Computational simulation and optimization methodology of an ammonia–water GAX absorption cooling system

  • Karlos R. S. Braga MartinsEmail author
  • José Ricardo Figueiredo
Review Paper


This paper presents a methodology for the steady-state simulation and optimization of a water–ammonia GAX cycle cooling system for residential and commercial air-conditioning applications. The study is based on an experimental GAX absorber unit described in the literature designed with a cooling capacity of 7.1 kW and uses ammonia–water mixture as the working fluid. The model uses thermodynamic relations of species conservation and energy conservation and general heat transfer expressions in terms of the product of the global heat transfer coefficient by the heat transfer area, UA. Thermodynamic state relations are analytically derived from two equations representing the Gibbs free energy in terms of pressure, temperature and concentration; vapor–liquid equilibrium of the ammonia–water mixture is computed in subroutines adopting the Newton–Raphson method with analytical computation of the Jacobian matrix. The resulting system of nonlinear equations was solved by the Substitution-Newton–Raphson method with a numerical estimate of the Jacobian matrix. The model was first used to simulate the performance of the experimental system, calibrating the necessary component parameters. After that, an optimization study was carried out from the experimental prototype based on the evaluation of the effect of varying the UA product of each GAX cycle component on the refrigeration effect, adopting the criterion of maintaining the overall system size represented by the sum of the UA products. Optimization results show an increased fridge effect and COP of 10.75% and 31%, respectively, together with a simplification of the systems.


Absorption refrigeration GAX cycle Computational simulation Optimization 

List of symbols

Latin symbols


Mass transfer area or heat transfer area (m2)


Specific molar heat (kJ/kmol K or kJ/kg °C)


Circulation ratio (dimensionless)


Flow ratio (dimensionless)


Real function or vector


Real function or vector


Specific enthalpy (kJ/mol or kJ/kg)


Molar flow of liquid (mol/s)


Mass flow rate (kg/s)


Number of physically relevant variables


Number of effective variables in the Substitution-Newton–Raphson method (n < N)


Pressure (absolute) (Pa or bar)


Heat flow (kW)


Temperature (°C or K)


Global coefficient of heat transfer (W/m2 K)


Molar vapor flow (mol/s)


Power (W)


Molar fraction of ammonia in the liquid phase (mol/mol)


Molar fraction of ammonia in the vapor phase (mol/mol)

Greek symbols


Mechanical efficiency of pump (fraction)


Variable change




Specific molar volume (m3/kmol)





Absorber heat exchange


Environment cooled


Cooling air


Solution pump




Reflux condenser








Generator absorber heat exchange


Generator heat exchange






Sorting index or initial condition


Sorting index or constant








Rectification column








Thermostatic expansion valve


Saturation conditions



Auxiliary, theoretical or previous value

\(k,k + 1\)

Interaction index


Vapor phase


Liquid phase



Coefficient of performance


Control volume


Product UA in initial condition



The authors would like to thank the Foundation for the Maranhao State Research (FAPEMA) for their support and funding for this work.

Compliance with ethical standards

Conflict of interest

We, the authors of the paper entitled “optimization methodology and computer simulation of the GAX cycle cooling system,” declare to the Journal of the Brazilian Society of Mechanical Sciences and Engineering (BMSE) for the proper purposes that we have no potential conflict of interest in relation to the present manuscript, specific financial interests and relationships and affiliations relevant to the topic or materials discussed in the manuscript. We also declare that we have no potential or actual conflicts of interest, whether personal or institutional.


