Arch. Min. Sci. 62 (2017), 1, 55-72

Arch. Mi. Sci. 62 (2017), 1, 55-72 Electroic versio (i color) of this paper is available: http://miig.archives.pl DOI 10.1515/amsc-2017-0005 BERNARD NOWAK*, PIOTR ŻYCZKOWSKI*, RAFAŁ ŁUCZAK* FUNCTIONAL DEPENDENCE OF THERMODYNAMIC AND THERMOKINETIC PARAMETERS OF REFRIGERANTS USED IN MINE AIR REFRIGERATORS. PART 1 REFRIGERANT R407C ZALEŻNOŚCI FUNKCYJNE PARAMETRÓW TERMODYNAMICZNYCH I TERMOKINETYCZNYCH CZYNNIKÓW CHŁODNICZYCH STOSOWANYCH W GÓRNICZYCH CHŁODZIARKACH POWIETRZA. CZĘŚĆ 1 CZYNNIK CHŁODNICZY R407C The authors of this article dealt with the issue of modelig the thermodyamic ad thermokietic properties (parameters) of refrigerats. The kowledge of these parameters is essetial to desig refrigeratio equipmet, to perform their eergy efficiecy aalysis, or to compare the efficiecy of air refrigerators usig differet refrigerats. Oe of the refrigerats used i mie air compressio refrigerators is R407C. For this refrigerat, 23 depedecies were developed, determiig its thermodyamic ad thermokietic parameters i the states of saturated liquid, dry saturated, superheated vapor, subcooled liquid, ad i the two-phase regio. The created formulas have bee preseted i Tables 2, 5,, 10 ad 12, respectively. It should be oted that the scope of applicatio of these formulas is wider tha the rage of chages of that refrigerat durig the ormal operatio of mie refrigeratio equipmet. The article eds with the statistical verificatio of the developed depedecies. For this purpose, for each model correlatio coefficiets ad coefficiets of determiatio were calculated, as well as absolute ad relative deviatios betwee the give values from the program REFPROP 7 (Lemmo et al., 2002) ad the calculated oes. The results of these calculatios have bee cotaied i Tables 14 ad 15. Keywords: refrigerats, R407C, thermodyamic ad thermokietic parameters Autorzy iiejszego artykułu zajęli się zagadieiem modelowaia właściwości (parametrów) termodyamiczych i termokietyczych czyików chłodiczych. Zajomość tych parametrów jest iezbęda do projektowaia urządzeń chłodiczych, ich aalizy eergetyczej, a także do porówaiu efektywości pracy chłodziarek powietrza wykorzystujących róże czyiki chłodicze. Jedym ze stosowaych w góriczych sprężarkowych chłodziarkach powietrza czyikiem chłodiczym jest R407C. Dla wymieioego czyika chłodiczego opracowao 23 zależości określające jego parametry termodyamicze i termokietycze w staie cieczy asycoej, w staie pary asycoej suchej, w staie pary przegrzaej, w staie cieczy przechłodzoej oraz w staie pary mokrej. Utworzoe wzory podao odpowiedio w tabelach: 2, 5,, 10 i 12. Należy zazaczyć, że zakresy obowiązywaia tych wzorów są szersze od zakresów zmia * AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY, FACULTY OF MINING AND GEOENGINEERING, DEPARTMENT OF UNDERGROUND MINING, AL. A. MICKIEWICZA 30, 30-059 KRAKOW, POLAND

56 tego czyika podczas ormalej pracy góriczych urządzeń chłodiczych. Artykuł kończy weryfikacja statystycza utworzoych zależości. W tym celu dla każdego wzoru obliczoo współczyiki korelacji, determiacji oraz odchyłki bezwzględe i względe między wartościami daymi z programu REFPROP 7 (Lemmo i i., 2002) a obliczoymi. Rezultaty tych obliczeń zamieszczoo w tabelach 14 i 15. Słowa kluczowe: czyiki chłodicze, R407C, parametry termodyamicze i termokietycze 1. Itroductio I order to improve thermal workig coditios i udergroud mie workigs, air compressio refrigerators are ofte used. Regardig the maer of heat receptio, the followig refrigerators ca be distiguished: direct actio refrigerators, i which the evaporator is directly used to cool the air, idirect actio refrigerators, i which the evaporator is used to cool the water supplied to the gallery or logwall air refrigerators. Regardless of the maer of heat receptio, the refrigerators use low-boilig workig fluids kow as refrigerats. With respect to their compositio, refrigerats are divided ito sigle-compoet refrigerats (atural ad sythetic, divided ito the followig groups: CFC chlorofluorocarbo, HCFC hydrochlorofluorocarbo ad HFC hydrofluorocarbo), ad multi-compoet refrigerats (azeotropic, zeotropic, ear-azeotropic) Figure 1. REFRIGERANTS SINGLE-COMPONENT MULTI-COMPONENT e.g.: R717, R744, R290, R600a NATURAL SYNTHETIC CFC HCFC HFC e.g.: R22, R23, R24, R123 e.g.: R11, R12, R13, R113 e.g.: R134a, R32, R143a, R152a AZEOTROPIC e.g.: R502, R507, R50, R509 NEAR-AZEOTROPIC e.g.: R404A, R410A, R406A, R407A ZEOTROPIC e.g.: R407C, R401A, R402A, R409A Fig. 1. Divisio of refrigerats due to their compositio (Boca et al., 2004) The ew group of refrigerats based o fluories HFO (hydrofluoroolefi) should also be metioed. They have a lower GWP coefficiet (global warmig potetial) tha HFCs. Curretly, two refrigerats belogig to this group: R1234yf ad R1234ze were lauched o the market. The first oe is plaed as a replacemet for R134a i mobile air coditioig (MAC) systems. The refrigerators i udergroud miig use sythetic refrigerats both sigle-compoet ad multi-compoet. Depedig o the type of the device ad its omial power, these are the followig refrigerats: R407C, R404A, R507 ad R134a (Elgór+ Hase, 2014; Eurotech, 2013; IMKiUS, 2013; Gajosiński & Jakowska-Groch, 2011; Termospec, 2004; Wojciechowski, 2013). The uits operatig with the refrigerat R22 ca still be foud. Such devices may be used,

