DETERMINATION THERMODYNAMIC PROPERTIES OF WATER AND STEAM

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1 DETERMINATION THERMODYNAMIC PROPERTIES OF WATER AND STEAM S. Sngr, J. Spal Afflaton Abstract Ths work presents functons of thermodynamc parameters developed n MATLAB. There are functons to determne: saturaton pressure on the temperature and conversely, enthalpy on the temperature and pressure, entropy on the temperature and pressure. All functons based on formulaton IAPWS-IF97. Functons for saturaton pressure and temperature are a smple functons wth one varable. Determnaton enthalpy and entropy to the temperature and pressure requred soluton of equaton wth dfferentals. 1 Theoretcal bass The Industral Formulaton IAPWS-IF97 consst from set of equatons for dfferent regons. At the Fgure 1 shows dagram state of water and steam. Regon 1 s a lqud phase; regon 2 s a vapor phase; regon 3 s a phase of the crtcal state. Lne ABC s saturaton lne; lne BD s sotherm, whch s boundary bee twn lqud and crtcal phase; lne BE s boundary bee twn crtcal and vapor phase, ths lne descrbes by specal equaton. Pont C s a crtcal pont. For regons 1, 2 uses the fundamental equaton for the Gbbs energy. For regon 3 fundamental equaton Helmholtz free energy. Fgure1 - Dagram water and steam. 1.1 Regon 1- lqud phase For regon 1 uses equaton for the Gbbs energy [1]: g( p, ) R 34 n 1 (, ) (7,1- ) ( -1, 222) J (1) R- specfc gas constant,, [kj/(kgk)];

2 p / p [1], p 16,53 [Mpa]; T / T [1], T 1386 [K]; n - specfc coeffcents for regon 1 [1]; I, J - specfc exponents for regon 1 [1]. Equaton for determne enthalpy [1]: h/( RT) (2) h- enthalpy, [kj/kg]; Equaton for determne entropy [1]: s/( RT) (3) s- entropy [kj/(kgk)]; 1.2 Regon 2- vapor phase For regon 2 uses equaton for the Gbbs energy, conssted of two part: (, )- deal gas r part, (, )- real part [1]: g( p, ) R r (, ) (, ) (, ) (4) (, ) ln 9 J n (5) 1 T / T [1], T 54 [K]; n - specfc coeffcents for regon 2 [1]; J - specfc exponents for regon 2 [1]. 43 r I J (, ) n (,5) (6) 1 p / p [1], p 1 [MPa]; n - specfc coeffcents for regon 2 [1];

3 I, J - specfc exponents for regon 2 [1]. Enthalpy and entropy determnng by equatons (2) and (3). 1.3 Regon 3- phase of crtcal state For regon 3 uses fundamental energy equaton Helmholtz. [1]: f (, ) J (, ) ln (7) R 4 n1 n I 2 / c [1], - densty [kg/m 3 ], c - densty n crtcal pont, 322 [kg/m 3 ]; T / Tc [1], Tc -temperature n crtcal pont, [K]; n - specfc coeffcents for regon 3 [1]; I, J - specfc exponents for regon 3 [1]. Equaton for determne enthalpy [1]: h/( RT) (8) Equaton for determne entropy [1]: s/( RT) (9) For determne, consstency to pressure and temperature uses equatons system from (2). 1.4 Saturaton lne Man equaton for saturaton lne [1]: (1) n1 n2 n3 n4 n5 n6 n7 n8 p p 1/4 ( s / ) (11) T / T n /(( T / T ) n ) (12) s 9 s 1 P s - saturaton pressure, [MPa]; T s - saturaton temperature, [K];

