Döner tip rejeneratör diferansiyel denklemlerinin çözümü için en uygun sınır şartlarının belirlenmesi
Şaban ÜNAL
2020
Gazi Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi
Highlights: Graphical/Tabular Abstract Use of rotary type regenerators in energy saving Solution of rotary type regenerator differential equations with finite differences method Determination of optimal boundary conditions for finite differences method Figure A. The use of rotary type regenerator in air contioning system Purpose: The purpose of the present work is to determine the optimal boundary conditions for the solution of rotary type regenerator differential equations by using the
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... nite difference method. Theory and Methods: The first law of the thermodynamics and the continuity equation are applied to the rotary type regenerator control volume element and the differential equations are written in terms of dimensionless to calculate of the fluid and wall temperatures. These differential equations are solved by using finite difference method. Two different boundary conditions have been used to solve the differential equations. The first one is to assign the fluid temperature at the transition points between the periods. The second one is based on the assumption that there is no heat transfer in the fluid through the flow direction at these points. Fluid and wall boundary conditions are also expressed by finite differences and the fluid and wall temperature are calculated with the solution of equations. Results: When it is assumed that the fluid temperature is assigned at the transition points between periods, which is called the first boundary condition, the obtained temperature distribution is not smooth. Also there are significant fluctuations in temperature especially in cold and hot period transition points. On the other hand, according to the assumption that there is no heat transfer in the fluid through the flow direction at the transition points between the periods, which is called the second boundary condition, it is seen that the obtained temperature distributions are quite smooth. Conclusion: In the mathematical models of various types of rotary type regenerators to be used in air conditioning systems, many simple assumptions were made, and analytical solutions were obtained accordingly. In the literature, solutions have been developed by using numerical methods besides analytical methods. In this study, two different boundary conditions were used for the solution of the mathematical model for rotary type regenerators with the finite difference method and the obtained results were compared. Accordingly, it was found that assigning the fluid temperature as a boundary condition at the transition points from the hot period to the cold period or vice versa was not suitable. Instead, it is seen from the obtained temperature distribution graphs that the assumption of there is no heat transfer in the fluid through the flow direction at the transition points between the periods, gives more accurate results. DOI: Rotary type regenerators are used for energy recovery from waste heat, especially in low temperature applications such as air conditioning systems. In this study, the developed mathematical model for rotary type regenerators has been solved with finite difference method using two different boundary conditions and the effects of the boundary conditions on the results have been investigated. Two different boundary conditions have been used at transition points between periods. It has been shown that the assumption of there is no heat transfer in the fluid at these points yields better results rather than assigned fluid temperature as a boundary condition at the transition points from one period to the other period (from the hot period to the cold period or from the cold period to the warm period).
doi:10.17341/gazimmfd.563263
fatcat:rfjk7qczmfb7xczpk7622skg3q