ÏÐÅÄÅËÜÍÀß ÝÔÔÅÊÒÈÂÍÎÑÒÜ ÀÄÑÎÐÁÖÈÎÍÍÎÃÎ ÒÅÏËÎÂÎÃÎ ÍÀÑÎÑÀ

12
ÂÅÑÒÍ. ÌÎÑÊ. ÓÍ-ÒÀ. ÑÅÐ. 2. ÕÈÌÈß. 2007. Ò. 48. ¹ 1
ÓÄÊ 541.183+621.577
ÏÐÅÄÅËÜÍÀß ÝÔÔÅÊÒÈÂÍÎÑÒÜ ÀÄÑÎÐÁÖÈÎÍÍÎÃÎ
ÒÅÏËÎÂÎÃÎ ÍÀÑÎÑÀ
Â.Ë. Çåëåíêî, Ë.È. Õåéôåö
(êàôåäðà õèìè÷åñêîé òåõíîëîãèè è íîâûõ ìàòåðèàëîâ; e-mail: heifets@tech.chem.msu.ru)
Íà îñíîâå ïðåäñòàâëåíèÿ î íåðåêóïåðèðóåìûõ ïîòåðÿõ ýíåðãèè â äèññèïàòèâíûõ ïðîöåññàõ
ìàëîãî ìàñøòàáà ïðîâåäåíà îöåíêà âåðõíåé ãðàíèöû ýôôåêòèâíîñòè òåïëîâîãî íàñîñà, äîñòèæèìîé â îòñóòñòâèè ïîòåðü ïðè òåïëîîáìåíå ñ òåïëîíîñèòåëåì, íî ñ ó÷åòîì íåðàâíîâåñíîñòè ïðîöåññà íåèçîòåðìè÷åñêîãî ïåðåíîñà ïàðà. Ýòà âåëè÷èíà ìåíüøå òåðìîäèíàìè÷åñêè
ðàâíîâåñíîé ýôôåêòèâíîñòè è ÿâëÿåòñÿ áîëåå òî÷íûì îðèåíòèðîì ïðè ïîèñêå ðàöèîíàëüíûõ ñõåì îðãàíèçàöèè ïðîöåññà.
Ïîñòàíîâêà çàäà÷è
 ðåàëüíûõ äèíàìè÷åñêèõ ñèñòåìàõ âîçíèêàþò
äèññèïàòèâíûå ïðîöåññû ñòîëü ìàëîãî ìàñøòàáà,
÷òî íåâîçìîæíî â ïðèíöèïå èëè ïî òåõíè÷åñêèì è
ýêîíîìè÷åñêèì ïðè÷èíàì ðåêóïåðèðîâàòü äèññèïèðóåìóþ â ýòèõ ïðîöåññàõ ýíåðãèþ. Äàëåå òàêèå ïðîöåññû áóäåì íàçûâàòü äèññèïàòèâíûìè ïðîöåññàìè ñ
íåðåêóïåðèðóåìûìè ïîòåðÿìè ýíåðãèè (ÄÏÍÝ). Ýòè
ïðîöåññû, êàê âïðî÷åì è ëþáûå äèññèïàòèâíûå
ïðîöåññû, ÿâëÿþòñÿ èñòî÷íèêàìè ýíòðîïèè â ñèñòåìå.  êîðîòêîöèêëîâûõ àäñîðáöèîííûõ ñèñòåìàõ ðàçäåëåíèÿ ãàçîâ ìàñøòàáîì ÄÏÍÝ ÿâëÿåòñÿ ïðîòÿæåííîñòü ôðîíòà àäñîðáöèè [1], â ýíåðãîóñòàíîâêàõ ñ õèìè÷åñêèì îêèñëåíèåì òîïëèâà – ðàçìåð êàòàëèòè÷åñêîé âñòàâêè, ñèíõðîíèçèðóþùåé ñêîðîñòè îêèñëåíèÿ òîïëèâà è ðàñøèðåíèÿ ãàçîâîé ñìåñè â òóðáèíå
[2]. Ó÷åò ïðîèçâîäñòâà ýíòðîïèè â ÄÏÍÝ ïîçâîëÿåò
îöåíèòü ïðåäåëüíî äîñòèæèìóþ ýôôåêòèâíîñòü, êîòîðàÿ â îòëè÷èå îò ýôôåêòèâíîñòè ðàâíîâåñíîé ñèñòåìû îïðåäåëÿåò áîëåå ðåàëèñòè÷íóþ ãðàíèöó âîçìîæíîãî ïîâûøåíèÿ ýôôåêòèâíîñòè ðåàëüíûõ ñèñòåì.
Ïðîèëëþñòðèðóåì ýòî íà ïðèìåðå àäñîðáöèîííîãî
òåïëîâîãî íàñîñà. Íà ðèñ. 1 ïîêàçàíà ïðèíöèïèàëüíàÿ
ñõåìà òåïëîâûõ ïîòîêîâ â àäñîðáöèîííîì òåïëîâîì
íàñîñå.  óñòàíîâèâøåìñÿ ïåðèîäè÷åñêîì ðåæèìå
óñòðîéñòâî ïîëó÷àåò òåïëîòó Q hs îò èñòî÷íèêà ñ
òåìïåðàòóðîé T hs , òåïëîòó Q ev – îò õîëîäèëüíîé êàìåðû ñ òåìïåðàòóðîé T ev è îòäàåò ïîëó÷åííóþ òåïëîòó Qs âî âíåøíþþ ñðåäó ñ òåìïåðàòóðîé T env .
Ýôôåêòèâíîñòü ðàáî÷åãî öèêëà àäñîðáöèîííîãî òåïëîâîãî íàñîñà õàðàêòåðèçóåò ïàðàìåòð η = Q ev /Q hs ,
ðàâíûé êîëè÷åñòâó ïðîèçâåäåííîãî õîëîäà íà åäèíèöó
çàòðà÷åííîé òåïëîòû è îáîçíà÷àåìûé â ëèòåðàòóðå
àíãëèéñêîé àááðåâèàòóðîé ÑÎÐ (coefficent of perfomancy) [3]. Äëÿ ðàâíîâåñíîãî öèêëà ýôôåêòèâíîñòü
(ηc) àäñîðáöèîííîãî òåïëîâîãî íàñîñà ìîæíî âûðàçèòü ÷åðåç óêàçàííûå çíà÷åíèÿ òåìïåðàòóðû [3]:
ηɫ =
Qev Tev Ths − Tenv
.