4 Decde ths equaton relatve to P s, determne depend saturaton pressure to saturaton temperature; decde ths equaton relatve to T s, determne depend saturaton temperature to saturaton pressure. To determne enthalpy and entropy for saturated lqud uses equaton for regon 1. For saturated dry steam equaton for regon 2. 2 MATLAB functons Based on the prevous equatons were developed functons to determne enthalpy and entropy from temperature and pressure. 2.1 Bass Structure of ths program prefer on Fgure 2. Fgure 2 - Structure of the MATLAB functon h(p,t),s(p,t) The frst one functon requred enter nlet parameters: pressure p [MPa], temperature t [ o C]. For nlet varables can be use vectors wth the same dmenson, result wll be vector of values elementwse calculaton enthalpy (entropy). After checkng the dmensons of ncomng varables t runs the cycle of calculaton for correspondng elements. In the loop based on the values of nlet parameters selectng the area n whch located the pont and solve the correspondng equaton for enthalpy (entropy). Boundares of the regon: Regon 1: o C<t<35 o C; P s (t)<p<1 MPa.

5 Regon 2: o C<t<35 o C; P s (t) p;. 35 o C<t<8 o C; P 97 (t)> p. Regon 3: 35 o C<t<8 o C; P 97 (t) p. As for the crtcal regon enthalpy equaton has form, for calculaton s also used equaton of the form to fndng value of densty at the pont. Equatons (2),(3),(8),(9) were dfferentated before and wrtten n symbolc form wthout dfferentals. Ths s ncreasng calculatng speed. 2.2 Interface For appled use functons were developed nterface program, whch calculate enthalpy (entropy) to temperature and pressure and mark ths pont on dagram. Interface prefer at Fgure 3. Fgure 3 - Interface for developed functons Input data felds for nput data: pressure p [MPa] and temperature t [ o C] for calculaton. Output data felds for output data: enthalpy h [kj/kg ] and entropy s [kj/(kgk)]. Graphc wndow s dagram wth thermodynamc propertes n coordnate axes. On ths dagram dsplayed saturaton lne and markng gven pont. Propertes on axes can be change by menu Type of dagram. Button Calculate should be clck after nput pressure and temperature. Menu Type of dagram for change parameters of coordnate axes. Menu About program for call help fle. Buttons Englsh and Češtna s for change program language on approprate.

6 3 Results These functons were developed wthn the framework of dssertaton. Durng buldng a model of heat exchanger became necessary determnng enthalpy of heat carrers at a certan temperature and pressure to solve the equatons of thermal balance. Usng developed functons are not restrcted a sngle model. As the water the man operatng flud n power equpment: heat carrer n bolers and heat exchanger, operatng body n turbnes, etc these functons also can be used to buld model of these equpment. In constructon these models the need arses to dentfy other water parameters (entropy, densty, specfc volume, thermal conductvty, etc.) wth other ntal values (enthalpy, entropy, specfc volume) and therefore were have been developed other functons n a smlar method. Functons can be used to buld varous fgures because of ther support as nput a set of values (vector). For the appled use functons outsde Matlab has been desgned program wth user nterface. It can rapdly calculate enthalpy and entropy of water (steam) and notes poston of the pont wth the specfed parameters to the dfferent dagrams. For better percepton on the dagrams ndcate saturaton lne and crtcal pont, at the p-t dagram also ndcate boundares of the varous phases of water: lqud, vapor and phase of crtcal state. Ths vsualzaton allows use the program as appled to calculatons nstead of tables and dagrams, to rapdly determne enthalpy and entropy and for learnng purposes for better understandng of thermodynamc process and phase transton. Language of program nterface can change between Englsh and Czech. References [1] Revsed Release on the IAPWS Industral Formulaton 1997 for the Thermodynamc Propertes of Water and Steam: Lucerne, Swtzerland 27. [2] Supplementary Release on Backward Equatons for Specfc Volume as a Functon of Pressure and Temperature v(p,t) for Regon 3 of the IAPWS Industral Formulaton 1997 for the Thermodynamc Propertes of Water and Steam: Santorn, Greece July 25. Ing Sergey Sngr; UJEP; Faculty of Producton Technology and Management; Department of Machnery and Mechancs; Na okraj 11; 496 Ust nad Labem; Doc. Ing. Jaroslav Spal, Ph. D.; UJEP, Faculty of Producton Technology and Management, Department of Machnery and Mechancs; Na okraj 11; 496 Ust nad Labem;

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