k = i-isoentropic exponent
Ukubaluleka koku k ye-valve yokuphepha
ihlelwe ngu-Alessandro Ruzza
by Rentato Pintabona futhi I-Panio Colacicco
Ukulinganiswa kwamavalvu okuphepha aklanyelwe ukukhipha amagesi noma umhwamuko, ngokuya ngeqoqo le-lspesl “E”, kudinga ulwazi lwe-isoentropic exponent k ezimeni zokuphuma.
Ukusetshenziswa ngokunganaki kwe-lspesl Collection “E” isahluko “E.1”, mayelana nosayizi wamavalvu okuphepha, kungaholela ekucabangeni ngokweqile kwamandla okukhipha ama-valve namadiski okuqhuma.
Lesi sihloko sinikeza iziqondiso ezithile zokulinganisa inani lika-k lamagesi wangempela kanye
igqamisa iphutha ngokucabangela u-k olingana nesilinganiso sokushisisa okuthile Cp/Cv
Ukuphuma kwe-isoentropic ngombhobho
Ifomula [1] esetshenziswa eqoqweni elithi “E”, kanye nakwesinye isiNtaliyane [2] nangaphandle [3] standama-ardi, ekubaleni ama-valve okuphepha okufanele akhiphe amagesi noma umhwamuko, yilokho okuphuma kwe-isoentropic ngombhobho ngaphansi kwezimo ezibucayi zokugxuma, okuthi igesi efanelekile ibe yile:
lapho i-expansiku-coefficient C inikezwa ngu:
ngokuba k i-eksponenti ye-isoentropic expansikwi-equation: 
| Fluid | I-P1 (bar) | I-T1 (°C) | q' (kg/h) | q (kg/h) | (q'/q) x 100 |
|---|---|---|---|---|---|
| IMethane | 12 | 50 | 1472 | 1466 | 100.4 |
| IMethane | 23 | 200 | 2314 | 2267 | 102.1 |
| propane | 12 | 100 | 2261 | 2181 | 103.7 |
| UHexane | 12 | 178 | 3099 | 2740 | 113.1 |
| UHexane | 23 | 220 | 6519 | 5111 | 127.5 |
| I-Heptane | 12 | 215 | 3232 | 2821 | 114.4 |
q'= izinga lokugeleza elibalwa nge-k = Cp/Cv (20 °C, 1 atm)
q = izinga lokugeleza elibalwa nge k = (Cp/Cv) • (Z/Zp)
Ngokwethula i-coefficient yokuhlola k yokuphuma kwe-valve yokuphepha, ebheka umhlaba wonke ukusebenza kwangempela kokuphuma kwe-valve, i-coefficient yokuphepha engu-0.9 kanye ne-compressibility factor Z1 ngoketshezi lwangempela, sifika ekwakhiweni kweqoqo elithi “E”:
I-exponent ye-isoentropic k ingavezwa ngokuthi:
![[2]](https://i0.wp.com/www.besa.it/wp-content/uploads/2022/06/Schermata-2022-06-30-alle-15.39.24.png?ssl=1)
Okokuqala igesi ekahle, ngalo P x V / R x T =1 , kuboniswa ukuthi k ilingana nesilinganiso se-Cp/Cv phakathi kokushisisa okuthile ngokucindezela okungaguquki nevolumu.
Okwe igesi yangempela, k ingavezwa (bheka Isithasiselo B) ngokuthi:
![[3]](https://i0.wp.com/www.besa.it/wp-content/uploads/2022/07/Schermata-2022-06-30-alle-15.39.46.png?ssl=1)
lapho u-Z eyisici esicindezelayo esichazwa ngu-Z=P x V / R x T futhi i-Zp “iyisici esicindezelayo esitholakalayo”. Uma usebenzisa ifomula [3], ngokuya ngeqoqo elithi “E”, amanani e-Cp/Cv, Z kanye ne-Zp kufanele ahlolwe ezimweni zokukhishwa P.1 no-T1.
I-compressibility factor Zp etholakalayo ichazwa kufomula [4] njenge:
![[3.1]](https://i0.wp.com/www.besa.it/wp-content/uploads/2022/07/Schermata-2022-06-30-alle-15.40.20.png?ssl=1)
I-compressibility factor Z ingavezwa kanje:
![[4]](https://i0.wp.com/www.besa.it/wp-content/uploads/2022/07/Schermata-2022-06-30-alle-15.40.29.png?ssl=1){kind=small}
futhi ngokufanayo, ingavezwa ngokuthi:
![[5]](https://i0.wp.com/www.besa.it/wp-content/uploads/2022/07/Schermata-2022-06-30-alle-15.40.36.png?ssl=1){kind=small}
lapho amanani okuthi Z^0, Z^1, Zp^0, Zp^1 afakwe kuthebula ku-Appendix A njengomsebenzi we-Pr kanye ne-Tr.
