Variational formulation of stationary two-phase flow distribution

Abstract This paper discusses the extremisation of the entropy production in fluidic networks to gain insight into using non-equilibrium thermodynamics for mathematically formulating thermal engineering transfer phenomena. In the study, a variational formulation of the two-phase flow distribution in a fluidic junction is developed. Moreover, based on the flow representation, it is shown that the flow is distributed such that the entropy production rate is either maximised or minimised. Specifically, considering a homogeneous representation of the flow in an adiabatic fluidic network, the flow rates are distributed to maximize the entropy generation rate. Contrarily, when a separate flow representation is adopted, the stationary flow rates are distributed to yield the minimum entropy generation rate. Additionally, various characteristics which affect the flow distribution ratio and phase separation, such as the geometric imbalance, the gravitational static head, the total inlet mass flux, different thermo-physical properties of the fluid, and a generalised number of parallel branches are explored. This supports the possibility of relying on non-equilibrium thermodynamics, instead of introducing case-specific empirical correlations, for obtaining general mathematical formulations of thermal engineering transfer phenomena.

[1]  Kiyoshi Saito,et al.  Cascade refrigeration system with inverse Brayton cycle on the cold side , 2017 .

[2]  Stéphane Lips,et al.  Local entropy generation for saturated two-phase flow , 2009 .

[3]  S. Zivi.  Estimation of Steady-State Steam Void-Fraction by Means of the Principle of Minimum Entropy Production , 1964 .

[4]  L. Martyushev,et al.  From dendrites and S-shaped growth curves to the maximum entropy production principle , 2003 .

[5]  A. Bejan,et al.  Optimal allocation of a heat-exchanger inventory in heat driven refrigerators , 1995 .

[6]  Davor Juretić,et al.  Kirchhoff's loop law and the maximum entropy production principle. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Y Kawazura,et al.  Entropy production rate in a flux-driven self-organizing system. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Jun Kyoung Lee.  Branching of two-phase flow from a vertical header to horizontal parallel channels , 2003 .

[9]  P. Neveu,et al.  A comprehensive non-equilibrium thermodynamic analysis applied to a vapor–liquid two-phase flow of a pure fluid , 2012 .

[10]  Leonid M. Martyushev,et al.  Some interesting consequences of the maximum entropy production principle , 2007 .

[11]  Y. Taitel,et al.  SPLITTING CHARACTERISTICS AND FLOW DISTRIBUTION OF GAS-LIQUID FLOW IN TWO PARALLEL PIPES , 2010 .

[12]  L. Saraceno,et al.  Capillary pressure influence on open channels pressure drop , 2013 .

[13]  Vikrant Aute,et al.  CoilDesigner: a general-purpose simulation and design tool for air-to-refrigerant heat exchangers , 2006 .

[14]  Nae-Hyun Kim,et al.  Refrigerant distribution in a parallel flow heat exchanger having vertical headers and heated horizontal tubes , 2011 .

[15]  Stijn Bruers,et al.  On the Validity of Entropy Production Principles for Linear Electrical Circuits , 2007 .

[16]  John Whitfield,et al.  Complex systems: Order out of chaos , 2005, Nature.

[17]  Thomas Christen,et al.  Application of the maximum entropy production principle to electrical systems , 2006 .

[18]  R. G. Endres.  Entropy production selects nonequilibrium states in multistable systems , 2017, Scientific Reports.

[19]  István Gyarmati,et al.  Non-equilibrium thermodynamics : field theory and variational principles , 1970 .

[20]  Chi-Chuan Wang,et al.  Optimization of the airside thermal performance of mini-channel-flat-tube radiators by using composite straight-and-louvered fins , 2020 .

[21]  Pega Hrnjak,et al.  Vapor–liquid separation in a vertical impact T-junction for vapor compression systems with flash gas bypass , 2014 .

[22]  L. Onsager.  Reciprocal Relations in Irreversible Processes. II. , 1931 .

[23]  P. Hrnjak,et al.  Effects of fluid properties on two-phase flow and refrigerant distribution in the vertical header of a reversible microchannel heat exchanger - Comparing R245fa, R134a, R410A, and R32 , 2014 .