provided that they are i good coditio, tight ad regularly serviced. It must be remembered, though, that as of 1 Jauary 2015, it is forbidde to use R22 i ay form (icludig recycled), so there is o possibility to fill up the istallatio operatig o such a refrigerat (OJ L 26/1 2009). The basic properties of the refrigerats used i mie refrigerators have bee illustrated i Table 1. 57 Properties of the refrigerats used i mie refrigerators (Lemmo et al, 2002) TABLE 1 Parameter Refrigerat R22 R134a R404A R407C R507 Group HCFC HFC HFC HFC HFC 52% C 2 H 2 F 4 25% C 2 HF 5 50% C 2 HF 5 23% CH 2 F 2 Chemical formula CHF 2 Cl C 2 H 2 F 4 44% C 2 HF 5 52% C 2 H 3 F 3 4% C 2 H 2 F 4 52% R143a Mixture 44% R125 4% R134a 52% R134a 25% R125 23% R32 50% C 2 H 3 F 3 50% R125 50% R143a Molar mass [kg/kmol] 6,46 102,03 97,604 6,204 9,59 Critical temperature [ C] 96,145 101,06 72,046 6,034 70,617 Critical pressure [bar] 49,9 40,593 37,29 46,29 37,05 Critical desity [kg/m 3 ] 523,4 511,9 46,53 44,23 490,77 Normal boilig poit [ C] 40,1 26,074 46,5 43,63 46,74 Temperature of the triple poit [ C] 157,42 103,3 73,15 73,15 73,15 ODP (ozoe depletio potetial) 0,05 0 0 0 0 GWP (global warmig potetial) 1700 1300 374 1609 300 It is ot possible to carry out the calculatios of refrigeratio circuits, or the workig parameters of the devices i the refrigeratio circuits, without the kowledge of the thermodyamic ad thermokietic properties (parameters) of the refrigerats used i these devices. This kowledge is essetial i the aalysis of eergy efficiecy, durig the modelig or desigig ew, more efficiet refrigeratio equipmet. 2. Thermodyamic ad thermokietic properties of refrigerats Numerical values of various thermodyamic parameters of refrigerats, most commoly, are cotaied i graphs or tables. Such data ca be foud i umerous works dealig exclusively with the subject of refrigerats, such as (Boca et al., 199, 2004; Laroiya & Bawait, 2007; Grzebielec et al., 2011; Kothadarama, 2011), i the publicatios of the maufacturers of refrigerats, for example (DuPot, 2004; Buchwald et al., 200; Arkema, 2010, Mexichem, 2010), or i umerous books related to the refrigeratio ad air coditioig, such as (Ullrich, 199, 1999; Bohdal et al., 2003; Radermacher & Hwag 2005; Reckagel et al., 200; ASHRAE, 2010; Baumgarth et al., 2010; Butrymowicz et al., 2014). Detailed thermodyamic ad thermokietic parameters of refrigerats ca be foud usig commercially available computer programs, such as Refrigerats 3.0 (Boca et al, 199), Thermodyamics Heat Trasfer (Domański et al., 2000), Duprex 3.2

