A modified model parametrization algorithm for solving a special type of heat and mass transfer systems

Drąg, Paweł; Drąg, Marlena; Worek, William; Pandelidis, Demis

doi:10.1016/j.icheatmasstransfer.2022.106224

A modified model parametrization algorithm for solving a special type of heat and mass transfer systems

Journal Article · Sun Jul 03 00:00:00 EDT 2022 · International Communications in Heat and Mass Transfer

DOI:https://doi.org/10.1016/j.icheatmasstransfer.2022.106224· OSTI ID:1995495

Drąg, Paweł ^[1]; Drąg, Marlena ^[1]; Worek, William ^[2]; Pandelidis, Demis ^[1]

Wroclaw University of Science and Technology (Poland)
Argonne National Laboratory (ANL), Argonne, IL (United States)

A new method for solving nonlinear heat and mass transfer design tasks was considered. Systems using the Number of Transfer Units (NTU) method are a special type of mathematical model of heat and mass exchangers. It was observed, that the NTU models in a form of differential-algebraic equations (DAEs) cannot be directly solved with higher values of NTU. The requirements for consistent initial conditions, as well as numerical limitations of DAEs solvers, result, that the solution to the considered design problems that cannot be obtained by a classical direct shooting procedure. To overcome the presented difficulties, the αDAE model optimization algorithm was adjusted for solving NTU-based models. The new approach consists of 3 main steps: 1) task discretization by a multiple-shooting approach, 2) design an appropriate function $$f_{NTU}$$(α) to effectively influence the variability of the state variables described by dynamical relations, 3) the iterative numerical optimization algorithm for the new parametrized system. Moreover, computations can be performed by a chosen numerical optimization approach, which can be communicated with an available outer procedure for solving differential-algebraic equations. The presented algorithm was implemented and applied to solve the design task with the NTU model of a counter-flow exchanger. Here, the new approach was used to modify the system dynamics to influence the difficulty of the considered problem. Finally, the presented method enabled failure-free numerical computations for the higher values of the NTU parameter.

View Accepted Manuscript (DOE)

Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: European Regional Development Fund (ERDF); Polish National Agency for Academic Exchange; Polish National Centre for Research and Development; USDOE

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1995495

Journal Information:: International Communications in Heat and Mass Transfer, Journal Name: International Communications in Heat and Mass Transfer Vol. 137; ISSN 0735-1933

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
Differential-algebraic equations
Heat and mass transfer
Multiple shooting method
Numerical optimization
α-model parametrization

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