09_Чистов_АС.pmd

ÏÐÎÁËÅÌÛ ÏÐÎ ÍÎÑÒÈ È ÏËÀÑÒÈ ÍÎÑÒÈ, ò. 80, ¹, 08 ã. ÓÄÊ 6.039.54 ÈÑËÅÍÍÎÅ ÌÎÄÅËÈÐÎÂÀÍÈÅ ÒÅÏËÎÌÀÑÑÎÏÅÐÅÍÎÑÀ Â ÏÀÐÎÃÅÍÅÐÀÒÎÐÅ ÐÅÀÊÒÎÐÍÎÉ ÓÑÒÀÍÎÂÊÈ ÒÈÏÀ ÁÐÅÑÒ ÏÐÈ ÂÎÇÍÈÊÍÎÂÅÍÈÈ ÊÐÈÑÒÀËËÈÇÀÖÈÈ ÑÂÈÍÖÎÂÎÃÎ ÒÅÏËÎÍÎÑÈÒÅËß * 08 ã. èñòîâ À.Ñ., Ñàâèõèí Î.Ã., Îâ èííèêîâ Â.Ô., Êèðþøèíà Å.Â. Íàó íî-èññëåäîâàòåëüñêèé èíñòèòóò ìåõàíèêè Íàöèîíàëüíîãî èññëåäîâàòåëüñêîãî Íèæåãîðîäñêîãî ãîñóäàðñòâåííîãî óíèâåðñèòåòà èì. Í.È. Ëîáà åâñêîãî, Íèæíèé Íîâãîðîä, Ðîññèéñêàÿ Ôåäåðàöèÿ Íàöèîíàëüíûé èññëåäîâàòåëüñêèé Íèæåãîðîäñêèé ãîñóäàðñòâåííûé óíèâåðñèòåò èì. Í.È. Ëîáà åâñêîãî, Íèæíèé Íîâãîðîä, Ðîññèéñêàÿ Ôåäåðàöèÿ chistov@mech.unn.ru Ïîñòóïèëà â ðåäàêöèþ 04..07 Ðàçðàáîòàíà ìåòîäèêà èñëåííîãî ìîäåëèðîâàíèÿ íåñòàöèîíàðíîãî òåïëîìàññîïåðåíîñà è òåïëîïåðåäà è â ïàðîãåíåðàòîðå ñ æèäêîìåòàëëè åñêèì òåïëîíîñèòåëåì ïðè âîçíèêíîâåíèè ïðîöåññà êðèñòàëëèçàöèè. Ìåòîäèêà ó èòûâàåò ðàçëè èÿ ïðîòåêàíèÿ ïðîöåññà â çàâèñèìîñòè îò ñîñòîÿíèÿ êîíòàêòíûõ ïîâåðõíîñòåé. Íà åå îñíîâå èññëåäîâàíà äèíàìèêà îáðàçîâàíèÿ òâåðäîé ôàçû â ñâèíöîâîì òåïëîíîñèòåëå ðåàêòîðíîé óñòàíîâêè òèïà ÁÐÅÑÒ â àâàðèè ñ ðàçãåðìåòèçàöèåé ïàðîïðîâîäà ïàðîãåíåðàòîðà. Ðàñ åòû âûïîëíåíû ñ ïîìîùüþ ïðîãðàììíîãî êîìïëåêñà ÐÀÑÏËÀÂ, êîòîðûé ïîçâîëÿåò ìîäåëèðîâàòü âçàèìîñâÿçàííóþ äèíàìèêó òåïëîãèäðàâëè- åñêèõ ïðîöåññîâ â ïåðâîì è âòîðîì êîíòóðàõ â îäíîìåðíîì ðàâíîâåñíîì ïðèáëèæåíèè. Ïîêàçàíî, òî ïðè îòêàçå çàïîðíî-ðåãóëèðóþùåé àðìàòóðû ïî ïèòàòåëüíîé âîäå ïðîèñõîäèò ïîëíîå ïåðåêðûòèå ïðîõîäíîãî ñå åíèÿ àâàðèéíîãî ïàðîãåíåðàòîðà òâåðäîé ôàçîé. Â çàâèñèìîñòè îò ñîñòîÿíèÿ çàùèòíîãî îêñèäíîãî ñëîÿ òåïëîîáìåííîé ïîâåðõíîñòè çàòâåðäåâàíèå ñâèíöîâîãî òåïëîíîñèòåëÿ ïðîèñõîäèò ëèáî íà òåïëîîáìåííûõ òðóáàõ, ëèáî â íèæíåé àñòè øàõòû ïàðîãåíåðàòîðà. Â îáîèõ ñëó àÿõ âîçíèêàåò óãðîçà ïðåêðàùåíèÿ öèðêóëÿöèè â àâàðèéíîé ïåòëå. Äàíî êðàòêîå îïèñàíèå ìàòåìàòè åñêîé ìîäåëè ïàðîãåíåðàòîðà è êîíòóðà öèðêóëÿöèè óñòàíîâêè â öåëîì. Èñïîëüçóåòñÿ îäíîìåðíîå îïèñàíèå òåïëîìàññîïåðåíîñà. Ïîñòóëèðóåòñÿ òåðìîäèíàìè åñêîå ðàâíîâåñèå ôàç íà ãðàíèöå ôàçîâîãî ïåðåõîäà. Ïðèâîäÿòñÿ ðåçóëüòàòû òåñòèðîâàíèÿ ïðîãðàììíîãî êîìïëåêñà. Ðàñ åò ðàçðûâà òðóáîïðîâîäà âûñîêîãî äàâëåíèÿ ïðîòåñòèðîâàí íà ýêñïåðèìåíòàëüíûõ äàííûõ. Ðàñ åò äèíàìèêè îáðàçîâàíèÿ òâåðäîãî ñëîÿ íà ïîâåðõíîñòè òåï- * Âûïîëíåíî ïðè ôèíàíñîâîé ïîääåðæêå ÐÔÔÈ (ãðàíò ¹6-08-04 à). 67