5 (DuPot, 2011), released by the US Natioal Istitute of Stadards ad Techology, the program REFPROP 9.1 (Lemmo et al., 2013), or the program CoolProp 4.0 (Bell et al., 2014). I egieerig calculatios, parameters of refrigerats read from tables or graphs may be subject to sigificat errors. Their readig for the measuremet series is icoveiet ad timecosumig. The values of these parameters ca also be calculated usig appropriate computer software. It ivolves, however, a eed to purchase the licese ad is associated with the problem of the automatio of obtaiig required parameters for give iput values. Numerical calculatios use various kids of equatios of state, describig the relatioships betwee the various parameters. Today, Helmholtz equatio of state is the most commoly used for this purpose (Bell et al., 2014). I the literature it is possible to fid depedecies describig the parameters of refrigerats i the form which does ot require the use of umerical calculatios but, most frequetly, they oly refer to the refrigerats i the state of saturated liquid or dry saturated. The complex character of these depedecies makes it virtually impossible to use them i simple egieerig calculatios. The accuracy of the results should also be metioed, which may differ sigificatly from the values obtaied based o the equatios of state. I the work (Boca et al., 199), simple correlatios ca be foud, describig the thermodyamic parameters ad coefficiets of trasport of the refrigerats i the state of saturated liquid ad dry saturated as a fuctio of their saturatio temperature. They were obtaied by approximatio of the tabular data of the refrigerats with fifth degree polyomials. The author of the work (de Mote, 2002a), basig o the Marti-Hou equatio of state, developed the equatios describig the thermodyamic parameters of the refrigerats R407C ad R410A i the superheated regio. The resultig equatios are fuctios of the specific volume ad temperature of the refrigerat. Cotiuig his research (de Mote, 2002b), F. de Mote compares calculatio results obtaied from the solutios to these equatios compared with those obtaied with the REFPROP computer program. For the various properties of R407C, the calculated relative deviatios are icluded i the rage of 0.4% to 9.7%. V. Feroiu ad D. Geaa i their works (Feroiu & Geaa, 2003, 2011) preseted the calculatios results of thermodyamic parameters of the refrigerats R32, R125 ad R134a ad their mixtures usig GEOS3C equatios (Geeral Cubic Equatio of State with 3 Costats), the Soave-Redlich-Kwog equatio ad the Peg-Robiso equatio. They compared the obtaied results with the database of refrigerats available i the literature. I order to determie the relatioships describig thermodyamic parameters of refrigerats (R22 ad R407C), G. Dig et al. (2005) used a curve fittig method (implicit curve-fittig). The resultig formulas allow to determie the ethalpy, temperature, etropy, desity ad specific heat capacity for the refrigerats i the subcooled liquid state, the state of saturated liquid, twophase regio, dry saturated ad superheated. The disadvatage of the formulas developed by the authors is their very complicated form, which makes it impossible to use them i simple egieerig calculatios. Usig the techiques of artificial eural etworks (ANN), A. Soze et al. (2009) came up with slightly less complicated equatios, but also limitig their use fast egieerig calculatios. The depedecies which they provide are for the two-phase regio ad for the superheated regio. For the refrigerat i the two-phase regio, the kowledge of the temperature ad the degree of dryess is required, while i the state of the superheated of the temperature ad pressure. This allows the calculatio of the specific volume, ethalpy, etropy, the dyamic coefficiet of viscosity as well as thermal coductivity. E.U. Kucuksille et al. (2009, 2011), usig various data miig techiques, obtaied simple equatios for determiig the ethalpy, etropy, specific volume, specific heat capacity, the

coefficiet of dyamic viscosity, thermal coductivity ad desity of refrigerats at saturatio state. The formulas were developed for R134a, R404a, R407C ad R410A. A disadvatage of the developed depedecies is the eed to kow two parameters of the refrigerat o the saturatio lie: the temperature ad the pressure. I the literature, the depedecies describig the performace of refrigerats, either relate oly to the regio of saturated liquid ad dry saturated or, with its complicated form, make them impossible to be used i simple egieerig calculatios. Therefore, i this paper, the authors have developed the depedecies to determie the thermodyamic ad thermokietic parameters of the refrigerats i all regios, which have high accuracy ad simple form. 59 3. Calculatio formulas of thermodyamic ad thermokietic parameters of R407C Depedig o the state of a refrigerat, i order to uambiguously determie its thermodyamic ad thermokietic parameters, oe idepedet variable is required (saturated liquid, dry saturated ) or two idepedet variables (superheated, subcooled liquid, two-phase regio). As previously metioed, the literature lists quite a umber of depedecies describig the parameters of a refrigerat i the state of saturated liquid ad dry saturated. However, calculatio formulas for thermodyamic parameters for the regios of superheated, subcooled liquid ad two-phase regio, are usually very complicated, which makes them impossible to be used i egieerig practice. Part 1 of the paper presets the fuctioal depedecies describig the thermodyamic ad thermokietic parameters of oe of the most frequetly used refrigerats i mie air refrigerators R407C. The iput ad output data of the R407C parameters required for the aalysis were obtaied from REFPROP 7 (Lemmo et al, 2002). The sought thermodyamic ad thermokietic parameters were described usig polyomials of the 4, 5, 6, 7 or degree, whose coefficiets were determied usig STATISTICA 10 (StatSoft, 2011). For this purpose, oe of the oliear estimatio methods of least squares was used the Leveberg-Marquardt method. Leveberg-Marquardt is a modificatio (extesio) of the Gauss-Newto algorithm. Usig the loss fuctio of least squares, as i the case of the Gauss-Newto algorithm, to fid the parameter estimates of least squares, the partial derivatives of the secod order do ot eed to be calculated (or estimated approximately), as for each iteratio, to calculate the gradiet, a correspodig system of liear equatios is solved (StatSoft, 2006). The depedecies describig specific parameters of the refrigerat R407C were selected so as to obtai the largest possible values of the correlatio coefficiets ad coefficiets of determiatio ad, at the same time, the smallest possible values of both mea ad maximum deviatios (absolute ad relative). Thus, the obtaied polyomial coefficiets were give to the earest 12 digits i the literature, the authors typically defie coefficiets with greater accuracy, for example i (de Mote, 2002) to 15 digits, ad i (Dig et al., 2005) to 20 digits. Depedig o the parameter of the refrigerat, 3 to 6 polyomials were tested i order to obtai the most accurate calculatio results possible. The rest of this article presets oly these depedecies for which the statistical aalysis showed the highest correlatio coefficiets ad coefficiets of determiatio ad the lowest values of deviatios.