=
⋅
Qhs Ths Tenv − Tev
(1)
Òèïîâîé öèêë àäñîðáöèîííîãî òåïëîâîãî íàñîñà
ñîñòîèò èç äâóõ èçîáàð (ñòàäèè àäñîðáöèè è ðåãåíåðàöèè àäñîðáåíòà) è äâóõ èçîñòåð (ñòàäèè íàãðåâà è
Ðèñ. 1. Ïðèíöèïèàëüíàÿ ñõåìà òåïëîâûõ ïîòîêîâ â òåïëîâîì íàñîñå: hs – èñòî÷íèê òåïëîòû
(íàãðåâàþùàÿ ñèñòåìà), env – îêðóæàþùàÿ ñðåäà; ev – èñïàðèòåëü õîëîäèëüíîé êàìåðû
ÂÅÑÒÍ. ÌÎÑÊ. ÓÍ-ÒÀ. ÑÅÐ. 2. ÕÈÌÈß. 2007. Ò. 48. ¹ 1
13
Ðèñ. 2. Äåòàëèçèðîâàííàÿ ñõåìà òåïëîâîãî íàñîñà: 1, 2 – àäñîðáåðû, 3 – êîíäåíñàòîð, 4 –
èñïàðèòåëü, 5 – íàãðåâàþùàÿ ñèñòåìà äëÿ òåïëîíîñèòåëÿ, 6 – îõëàæäàþùàÿ ñèñòåìà äëÿ
òåïëîíîñèòåëÿ (ñs), 7 – öèðêóëÿöèîííûé êîíòóð òåïëîíîñèòåëÿ, 8 – æèäêîñòü (ðàáî÷åå òåëî),
9 – êîíòóð ðàáî÷åé æèäêîñòè ñ õîëîäèëüíèêîì 10 (Tcs = Tenv, q – òåïëîîáìåí)
îõëàæäåíèÿ àäñîðáåíòà) [3–7]. Íà ñòàäèè èçîáàðè÷åñêîé àäñîðáöèè àäñîðáåð ñîåäèíåí ïî ãàçîâîé ôàçå ñ
èñïàðèòåëüíûì îòäåëåíèåì õîëîäèëüíîé êàìåðîé, â
êîòîðîé ïîääåðæèâàåòñÿ ïîñòîÿííàÿ òåìïåðàòóðà Tev è
ñîîòâåòñòâóþùåå ýòîé òåìïåðàòóðå ðàâíîâåñíîå äàâëåíèå ïàðà ðàáî÷åãî òåëà pev = p(T ev ). Íà ñòàäèè
èçîáàðè÷åñêîé ðåãåíåðàöèè àäñîðáåð ñîåäèíåí ñ êîíäåíñàòîðîì, â êîòîðîì â óñëîâèÿõ êîíäåíñàöèè ïàðà
ïîääåðæèâàþòñÿ ïîñòîÿííàÿ òåìïåðàòóðà Tc , ðàâíàÿ
òåìïåðàòóðå îêðóæàþùåé ñðåäû (Tc = Tenv), è ñîîòâåòñòâóþùåå ýòîé òåìïåðàòóðå ðàâíîâåñíîå äàâëåíèå
ïàðà pc = p(T c). Äëÿ ïîâûøåíèÿ ýôôåêòèâíîñòè àäñîðáöèîííîãî òåïëîâîãî íàñîñà ïðåäëîæåíî ðåãåíåðèðîâàòü òåïëîòó àäñîðáöèè [3, 4].
Òåïëîâîé íàñîñ ñ ðåãåíåðàöèåé òåïëîòû àäñîðáöèè
èìååò äâà âíóòðåííèõ öèðêóëÿöèîííûõ êîíòóðà
(ðèñ. 2): êîíòóð ðàáî÷åé æèäêîñòè, ïî êîòîðîìó ñêîíäåíñèðîâàííîå âåùåñòâî âîçâðàùàåòñÿ èç êîíäåíñàòîðà â èñïàðèòåëüíóþ êàìåðó, è êîíòóð òåïëîíîñèòåëÿ
[6]. Â ïðîöåññå àäñîðáöèè àäñîðáåíò îõëàæäàåòñÿ
ïîòîêîì òåïëîíîñèòåëÿ, ÷òî ñïîñîáñòâóåò óâåëè÷åíèþ êîëè÷åñòâà àäñîðáàòà.  ïðîöåññå ðåãåíåðàöèè
àäñîðáåíò íàãðåâàåòñÿ ïîòîêîì òåïëîíîñèòåëÿ, ÷òî
ñïîñîáñòâóåò óìåíüøåíèþ êîëè÷åñòâà àäñîðáàòà.
Ðàñ÷åòíûì ïóòåì â ðàáîòàõ [4–7] è ýêñïåðèìåíòàëüíî â ðàáîòàõ [8, 9] ïîêàçàíî, ÷òî îïòèìèçèðóÿ ïðîöåññû òåïëîîáìåíà â ðàçíûõ ýëåìåíòàõ òåïëîâîãî
7 ÂÌÓ, õèìèÿ, ¹ 1
íàñîñà íå óäàåòñÿ äîñòèãíóòü ðàâíîâåñíîãî çíà÷åíèÿ
ηc. Ïðîöåññû íàãðåâà è îõëàæäåíèÿ àäñîðáåíòà è
òåïëîíîñèòåëÿ ìîãóò áûòü ðàâíîâåñíûìè. Ïîòåðÿìè
ïðè îõëàæäåíèè ðàáî÷åé æèäêîñòè â èñïàðèòåëüíîé
êàìåðå ìîæíî ïðåíåáðå÷ü, ïîñêîëüêó èõ çíà÷åíèå
ìàëî ïî ñðàâíåíèè ñ òåïëîòîé èñïàðåíèÿ. Òåì íå
ìåíåå çíà÷èòåëüíàÿ ðàçíèöà ìåæäó ðàâíîâåñíîé ýôôåêòèâíîñòüþ è ýôôåêòèâíîñòüþ, äîñòèãíóòîé ýêñïåðèìåíòàëüíî èëè âû÷èñëåííîé òåîðåòè÷åñêè, óêàçûâàåò íà òî, ÷òî â ðàáî÷åì öèêëå òåïëîâîãî íàñîñà
ïðèñóòñòâóþò äèññèïàòèâíûå ñòðóêòóðû, õàðàêòåðíûé ìàñøòàá êîòîðûõ ìíîãî ìåíüøå ðàçìåðà òåïëîîáìåííûõ óñòðîéñòâ. Ñóùåñòâåííîé îñîáåííîñòüþ
èçîáàðè÷åñêèõ ñòàäèé àäñîðáöèè è ðåãåíåðàöèè ÿâëÿåòñÿ ïîñòîÿíñòâî äàâëåíèÿ ïàðà ðàáî÷åãî òåëà â
ñëîå àäñîðáåíòà. Â óñëîâèÿõ ïðèåìëåìîé ïðîèçâîäèòåëüíîñòè òåïëîâîãî íàñîñà ïîòîê ïàðà äîñòèãàåò
òàêîé âåëè÷èíû, ïðè êîòîðîé ôîðìèðóåòñÿ òîíêèé
òåìïåðàòóðíûé ïîãðàíè÷íûé ñëîé âáëèçè ôàçû ëèáî
àäñîðáåíòà (ñòàäèÿ àäñîðáöèè), ëèáî êîíäåíñàòà
(ñòàäèÿ ðåãåíåðàöèè). Èìåííî ýòè ïîãðàíè÷íûå ñëîè
îòâåòñòâåííû çà äèññèïàòèâíûå ïðîöåññû, à èõ ìàñøòàá íå ïîçâîëÿåò ðåêóïåðèðîâàòü äèññèïèðóåìóþ â
íèõ ýíåðãèþ. Âîò ïî÷åìó ïðîöåññû â ýòèõ ïîãðàíè÷íûõ ñëîÿõ ÿâëÿþòñÿ íåóñòðàíèìûìè äèññèïàòèâíûìè
ïðîöåññàìè. Ïî àíàëîãèè ñ ðàáîòîé [6] îöåíèì ïðîèçâîäñòâî ýíòðîïèè ïðè ïåðåíîñå ïàðà.