ëîîáìåííûõ òðóá ïðîòåñòèðîâàí ïóòåì ñðàâíåíèÿ èñëåííîãî ðåøåíèÿ ñ àíàëèòè åñêèì ðåøåíèåì çàäà è Ñòåôàíà. Ðåçóëüòàòû èññëåäîâàíèÿ ìîãóò áûòü èñïîëüçîâàíû ïðè ðàçðàáîòêå ïðîåêòîâ ðåàêòîðîâ ñî ñâèíöîâûì òåïëîíîñèòåëåì. Êëþ åâûå ñëîâà: çàäà à Ñòåôàíà, çàïîðíûé êëàïàí, ìàòåìàòè åñêàÿ ìîäåëü, ïàðîãåíåðàòîð, ðåàêòîðíàÿ óñòàíîâêà, ñâèíöîâûé òåïëîíîñèòåëü, ñìà- èâàåìîñòü ïîâåðõíîñòè, ñìåøèâàþùèé ïîäîãðåâàòåëü ïèòàòåëüíîé âîäû, ïðîöåññ êðèñòàëëèçàöèè, ôàçîâûé ïåðåõîä. Ââåäåíèå Â íàñòîÿùåå âðåìÿ íà ïëîùàäêå Ñèáèðñêîãî õèìè åñêîãî êîìáèíàòà íà àòà ðåàëèçàöèÿ ïðîåêòà Ðîñàòîìà «Ïðîðûâ» [], ïðåäóñìàòðèâàþùåãî ñòðîèòåëüñòâî îïûòíî-äåìîíñòðàöèîííîãî ðåàêòîðà íà áûñòðûõ íåéòðîíàõ ñî ñâèíöîâûì òåïëîíîñèòåëåì ÁÐÅÑÒ-ÎÄ-300 ýëåêòðè åñêîé ìîùíîñòüþ 300 ÌÂò è ñîïóòñòâóþùåãî òåõíîëîãè åñêîãî êîìïëåêñà çàìêíóòîãî òîïëèâíîãî öèêëà. ÁÐÅÑÒ-ÎÄ-300 ðåàêòîð, â êîòîðîì ðåàëèçóåòñÿ ïðèíöèï åñòåñòâåííîé ñàìîçàùèùåííîñòè, ñ êîýôôèöèåíòîì âîñïðîèçâîäñòâà, áîëüøèì åäèíèöû, ñ äâóõêîíòóðíîé ñõåìîé îòâîäà òåïëà è ïàðîòóðáèííûì öèêëîì ïðåîáðàçîâàíèÿ ýíåðãèè. Îñíîâíûå ïîëîæåíèÿ ïðîåêòà èçëîæåíû â [ 5]. Ïðè îáîñíîâàíèè áåçîïàñíîñòè ÿäåðíûõ ýíåðãåòè åñêèõ óñòàíîâîê ñ òÿæåëûìè æèäêîìåòàëëè åñêèìè òåïëîíîñèòåëÿìè [, 6], èìåþùèìè âûñîêóþ òåìïåðàòóðó ïëàâëåíèÿ, ìîæíî âûäåëèòü ñïåöèôè åñêèé êëàññ àâàðèé, â êîòîðûõ ïðîèñõîäèò îáðàçîâàíèå òâåðäîé ôàçû â ïåðâîì êîíòóðå ïàðîãåíåðàòîðîâ (ÏÃ). Ïîëíîå ïåðåêðûòèå ïðîõîäíîãî ñå åíèÿ îäíîãî èëè íåñêîëüêèõ ïàðîãåíåðàòîðîâ òâåðäîé ôàçîé ìîæåò ïðèâåñòè ê ñàìûì òÿæåëûì ïîñëåäñòâèÿì: îò ðàçðûâà òåïëîîáìåííûõ òðóá äî ïîëíîãî ïðåêðàùåíèÿ öèðêóëÿöèè åðåç ðåàêòîð. Èññëåäîâàíèå ýòîãî êëàññà àâàðèé òðåáóåò äåòàëüíîãî îïèñàíèÿ ïðîöåññà çàòâåðäåâàíèÿ òåïëîíîñèòåëÿ â ïàðîãåíåðàòîðå. Â ñòàòüå ïðåäñòàâëåíà ìåòîäèêà èñëåííîãî ìîäåëèðîâàíèÿ äèíàìèêè êðèñòàëëèçàöèè æèäêîìåòàëëè åñêîãî òåïëîíîñèòåëÿ â ïàðîãåíåðàòîðå, îñíîâàííàÿ íà ìàòåìàòè åñêîé ìîäåëè [7]. Ìåòîäèêà ïîçâîëÿåò ó èòûâàòü íåîïðåäåëåííîñòü, îáóñëîâëåííóþ ñîñòîÿíèåì