60 3.1. Saturated liquid regio For the R407C refrigerat i a saturated liquid state, depedecies were determied describig the basic thermodyamic parameters as a fuctio of pressure: temperature T' [K], specific ethalpy h' [kj/kg], specific heat c p ' [kj/(kg K)], desity ρ' [kg/m 3 ], as well as thermodyamic ad thermokietic parameters: thermal coductivity λ' [W/(m K)] 10 3, the coefficiet of dyamic viscosity μ' [kg/(m s)], Pradtl umber Pr [-], surface tesio σ' [N/m]. Usig the program REFPROP 7 for the pressures of 0.5 40 bar with variability of 0.05 bar, the values of the correspodig parameters of saturated liquid were read. A total of 791 data was used for the calculatios for each of the aalyzed properties of the refrigerat. The give rage of pressure chages is sigificatly exteded whe compared to the observed chages i the refrigerat pressure durig a trouble-free operatio of mie air compressio refrigerators. Table 2 illustrates the depedecies. Calculatio formulas for the thermodyamic ad thermokietic parameters of the R407C refrigerat i a saturated liquid state TABLE 2 No. Parameter Uit Formula Formula No. 1 2 3 4 5 1 Temperature [K] 2 Specific ethalpy [kj/kg] 3 Specific heat [kj/(kg K)] 4 Desity [kg/m 3 ] 6 l 0 (1) 1 T a p a l 0 (2) 1 h a p a ' p (3) 0 c a p a l p a0 (4) 1 5 Coefficiet of thermal coductivity [W/(m K)] 10 3 ' a l p a0 (5) 1 6 Coefficiet of dyamic viscosity [kg/(m s)] a l p a0 (6) 1

61 1 2 3 4 5 7 Pradtl umber [-] Surface tesio [N/m] a l p a0 (7) 1 a l p a0 () 1 Pr' The determied coefficiets of the polyomial for the specific properties of the refrigerat have bee summarized i Table 3 (thermodyamic parameters) ad Table 4 (thermokietic parameters). Coefficiets of polyomials describig the thermodyamic parameters of saturated liquid of the R407C refrigerat TABLE 3 No. Coefficiets Formula T' = f (p) h' = f (p) c p ' = f (p) ρ' = f (p) (1) (2) (3) (4) 1 a 0 2,29250321067E+02 1,40422220472E+02 1,252960459E+00 1,305616075E+03 2 a 1 2,07331294777E+01 2,73191911150E+01 2,7379364921E-02 6,4273062633E+01 3 a 2 2,1619095543E+00 1,6732501997E+00 1,427611661E-04 5,32615534727E+00 4 a 3 2,3177174095E-01 1,475950451E+00 2,62736927675E-04 1,10497623222E+01 5 a 4 5,0399944951E-03 2,15960117966E+00 4,1291061261E-05 1,9404030402E+01 6 a 5 9,04543420167E-03 3,221001106E+00 2,060607457E-06 2,95276767573E+01 7 a 6 1,16532121747E-03 1,70547615957E+00 1,0032729701E-07 1,56232932645E+01 a 7 4,01149194E-01 1,334091355E-09 3,63402404E+00 9 a 3,59632334415E-02 1,36404350024E-11 3,297555664E-01 Coefficiets of polyomials describig the thermokietic parameters of saturated liquid of the R407C refrigerat TABLE 4 Formula No. λ' = f (p) μ' = f (p) Pr' = f (p) σ' = f (p) (5) (6) (7) () 1 a 0 1,24697265723E+02 4,0431461193E-04 4,29410020046E+00 1,773125769E-02 2 a 1 1,19153244076E+01 1,3964947413E-04 9,3059757759E-01 3,57224306557E-03 3 a 2 1,6914297365E+00 2,07000553E-05 3,59549913515E-01 3,2025739969E-04 4 a 3 3,491941516E-01 2,7772239213E-06 3,29394521967E-01 4,3146435591E-06 5 a 4 9,57437765626E-01 1,64363225291E-06 7,31145922262E-01 2,9930077241E-05 6 a 5 1,3797551090E+00 2,67233304436E-06 1,02550064E+00 4,7770267702E-05 7 a 6 7,07926072507E-01 1,41917623695E-06 5,607232549E-01 2,6252209510E-05 a 7 1,61712602790E-01 3,3425914299E-07 1,2955040799E-01 6,364715939E-06 9 a 1,3991606597E-02 2,9792202377E-0 1,1356407643E-02 5,997619606E-07 Coefficiet

