Equation of state based analytical formulation for optimization of sCO2 Brayton cycle

Abstract Real gas thermodynamic cycles employ state-of-the-art property routines to compute the state properties as ideal gas relations are inaccurate. Multiparameter equation of state (EOS), though accurate, is computationally time consuming due to iterative solutions needed for complex cycles. Alternatively, look-up tables alleviate the computational time but compromise the accuracy due to interpolation and extrapolation schemes. This paper proposes a novel analytical formulation to overcome the tradeoff between accuracy and computation cost. Helmholtz energy-based EOS in combination with Jacobian transformations and real gas thermodynamics is used to arrive at a single equation linking the state points of a thermodynamic cycle. The efficacy of the formulation is demonstrated to deduce the optimum pressure ratio while maximizing specific work or efficiency of a simple recuperated supercritical CO2 Brayton cycle. The difference in optimum pressure ratio predicted by the analytical formulation and conventional property-routine is inconsequential compared to an order of gain in the computational time.

[1]  Manson Benedict,et al.  An Empirical Equation for Thermodynamic Properties of Light Hydrocarbons and Their Mixtures I. Methane, Ethane, Propane and n‐Butane , 1940 .

[2]  Richard T. Jacobsen,et al.  Thermodynamic Properties of Nitrogen Including Liquid and Vapor Phases from 63K to 2000K with Pressures to 10,000 Bar, , 1973 .

[3]  S. G. Penoncello,et al.  18 Multiparameter equations of state , 2000 .

[4]  D. A. Kouremenos,et al.  The three isentropic exponents of dry steam , 1985 .

[5]  Z. Spakovszky,et al.  An Investigation of Real Gas Effects in Supercritical CO2 Centrifugal Compressors , 2015 .

[6]  D. A. Kouremenos,et al.  A correlation of the isentropic exponents of real gases , 1988 .

[7]  K. Srinivasan,et al.  A trade-off between maxima in efficiency and specific work output of super- and trans-critical CO2 Brayton cycles , 2015 .

[8]  Ali Saadat,et al.  Partial derivatives of thermodynamic state properties for dynamic simulation , 2013, Environmental Earth Sciences.

[9]  Roland Span,et al.  A New Equation of State for Argon Covering the Fluid Region for Temperatures From the Melting Line to 700 K at Pressures up to 1000 MPa , 1999 .

[10]  Vincent Lemort,et al.  Pure and Pseudo-pure Fluid Thermophysical Property Evaluation and the Open-Source Thermophysical Property Library CoolProp , 2014, Industrial & engineering chemistry research.

[11]  Y. Duan,et al.  Part-load performance analysis and comparison of supercritical CO2 Brayton cycles , 2020 .

[12]  W. Wagner,et al.  A method for optimizing the structure of equations of state and its application to an equation of state for oxygen , 1982 .

[13]  I. Bell,et al.  Helmholtz Energy Transformations of Common Cubic Equations of State for Use with Pure Fluids and Mixtures. , 2016, Journal of research of the National Institute of Standards and Technology.

[14]  W. Wagner,et al.  The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use , 2002 .

[15]  W. Wagner,et al.  A Reference Quality Equation of State for Nitrogen , 1998 .

[16]  Guoliang Ding,et al.  An implicit curve-fitting method for fast calculation of thermal properties of pure and mixed refrigerants , 2005 .

[17]  Vincent Lemort,et al.  ThermoCycle: A Modelica library for the simulation of thermodynamic systems , 2014 .

[18]  W. Wagner,et al.  A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple‐Point Temperature to 1100 K at Pressures up to 800 MPa , 1996 .

[19]  Nathan Carstens.  Control strategies for supercritical carbon dioxide power conversion systems , 2007 .

[20]  James J. Sienicki,et al.  Dynamic Analysis of S-CO2 Cycle Control With Coupled PDC-SAS4A/SASSYS-1 Codes , 2012 .

[21]  Pramod Kumar,et al.  Analysis of a 10 MW recompression supercritical carbon dioxide cycle for tropical climatic conditions , 2021 .

[22]  Ali Saadat,et al.  HelmholtzMedia — A Fluid Properties Library , 2012 .

[23]  M. McLinden,et al.  NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.1 | NIST , 2013 .

[24]  Vaclav Dostal,et al.  A supercritical carbon dioxide cycle for next generation nuclear reactors , 2004 .

[25]  A. Shaw.  The Derivation of Thermodynamical Relations for a Simple System , 1935 .

[26]  James J. Sienicki,et al.  Control system options and strategies for supercritical CO2 cycles. , 2009 .

[27]  Seungjoon Baik,et al.  Review of supercritical CO2 power cycle technology and current status of research and development , 2015 .

[28]  C. Turchi,et al.  Thermodynamic Study of Advanced Supercritical Carbon Dioxide Power Cycles for Concentrating Solar Power Systems , 2013 .

[29]  Pramod Kumar,et al.  Simple Recuperated s-CO2 Cycle Revisited: Optimization of Operating Parameters for Maximum Cycle Efficiency , 2019 .

[30]  Y. Duan,et al.  Crossover multiparameter equation of state: General procedure and demonstration with carbon dioxide , 2019, Fluid Phase Equilibria.

[31]  B. Armstrong,et al.  A method of correlation using a search procedure, based on a step-wise least-squares technique, and its application to an equation of state for propylene , 1979 .

[32]  D. Nikovski,et al.  Fast Refrigerant Property Calculations Using Interpolation-Based Methods , 2012 .

[33]  Kun Wang,et al.  Thermodynamic analysis and comparison for different direct-heated supercritical CO2 Brayton cycles integrated into a solar thermal power tower system , 2017 .

[34]  Wolfgang Wagner,et al.  A New Equation of State and Tables of Thermodynamic Properties for Methane Covering the Range from the Melting Line to 625 K at Pressures up to 100 MPa , 1991 .