  1. 1.
    Altenkirch E (1913) Reversible absorptions maschinen. Zeitschrift for die gesamte Kalte-Industrie, XX. Jahrgang. Heft 1: 1–9, Heft 6:114–119Google Scholar
  2. 2.
    Engler M, Grossman G, Hellmann HM (1997) Comparative simulation and investigation of ammonia water absorption cycles for heat pump applications. Int J Refrig 20(7):504–516CrossRefGoogle Scholar
  3. 3.
    Erickson DC, Anand G, Papar RA (1996) Branched GAX cycle gas fired heat pump. In: Proceedings of the intersociety energy conversion engineering conferenceGoogle Scholar
  4. 4.
    Fernandes BG (2012) Otimização econômica de um sistema bomba de calor e reservatório térmico para aquecimento de água para fins domésticos em edifício. Dissertação (Mestrado). Faculdade de Engenharia Mecânica, Universidade Estadual de Campinas, CampinasGoogle Scholar
  5. 5.
    Figueiredo JR, Santos RG, Favaro C, Silva AFS, Sbravati A (2002) Substitution-Newton–Raphson method applied to the modeling of a vapour compression refrigeration system using different representations of th thermodynamic properties of R-134A. J Braz Soc Mech Sci XXIV(158):168Google Scholar
  6. 6.
    Figueiredo JR, Fernandes BL, Silverio RJR (2006) Nonequilibrium modeling of an ammonia–water rectifying column via fundamental thermodynamic and transport relations. Braz J Chem Eng 23(4):539–553CrossRefGoogle Scholar
  7. 7.
    García-Arellano C, García-valladares O, Gómez VH (2010) Experimental analysis of a transfer function for the transiente response of an evaporator in an absorption refrigeration GAX system. Applied Thermal Engineering 30:2026–2033CrossRefGoogle Scholar
  8. 8.
    Gómez VH, Vidal A, Best R, Garcia-Valladares O, Velázquez N (2008) Theoretical and experimental evaluation of an indirect-fired GAX cycle cooling system. Appl Therm Eng 28(8–9):975–987CrossRefGoogle Scholar
  9. 9.
    Jawahar CP, Saravanan R (2010) Generator absorber heat exchange based absorption cycle—a review. Renew Sustain Energy Rev 14:2372–2382CrossRefGoogle Scholar
  10. 10.
    Kim D (1990) Advanced regenerative absorption refrigeration cycles. US Patent 4921515Google Scholar
  11. 11.
    Kang YT, Kunugi Y, Kashiwagi T (1999) Advanced absorption systems for low temperature applications. In: Proceedings of the international absorption heat pump conferenceGoogle Scholar
  12. 12.
    Lobatón OAC (2011) Otimização térmica e econômica de bomba de calor para aquecimento de água, utilizando programação quadrática sequencial e simulação através do método de substituição Newton Raphson. Dissertação (Mestrado). Faculdade de Engenharia Mecânica, Universidade Estadual de Campinas, CampinasGoogle Scholar
  13. 13.
    Makiyama PA (2008) Aperfeiçoamento de um simulador de sistemas de refrigeração de absorção água-amônia e sua aplicação para projeto de um sistema movido a gás de escape de motor diesel. Tese (Doutorado). Faculdade de Engenharia Mecânica, Universidade Estadual de Campinas, CampinasGoogle Scholar
  14. 14.
    Martins KRSB (2014) Simulação e Otimização Computacional de Diferentes Comfigurações de Sistema de Refrigeração por Absorção Água-Amônia tipo GAX. Tese (Doutorado). Faculdade de Engenharia Mecânica, Universidade Estadual de Campinas, CampinasGoogle Scholar
  15. 15.
    Mehr AS, Yari M, Mahmoudi SMS, Soroureddin A (2012) A comparative study on the GAX based absorption refrigeration systems: SGAX, GAXH and GAX-E. Appl Therm Eng 44:29–38CrossRefGoogle Scholar
  16. 16.
    Mehr AS, Zare V, Mahmoudi SMS (2013) Standard GAX versus hybrid GAX absorption refrigeration cycle: from the view point of thermoeconomics. Energy Convers Manag 76:68–82CrossRefGoogle Scholar
  17. 17.
    Rameshkumar A, Udaya Kumar M (2009) Simulation studies on GAX absorption compression cooler. Energy Convers Manag 48(9):2604–2610CrossRefGoogle Scholar
  18. 18.
    Saravanan R, Rengasamy G, Arivazhagan S, Sivakumar K, Narendran C (2008) Renewable based 40 TR ammonia water GAX absorption cooling system. In: Proceedings of the international sorption heat pump conferenceGoogle Scholar
  19. 19.
    Shi Y, Wang Q, Hong D, Chen G (2017) Thermodynamic analysis of a novel GAX absorption refrigeration cycle. Int J Hydrog Energy 42(7):4540–4547CrossRefGoogle Scholar
  20. 20.
    Stoicovici MD (1995) Polybranched regenerative GAX cooling cycles. Int J Refrig 18(5):318–329CrossRefGoogle Scholar
  21. 21.
    Srikhirin P, Aphornratana S, Chungpaibulpatana S (2001) A review of absorption refrigeration technologies. Renew Sustain Energy Rev 5:343–372CrossRefGoogle Scholar
  22. 22.
    Stoecker WF, Jones JW (1985) Refrigeração e ar condicionado. Mc-Graw-Hill, New YorkGoogle Scholar
  23. 23.
    Velazquez N, Best R (2002) Methodology for the energy analysis of an air cooled GAX absorption heat pump operated by natural gas and solar energy. Appl Therm Eng 22(10):1089–1103CrossRefGoogle Scholar
  24. 24.
    Yari M, Zarin A, Mahmoudi SMS (2011) Energy and exergy analyses of GAX and GAX hybrid absorption refrigeration cycles. Renew Energy 36(7):2011–2020CrossRefGoogle Scholar
  25. 25.
    Zaltash A, Grossman G (1996) Simulation and performance analysis of basic GAX and advanced GAX cycles with ammonia water and ammonia water LiBr absorption fluids. In: Proceedings of the international absorption heat pump conferenceGoogle Scholar
  26. 26.
    Zheng D, Deng W, Jin H, Ji J (2007) a–h diagram and principle of exergy coupling of GAX cycle. Appl Therm Eng 27(11–12):1771–1778CrossRefGoogle Scholar
  27. 27.
    Ziegler B, Trepp CH (1984) Equation of state for ammonia–water mixtures. Int J Refrig 7(2):101–106CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Departamento de MecânicaInstituto Federal de São Paulo – IFSPHortolândiaBrazil
  2. 2.Faculdade de Engenharia MecânicaUniversidade Estadual de Campinas – UNICAMPCampinasBrazil

Personalised recommendations