62 3.2. Dry saturated regio For the dry saturated regio, aalogous depedecies were determied as for the refrigerat i a saturated liquid state: temperature T'' [K], specific ethalpy h'' [kj/kg], specific heat c p '' [kj/(kg K)], desity ρ'' [kg/m 3 ], thermal coductivity λ'' [W/(m K)] 10 3, the coefficiet of dyamic viscosity μ'' [kg/(m s)], Pradtl umber Pr'' [-], surface tesio σ'' [N/m]. The depedecies have bee developed as for the saturated liquid state, i.e. based o 791 data for each of the properties. Similarly as before, the give formulas are valid for the pressures of 0.5 to 40 bar. The followig tables summarize: calculatio formulas of the thermodyamic ad thermokietic parameters of the R407C refrigerat i the state of dry saturated Table 5, polyomial coefficiets of the depedecies that describe the thermodyamic parameters of dry saturated of the refrigerat Table 6, polyomial coefficiets of the depedecies that describe the thermokietic parameters of dry saturated of the refrigerat Table 7. TABLE 5 Calculatio formulas of the thermodyamic ad thermokietic parameters of the R407C refrigerat i the state of dry saturated No. Parameter Uit Formula Formula No. 1 2 3 4 5 1 Temperature [K] 6 l 0 (9) 1 T a p a 2 Specific ethalpy [kj/kg] 3 Specific heat 5 l 0 (10) 1 h a p a '' p 7 (11) 0 c a p 4 Desity [kg/m 3 ] 7 0 a p (12) 5 Coefficiet of thermal coductivity [W/(m K)] 10 3 '' a p (13) 0 6 Coefficiet of dyamic viscosity [kg/(m s)] 0 a p (14)

63 1 2 3 4 5 7 Pradtl umber [-] Surface tesio [N/m] Pr'' a p (15) 0 a l p a0 (16) 1 Polyomial coefficiets describig the thermodyamic parameters of dry saturated of the R407C refrigerat TABLE 6 Formula No. T'' = f (p) h'' = f (p) c p '' = f (p) ρ'' = f (p) (9) (10) (11) (12) 1 a 0 2,3626067925E+02 3,9436315999E+02 7,00107253561E-01 2,247240711E-01 2 a 1 2,0279797499E+01 1,1756417070E+01 9,61657195713E-02 4,40797044E+00 3 a 2 2,1299526127E+00 3,06023346166E+00 1,4336014475E-02 7,7969653753E-02 4 a 3 4,41905476479E-01 1,5921507467E+00 1,62570416E-03 1,09249091955E-02 5 a 4 2,273240762E-01 3,053170147E+00 1,04431734622E-04 6,50450529756E-04 6 a 5 9,193764425E-02 4,7275556674E+00 3,1391572933E-06 2,35393536693E-05 7 a 6 1,17214121233E-02 2,51140699763E+00 7,2973633399E-0 4,4721401100E-07 a 7 5,9426044223E-01 5,7577577269E-10 3,591912073E-09 9 a -5,3493975696E-02 Coefficiet Polyomial coefficiets describig the thermokietic parameters of dry saturated of the R407C refrigerat TABLE 7 Formula No. λ'' = f (p) μ'' = f (p) Pr'' = f (p) σ'' = f (p) (13) (14) (15) (16) 1 a 0 7,732196700E+00 9,07465795E-06,15095257062E-01 1,6962463919E-02 2 a 1 1,61150931127E+00 1,110016454E-06 3,6122364256E-02 3,35402490636E-03 3 a 2 2,605711610E-01 1,74651516494E-07 1,097796246E-03 3,2246202505E-04 4 a 3 3,0490524277E-02 1,609309104E-0 3,06064660413E-04 2,6614172933E-06 5 a 4 2,1107596900E-03 9,3532559774E-10 5,7041245411E-05 3,15456114972E-05 6 a 5,0934272E-05 3,060036095E-11 3,7699465436E-06 5,0962127952E-05 7 a 6 2,1566694077E-06 5,95296576200E-13 1,259936562E-07 2,0424020706E-05 a 7 2,464905033E-0 6,1410370300E-15 2,1263616015E-09 6,0265455746E-06 9 a 1,55766549265E-10 2,56315570371E-17 1,4615666017E-11 6,392122756E-07 Coefficiet

64 3.3. Superheated regio I the superheated regio, the thermodyamic state of the refrigerat is give uiquely by two parameters of state. Therefore, determiatio of the depedece characterized by the highest possible value of the correlatio (determiatio) coefficiet, ad possibly small deviatios, is becomig more complicated. First of all, the umber of data eeded to coduct estimatios icreases sigificatly, ad the time of calculatio legthes cosiderably. For further calculatios, the authors developed 4 depedecies describig the parameters of the refrigerat i the superheated regio: specific ethalpy as a fuctio of pressure ad temperature: h = f(p,t), specific ethalpy as a fuctio of pressure ad specific etropy: h = f(p,s), specific etropy as a fuctio of pressure ad temperature: s = f(p,t), temperature as a fuctio of pressure ad specific ethalpy: T = f(p,h). Also here, these depedecies apply to he pressures of 0.5 to 40 bar, ad the temperatures from the dry saturated temperature to 100 C. Usig the REFPROP program for variable pressure of 0.1 bar ad a variable temperature of 1 C, the correspodig values of the specific ethalpy ad the specific etropy were read. I this way, to determie idividual calculatio formulas, 23,033 data were used. The resultig calculatio formulas have bee illustrated i Table, ad the coefficiets for the specific equatios i Table 9. Calculatio formulas of the thermodyamic parameters of the R407C refrigerat i a superheated vapor state TABLE No. Parameter Uit Formula Formula No. 1 2 3 4 Specific ethalpy as a fuctio of pressure ad temperature Specific ethalpy as a fuctio of pressure ad specific etropy Specific etropy as a fuctio of pressure ad temperature Temperature as a fuctio of pressure ad specific ethalpy 5 (17) 1 [kj/kg] h a p b t c 6 (1) 1 [kj/kg] h a p b s c 4 (19) 1 [kj/(kg K)] s a p b t c 4 (20) 1 [K] T a p b h c 3.4. Subcooled liquid regio I the subcooled liquid regio, the thermodyamic state of the refrigerat is also give uiquely by two state parameters. Therefore, the depedece was determied, describig the specific ethalpy of the refrigerat i the subcooled liquid regio as a fuctio of pressure ad temperature, as well as the depedece describig the temperature as a fuctio of pressure ad specific ethalpy. The value of the depedet variable (specific ethalpy) was read for the