çàùèòíîãî îêñèäíîãî ñëîÿ íà ïîâåðõíîñòè òåïëîîáìåííûõ òðóá, êîíòàêòèðóþùèõ ñ æèäêèì ìåòàëëîì. Èç [8, 9] ñëåäóåò, òî íåñìà èâàåìîñòü ïîâåðõíîñòè òåïëîîáìåíà ìåòàëëîì èç-çà íàëè èÿ íà íåé îêñèäíîãî ñëîÿ ïðåïÿòñòâóåò îáðàçîâàíèþ öåíòðîâ êðèñòàëëèçàöèè. Â ýòîì ñëó àå ëèáî êðèñòàëëè åñêèå îáðàçîâàíèÿ äðåéôóþò â òóðáóëåíòíîì ïîòîêå â âèäå æèäêîìåòàëëè åñêîé ñóñïåíçèè, ëèáî ïðîèñõîäèò ïåðåîõëàæäåíèå ïîòîêà. Íàêîïëåíèå êðèñòàëëîâ â ïîëîñòè íà âûõîäå ÏÃ òàê æå îïàñíî, êàê è âíåçàïíîå çàòâåðäåâàíèå ïåðåîõëàæäåííîãî ðàñïëàâà â ýòîé ïîëîñòè. Ïðè îòñóòñòâèè îêñèäíîãî ñëîÿ íà êîíòàêòíîé ïîâåðõíîñòè çàòâåðäåâàíèå ìåòàëëà ïðîèñõîäèò íà òåïëîîáìåííûõ òðóáàõ. Ñ èñïîëüçîâàíèåì ðàçðàáîòàííîé ìåòîäèêè ïðîâåäåí ðàñ åòíûé àíàëèç àâàðèè ñ àñòè íîé ðàçãåðìåòèçàöèåé ïàðîïðîâîäîâ îäíîãî èç åòûðåõ ÏÃ ðåàêòîðíîé óñòàíîâêè òèïà ÁÐÅÑÒ-ÎÄ-300. Ðàñ åòû âûïîëíåíû ñ ïîìîùüþ ïðîãðàììíîãî êîìïëåêñà ÐÀÑÏËÀÂ [0, ], êîòîðûé ïîçâîëÿåò ìîäåëèðîâàòü âçàèìîñâÿçàííóþ äèíàìèêó òåïëîãèäðàâëè åñêèõ ïðîöåññîâ â ïåðâîì è âòîðîì êîíòóðàõ â îäíîìåðíîì ðàâíîâåñíîì ïðèáëèæåíèè. Ïîêàçàíî, òî ïðè íåñðàáàòûâàíèè îòñå íîé àðìàòóðû ïî ïèòàòåëüíîé âîäå ïðîèñõîäèò ïîëíîå ïåðåêðûòèå ïðîõîäíîãî ñå åíèÿ ïåðâîãî 68

êîíòóðà àâàðèéíîãî ÏÃ òâåðäîé ôàçîé ñâèíöà, âñëåäñòâèå åãî âîçìîæíî ïðåêðàùåíèå öèðêóëÿöèè â àâàðèéíîé ïåòëå. Ïðèâîäÿòñÿ ðåçóëüòàòû òåñòèðîâàíèÿ ïðîãðàììíîãî êîìïëåêñà. Ðàñ åò ðàçðûâà òðóáîïðîâîäà âûñîêîãî äàâëåíèÿ ïðîòåñòèðîâàí íà ýêñïåðèìåíòàëüíûõ äàííûõ []. Ðàñ åò äèíàìèêè îáðàçîâàíèÿ òâåðäîãî ñëîÿ íà ïîâåðõíîñòè òåïëîîáìåííûõ òðóá ïðîòåñòèðîâàí ïóòåì ñðàâíåíèÿ èñëåííîãî ðåøåíèÿ ñ àíàëèòè åñêèì ðåøåíèåì çàäà è Ñòåôàíà [3].. Ìàòåìàòè åñêàÿ ìîäåëü Ïåðâûé êîíòóð ÁÐÅÑÒ-ÎÄ-300 âêëþ àåò â ñåáÿ ðåàêòîð è åòûðå ïåòëè öèðêóëÿöèè òåïëîíîñèòåëÿ, êàæäàÿ èç êîòîðûõ ñîäåðæèò îäèí ïàðîãåíåðàòîð, îäèí ãëàâíûé öèðêóëÿöèîííûé íàñîñ (ÃÖÍ) è òðàêòû öèðêóëÿöèè òåïëîíîñèòåëÿ. Âòîðîé êîíòóð ïðåäñòàâëåí ïàðîâîäÿíûìè òðàêòàìè ïàðîãåíåðàòîðîâ îò ñìåøèâàþùåãî ïîäîãðåâàòåëÿ ïèòàòåëüíîé âîäû (ÑÏÏÂ) äî òóðáèíû. Âëèÿíèå îñòàëüíîé àñòè âòîðîãî êîíòóðà ó èòûâàåòñÿ åðåç ãðàíè íûå óñëîâèÿ. Ìîäåëèðîâàíèå äèíàìèêè åòûðåõïåòëåâîãî êîíòóðà ðåàêòîðíîé