A network approach was used to develop a thermofluid process model of a cross-flow primary superheater heat exchanger with complex flow arrangement in the convective pass of a coal-fired boiler. The model solves the transient one-dimensional forms of the conservation equations for mass, energy, and momentum, combined with the applicable closure relations, boundary values, and initial values. The dual-tube 12-pass superheater was discretized along the flue gas flow path as well as along the steam flow path. The model accounts for the convective thermal resistance on the steam side, the conductive thermal resistances of the tube wall, and scaling or fouling on the tube walls, as well as the convective and radiative thermal resistances on the flue gas side. The model was qualitatively validated using real plant data and for reference purposes also systematically compared to conventional lumped parameter models. The ability of the model to analyze the effect of the ramp rate during load changes on the tube metal temperature was demonstrated, as well as the ability to determine the maldistribution of flow and temperature on the steam and flue gas sides. Models such as this can be employed to study complex thermofluid process phenomena that may occur during intermittent, transient, and low-load operation of power plants. This could form the basis for improving operations and for the development of advanced tools for online process condition monitoring.

Integrated whole-boiler process models are useful in the design of biomass and coal-fired boilers, and they can also be used to analyse different scenarios such as low load operation and alternate fuel firing. Whereas CFD models are typically applied to analyse the detail heat transfer phenomena in furnaces, analysis of the integrated whole-boiler performance requires one-dimensional thermofluid network models. These incorporate zero-dimensional furnace models combined with the solution of the fundamental mass, energy, and momentum balance equations for the different heat exchangers and fluid streams. This approach is not new, and there is a large amount of information available in textbooks and technical papers. However, the information is fragmented and incomplete and therefore difficult to follow and apply. The aim of this review paper is therefore to: (i) provide a review of recent literature to show how the different approaches to boiler modelling have been applied; (ii) to provide a review and clear description of the thermofluid network modelling methodology, including the simplifying assumptions and its implications; and (iii) to demonstrate the methodology by applying it to two case study boilers with different geometries, firing systems and fuels at various loads, and comparing the results to site measurements, which highlight important aspects of the methodology. The model results compare well with values obtained from site measurements and detail CFD models for full load and part load operation. The results show the importance of utilising the high particle load model for the effective emissivity and absorptivity of the flue gas and particle suspension rather than the standard model, especially in the case of a high ash fuel. It also shows that the projected method provides better results than the direct method for the furnace water wall heat transfer.

Physics-informed neural networks (PINNs) were developed to overcome the limitations associated with the acquisition of large training data sets that are commonly encountered when using purely data-driven machine learning methods. This paper proposes a PINN surrogate modeling methodology for steady-state integrated thermofluid systems modeling based on the mass, energy, and momentum balance equations, combined with the relevant component characteristics and fluid property relationships. The methodology is applied to two thermofluid systems that encapsulate the important phenomena typically encountered, namely: (i) a heat exchanger network with two different fluid streams and components linked in series and parallel; and (ii) a recuperated closed Brayton cycle with various turbomachines and heat exchangers. The results generated with the PINN models were compared to benchmark solutions generated via conventional, physics-based thermofluid process models. The largest average relative errors are 0.17% and 0.93% for the heat exchanger network and Brayton cycle, respectively. It was shown that the use of a hybrid Adam-TNC optimizer requires between 180 and 690 fewer iterations during the training process, thus providing a significant computational advantage over a pure Adam optimization approach. The resulting PINN models can make predictions 75 to 88 times faster than their respective conventional process models. This highlights the potential for PINN surrogate models as a valuable engineering tool in component and system design and optimization, as well as in real-time simulation for anomaly detection, diagnosis, and forecasting.