65 Polyomial coefficiets describig the thermodyamic parameters of superheated of the R407C refrigerat TABLE 9 Formula No. h = f(p,t) h = f(p,s) s = f(p,t) T = f(p,h) (17) (1) (19) (20) 1 a 1 1,65294961595E+03 2,9415441995E+01 1,999364561E+00 1,47750291327E+02 2 a 2 1,79926636274E+00 7,6456222377E-01,53411671460E-02 7,272094227E-01 3 a 3 2,7465125363E-01 1,0995420102E-01 1,960452945E-02 5,23261034313E-02 4 a 4 1,0274159915E-01 1,7015024797E-01 3,124215641E-02 1,22277763E-02 5 a 5 4,1653976167E-02 9,973547721E-02 6 a 6,55235139267E-03 7 b 1 7,264642690E+02,06701613754E+02 2,3245244605E-01 2,64445732330E+02 b 2,309332279E-01 3,5377935763E+01 1,0529055396E-02 9,40969469435E-01 9 b 3 1,119255401E-01 5,34215907946E+00 2,45520632113E-03 6,3941362736E-02 10 b 4 3,74464624306E-02 3,40469100403E+00 4,69577711025E-04 1,9211550901E-02 11 b 5 1,4413353477E-02 1,764037523E+00 12 b 6 7,34029559766E-02 13 c 1 7,27933120437E+04 1,46323609794E+03 3,56423749994E+02 1,42106976399E+04 14 c 2 1,430773506E+02 1,53111291910E+01 2,4541953620E+01 4,53230023E+02 15 c 3 5,24100047947E+01 2,6175009115E+00 6,25022392690E+00 6,00695000076E+01 16 c 4 1,799447937E+01 5,576617227E-01 7,2374202256E-01 1,20494117267E+00 17 c 5,3177713710E+00,72963953015E-01 1 c 6 4,2095710375E-01 Coefficiet pressures of 0.5 to 40.0 bar (i icremets of 0.1 bar) ad the temperatures of 100 C to the temperature of a saturated liquid (i icremets of 1 C). I this way, 55,524 data were obtaied for the aalysis. The same data was also used to determie the formula for the refrigerat temperature. The forms of these two fuctios have bee illustrated i Table 10, ad the coefficiets of the polyomial i Table 11. Calculatio formulas of the thermodyamic parameters of the R407C refrigerat i a subcooled liquid state TABLE 10 No. Parameter Uit Formula Formula No. 1 Specific ethalpy as a fuctio of pressure ad temperature 6 (21) 1 [kj/kg] h a p b t c 2 Temperature as a fuctio of pressure ad specific ethalpy 4 (22) 1 [K] T a p b h c

66 Polyomial coefficiets describig the thermodyamic parameters of the subcooled liquid of the R407C refrigerat TABLE 11 Formula No. h = f(p,t) T = f(p,h) (21) (22) 1 a 1 4,979642744E+00 4,171939615E+00 2 a 2 5,7501423043E-02 4,16292119152E-03 3 a 3 1,471491946E-02 2,05420514E-03 4 a 4 6,549431332E-03 1,401941292E-03 5 a 5 3,50217321209E-03 6 a 6 1,7370921417E-03 7 b 1 2,9134107427E+01 1,6030397764E+01 b 2 3,22116370517E-01,727603940E-05 9 b 3 7,947456227E-02 7,0949773051E-03 10 b 4 3,3477132455E-02 4,95516120731E-03 11 b 5 2,215397674E-02 12 b 6 1,53791260925E-02 13 c 1 4,147066030E+01 2,344143079E+04 14 c 2 2,5404314572E+01,25333111E+01 15 c 3 7,7003553422E+00 3,1610776407E+01 16 c 4 2,703292712E+00 6,1073369249E+00 17 c 5 1,0399077301E+00 1 c 6 4,9633399666E-01 Coefficiet 3.5. Two-phase regio For the two-phase regio, the authors developed a relatioship describig the heat of vaporizatio as a fuctio of pressure. The depedece was based upo the data obtaied i the same way as the parameters of the desity lie (791 data). The formula is preseted i Table 12, ad the polyomial coefficiets are cotaied i Table 13. Calculatio depedece describig the heat of vaporizatio of the R407C refrigerat TABLE 12 No. Parameter Uit Formula Formula No. 1 Heat of vaporizatio [kj/kg] l 0 (23) 1 r a p a