óñòàíîâêè ñâîäèòñÿ ê îïèñàíèþ äâóõ ïåòåëü: ýêâèâàëåíòíîé àâàðèéíîé è ýêâèâàëåíòíîé íåàâàðèéíîé. Êàæäàÿ èç íèõ ìîäåëèðóåò äèíàìèêó ãðóïï èäåíòè íûõ àâàðèéíûõ è èäåíòè íûõ íåàâàðèéíûõ ïåòåëü. Ðàñ åòíàÿ áëîê-ñõåìà êîíòóðà öèðêóëÿöèè ðåàêòîðíîé óñòàíîâêè òèïà ÁÐÅÑÒ ïðèâåäåíà íà ðèñ.. Ïàðîâîé êîëëåêòîð Ïàð íà òóðáèíó Êîëëåêòîð ïèòàòåëüíîé âîäû ÎÊÏ ÇÊÏ ÐÏÊ ÇÊÏÂ ÎÊÏÂ 9 3 6 ÃÖÍ 4 5 ÃÖÍ 6 3 8 Ïèòàòåëüíàÿ âîäà îò êàñêàäà ïîäîãðåâàòåëåé 7 7 3 ÑÏÏÂ 0 Íåàâàðèéíàÿ ïåòëÿ 0 Àâàðèéíàÿ ïåòëÿ ÏÝÍ- Ðèñ. Íàïðàâëåíèÿ äâèæåíèÿ òåïëîíîñèòåëåé ïîêàçàíû ñòðåëêàìè, ïðèíöèï öèðêóëÿöèè ïîäðîáíî îïèñàí â [, 4]. Ïåðâûé è âòîðîé êîíòóðû ïðåäñòàâëåíû â âèäå íàáîðà âçàèìîñâÿçàííûõ òåïëîãèäðàâëè åñêèõ ýëåìåíòîâ (êàíàëîâ): íà ñõåìå îáîçíà- åíû íîìåðàìè 4, 6, 8, 9, 3. Ïîñëåäîâàòåëüíîñòè êàíàëîâ îáðàçóþò òðàêòû öèðêóëÿöèè òåïëîíîñèòåëåé. Òðàêòû ñâèíöîâîãî òåïëîíîñèòåëÿ çàìûêàþòñÿ íà îáúåìû ñî ñâîáîäíûìè óðîâíÿìè:, 5 âõîäíàÿ è âûõîäíàÿ êàìåðû ðåàêòîðà, 7 âõîä- 69

íàÿ êàìåðà ÃÖÍ. Ñâîáîäíûå óðîâíè îáúåäèíåíû ïðîñòðàíñòâîì, çàïîëíåííûì àðãîíîì ïðè àòìîñôåðíîì äàâëåíèè P a. Ïàðîãåíåðàòîð ÁÐÅÑÒ-ÎÄ-300 ïðåäñòàâëÿåò ñîáîé òåïëîîáìåííèê ñ ïðîòèâîòî íûì äâèæåíèåì ñðåä [ 4, 4, 5]. Òåïëîîáìåííàÿ ïîâåðõíîñòü 0 íàáðàíà èç âèòûõ òðóá, âíóòðè êîòîðûõ ïèòàòåëüíàÿ âîäà íàãðåâàåòñÿ äî ñîñòîÿíèÿ ïåðåãðåòîãî ïàðà. Òðóáíàÿ ñèñòåìà ÏÃ èìååò îïóñêíîé ïîäâîäÿùèé ó àñòîê, çìååâèêîâûé ó àñòîê àêòèâíîãî òåïëîîáìåíà è ïàðîâîé ó àñòîê 3. Çìååâèê îáîãðåâàåòñÿ îïóñêíûì ïîòîêîì ñâèíöà â êîëüöåâîì ïðîñòðàíñòâå ìåæäó êîðïóñîì ÏÃ è âíóòðåííèì öèëèíäðè åñêèì êîæóõîì. Ó àñòîê ðàñïîëîæåí âíóòðè êîæóõà. Ïàðîãåíåðàòîðû ñîåäèíåíû ñ ïèòàòåëüíûì è ïàðîâûì êîëëåêòîðàìè òðóáîïðîâîäàìè, íà êîòîðûõ, ñîãëàñíî [4], óñòàíîâëåíû çàïîðíûå êëàïàíû ïî ïèòàòåëüíîé âîäå (ÇÊÏÂ) è ïî ïàðó (ÇÊÏ), à òàêæå ðåãóëèðóþùèå êëàïàíû ðàñõîäà ïèòàòåëüíîé âîäû (ÐÏÊ) è îáðàòíûå êëàïàíû ïî âîäå (ÎÊÏÂ) è ïî ïàðó (ÎÊÏ). Òåïëîìàññîïåðåíîñ â êàíàëàõ îïèñàí â îäíîìåðíîì ãîìîãåííîì ïðèáëèæåíèè. Àëãîðèòìû ðåøåíèÿ êîíå íî-ðàçíîñòíîé çàäà è äëÿ äàííîé ìàòåìàòè åñêîé ìîäåëè ðàññìîòðåíû â [6]. Óñëîâèÿìè ñøèâêè íà âûõîäå ïðåäûäóùåãî è âõîäå ïîñëåäóþùåãî êàíàëîâ ÿâëÿþòñÿ ðàâåíñòâà çíà åíèé