ȼȿɋɌɇ. ɆɈɋɄ. ɍɇ-ɌȺ. ɋȿɊ. 2. ɏɂɆɂə. 2007. Ɍ. 48. ʋ 1
14
qÆľ½¸ÄºÇÈ¸Ä ÓÃÈÆÄž¾ ö Çȶº¾¾ ¾½Ä·¶Æ¾Í»ÇÀÄ¿
¶ºÇÄƷ̾¾
Ⱥɞɫɨɪɛɟɪ ɩɨ ɮɚɡɟ ɩɚɪɚ ɫɨɟɞɢɧɟɧ ɫ ɢɫɩɚɪɢɬɟɥɶɧɨɣ
ɤɚɦɟɪɨɣ. ȼ ɢɫɩɚɪɢɬɟɥɶɧɨɣ ɤɚɦɟɪɟ ɩɪɢ ɩɨɫɬɨɹɧɧɵɯ
ɬɟɦɩɟɪɚɬɭɪɟ Tev ɢ ɞɚɜɥɟɧɢɢ ɧɚɫɵɳɟɧɧɨɝɨ ɩɚɪɚ pev
ƶ¸Ãĸ»ÇÃÄ ɢɫɩɚɪɹɸɬɫɹ dm ɦɨɥɟɣ ɪɚɛɨɱɟɝɨ ɬɟɥɚ,
ɧɚɩɪɢɦɟɪ ɜɨɞɵ. ɗɬɨɬ ɩɚɪ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɞɚɜɥɟɧɢɢ
pev ûƶ¸Ãĸ»ÇÃÄ ɧɚɝɪɟɜɚɟɬɫɹ ɜ ɚɞɫɨɪɛɟɪɟ ɞɨ ɬɟɤɭɳɟɣ ɬɟɦɩɟɪɚɬɭɪɵ ɫɥɨɹ ɚɞɫɨɪɛɟɧɬɚ T ɢ ɞɚɥɟɟ
ƶ¸Ãĸ»ÇÃÄ ɚɞɫɨɪɛɢɪɭɟɬɫɹ. ɋɥɨɣ ɚɞɫɨɪɛɟɧɬɚ, ɢɦɟɸɳɢɣ ɬɟɤɭɳɭɸ ɬɟɦɩɟɪɚɬɭɪɭ T > Tev , ɩɟɪɟɞɚɟɬ
ɩɚɪɭ cp⋅dm⋅( T–Tev) ɞɠɨɭɥɟɣ ɬɟɩɥɨɬɵ. ɉɪɢ ɷɬɨɦ ɷɧɬɪɨɩɢɹ ɫɥɨɹ ɭɦɟɧɶɲɚɟɬɫɹ ɧɚ ɜɟɥɢɱɢɧɭ
d 2s = –cp⋅dm⋅( T–Tev) /T,
ɚ ɷɧɬɪɨɩɢɹ ɩɚɪɚ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɧɚ ɜɟɥɢɱɢɧɭ
d 1s = cp⋅dm⋅ln(T/Tev) ,
ɝɞɟ cp (Ⱦɠ/ɦɨɥɶ.Ʉ) – ɦɨɥɶɧɚɹ ɬɟɩɥɨɟɦɤɨɫɬɶ ɩɚɪɚ.
ɉɨɥɧɨɟ ɢɡɦɟɧɟɧɢɟ ɷɧɬɪɨɩɢɢ ɩɪɢ ɩɟɪɟɧɨɫɟ dm ɦɨɥɟɣ
ɩɚɪɚ ɢɡ ɯɨɥɨɞɢɥɶɧɨɣ ɤɚɦɟɪɵ ɜ ɚɞɫɨɪɛɟɪ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ
T
T
d a s = d 1s + d 2 s = c p ¸ dm ¸ [ ev − ln ev − 1] .
T
T
(2)
ȿɫɥɢ ɜɜɟɫɬɢ ɜɟɥɢɱɢɧɭ q = (T–Tev) /Tev , ɬ ɨ, ɩɪɟɞɫɬɚɜɥɹɹ ɜɵɪɚɠɟɧɢɟ ɜ ɤɜɚɞɪɚɬɧɵɯ ɫɤɨɛɤɚɯ ɮɨɪɦɭɥɵ (2) ɜ
ɜɢɞɟ ɪɹɞɚ ɩɨ ɫɬɟɩɟɧɹɦ q, ɧɟɬɪɭɞɧɨ ɭɛɟɞɢɬɶɫɹ, ɱɬɨ
ɜɵɩɨɥɧɹɟɬɫɹ ɧɟɪɚɜɟɧɫɬɜɨ das > 0. Ɉɱɟɜɢɞɧɨ, ɧɚ ɜɯɨɞɟ
ɩɚɪɚ ɜ ɫɥɨɣ ɚɞɫɨɪɛɟɧɬɚ ɢɦɟɟɬɫɹ ɢɫɬɨɱɧɢɤ ɷɧɬɪɨɩɢɢ,
ɨɛɭɫɥɨɜɥɟɧɧɵɣ Ⱦɉɇɗ, ɜɨɡɧɢɤɲɟɣ ɩɪɢ ɧɟɪɚɜɧɨɜɟɫɧɨɦ
ɧɚɝɪɟɜɟ ɩɚɪɚ. Ⱦɢɮɮɟɪɟɧɰɢɚɥ dm ɦɨɠɧɨ ɜɵɪɚɡɢɬɶ ɱɟɪɟɡ ɞɢɮɮɟɪɟɧɰɢɚɥ ɢɡɨɛɚɪɵ ɚɞɫɨɪɛɰɢɢ w( T) p=const
dm m0
dw
dT
dT ,
(3)
T1
T2
dw
dT
p p ev
¸[
d d s d 1 s d 2 s c p ¸ dm ¸ [
T
T
ln
1] .
