Analytical calculation of adiabatic processes in real gases

Transcription

1 Journal of Physs: Conferene Seres PAPER OPEN ACCESS Analytal alulaton of adabat roesses n real gases o te ths artle: I B Amarskaja et al 016 J. Phys.: Conf. Ser Related ontent - Shortuts to quantum adabat roesses J G Muga, X Chen, E orrontegu et al. - Letters and Comments Joaqum Analeto and Máro G Perera - Rely to 'Comment on "Dssatve work n thermodynams"' Joaqum Analeto, Máro G Perera and J M Ferrera Vew the artle onlne for udates and enhanements. hs ontent was downloaded from IP address on 04/0/018 at 08:57

2 Journal of Physs: Conferene Seres 754 (016) IOP Publshng do: / /754/11/11003 Analytal alulaton of adabat roesses n real gases I B Amarskaja, V S Belousov, P S Flov Ural Federal Unversty, 19 Mra street, Ekaternburg, Russa E-mal: tot@urfu.ru Abstrat. he mat of gases nondealty n the omresson and exanson roesses on the sef heat rato and the heat aaty s analyzed. he sef heat rato varaton leads to temerature varaton durng omresson n the omressor and exanson n the turbne and, onsequently, the gas turbne yle effeny fator varaton. It s also essental to onsder the gases nondealty n the omresson and exanson roesses n the omresson roesses n omressor. Generally t s assumed durng alulatons that the heat aates deend only on temerature, n ths ase the referene data resented by varous authors dffers markedly. In the real roesses the heat aaty and the sef heat rato deend on temerature and wthn the artular temeratures and ressures range deend on ressure. Consequently, the oeratng flud nondealty n the gas turbne yle should be onsdered. 1. Introduton he roesses of gases omresson n the nonooled omressor and exanson n the turbne an be assumed as adabat to a good aroxmaton. Usually durng the thermodynam analyss of the roesses mentoned above t s assumed that the oeratng flud s an deal gas wth the thermohysal roertes deendng only on temerature. In real roesses the heat aaty and, onsequently, the sef heat rato deend heavly on temerature and wthn the artular temeratures and ressures range deend on ressure, t means that the oeratng flud nondealty n the gas turbne yle should be onsdered. he thermodynam effeny mrovement n the modern gas turbne unts s aheved by means of the nrease n the omresson ressure rato n the omressor and the ombuston roduts temerature rse before the turbne, whh an result n the neessty of the gas nondealty onsderaton. For nstane, the hange of % n the sef heat rato as omared to the k value beng equal to 1.4 at the omresson ressure rato 5,at the temerature before the turbne of 1600 K, at the relatve effeny of the omressor and the turbne 0, 85 results n the r r hange of 35 K and 30 K n temerature at the end of the omresson roess n the omressor and at the end of the exanson roess n the turbne resetvely, n ths ase the gas turbne yle effeny fator hanges n %. herefore the aurate determnaton of the sef heat rato values s of hgh mortane.. he ressure deendene of the sef heat rato for the nondeal gas Usually durng the alulatons the heat aaty s taken to be not deendng on ressure and the temerature deendenes at the ressure of 0.1 MPa, resented n the gudelnes [1-3] are used. It should be mentoned that sometmes the referene data resented by varous authors dffer markedly, as t s seen n Fg.1, where the deendenes mentoned above are gven for ar. t Content from ths work may be used under the terms of the Creatve Commons Attrbuton 3.0 lene. Any further dstrbuton of ths work must mantan attrbuton to the author(s) and the ttle of the work, journal taton and DOI. Publshed under lene by IOP Publshng Ltd 1

3 Journal of Physs: Conferene Seres 754 (016) IOP Publshng do: / /754/11/11003 Fgure 1. emerature deendene of the molar heat aaty at onstant ressure of 0.1 MPa he ressure deendene of the ar heat aaty was aroxmated n [4] by the olynomals, obtaned by the table data roessng, but the heat aaty at onstant volume, whh s nluded n the sef heat rato exresson was alulated by the Meyer relaton v R beng true only for the deal gas. he resent exresson s not arorate for the real gas and the relaton between the heat aates s wrtten as v v v v v v he dervatves n the sef heat exresson an be alulated only f the real gas state equaton s known. he ressure deendene at dfferent temeratures was onsdered wth a orreton, 0, 0,, the temerature deendene of the heat aaty at ressure of 0.1 MP, to. (1) he orreton to the ressure deendene was aroxmated by data [3] as follows 4, A ехр 0,1 a 0, () 50 where, A, b b a. (3) 0 1 j0 j 100 j

4 Journal of Physs: Conferene Seres 754 (016) IOP Publshng do: / /754/11/11003 he analytal temerature deendene at ressure of 0.1 MPa was aeted n aordane wth [3]: In ths ase the Redlh-Kwong and Dterh equatons [] are the most adequate equatons []. he devaton from dealty an be also taken nto onsderaton by the omressblty fator v z, the analytal exresson of whh an be obtaned by the referene data roessng [3]. R he roessng results for ar are resented n Fg.. Fgure. emerature deendene of the ar omressblty at dfferent ressures a In Dterh state equaton v b ex R the orretons for the nteratons Rv between moleules and ther volume, defned from the ondton that the frst and the seond order r r dervatves are equal to zero v v 0 n the rtal ont, are as follows v r a R v, b r r. he results of the sef heat rato alulaton by the Dterh equaton are resented n Fg.3. he nondealty onsderaton at the ressure of 4MPa results n the sef heat rato hange from k=1.4 to k=1.5 value, whh results n the temerature nrease from 83 to 93 K at the end of omresson at the omresson ressure rato 5 and at the relatve effeny of the omressor t 0, 85. r r 3

5 Journal of Physs: Conferene Seres 754 (016) IOP Publshng do: / /754/11/11003 Fgure 3. emerature deendene of the ar sef heat rato at dfferent ressures he ressure deendene of the heat aaty s suffent for temeratures less than ~ 700 K, whh are tyal for the end of omresson roesses n the omressor. 3. Conluson hus, the aurate determnaton of the sef heat rato values wth onsderaton of both temerature and ressure deendenes of the heat aaty s of hgh mortane. It s artularly true for the omresson roesses n the omressor as far as at the temeratures tyal for the exanson roesses n the turbne the ressure deendene s not so essental and the gas an be assumed to be deal, and n ths ase only the temerature deendene of the heat aates an be onsdered. hs work was arred out at UrFU and fnanally suorted by the Russan Sene Foundaton (rojet number ). Referenes [1] Rd R, Prausnots J and Shervud 198 he gases and lquds roertes (L.:Chemstry) 59 [] Vargaft N B 1963 he gudelnes for thermal and hysal roertes of gases and lquds (M. Physmathgz) 708 [3] Ravdel A 1983 Quk referene of the hysal and hemal values edted by A.A. Ravdel and A.M. Ponomareva (L. Chemstry) 3 [4] Hasanov N G and Shgaov A B 014 he real ar roertes mat on the statonary gas turbne unts erformane (he ower ndustry roblems N 9-10)