äàâëåíèÿ, óäåëüíîé ýíòàëüïèè è ðàñõîäà. Â êà åñòâå íà àëüíîãî óñëîâèÿ ïðè ðàñ åòàõ ïåðåõîäíûõ ïðîöåññîâ èñïîëüçóåòñÿ ñòàöèîíàðíûé ðåæèì ðàáîòû ðåàêòîðíîé óñòàíîâêè íà íîìèíàëüíîì óðîâíå ìîùíîñòè. Â êà åñòâå ãðàíè íûõ óñëîâèé èñïîëüçóþòñÿ äàâëåíèÿ íà âõîäå è âûõîäå òðàêòîâ öèðêóëÿöèè òåïëîíîñèòåëåé ïåðâîãî è âòîðîãî êîíòóðîâ. Èõ çíà åíèÿ ñîñòàâëÿþò: ïî ïåðâîìó êîíòóðó P = P a + P i, P = P a + P j ; ïî âòîðîìó êîíòóðó P = P 0 (t) + H(t), P = P T (t). Çäåñü P i, P j äàâëåíèÿ ñòîëáîâ óðîâíåé i, j; P 0 (t), P T (t) äàâëåíèÿ â ÑÏÏÂ è ïåðåä ñòîïîðíî-ðåãóëèðóþùèì êëàïàíîì òóðáèíû; H(t) íàïîð ïèòàòåëüíîãî ýëåêòðîíàñîñà ÏÝÍ-. Îñíîâíûå ãåîìåòðè åñêèå è ðåæèìíûå ïàðàìåòðû, êîòîðûå èñïîëüçîâàëèñü â ðàñ åòàõ, ïðåäñòàâëåíû â òàáëèöå è ñîîòâåòñòâóþò äàííûì èç [, 4, 4, 5]. Òàáëèöà Ýëåìåíò Äëèíà, ì Ïëîùàäü Îáúåì, ì 3 P âõ /ΔP òð, Òåìïåðàòóðà, Ðàñõîä, êîíòóðà ñå åíèÿ, ì ÌÏà Ñ, âõ/âûõ êã/ñ ÑÏÏÂ 45 9/0,0 340 40 -é êîíòóð ÏÃ 7,0,0 0,/0,07 540/40 000 -é êîíòóð ÏÃ 3,5 0, 7,05/0,05 340,5/506 05 Ðàñ åò ñòàöèîíàðíîãî ðåæèìà ÏÃ ïðîèçâîäèòñÿ ïî àëãîðèòìó, ïðèâåäåííîìó â [7]. Òåïëîâûäåëåíèå â àêòèâíîé çîíå ðàññ èòûâàåòñÿ â òî å íîì ïðèáëèæåíèè, îñòàòî íîå òåïëîâûäåëåíèå ïî ôîðìóëå Óíòåðìàéåðà Óýëëñà [8]. Ðàçðûâ ïàðîïðîâîäà ìîäåëèðóåòñÿ óìåíüøåíèåì äàâëåíèÿ â ñå åíèè ðàçðûâà ïàðîïðîâîäà ÏÃ àâàðèéíîé ïåòëè äî àòìîñôåðíîãî çà âðåìÿ 0,5 ñ. Ïîäðîáíåå ðàññìîòðèì ìåòîäèêó ðàñ åòà ñîäåðæàíèÿ òâåðäîé ôàçû â òåïëîíîñèòåëå. Òåïëîìàññîïåðåíîñ â ïåðâîì êîíòóðå ñ ó åòîì ìåæôàçíîãî îáìåíà åðåç ïîâåðõíîñòü ñî ñâîáîäíîé ãðàíèöåé ìîæíî ïðåäñòàâèòü ñèñòåìîé óðàâíåíèé ñîõðàíåíèÿ äëÿ îäíîôàçíîãî ïîòîêà ñ èñòî íèêîì J è ïåðåìåííîé ïëîùàäüþ ñå åíèÿ [7]: 70

u ρ t Sρ G + = J, t z i i S ρ + G = q t z, () u P ξ + u + + ρg z + 0 0, + ξ ρ u z z dγ () δ ρ Π δ), δ > 0, J = ( z 0, δ = 0, = Π( δ) α( Tcr T), δ > 0, q = Πα( Tw T), δ = 0, S( δ( t, z) ), δ > 0, S = * S, δ = 0, à âî âòîðîì êîíòóðå ñèñòåìîé óðàâíåíèé ãîìîãåííîé ìîäåëè ïîòîêà: S ρ G + = t z 0, i i Sρ + G q, q ( Tw T ), t z = = α Π () G t + z ξgu P ( Gu) + + + ( ρ) S Sg z dγ z = ãäå t âðåìÿ; z ïðîäîëüíàÿ êîîðäèíàòà; ρ ïëîòíîñòü; G ìàññîâûé ðàñõîä; i óäåëüíàÿ ýíòàëüïèÿ; u