Tc
Tc
(5)
ȿɫɥɢ ɜɜɟɫɬɢ ɜɟɥɢɱɢɧɭ g = (T–Tc) / Tc ɢ ɩɪɟɞɫɬɚɜɢɬɶ
ɜɵɪɚɠɟɧɢɟ ɜ ɤɜɚɞɪɚɬɧɵɯ ɫɤɨɛɤɚɯ ɮɨɪɦɭɥɵ (5) ɜ ɜɢɞɟ
ɪɹɞɚ ɩɨ ɫɬɟɩɟɧɹɦ g, ɛɭɞɟɬ ɜɵɩɨɥɧɹɬɶɫɹ ɧɟɪɚɜɟɧɫɬɜɨ
dds > 0. ɗɬɨ ɨɡɧɚɱɚɟɬ , ɱɬɨ ɧɚ ɜɯɨɞɟ ɩɚɪɚ ɜ ɤɨɧɞɟɧɫɚɬɨɪ ɢɦɟɟɬɫɹ ɢɫɬɨɱɧɢɤ ɷɧɬɪɨɩɢɢ, ɨɛɭɫɥɨɜɥɟɧɧɵɣ Ⱦɉɇɗ,
ɜɨɡɧɢɤɲɟɣ ɩɪɢ ɧɟɪɚɜɧɨɜɟɫɧɨɦ ɨɯɥɚɠɞɟɧɢɢ ɩɚɪɚ.
ȼ ɫɬɚɰɢɨɧɚɪɧɨɦ ɰɢɤɥɟ ɤɨɥɢɱɟɫɬɜɨ ɚɞɫɨɪɛɚɬɚ ɜ
ɫɥɨɟ ɧɚ ɫɬɚɞɢɢ ɪɟɝɟɧɟɪɚɰɢɢ ɭɦɟɧɶɲɚɟɬɫɹ ɨɬ w2 =
w( p c, T 3) ɞɨ w1 = w( pc, T4) . ɉɨ ɢɡɨɛɚɪɚɦ ɚɞɫɨɪɛɰɢɢ ɦɨɠɧɨ ɜɵɱɢɫɥɢɬɶ ɧɚɱɚɥɶɧɨɟ (T3) ɢ ɤɨɧɟɱɧɨɟ (T4)
ɡɧɚɱɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɫɥɨɹ ɧɚ ɫɬɚɞɢɢ ɪɟɝɟɧɟɪɚɰɢɢ
( T3 < T4). Ɉɛɳɟɟ ɩɪɨɢɡɜɨɞɫɬɜɨ ɷɧɬɪɨɩɢɢ ɧɚ ɫɬɚɞɢɢ
ɪɟɝɟɧɟɪɚɰɢɢ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟɦ ɜɵɪɚɠɟɧɢɹ (5) ɫ ɭɱɟɬɨɦ (3)
p
ɝɞɟ w – ɚɞɫɨɪɛɰɢɹ ɩɚɪɚ ɜ ɦɨɥɹɯ ɧɚ ɟɞɢɧɢɰɭ ɦɚɫɫɵ
ɫɭɯɨɝɨ ɚɞɫɨɪɛɟɧɬɚ, m0 – ɦɚɫɫɚ ɫɭɯɨɝɨ ɚɞɫɨɪɛɟɧɬɚ ɜ
ɚɞɫɨɪɛɟɪɟ (ɡɧɚɤ ɦɨɞɭɥɹ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɫ ɭɜɟɥɢɱɟɧɢɟɦ
ɬɟɦɩɟɪɚɬɭɪɵ ɚɞɫɨɪɛɟɧɬɚ ɜɟɥɢɱɢɧɚ ɚɞɫɨɪɛɰɢɢ ɭɦɟɧɶɲɚɟɬɫɹ). ȼ ɫɬɚɰɢɨɧɚɪɧɨɦ ɰɢɤɥɟ ɤɨɥɢɱɟɫɬɜɨ ɚɞɫɨɪɛɚɬɚ ɧɚ ɫɬɚɞɢɢ ɚɞɫɨɪɛɰɢɢ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɨɬ ɜɟɥɢɱɢɧɵ
w1 = w ( p ev, T 1) ɞɨ w 2 = w ( p ev, T 2 ) . Ɉɬɫɸɞɚ ɩɨ
ɢɡɜɟɫɬɧɨɣ ɢɡɨɛɚɪɟ ɚɞɫɨɪɛɰɢɢ ɦɨɠɧɨ ɜɵɱɢɫɥɢɬɶ ɧɚɱɚɥɶɧɨɟ (T1) ɢ ɤɨɧɟɱɧɨɟ (T2) ɡɧɚɱɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ
ɫɥɨɹ ɧɚ ɫɬɚɞɢɢ ɚɞɫɨɪɛɰɢɢ (T2 < T1). Ɉɛɳɟɟ ɩɪɨɢɡɜɨɞɫɬɜɨ ɷɧɬɪɨɩɢɢ ɧɚ ɫɬɚɞɢɢ ɚɞɫɨɪɛɰɢɢ ɩɨɥɭɱɢɦ, ɢɧɬɟɝɪɢɪɭɹ ɜɵɪɚɠɟɧɢɹ (2) ɫ ɭɱɟɬɨɦ (3)
Δs a c p m0 ¨
qÆľ½¸ÄºÇÈ¸Ä ÓÃÈÆÄž¾ ö Çȶº¾¾ ¾½Ä·¶Æ¾Í»ÇÀÄ¿
Æ»¹»Ã»Æ¶Ì¾¾
Ⱥɞɫɨɪɛɟɪ ɩɨ ɮɚɡɟ ɩɚɪɚ ɫɨɟɞɢɧɟɧ ɫ ɤɨɧɞɟɧɫɚɬɨɪɨɦ.
