Eventos Anais de eventos
ENCIT 2022
19th Brazilian Congress of Thermal Sciences and Engineering
Cubic Hermite interpolation function in supercritical heat exchanger modeling
Submission Author:
Luciano Amaury dos Santos , SC
Co-Authors:
Luciano Amaury dos Santos, Joaquim Manoel Gonçalves, Samuel Luna de Abreu, Carlos Boabaid Neto
Presenter: Luciano Amaury dos Santos
doi://10.26678/ABCM.ENCIT2022.CIT22-0040
Abstract
Most heat exchangers may be fairly accurately modeled using an analytical approach, generally presented in Heat Transfer textbooks as the Logarithmic Mean Temperature Difference and the efficiency-NTU methods (for design and analysis problems, respectively), with subtle adaptations when there is phase change involved. Concerning about the environmental impact of CFC and HFC working fluids in heating and refrigeration, and also the possibility of a better matching between heat source and working fluid temperatures in power generation has attracted attention to the possibility of using supercritical cycles, mostly using CO2 as working fluid. Above the critical temperature and/or pressure (point) the working fluid does not experience a phase change between liquid and vapor, it changes continuously its properties but, when the temperature and pressure get near the critical point, much more intensely than it changes in single phase fluids below the critical point. The intense variations of fluids properties accompanied by temperature (and less noticeable pressure) variations are much more difficult to model analytically than those observed in single phase or conventional two-phase heat exchangers, and so emerges the need for fully numerical approaches based on some sort of finite difference or approximate spectral methods. Since the computational demands of a one-dimensional discretization are not extremely high, the usual second and first-order accurate ones (central differences and upwind differences) are considered satisfactory and really an optimal balance between complexity and performance. The present paper shows that the use of fourth-order accurate cubic Hermite polynomials as interpolation functions does not increase the complexity too much and greatly improves the convergence of a control volume based finite element method for supercritical heat exchanger modeling. The results of the use of Hermite cubic (spline) interpolation function are compared with those of more conventional approaches and also other not so usual. To perform this comparison a test problem is solved using some different approaches, starting the use of an interpolation function based in analytical solution, not dismissing the classical linear interpolation, but then comparing the Hermite cubic spline interpolation function fourth order of convergence with the accuracy provided by other cubic polynomials.
Keywords
Interpolation function, Heat exchanger, Supercritical CO2