ñêîðîñòü; q òåïëîâàÿ ìîùíîñòü íà åäèíèöó äëèíû êàíàëà; P äàâëåíèå; g z ïðîåêöèÿ óñêîðåíèÿ ñâîáîäíîãî ïàäåíèÿ íà íàïðàâëåíèå äâèæåíèÿ; S ïëîùàäü ïðîõîäíîãî ñå åíèÿ; ξ êîýôôèöèåíò ãèäðàâëè åñêîãî ñîïðîòèâëåíèÿ òðåíèþ; ξ 0 = ( S / S( δ) ) ( + 0,707 S( δ) / S ) êîýôôèöèåíò ìåñò- * * íîãî ñîïðîòèâëåíèÿ ïðè ïåðåêðûòèè âûõîäíîãî ñå åíèÿ Ïà òâåðäîé ôàçîé [7]; d à ãèäðàâëè åñêèé äèàìåòð; δ òîëùèíà òâåðäîãî ñëîÿ ñâèíöà; T òåìïåðàòóðà; Π (δ), Π ïåðèìåòðû ïîâåðõíîñòåé òåïëîîáìåíà ñî ñòîðîíû ïåðâîãî è âòîðîãî êîíòóðîâ. Íèæíèå èíäåêñû îáîçíà àþò:, íîìåð êîíòóðà ÏÃ; w ïðèíàäëåæíîñòü ê ñòåíêå òðóáû ÏÃ; âåðõíèé èíäåêñ () ïðèíàäëåæíîñòü ê òâåðäîé ôàçå; cr ñîñòîÿíèå êðèñòàëëèçàöèè-ïëàâëåíèÿ. Ïðîöåññû () è () ñâÿçàíû åðåç ïðîöåññ òåïëîîáìåíà â òðóáàõ ÏÃ, êîòîðûé ñ ó åòîì îáðàçóþùåãîñÿ òâåðäîãî ñëîÿ ìîæíî îïèñàòü ñîãëàñíî [7]: ρc T T T = r +, r r r( t, z), r( t, z) r w < < = w λ t r r r z () δ T T qcrρ = α( T ( r) T) λ, α( T T w) λ t n r r= r 0, + δ( t, z), r= r w = 0, ãäå Ñ, λ ñîîòâåòñòâåííî óäåëüíàÿ èçîáàðíàÿ òåïëîåìêîñòü è êîýôôèöèåíò òåïëîïðîâîäíîñòè ìåòàëëà òåïëîïåðåäàþùåãî ñëîÿ; r ðàäèàëüíàÿ êîîðäèíàòà; r w ðà- (3) 7

äèóñ òåïëîîáìåííîé òðóáû; n íàïðàâëåíèå íîðìàëè ê ãðàíèöå ðàçäåëà ôàç; α êîýôôèöèåíòû òåïëîîòäà è; q cr ñêðûòàÿ òåïëîòà ïëàâëåíèÿ. Îáîçíà èâ l = L/, δ l = l r w, δ * = l/cos (π/6) r w, îïðåäåëèì S = S (δ(t, z)) è Π = Π (δ(t, z)) â () äëÿ òðóáíîé ñèñòåìû ÏÃ èç N òåïëîîáìåííûõ òðóá, ðàñïîëîæåííûõ â òðåóãîëüíîé ðåøåòêå ñ øàãîì L: * S πn( rw + δ) δ, r < l, S ( δ( t, z) ) = S( δl ) l π + r 3 * (4) 3 3arccos r, + δ, 3 π/ l l r r w r l l, r < l, Π ( δ( t, z)) = π( rw + δ) N K, K = 6arccos ( l / r) (5), r l. π Óñëîâèå íà ìåæôàçíîé ïîâåðõíîñòè çàäà è (3) óäîáíî âûðàçèòü åðåç ïîäâîäèìóþ â çàäàííîì ñå åíèè ìîùíîñòü δ = q, q T = q Π λ Σ () Σ t qcrρ Π n r= r èñëåííîå èíòåãðèðîâàíèå óðàâíåíèÿ òåïëîïðîâîäíîñòè (3) îñóùåñòâëÿåòñÿ ïî ÿâíîé ðàçíîñòíîé ñõåìå ñ ïåðåìåííûì èñëîì óçëîâ ïî ïðîñòðàíñòâåííîé êîîðäèíàòå. Â ñëó àå îáðàçîâàíèÿ æèäêîìåòàëëè åñêîé ñóñïåíçèè îáúåìíîå ñîäåðæàíèå òâåðäîé ôàçû îïðåäåëÿåòñÿ èç ñîîòíîøåíèé îñðåäíåíèÿ ãîìîãåííîé ìîäåëè (ñì. [7]). Ôóíêöèè ñîñòîÿíèÿ ñâèíöîâîãî