ȼ ɚɞɫɨɪɛɟɪɟ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɞɚɜɥɟɧɢɢ pc, ɪɚɜɧɨɦ
ɞɚɜɥɟɧɢɸ ɧɚɫɵɳɟɧɧɨɝɨ ɩɚɪɚ ɪɚɛɨɱɟɝɨ ɬɟɥɚ ɜ ɤɨɧɞɟɧɫɚɬɨɪɟ, ɢ ɬɟɤɭɳɟɣ ɬɟɦɩɟɪɚɬɭɪɟ ɚɞɫɨɪɛɟɪɚ T,
ɩɪɟɜɵɲɚɸɳɟɣ ɬɟɦɩɟɪɚɬɭɪɭ ɜ ɤɨɧɞɟɧɫɚɬɨɪɟ (T > Tc) ,
ƶ¸Ãĸ»ÇÃÄ ɞɟɫɨɪɛɢɪɭɸɬɫɹ dm ɦɨɥɟɣ ɪɚɛɨɱɟɝɨ
ɬɟɥɚ, ɤɨɬɨɪɵɟ ɡɚɬɟɦ ûƶ¸Ãĸ»ÇÃÄ ɨɯɥɚɠɞɚɸɬɫɹ ɜ
ɤɨɧɞɟɧɫɚɬɨɪɟ ɞɨ ɬɟɦɩɟɪɚɬɭɪɵ Tc. Ⱦɚɥɟɟ ɨɯɥɚɠɞɟɧɧɵɣ ɩɚɪ ƶ¸Ãĸ»ÇÃÄ ɤɨɧɞɟɧɫɢɪɭɟɬɫɹ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ Tc. ɉɪɢ ɨɯɥɚɠɞɟɧɢɢ ɩɚɪ ɨɬɞɚɟɬ ɤɨɧɞɟɧɫɚɬɨɪɭ
cp⋅dm⋅( T–Tc) ɞɠɨɭɥɟɣ ɬɟɩɥɚ, ɟɝɨ ɷɧɬɪɨɩɢɹ ɭɦɟɧɶɲɚɟɬɫɹ ɧɚ ɜɟɥɢɱɢɧɭ d1s = c p⋅dm⋅l n (T c T) , ɚ ɷɧɬɪɨɩɢɹ
ɤɨɧɞɟɧɫɚɬɨɪɚ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɧɚ ɜɟɥɢɱɢɧɭ d 2 s =
c p ⋅dm⋅( T–T c ) /T c . Ɉɛɳɟɟ ɢɡɦɟɧɟɧɢɟ ɷɧɬɪɨɩɢɢ ɧɚ
ɫɬɚɞɢɢ ɞɟɫɨɪɛɰɢɢ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ
Tev
T
ln ev 1]dT .
T
T
(4)
T4
dw
T
T
¸ [ ln
1] dT .
dT p p c Tc
Tc
T3
Δs d c p m 0 ¨
(6)
ɋɭɦɦɢɪɭɹ ɜɵɪɚɠɟɧɢɹ (4) ɢ (6), ɩɨɥɭɱɢɦ ɩɨɥɧɨɟ
ɩɪɨɢɡɜɨɞɫɬɜɨ ɷɧɬɪɨɩɢɢ ɜ ɫɬɚɰɢɨɧɚɪɧɨɦ ɰɢɤɥɟ ɬɟɩɥɨɜɨɝɨ ɧɚɫɨɫɚ ɫ ɭɱɟɬɨɦ Ⱦɉɇɗ (ΔS = ΔSa + ΔSd) .
ɂɫɩɨɥɶɡɭɟɦ ɞɥɹ ɭɩɪɨɳɟɧɢɹ ɜɵɤɥɚɞɨɤ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɩɨ ɱɚɫɬɹɦ:
Δs c p m0 {w2 [(
w1 [(
T1
¨
T2
Tev
T
T
T
ln ev ) ( 3 ln 3 ) 2] T2
T2
Tc
Tc
Tev
T
T
T
ln ev ) ( 4 ln 4 ) 2] T1
T1
Tc
Tc
T4
w( p ev , T )
T
w( p c , T ) T
(1 ev ) dT ¨
( 1) dT }.
T
T
T
Tc
T
3
(7)
ȼȿɋɌɇ. ɆɈɋɄ. ɍɇ-ɌȺ. ɋȿɊ. 2. ɏɂɆɂə. 2007. Ɍ. 48. ʋ 1
15
Ɂɚɦɟɬɢɦ, ɱɬɨ ɜɟɥɢɱɢɧɚ ΔS ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɬɟɩɥɨɜɨɝɨ ɢɫɬɨɱɧɢɤɚ Ths.
ÊÊ»ÀȾ¸ÃÄÇÈÒ Ì¾ÀÁ¶ Ç fqo
Ȼɚɥɚɧɫ ɷɧɬɪɨɩɢɢ ɬɟɩɥɨɜɨɝɨ ɧɚɫɨɫɚ ɡɚ ɨɞɢɧ ɫɬɚɰɢɨɧɚɪɧɵɣ ɰɢɤɥ (ɪɢɫ. 1) ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ:
Qev Qhs
Q Q hs
.
Δs ev
Tev
Ths
Tc
(9)
ɝɞɟ L – ɬɟɩɥɨɬɚ ɢɫɩɚɪɟɧɢɹ ɪɚɛɨɱɟɝɨ ɬɟɥɚ (Ⱦɠ/ɦɨɥɶ).
ɗɮɮɟɤɬɢɜɧɨɫɬɶ ɰɢɤɥɚ ɫ Ⱦɉɇɗ (ηL) ɧɚɡɨɜɟɦ ɩɪɟɞɟɥɶɧɨ ɞɨɫɬɢɠɢɦɨɣ ɷɮɮɟɤɬɢɜɧɨɫɬɶɸ ɬɟɩɥɨɜɨɝɨ ɧɚɫɨɫɚ (ηL
= Qev /Qhs ). Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɜɟɥɢɱɢɧɚ ηL ɦɟɧɶɲɟ ɜɟɥɢɱɢɧɵ ηc , ɩɨɫɤɨɥɶɤɭ ɭɱɢɬɵɜɚɟɬ ɞɢɫɫɢɩɚɰɢɸ ɷɧɟɪɝɢɢ ɜ Ⱦɉɇɗ. Ɋɚɡɞɟɥɢɜ ɨɛɟ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ (8) ɧɚ
Qev , ɩɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɪɟɞɟɥɶɧɨ ɞɨɫɬɢɠɢɦɨɣ ɷɮɮɟɤɬɢɜɧɨɫɬɢ:
1
1
1
J ¸ ΔS * ,
ηL
ηM a
ηc
(10)
ɝɞɟ Ja = cp.Tc /L – ɛɟɡɪɚɡɦɟɪɧɵɣ ɤɪɢɬɟɪɢɣ əɤɨɛɚ;
ΔS* = ΔS / (m0.cp.Δw) – ɛɟɡɪɚɡɦɟɪɧɨɟ ɩɪɨɢɡɜɨɞɫɬɜɨ
ɷɧɬɪɨɩɢɢ ɡɚ ɰɢɤɥ; ηM = 1 – Tc/Ths – ɤɩɞ ɬɟɩɥɨɜɨɣ
ɦɚɲɢɧɵ Ʉɚɪɧɨ, ɪɚɛɨɬɚɸɳɟɣ ɦɟɠɞɭ ɬɟɪɦɨɫɬɚɬɚɦɢ ɫ
ɬɟɦɩɟɪɚɬɭɪɨɣ Ths ɢ Tc. ȼɟɥɢɱɢɧɚ ηL ɹɜɥɹɟɬɫɹ ɜɟɪɯɧɟɣ ɝɪɚɧɢɰɟɣ ɡɧɚɱɟɧɢɣ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɬɟɩɥɨɜɨɝɨ ɧɚɫɨɫɚ ɜ ɨɬɫɭɬɫɬɜɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɬɟɩɥɨɩɟɪɟɧɨɫɭ ɜ ɤɪɭɩɧɨɦɚɫɲɬɚɛɧɵɯ ɷɥɟɦɟɧɬɚɯ.
