiments.

Abstract

A new formulation of physical thermal models for variable plug flow through a pipe is proposed. The derived model is based on a commonly used one-dimensional distributed parameter model, which explicitly takes into account the heat capacity of the jacket of the pipe. The main result of the present contribution is the constitution of the equivalence of this model with a serial connection of a pure delay or transport system and another partial differential equation (PDE), subsequently called delay-partial-differential equation (DPDE)-model. The means for obtaining the proposed model comprise operational calculus in the Laplace domain as well as classical theory of characteristics. The finite-dimensional approximation of the DPDE-model leads to a delay-differential equation (DDE)-system, which can be seen as a generalization of commonly used DDE-models consisting of a first-order low-pass filter subject to an input delay. The proposed model is compared to several alternative models in simulations and experimental studies.