è ïàðîâîäÿíîãî òåïëîíîñèòåëåé ðàññ èòûâàþòñÿ â âèäå ρ = ρ(i, P), T = T(i, P) è àïïðîêñèìèðóþòñÿ ñîãëàñíî [9, 0].. Òåñòîâûå ðàñ åòû Òåñòèðîâàíèå êîìïüþòåðíîé ìîäåëè ïðè ðàñ åòå ðàçðûâà òðóáîïðîâîäà âûñîêîãî äàâëåíèÿ ïðîâåäåíî ñ èñïîëüçîâàíèåì ýêñïåðèìåíòàëüíûõ äàííûõ []. Íà ðèñ. ìîæíî âèäåòü ïðèåìëåìîå ñîîòâåòñòâèå ðàññ èòàííîãî ïåðåõîäíîãî ïðîöåññà, âûçâàííîãî ðåçêîé ðàçãåðìåòèçàöèåé òðóáû ñ âîäîé ïîä äàâëåíèåì ~6,9 ÌÏà è òåìïåðàòóðîé 4 Ñ, ýêñïåðèìåíòàëüíûì äàííûì.. P, ÌÏà 6 4 Ðàñ åò Ýêñïåðèìåíò T, C 50 00 50 Ðàñ åò Ýêñïåðèìåíò 00 50 0 0, 0, 0,3 0,4 0,5 t, c 0 0, 0, 0,3 0,4 0,5 t, c à) á) Ðèñ. 7

Íà âðåìåííîì èíòåðâàëå, ñîîòâåòñòâóþùåì èñòå åíèþ ïàðîâîäÿíîé ñìåñè (P const, T const), èìååò ìåñòî íåêîòîðîå ïðåâûøåíèå ðàññ èòàííûõ çíà åíèé äàâëåíèÿ è òåìïåðàòóðû ïî ñðàâíåíèþ ñ ýêñïåðèìåíòàëüíûìè çíà åíèÿìè. Ïðè ðàñ åòå àâàðèè ñ ðàçãåðìåòèçàöèåé ïàðîïðîâîäà ÏÃ ÁÐÅÑÒ-ÎÄ-300 ýòî îáñòîÿòåëüñòâî ïîçâîëèò ïîëó èòü áîëåå êîíñåðâàòèâíûå îöåíêè ïðîöåññà îáðàçîâàíèÿ òâåðäîé ôàçû â ñâèíöîâîì òåïëîíîñèòåëå. Äëÿ òåñòèðîâàíèÿ ìîäåëè, îïèñûâàþùåé îáðàçîâàíèå òâåðäîãî ñëîÿ íà òðóáàõ ÏÃ, ðàññìîòðèì êâàçèñòàöèîíàðíûé ïðîöåññ òåïëîîáìåíà, âîçíèêàþùèé â èçîëèðîâàííîì ÏÃ â ðåçóëüòàòå ñèíõðîííîãî ñíèæåíèÿ òåìïåðàòóðû ñðåäû âî âòîðîì êîíòóðå ñ íîìèíàëüíûõ çíà åíèé äî çíà åíèÿ 0 Ñ çà 0 ñ (ðèñ. 3). T, C 500 400 300 00 00 3 4 0 0 0 30 t, c à) f i 0 00 Ëèíèè, íà ðèñ. 3à ïîêàçûâàþò èçìåíåíèå òåìïåðàòóð âî âòîðîì êîíòóðå, èíèöèèðóþùåå ïåðåõîäíûé ïðîöåññ. Òåìïåðàòóðà æèäêîãî ñâèíöà íà âõîäå ïåðâîãî êîíòóðà îñòàåòñÿ ïîñòîÿííîé (ðèñ. 3à, ëèíèÿ 3), à íà âûõîäå äîñòèãàåò òåìïåðàòóðû êðèñòàëëèçàöèè T cr = 37,5 Ñ ê 9-é ñåêóíäå (ðèñ. 3à, êðèâàÿ 4). Ñ ýòîãî ìîìåíòà íà èíàåòñÿ îáðàçîâàíèå òâåðäîãî ñâèíöîâîãî ñëîÿ íà âíåøíèõ ïîâåðõíîñòÿõ òåïëîîáìåííûõ òðóá. Êðèâûå, 3 íà ðèñ. 3á ïîêàçûâàþò äèíàìèêó íàðàñòàíèÿ òâåðäîãî ñëîÿ è äèíàìèêó ïåðåêðûòèÿ ïðîõîäíîãî ñå åíèÿ òâåðäîé ôàçîé íà âûõîäå ÏÃ. Â ñóæàþùåìñÿ ñå åíèè âîçíèêàåò äîïîëíèòåëüíîå ãèäðàâëè åñêîå ñîïðîòèâëåíèå ïîòîêó òåïëîíîñèòåëÿ è, êàê ñëåäñòâèå, óìåíüøåíèå åãî ðàñõîäà (ðèñ. 3á, êðèâàÿ 4). Çäåñü è äàëåå ïåðåìåííûå f i, i >, íîðìèðóþòñÿ íà íîìèíàëüíûå çíà