Energy Convers. Mgmt Vol. 25, No. 3, pp. 273-275, 1985 0196-8904/85 $3.00 + 0.00 Printed in Great Britain. All rights reserved Copyright © 1985 Pergamon Press Ltd AN EQUATION OF STATE FOR STEAM FOR SYSTEMS ANALYSIS TARIQ MUNEER* Mechanical Engineering Department, Garyounis University, Benghazi, Libya (Received 1 August 1984) Abstract--For engineers involved in the analysis of thermal systems, it may be desirable to compute thermodynamic properties using an equation of state rather than tables or charts. In this work, a pressure explicit equation of state for steam is developed by curve fitting of P- V-T data. An etticient optimization method was used for the least-squares minimization. The five-constant, Beattie-Bridgeman equation developed here was found to perform well in computation of a property when the other two were provided. The equation is inherently simple in form, and therefore, computation of other thermodynamic properties such as enthalpy and entropy will be an easy matter. Thus, the equation will be invaluable in design and optimization of steam-based thermal systems. Thermodynamics Steam Properties of steam Equation of state NOMENCLATURE dynamic properties. In some instances, it is possible to store a widely spaced network of thermodynamic A =constant in the Beattie-Bridgeman equation (l) data in computer memory and perform three- A' = dimensionless constant defined by equation (9) dimensional interpolations to obtain the desired val- a = constant in the Beattie-Bridgeman equation (l) ues. Alternatively, it may be desirable to compute all a' = dimensionless constant defined by equation (6) other properties from an equation of state and the B = constant in the Beattie-Bridgeman equation (l) B' = dimensionless constant defined by equation (10) ideal gas properties [1]. A thermodynamic equation B/ = variable defined by equation (5) of state is an equation relating pressure, specific b = constant in the Beattie-Bridgeman equation (I) volume and temperature of a substance in the satur- b' = dimensionless constant defined by equation (7) ated vapour/superheated state. c = constant in the Beattie-Bridgeman equation (l) In this work, an equation of state for steam will be c' = dimensionless constant defined by equation (8) f= function to be minimized developed. Once the equation of state is established, gr = gradient vector at the rth iteration equations for computation of other thermodynamic gr r = transpose of the the gradient vector at the rth properties, such as enthalpy and entropy, may be iteration easily obtained by use of thermodynamic relations. N = number of data points P = pressure, kPa Any good treatise on thermodynamics may be used P,. = pressure at critical point, kPa for an account of these relations. Pr = vector defined by equations (3) and (4) R = gas constant for steam, J/kg °K S = sum of squares of the residual BEA'I*FIE--BRIDGEMAN EQUATIONS T = temperature, °K T, = temperature at critical point, °K The equation developed here will be of the same v = specific volume, m3/kg form as the Beattie-Bridgeman equation of state X = vector of variables being optimized which has only five constants to be determined by least-squares curve fitting of thermodynamic data for INTRODUCTION steam. This equation is correct up to 0.8 times the critical density [2]. Correspondingly, the data used in Thermodynamic tables and charts find their use in a this work involve pressures up to 20 MPa. Therefore, wide range of engineering applications such as heat the equation can be used quite confidently for pres- transfer, power plant engineering, refrigeration, air- sures up to this limit, which is quite satisfactory for conditioning, fluid mechanics and solar energy en- practical applications. gineering. The equation is of simple form and, therefore, can However, an engineer involved in the analysis, be easily used for computation of other thermo- design and optimization of thermal systems often dynamic properties. It requires only a small computer requires an equation for computation of thermo- storage, and computations involving a large number of calculations require relatively short execution time. The values of the constants of the *Present address: School of Surveying, Robert Gordon's Institute of Technology, Garthdee Road, Aberdeen AB9 Beattie--Bridgeman equation for steam will be ob- 2QB, Scotland. tained by use of an efficient optimization method. 273