qÆ¾Â»Æ 1. Ɋɚɫɫɦɨɬɪɢɦ ɚɞɫɨɪɛɰɢɨɧɧɵɣ ɬɟɩɥɨɜɨɣ
ɧɚɫɨɫ, ɜ ɤɨɬɨɪɨɦ ɜ ɤɚɱɟɫɬɜɟ ɪɚɛɨɱɟɣ ɩɚɪɵ ɢɫɩɨɥɶɡɭɸɬɫɹ ɜɨɞɚ ɢ ɰɟɨɥɢɬ NaX. ɗɬɚ ɫɢɫɬɟɦɚ ɛɵɥɚ ɢɡɭɱɟɧɚ
ɬɟɨɪɟɬɢɱɟɫɤɢ [4–6] ɢ ɢɫɫɥɟɞɨɜɚɧɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ
[8]. Ⱥɞɫɨɪɛɰɢɸ ɜɨɞɵ w ɧɚ ɰɟɨɥɢɬɟ NaX ɚɜɬɨɪɵ
ɩɪɟɞɫɬɚɜɢɥɢ ɦɨɞɢɮɢɰɢɪɨɜɚɧɧɵɦ ɭɪɚɜɧɟɧɢɟɦ Ⱦɭɛɢɧɢɧɚ–Ⱥɫɬɚɯɨɜɚ [8]:
w 0, 261 ¸ exp{5, 36 ¸ (
T
1)1,73 } ,
Ts
W2 = 0,0086 ɦɨɥɶ/ɝ
tev = 7°ɋ
T1 = 423 Ʉ
T2 = 353 Ʉ
tɫ = 40°ɋ
T4 = 473 Ʉ
T3 = 395 Ʉ
ɢ Ts = Tc . Ɉɤɚɡɚɥɨɫɶ, ɱɬɨ w1 = 0,0027 ɦɨɥɶ ɜɨɞɵ/ɝ.
Ɇɚɤɫɢɦɚɥɶɧɨɟ ɜɥɚɝɨɫɨɞɟɪɠɚɧɢɟ (w2) ɩɨɥɨɠɢɦ ɪɚɜɧɵɦ 0,0086 ɦɨɥɶ ɜɨɞɵ/ɝ. ɂɫɩɨɥɶɡɭɹ ɮɨɪɦɭɥɭ (11), ɜɵɱɢɫɥɢɦ ɡɧɚɱɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪ ɜ ɧɚɱɚɥɟ ɢ ɤɨɧɰɟ ɢɡɨɛɚɪɢɱɟɫɤɢɯ ɫɬɚɞɢɣ ɚɞɫɨɪɛɰɢɢ (T1, T2) ɢ ɪɟɝɟɧɟɪɚɰɢɢ
( T3, T4), ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɜɵɛɪɚɧɧɵɦ ɜɟɥɢɱɢɧɚɦ
ɚɞɫɨɪɛɰɢɢ (w1, w2). ɗɬɢ ɞɚɧɧɵɟ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥ. 1.
Ɋɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɣ (7) ɢ (10) ɩɨɡɜɨɥɢɥɨ ɭɫɬɚɧɨɜɢɬɶ,
ɱɬɨ ηL = 2,33. ɗɬɨ ɡɧɚɱɟɧɢɟ ɧɚ 25% ɦɟɧɶɲɟ ɜɟɥɢɱɢɧɵ ηc, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢ ɪɚɜɧɨɜɟɫɧɨɦɭ ɰɢɤɥɭ. ȼ ɬɨ ɠɟ ɜɪɟɦɹ ɨɧɨ ɜ 1,5 ɪɚɡɚ ɛɨɥɶɲɟ
ɦɚɤɫɢɦɚɥɶɧɨɣ ɷɮɮɟɤɬɢɜɧɨɫɬɢ (1,6), ɜɵɱɢɫɥɟɧɧɨɣ ɧɚ
ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ ɭɪɚɜɧɟɧɢɣ ɬɟɩɥɨɩɟɪɟɧɨɫɚ ɜ ɪɚɡɧɵɯ
ɷɥɟɦɟɧɬɚɯ ɬɟɩɥɨɜɨɝɨ ɧɚɫɨɫɚ [4], ɢ ɜ 3,5 ɪɚɡɚ ɛɨɥɶɲɟ
ɦɚɤɫɢɦɚɥɶɧɨɣ ɷɮɮɟɤɬɢɜɧɨɫɬɢ (0,6), ɞɨɫɬɢɝɧɭɬɨɣ ɜ ɷɤɫɩɟɪɢɦɟɧɬɚɯ [8].
qÆ¾Â»Æ 2. Ɋɚɫɫɦɨɬɪɢɦ ɚɞɫɨɪɛɰɢɨɧɧɵɣ ɬɟɩɥɨɜɨɣ
ɧɚɫɨɫ, ɜ ɤɨɬɨɪɨɦ ɜ ɤɚɱɟɫɬɜɟ ɪɚɛɨɱɟɣ ɩɚɪɵ ɢɫɩɨɥɶɡɭɸɬɫɹ ɜɨɞɚ ɢ ɤɨɦɩɨɡɢɬɧɵɣ ɚɞɫɨɪɛɟɧɬ, ɩɪɟɞɫɬɚɜɥɹɸɳɢɣ ɫɨɛɨɣ ɢɦɩɪɟɝɧɢɪɨɜɚɧɧɵɣ ɜ ɩɨɪɢɫɬɭɸ ɫɢɥɢɤɚɝɟɥɶɧɭɸ ɦɚɬɪɢɰɭ ɯɥɨɪɢɞ ɤɚɥɶɰɢɹ. ɋɟɪɢɹ ɬɚɤɢɯ ɫɨɪɛɟɧɬɨɜ
ɪɚɡɪɚɛɨɬɚɧɚ ɜ ɂɧɫɬɢɬɭɬɟ ɤɚɬɚɥɢɡɚ ɋɈ ɊȺɇ [10, 11].
