Unified 1D Dynamic Modelling of Three Heat Exchanger Types with Numerical Verification and PI Control

Abstract

This study develops a unified dynamic thermal simulator for double-pipe, shell-and-tube, and plate types within a single Partial Differential Equation (PDE) modeling framework. The primary issue with conventional HE simulators is their limitation to steady-state simulations and the lack of integration with dynamic control modules. The developed simulator integrates a three-domain PDE model with an Adaptive Nusselt Correlation Engine and a Feedforward-Feedback (PI-SIMC) control system. Numerical verification using the Grid Convergence Index (GCI) confirms a convergence order of  with a spatial error of ≤ 0.26%. System-level validation demonstrates high accuracy in the double-pipe model, showing a 0.01% heat transfer deviation against analytical data, whereas a 7.6% deviation in the shell-and-tube model is identified as originating from the conceptual 1-1 pass assumption of the PDE model. Transient thermal performance testing through the simulation of disturbance injection in the upstream flow (10% temperature drop) proves that the integration of the Feedforward-SIMC PI control significantly accelerates thermal stabilization. The system successfully restores the outlet temperature to the setpoint with a recovery time ranging from 5 to 31 seconds, depending on the HE type. This simulator architecture contributes to providing a preliminary analysis tool for testing thermal control strategies in manufacturing industrial facilities.