67 Polyomial coefficiets describig the heat of vaporizatio of the R407C refrigerat TABLE 13 Formula No. r = f (p) (23) 1 a 0 2,4901409447E+02 2 a 1 1,556217972E+01 3 a 2 1,3709019024E+00 4 a 3 3,0607965E+00 5 a 4 5,24512520779E+00 6 a 5 7,9490397037E+00 7 a 6 4,21695552902E+00 a 7 9,960900769E-01 9 a,9452179330e-02 Coefficiet 4. Statistical verificatio of calculatio formulas of the thermodyamic ad thermokietic parameters of the R407C refrigerat I order to verify the correctess of the developed depedecies describig the thermodyamic ad thermokietic parameters, for each model, correlatio coefficiets, coefficiets of determiatio, as well as absolute ad relative deviatios were calculated betwee the values give from the program REFPROP 7 (Lemmo et al, 2002) ad the calculated oes. The values of the correlatio coefficiets ad the coefficiets of determiatio have bee illustrated i Table 14. TABLE 14 Correlatio coefficiets ad coefficiets of determiatio of the calculatio formulas for the thermodyamic ad thermokietic parameters of the R407C refrigerat No. Formula Regio Correlatio coefficiet R [-] Coefficiet of determiatio R 2 [-] 1 2 3 4 5 6 1 T' = f (p) (1) Saturated liquid 0,9999999951 0,9999999901 2 h' = f (p) (2) Saturated liquid 0,999999434 0,99999696 3 c p ' = f (p) (3) Saturated liquid 0,999992169 0,9999964337 4 ρ' = f (p) (4) Saturated liquid 0,9999951614 0,999990322 5 λ' = f (p) (5) Saturated liquid 0,999992677 0,9999965355 6 μ' = f (p) (6) Saturated liquid 0,999999329 0,999999665 7 Pr' = f (p) (7) Saturated liquid 0,996101992 0,9972223299 σ' = f (p) () Saturated liquid 0,999999990 0,999999971 9 T'' = f (p) (9) Dry saturated 0,9999999307 0,999999614 10 h'' = f (p) (10) Dry saturated 0,9999594306 0,9999162

6 1 2 3 4 5 6 11 c p '' = f (p) (11) Dry saturated 0,9999964909 0,99999291 12 ρ'' = f (p) (12) Dry saturated 0,999999976 0,9999999753 13 λ'' = f (p) (13) Dry saturated 0,9999962025 0,9999924050 14 μ'' = f (p) (14) Dry saturated 0,999945443 0,99996909 15 Pr'' = f (p) (15) Dry saturated 0,9999972450 0,9999944900 16 σ'' = f (p) (16) Dry saturated 0,999999952 0,9999999705 17 h = f(p,t) (17) Superheated 0,9999221669 0,999443400 1 h = f(p,s) (1) Superheated 0,997110270 0,9942443597 19 s = f(p,t) (19) Superheated 0,995500924 0,9910220913 20 T = f(p,h) (20) Superheated 0,9999634400 0,99992613 21 h = f(p,t) (21) Subcooled liquid 0,9999993192 0,99999633 22 T = f(p,h) (22) Subcooled liquid 0,999997179 0,999994375 23 r = f(p) (23) Two-phase 0,999995946 0,999991792 The developed depedecies are characterized by very high values of correlatio coefficiets i all cases they exceed 99%, ad they are frequetly close to oe. Also, the coefficiets of determiatio are characterized by the values close to oe, provig that the models almost etirely explai the variability of the depedet variable. The lowest values of the correlatio coefficiets ad the coefficiets of determiatio exist for the depedece describig the specific etropy i superheated regio (formula 19) ad are, respectively, 0.995500924 ad 0.9910220913. Such good fittig of the calculatio results to the data meas that, i most cases, the absolute ad the relative deviatio, listed i Table 15, betwee the data from the program REFPROP 7 (Lemmo et al., 2002) ad the calculated oes, are very small. Absolute ad relative deviatios betwee the give ad calculated values TABLE 15 No. Formula Regio Absolute deviatio Relative deviatio [%] 1 2 3 4 5 6 7 9 Saturated mea 0,002625 mea 0,00044 1 T' = f (p) (1) [K] liquid maximum 0,009304 maximum 0,002652 2 h' = f (p) (2) 3 c p ' = f (p) (3) 4 ρ' = f (p) (4) 5 λ' = f (p) (5) 6 μ' = f (p) (6) 7 Pr' = f (p) (7) Saturated liquid Saturated liquid Saturated liquid Saturated liquid Saturated liquid Saturated liquid mea 0,042417 mea 0,01605 [kj/kg] maximum 0,246513 maximum 0,17441 mea 0,000791 mea 0,041573 [kj/(kg K)] maximum 0,006444 maximum 0,302075 mea [kg/m 3 0,3660 mea 0,0390 ] maximum 2,20495 maximum 0,206 mea [W/(m K)] 10 3 0,022564 mea 0,03020 maximum 0,164756 maximum 0,266265 mea [kg/(m s)] 10 3 0,000035 mea 0,033062 maximum 0,000196 maximum 0,305177 mea 0,015927 mea 0,536250 [-] maximum 0,107617 maximum 2,43924