Ⱥɞɫɨɪɛɰɢɹ ɜɨɞɵ ɧɚ ɷɬɢɯ ɫɨɪɛɟɧɬɚɯ ɜ ɲɢɪɨɤɨɦ ɢɧɬɟɪɜɚɥɟ ɡɧɚɱɟɧɢɣ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɞɚɜɥɟɧɢɹ ɩɚɪɚ ɜɨɞɵ
ɛɵɥɚ ɞɟɬɚɥɶɧɨ ɢɡɭɱɟɧɚ ɘ.ɂ. Ⱥɪɢɫɬɨɜɵɦ [12]. Ɉɛɪɚɛɚɬɵɜɚɹ ɞɚɧɧɵɟ ɢɡ ɪɚɛɨɬɵ [12] ɦɟɬɨɞɨɦ ɧɚɢɦɟɧɶɲɢɯ ɤɜɚɞɪɚɬɨɜ ɜ ɢɧɬɟɪɜɚɥɟ ɜɥɚɝɨɫɨɞɟɪɠɚɧɢɹ ɨɬ 0,006
ɞɨ 0,04 ɦɨɥɶ ɜɨɞɵ/ɝ, ɩɨɥɭɱɢɦ ɚɫɢɦɩɬɨɬɢɱɟɫɤɨɟ ɜɵɪɚɠɟɧɢɟ, ɩɪɟɞɫɬɚɜɥɹɸɳɟɟ ɚɞɫɨɪɛɰɢɸ ɜɨɞɵ ɧɚ ɫɨɪɛɟɧɬɟ
ɫ 33,7 ɦɚɫ.% ɯɥɨɪɢɞɚ ɤɚɥɶɰɢɹ:
w 0, 0486 ¸ exp(0, 0003 ¸ F ) .
(12)
(11)
ɝɞɟ Ts – ɬɟɦɩɟɪɚɬɭɪɚ ɪɚɜɧɨɜɟɫɧɨɣ ɫɢɫɬɟɦɵ ɠɢɞɤɨɫɬɶ–ɩɚɪ (T > Ts) .
Ʉɚɤ ɢ ɜ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɪɚɛɨɬɟ [8], ɩɪɢɦɟɦ,
ɱɬɨ ths = 200°ɋ, tev = 7°ɋ, tc = 40°ɋ. ɉɪɢ ɜɵɛɪɚɧɧɵɯ ɡɧɚɱɟɧɢɹɯ ɬɟɦɩɟɪɚɬɭɪɵ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɚɹ ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɪɚɜɧɨɜɟɫɧɨɝɨ ɰɢɤɥɚ (ηc) ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ
ɫ ɮɨɪɦɭɥɨɣ (1) ɛɭɞɟɬ ɫɨɫɬɚɜɥɹɬɶ 2,87. Ɇɢɧɢɦɚɥɶɧɭɸ
ɝɪɚɧɢɰɭ ɜɥɚɝɨɫɨɞɟɪɠɚɧɢɹ ɰɟɨɥɢɬɚ (w1) ɦɨɠɧɨ ɜɵɱɢɫɥɢɬɶ ɩɨ ɮɨɪɦɭɥɟ (11), ɢɫɩɨɥɶɡɭɹ ɡɧɚɱɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪ
ɬɟɩɥɨɜɨɝɨ ɢɫɬɨɱɧɢɤɚ ɢ ɤɨɧɞɟɧɫɚɬɨɪɚ, ɬ.ɟ. ɩɪɢ T = Ths
8 ȼɆɍ, ɯɢɦɢɹ, ʋ 1
w1 = 0,0027 ɦɨɥɶ/ɝ
(8)
Ɍɟɩɥɨɬɭ Qev , ɨɬɛɢɪɚɟɦɭɸ ɢɡ ɯɨɥɨɞɢɥɶɧɨɣ ɤɚɦɟɪɵ,
ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ
Qev = L.m0( w2 – w1) = L.m0.Dw,
Ɍɚɛɥɢɰɚ 1
Ɂɞɟɫɶ F – ɚɞɫɨɪɛɰɢɨɧɧɵɣ ɩɨɬɟɧɰɢɚɥ ɉɨɥɹɧɢ
( F = RT ⋅ ln
ps (T )
), R – ɭɧɢɜɟɪɫɚɥɶɧɚɹ ɝɚɡɨɜɚɹ ɩɨɫɬɨp
ɹɧɧɚɹ, ɪɚɜɧɚɹ 8,314.10–3 ɤȾɠ/ɦɨɥɶ.Ʉ, ps( T) – ɪɚɜɧɨɜɟɫɧɨɟ ɞɚɜɥɟɧɢɟ ɩɚɪɚ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ T, p – ɞɚɜɥɟɧɢɟ ɩɚɪɚ ɜ ɫɥɨɟ ɚɞɫɨɪɛɟɧɬɚ.
Ʉɚɤ ɢ ɜ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɪɚɛɨɬɟ [9], ɩɪɢɦɟɦ, ɱɬɨ
ɢɫɬɨɱɧɢɤ ɬɟɩɥɨɬɵ ɢɦɟɟɬ ɬɟɦɩɟɪɚɬɭɪɭ ths = 90°ɋ, ɜ ɯɨɥɨɞɢɥɶɧɨɣ ɤɚɦɟɪɟ ɩɨɞɞɟɪɠɢɜɚɟɬɫɹ ɬɟɦɩɟɪɚɬɭɪɚ tev =
10°ɋ, ɜ ɤɨɧɞɟɧɫɚɬɨɪɟ – tc = 35°ɋ. ɉɪɢ ɜɵɛɪɚɧɧɵɯ
16
ÂÅÑÒÍ. ÌÎÑÊ. ÓÍ-ÒÀ. ÑÅÐ. 2. ÕÈÌÈß. 2007. Ò. 48. ¹ 1
çíà÷åíèÿõ òåìïåðàòóðû â ñîîòâåòñòâèè ñ ôîðìóëîé (1)
ηc = 1,715. Äàâëåíèå íàñûùåííîãî ïàðà âîäû â õîëîäèëüíîé êàìåðå (pev) è â êîíäåíñàòîðå (pc) ïðè âûáðàííîì çíà÷åíèè òåìïåðàòóðû, âû÷èñëåííîå ïî óðàâíåíèþ
Êëàïåéðîíà–Êëàóçèóñà [13], îêàçàëîñü ðàâíûì 12,1 è
54,2 ìáàð â õîëîäèëüíîé êàìåðå è â êîíäåíñàòîðå ñîîòâåòñòâåííî. Ìèíèìàëüíóþ ãðàíèöó âëàãîñîäåðæàíèÿ öåîëèòà (w1) ìîæíî âû÷èñëèòü ïî ôîðìóëå (12), èñïîëüçóÿ çíà÷åíèÿ äàâëåíèÿ ïàðà â êîíäåíñàòîðå è ðàâíîâåñíîãî äàâëåíèÿ ïàðà âîäû ïðè òåìïåðàòóðå òåïëîâîãî èñòî÷íèêà (w1 = 0,0068 ìîëü âîäû/ã). Ìàêñèìàëüíîå âëàãîñîäåðæàíèå (w2) ïîëîæèì ðàâíûì 0,012 ìîëü âîäû/ã.