[24]  Kiyoshi Saito,et al.  Characterization of two-phase flow distribution in microchannel heat exchanger header for air-conditioning system , 2019, Experimental Thermal and Fluid Science.

[25]  Richard A. Gaggioli,et al.  Some observations of entropy extrema in fluid flow , 2004 .

[26]  Indranil Ghosh,et al.  Review of micro- and mini-channel heat sinks and heat exchangers for single phase fluids , 2015 .

[27]  N. Giannetti,et al.  Irreversibility analysis of falling film absorption over a cooled horizontal tube , 2015 .

[28]  Jae Sung Yoon,et al.  Modeling and simulation on the mass flow distribution in microchannel heat sinks with non-uniform heat flux conditions , 2010 .

[29]  Syed M. Zubair,et al.  Efficient energy utilization through proper design of microchannel heat exchanger manifolds: A comprehensive review , 2017 .

[30]  Rolf Landauer,et al.  Inadequacy of entropy and entropy derivatives in characterizing the steady state , 1975 .

[31]  E. Jaynes.  The Minimum Entropy Production Principle , 1980 .

[32]  Robert K. Niven,et al.  Simultaneous extrema in the entropy production for steady-state fluid flow in parallel pipes , 2009, 0911.5014.

[33]  K. Janáček.  [Introduction to thermodynamics]. , 1973, Ceskoslovenska fysiologie.

[34]  R. Landauer.  Stability and entropy production in electrical circuits , 1975 .

[35]  Zhihao Liang,et al.  Circuitry arrangement optimization for multi-tube phase change material heat exchanger using genetic algorithm coupled with numerical simulation , 2018, Energy Conversion and Management.

[36]  M. Arie,et al.  Experimental characterization of an additively manufactured heat exchanger for dry cooling of power plants , 2018 .

[37]  Adrian Bejan,et al.  Second-Law Analysis in Heat Transfer and Thermal Design , 1982 .

[38]  Sholahudin,et al.  Prediction of two-phase flow distribution in microchannel heat exchangers using artificial neural network , 2020, International Journal of Refrigeration.

[39]  Yu. E. Nikolaenko,et al.  Research on two-phase heat removal devices for power electronics , 2018, Thermal Science and Engineering Progress.

[40]  M. Bahrami,et al.  Development of novel plate heat exchanger using natural graphite sheet , 2019, International Journal of Heat and Mass Transfer.

[41]  Kiyoshi Saito,et al.  Experimental performance of a double-lift absorption heat transformer for manufacturing-process steam generation , 2017 .

[42]  Clark W. Bullard,et al.  Header design tradeoffs in microchannel evaporators , 2004 .

[43]  A. Bejan,et al.  The constructal law and the evolution of design in nature. , 2011, Physics of life reviews.

[44]  Pega Hrnjak,et al.  Enhancement of vapor–liquid separation in vertical impact T-junctions for vapor compression systems with flash gas bypass , 2014 .

[45]  T. Christen.  Modelling diffusion in nonuniform solids using entropy production rate , 2007 .

[46]  Ilya Prigogine,et al.  Introduction to Thermodynamics of Irreversible Processes , 1967 .

[48]  H. Yoshimura,et al.  Semitheoretical formulation of annular flow void fraction using the principle of minimum entropy production , 2020 .

[49]  Niccolo Giannetti,et al.  Thermodynamic analysis of regenerated air-cycle refrigeration in high and low pressure configuration , 2014 .

[50]  Nae-Hyun Kim,et al.  Two-phase refrigerant distribution in a two row/four pass parallel flow minichannel heat exchanger , 2016 .

[51]  N. Egrican,et al.  Theoretical and experimental examination of air conditioner heat exchangers , 2010 .

[52]  Shuangfeng Wang,et al.  Gas-liquid two-phase flow distribution in parallel micro-channels with different header and channels' orientations , 2017 .

[53]  Mark Naylor,et al.  Maximum entropy production and earthquake dynamics , 2008 .

[54]  A. Rinaldo,et al.  Maximum entropy production, carbon assimilation, and the spatial organization of vegetation in river basins , 2012, Proceedings of the National Academy of Sciences.

[55]  Kiyoshi Saito,et al.  Seasonal performance evaluation of CO2 open refrigerated display cabinets , 2019 .