69 1 2 3 4 5 6 7 9 σ' = f (p) () Saturated mea [N/m] 10 liquid 0,000522 mea 0,025271 maximum 0,00226 maximum 0,449592 9 T'' = f (p) (9) Dry saturated mea 0,00959 mea 0,0026 [K] maximum 0,057946 maximum 0,025976 10 h'' = f (p) (10) Dry saturated mea 0,060356 mea 0,014449 [kj/kg] maximum 0,345470 maximum 0,03516 11 c p '' = f (p) (11) Dry saturated mea 0,001753 mea 0,10401 [kj/(kg K)] maximum 0,01429 maximum 0,7443 12 ρ'' = f (p) (12) Dry saturated mea [kg/m 0,00607 mea 0,019952 ] maximum 0,06065 maximum 1,10745 13 λ'' = f (p) (13) Dry saturated mea [W/(m K)] 10 0,012122 mea 0,0295 maximum 0,203014 maximum 2,412664 14 μ'' = f (p) (14) Dry saturated mea [kg/(m s)] 10 0,00000 mea 0,06705 maximum 0,000130 maximum 1,36215 15 Pr'' = f (p) (15) Dry saturated mea 0,000649 mea 0,05775 [-] maximum 0,005052 maximum 0,494715 16 σ'' = f (p) (16) Dry saturated mea [N/m] 10 0,000577 mea 0,031054 maximum 0,003341 maximum 0,573553 17 h = f(p,t) (17) Superheated mea 0,17762 mea 0,039434 [kj/kg] maximum 3,26536 maximum 0,7949 1 h = f(p,s) (1) Superheated mea 1,214291 mea 0,266967 [kj/kg] maximum 11,695349 maximum 3,062732 19 s = f(p,t) (19) Superheated mea 0,007443 mea 0,393223 [kj/(kg K)] maximum 0,062769 maximum 2,94750 20 T = f(p,h) (20) Superheated mea 0,179120 mea 0,05471 [K] maximum 2,54147 maximum 1,15447 21 h = f(p,t) (21) Subcooled mea 0,041994 mea 0,026519 [kj/kg] liquid maximum 1,99072 maximum 0,596669 22 T = f(p,h) (22) Subcooled mea 0,067250 mea 0,0261 [K] liquid maximum 1,936642 maximum 0,55102 23 r = f(p) (23) Two-phase mea 0,091531 mea 0,07623 [kj/kg] maximum 0,59191 maximum 0,739791 The mea relative deviatios are from 0.00044% to 0.536250%, but for oly 4 out of 23 depedecies they exceed 0.1%. The smallest maximum deviatio value is 0.002652% ad cocers the depedece defiig the saturated liquid temperature chage as a fuctio of pressure. The largest oe is 3.062732% ad cocers specific ethalpy chages of the superheated as a fuctio of pressure ad specific etropy. For the 7 depedecies, the maximum deviatios exceed 1% this is due to the wide rage of the applicability of the depedece (especially at low pressures). Table 16 cotais the maximum relative deviatios for these depedecies for differet pressure rages.

70 Maximum relative deviatios for differet pressure rages TABLE 16 No. Formula Regio 1 Pr' = f (p) (7) Saturated liquid 2 ρ'' = f (p) (12) Dry saturated 3 λ'' = f (p) (13) Dry saturated 4 μ'' = f (p) (14) Dry saturated 5 h = f(p,s) (1) Superheated 6 s = f(p,t) (19) Superheated 7 T = f(p,h) (20) Superheated Maximum relative deviatio [%] 0,5 40 bar 1,0 40 bar 0,5 35 bar 1,0 35 bar 1,0 30 bar 2,43924 2,43924 1,453629 1,05310 0,755 1,10745 0,21539 1,10745 0,21539 0,21539 2,412664 0,63521 2,412664 0,63521 0,63521 1,36215 0,427316 1,36215 0,427316 0,427316 3,062732 1,606049 3,062732 0,94036 0,94036 2,94750 1,937215 2,94750 1,30641 1,30641 1,15447 0,367569 1,15447 0,367569 0,367569 A decrease i the pressure rage reduces the umber of maximum relative deviatios exceedig 1%. Ad so, for a chage of pressure i the rage of 1.0 30 bar, oly for the depedece describig the specific etropy of superheated as a fuctio of pressure ad temperature, the aforemetioed deviatio is slightly higher tha 1% (1.30%). 5. Summary The kowledge of the thermodyamic ad thermokietic parameters of refrigerats is ecessary for the aalysis of refrigeratio circuits, for the modelig ad desigig of refrigerators ad heat exchagers. The mie air compressio refrigerators curretly use the followig refrigerats: R407C, R404A, R507 ad R134a. This work discusses the first of the above refrigerats. The thermodyamic ad thermokietic parameters of this refrigerat (R407C) were described by a total of 23 depedecies applicable i the regios of subcooled liquid, saturated liquid, twophase regio, dry saturated ad superheated. The depedecies i the subcooled liquid regio ad the superheated regio are especially useful i aalyzig the work of refrigeratio equipmet where, i order to uambiguously determie the state of a refrigerat, the kowledge of two of thermodyamic parameters is required. All the formulas are applicable i the wide rage of pressures (0.5 40.0 bar) ad are characterized by very high values of the correlatio coefficiets ad coefficiets of determiatio. I additio, their simple formula should be metioed. Give the above, it may be stated that these relatioships ca be widely applied i all calculatios relatig to the refrigeratio ad air coditioig systems, both i miig ad i evirometal egieerig.

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