Èñïîëüçóÿ ôîðìóëó (12), âû÷èñëèì çíà÷åíèÿ òåìïåðàòóðû â íà÷àëå è êîíöå èçîáàðè÷åñêèõ ñòàäèé àäñîðáöèè
(T1, T2) è ðåãåíåðàöèè (T3, T4), ñîîòâåòñòâóþùèå âûáðàííûì âåëè÷èíàì àäñîðáöèè w1, w2 (òàáë. 2).
Ðåøåíèå óðàâíåíèé (7) è (10) ïîçâîëèëî îïðåäåëèòü çíà÷åíèå ïðåäåëüíî äîñòèæèìîé ýôôåêòèâíîñòè
(ηL = 1,52). Îíî íà 13% ìåíüøå âû÷èñëåííîãî ïî
ôîðìóëå (1) çíà÷åíèÿ òåðìîäèíàìè÷åñêè ðàâíîâåñíîé
ýôôåêòèâíîñòè η, íî â 2,5 ðàçà áîëüøå ìàêñèìàëüíîé
ýôôåêòèâíîñòè (0,6), äîñòèãíóòîé â ýêñïåðèìåíòàõ [9].
Çàìåòíóþ ðàçíèöó ìåæäó ηL è ìàêñèìàëüíîé ýôôåêÐàáîòà âûïîëíåíà ïðè ÷àñòè÷íîé
Òàáëèöà 2
w1 = 0,0068 ìîëü/ã
w2 = 0,012 ìîëü/ã
tev = 10°Ñ
T1 = 335 Ê
T2 =318 Ê
tñ = 35°Ñ
T4 = 363 Ê
T3 =344 Ê
òèâíîñòüþ, âû÷èñëåííîé íà îñíîâå ðåøåíèÿ óðàâíåíèé
òåïëîïåðåíîñà èëè ïîëó÷åííîé ýêñïåðèìåíòàëüíî, ìîæíî ÷àñòè÷íî îáúÿñíèòü ïîòåðÿìè òåïëîòû íà íàãðåâ ñ
ïîñëåäóþùèì îõëàæäåíèåì ýëåìåíòîâ êîíñòðóêöèè
òåïëîâîãî íàñîñà.
Òàêèì îáðàçîì, ó÷åò íåðàâíîâåñíîñòè, ñâÿçàííîé ñ
ïåðåíîñîì ïàðà, ïîçâîëÿåò îöåíèòü âåðõíþþ ãðàíèöó
ýôôåêòèâíîñòè òåïëîâîãî íàñîñà, äîñòèæèìóþ â îòñóòñòâèè ïîòåðü ïðè òåïëîîáìåíå ñ òåïëîíîñèòåëåì.
 ðàññìîòðåííûõ ïðèìåðàõ óêàçàííàÿ ãðàíèöà çíà÷èòåëüíî ïðåâîñõîäèò ýôôåêòèâíîñòü, äîñòèãíóòóþ â
ýêñïåðèìåíòàõ, ïîäòâåðæäàÿ òåì ñàìûì, ÷òî ñóùåñòâóþò çíà÷èòåëüíûå ðåçåðâû ñîâåðøåíñòâîâàíèÿ
ðåàëüíûõ óñòðîéñòâ.
Àâòîðû áëàãîäàðÿò Á.Í. Îêóíåâà çà êîíñòðóêòèâíîå îáñóæäåíèå ïðîáëåìû.
ïîääåðæêå ãðàíòà INTAS 03-51-6260.
CÏÈÑÎÊ ËÈÒÅÐÀÒÓÐÛ
1. Çåëåíêî Â.Ë., Õåéôåö Ë.È. // Âåñòí. Ìîñê. óí-òà. Ñåð. 2.
Õèìèÿ. 2005. 46. Ñ. 37.
2. Ñàôîíîâ Ì.Ñ., Îêóíåâ Á.Í., Æàòèêîâ Ï.À. // ÆÔÕ. 2003. 77.
¹ 8. Ñ. 1393.
3. Meunier F. // Heat Recovery System. 1985. 5. N 2. Ð. 133.
4. Pons M. // Int. J. Refrigeration. 1997. 20. N 6. Ð. 411.
5. Pons M. //Adsorption. 1998. 4. N. 2. Ð. 299.
6. Pons M. // J. Energy Resources Technology. 1996. 118. N 9.
Ð. 229.
7. Ñàôîíîâ Ì.Ñ., Îêóíåâ Á.Í. // ÈÔÆ. 2006 (â ïå÷àòè).
8. Lu Y.Z., Wang R.Z., Jianzhou S. et al. // Adsorption. 2004. 10.
N. 1. Ð. 57.
9. Påñòó÷÷à Ä., Ôðåíè À., Âàñòà Ñ. è äð. Õîëîäèëüíàÿ òåõíèêà.
2005. ¹ 1. C. 2.
10. Levitskij E.A., Aristov Yu.A., Tokarev M.M., Parmon V.N. //
Solar Energy Materials and Solar Cells. 1996. 44. N 1. Ð. 219.
11.Aristov Yu.I., Tokarev M.M., Cacciola G., Restuccia G. //
React. Kinet. Catal. Lett. 1996. 59. N 2. Ð. 325.
12. Àðèñòîâ Þ.È. Äèñ. ... äîêò. õèì. íàóê. Íîâîñèáèðñê, 2003.
13. Êóðñ ôèçè÷åñêîé õèìèè / Ïîä ðåä. ÷ë.-êîðð. ÀÍ ÑÑÑÐ
ïðîô. ß.È. Ãåðàñèìîâà. Ò. 1. Ì., 1969 .
Ïîñòóïèëà â ðåäàêöèþ 03.11.2005
LIMITING EFFICIENCY OF THE ADSORPTION HEAT PUMP
V.L. Zelenko, L.I. Heifets
(Division of Chemical Technology and New Materials)
The theoretical model basing on the conception of an unrecoverable dissipative structure is
suggested to estimate the adsorption thermal pump limiting efficiency (LE). The LE is
attainable at assumptions of both the nonequilibrium vapor transfer and negligible heat
exchange resistance. The LE value is less than the thermodynamically equilibrium efficiency
and is the more precise reference-point in selection of the optimal designs of the process
arrangement. Within the considered examples the LE substantially exceeds the efficiency
realized in experiments, thus confirming that there is the significant potential for improvement
of the practical devices.