In [4] futhi [5], Ω i-acentric factor ka-Pitzer echazwa ngokuthi:
![[10]](https://i0.wp.com/www.besa.it/wp-content/uploads/2022/07/Schermata-2022-06-30-alle-15.40.44.png?ssl=1){kind=small}
Lapho i-Pr^SAT ingumfutho we-vapor owehlisiwe ohambisana nenani elincishisiwe lokushisa Tr=T/Tc=0,7. I-Appendix A ibonisa amanani angu-Ω oketshezi oluthile. I-Z e Zp ingaphinda ithathwe ngokuqondile kuzibalo zokuhlaziya zombuso.
Isibonelo sezinombolo
Ukuphendukela esibonelweni sezinombolo, ake sithi sidinga ukubala umthamo wokukhipha we-valve yokuphepha ngaphansi kwezimo ezilandelayo:
| Fluid | n-Butano | |
| Isimo somzimba | umhwamuko oshisa kakhulu | |
| Isisindo samangqamuzana | M | 58,119 |
| Setha ingcindezi | P | 19,78 bar |
| Ukucindezela ngokweqile | 10% | |
| Izinga lokushisa loketshezi | T | I-400 K |
| I-coefficient ye-Efflux | 0,9 | |
| Ububanzi be-Orifice | Do | 100 mm |
ingcindezi yokukhipha inikezwa ngu:
okuka-n-Butane: Tc=425,18 K kanye ne-Pc=37,96 bar, Sine:
futhi sisebenzisa amathebula akuSithasiselo A, sina:
Ukwazi umthamo othize womhwamuko ezimeni zokuphuma (P1, T1) olingana no-0,01634 m^3/kg (0,0009498 m^3/g-mole), singaphinda sibale u-Z kusukela kulokhu:
Uma kubhekwa isilinganiso sokushisisa okuthile ngokucindezelwa okungaguquki kanye nevolumu, ezimeni zokukhishwa (P1, T1), elilingana no-1,36, lisuka kufomula [3] Sine:
147060
Ukusebenzisa ifomula [1], esixazululwe ekubalweni kwesilinganiso sokugeleza, sinenani lesilinganiso sokugeleza kokukhipha 147.060 kg / h.
174848
Ukube esikhundleni salokho sasebenzisa inani le-Cp/Cv ku-1 atm no-20 °C, ngabe k =1,19 futhi kusukela kufomula [1] izinga lokugeleza kokukhishwa kwe 174.848 kg / h.
Lokhu bekuzosiholela ekutheni overestimate ukukhishwa umthamo we-valve yokuphepha ngokuzungezile 19%
ISEXWAYISO:
Iphutha elingenziwa ngokunikeza inani Cp/Cv ku-k lingaba phezulu kakhulu kunalesi sibonelo.
NGAPHEZU kuka-20%
Ukuze unikeze umbono, ithebula elilandelayo libonisa izilinganiso zokugeleza ze-orifice engu-18-mm kwamanye ama-hydrocarbon agcwele, abalwe ezimweni ezimbili. Izibalo zenziwe nge-develo ekhethekileped isofthiwe.
| Fluid | I-P1 (bar) | I-T1 (°C) | q' (kg/h) | q (kg/h) | (q'/q) x 100 |
|---|---|---|---|---|---|
| IMethane | 12 | 50 | 1472 | 1466 | 100.4 |
| IMethane | 23 | 200 | 2314 | 2267 | 102.1 |
| propane | 12 | 100 | 2261 | 2181 | 103.7 |
| UHexane | 12 | 178 | 3099 | 2740 | 113.1 |
| UHexane | 23 | 220 | 6519 | 5111 | 127.5 |
| I-Heptane | 12 | 215 | 3232 | 2821 | 114.4 |
Isofthiwe ayisebenzisi amafomula [4] [5] kodwa, kusukela kokushintshiwe I-Redlich ne-Kwong equation yezwe, ibala inani le-eksponenti ye-isoentropic kusetshenziswa izixhumanisi ze-thermodynamic.
