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

Review Paper

## Abstract

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.

## Keywords

Absorption refrigeration GAX cycle Computational simulation Optimization

## Latin symbols

A

Mass transfer area or heat transfer area (m2)

$$c_{\text{p}}$$

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

CR

Circulation ratio (dimensionless)

FR

Flow ratio (dimensionless)

f

Real function or vector

g

Real function or vector

h

Specific enthalpy (kJ/mol or kJ/kg)

$$l$$

Molar flow of liquid (mol/s)

$$\dot{m}$$

Mass flow rate (kg/s)

N

Number of physically relevant variables

n

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

p

Pressure (absolute) (Pa or bar)

$$\dot{Q}$$

Heat flow (kW)

T

Temperature (°C or K)

$$U$$

Global coefficient of heat transfer (W/m2 K)

$$v$$

Molar vapor flow (mol/s)

$$\dot{W}$$

Power (W)

x

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

y

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

## Greek symbols

η

Mechanical efficiency of pump (fraction)

$$\Delta$$

Variable change

ε

Effectiveness

ν

Specific molar volume (m3/kmol)

## Subscribed

AB

Absorber

AHX

Absorber heat exchange

$${\text{amb}}$$

Environment cooled

$${\text{ar}}$$

Cooling air

$${\text{SP}}$$

Solution pump

CO

Condenser

$${\text{RC}}$$

Reflux condenser

e

Input

EV

Evaporator

f

Cold

GAXA

Generator absorber heat exchange

GAXD

Generator heat exchange

GE

Generator

H2O

Water

$$i$$

Sorting index or initial condition

j

Sorting index or constant

min

Minimum

NH3

Ammonia

q

Hot

$${\text{RE}}$$

Rectification column

s

Out

PR

Pre-cooler

suc

Suction

$${\text{vet}}$$

Thermostatic expansion valve

$${\text{sat}}$$

Saturation conditions

## Superscripts

*

Auxiliary, theoretical or previous value

$$k,k + 1$$

Interaction index

v

Vapor phase

l

Liquid phase

## Abbreviations

COP

Coefficient of performance

VC

Control volume

$${\text{UA}}_{i}$$

Product UA in initial condition

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© The Brazilian Society of Mechanical Sciences and Engineering 2019

## Authors and Affiliations

• Karlos R. S. Braga Martins
• 1
• José Ricardo Figueiredo
• 2
1. 1.Departamento de MecânicaInstituto Federal de São Paulo – IFSPHortolândiaBrazil