åíèÿ, à f = = δ/δ * (ñì. (4)). Çàäà à Ñòåôàíà î äâèæåíèè ãðàíèöû ðàçäåëà ôàç ïðè ñòàöèîíàðíûõ ãðàíè íûõ óñëîâèÿõ èìååò àíàëèòè åñêîå ðåøåíèå δ ( t) = A t t0, A = const, t 0 ìîìåíò íà àëà êðèñòàëëèçàöèè [3]. Íà ó àñòêå ÏÃ, ãäå èäåò ïðîöåññ êðèñòàëëèçàöèè, íà ãðàíèöàõ òåïëîîáìåííîãî ñëîÿ ðåàëèçóþòñÿ ñòàöèîíàðíûå óñëîâèÿ, è ðàññ èòàííàÿ êðèâàÿ ðèñ. 3á ñîâïàäàåò ñ àíàëèòè åñêèì ðåøåíèåì (ðèñ. 3á, êðèâàÿ ) ñ îòíîñèòåëüíîé ïîãðåøíîñòüþ ~5%. Êðèâûå 3 è 5 íà ðèñ. 3á ïîçâîëÿþò ñîïîñòàâèòü äèíàìèêó îáúåìíîãî ñîäåðæàíèÿ òâåðäîé ôàçû â ïåðåõîäíîì ïðîöåññå â ñëó àå ñìà èâàåìîé è íåñìà èâàåìîé êîíòàêòíîé ïîâåðõíîñòè ðàñïëàâîì. 3. Àâàðèÿ ñ ðàçãåðìåòèçàöèåé ïàðîïðîâîäà ïàðîãåíåðàòîðà Ðàññìàòðèâàåòñÿ ñëåäóþùèé ñöåíàðèé àâàðèè. Çà 0,5 ñ äàâëåíèå â ñå åíèè ðàçðûâà (ïåðåä ÎÊÏ) óìåíüøàåòñÿ äî àòìîñôåðíîãî. Ðàñõîä ïàðà â ðàçðûâ èç îñòàëü- 80 60 40 0 Ðèñ. 3 3 4 5 0 0 0 30 t, c á) 73

íûõ ÏÃ îòñåêàåòñÿ îáðàòíûì êëàïàíîì ïî ïàðó. Ïî ïðè èíå ïðîâàëà äàâëåíèÿ âî âòîðîì êîíòóðå çàêðûâàåòñÿ ñòîïîðíî-ðåãóëèðóþùèé êëàïàí òóðáèíû è îòêëþ àþòñÿ ïèòàòåëüíûå íàñîñû, ïðîèçâîäèòñÿ ñáðîñ àâàðèéíîé çàùèòû ðåàêòîðà è îòêëþ åíèå ÃÖÍ. Äàëåå ïðîèñõîäèò îïîðîæíåíèå ÑÏÏÂ åðåç àâàðèéíûé ÏÃ ñàìîòåêîì. Íà ðèñ. 4 ïîêàçàíà äèíàìèêà ðàñõîäîâ è äàâëåíèé âî âòîðîì êîíòóðå. Ðàñõîäû îáîçíà åíû: â ðàçðûâ;, 5 âîäû è ïàðà â ÑÏÏÂ; 3 íà òóðáèíó; 4 ñóììàðíûé ðàñõîä åðåç íåàâàðèéíûå ÏÃ (ñì. ðèñ. 4à). Äàâëåíèÿ îáîçíà åíû: 6 íà âûõîäå ÏÝÍ-; 7 â ÑÏÏÂ; 8 â ñå åíèè ðàçðûâà (ñì. ðèñ. 4á). G, êã/ñ 600 500 400 300 00 00 3 4 5 0 0 0 30 40 t, c à) P, ÌÏà 6 6 8 7 4 8 0 0 0 30 40 t, c á) Ðèñ. 4 Ìîæíî âèäåòü, òî âî âòîðîì êîíòóðå ÏÃ åðåç 0 ñ óñòàíàâëèâàåòñÿ êâàçèñòàöèîíàðíûé ðåæèì ñ ðàñõîäîì, áëèçêèì ê íîìèíàëüíîìó, è äàâëåíèåì â ÑÏÏÂ ~6 ÌÏà. Ê ýòîìó ìîìåíòó òåìïåðàòóðû òåïëîíîñèòåëåé íà âõîäå ïåðâîãî è âòîðîãî êîíòóðîâ äîñòèãàþò çíà åíèé ñîîòâåòñòâåííî ~475 Ñ è ~75 Ñ (ðèñ. 5à). Ïðîöåññ êðèñòàëëèçàöèè â ïåðâîì êîíòóðå íà èíàåòñÿ íà 6-é ñåêóíäå è çàâèñèò îò ñîñòîÿíèÿ ïîâåðõíîñòè, êîíòàêòèðóþùåé ñî ñâèíöîâûì òåïëîíîñèòåëåì. Äèíàìèêà ïðè îòñóòñòâèè îêñèäíîãî ñëîÿ íà êîíòàêòíîé ïîâåðõíîñòè. Â ýòîì ñëó àå ïîâåðõíîñòü ïðèîáðåòàåò ñâîéñòâî ñìà èâàåìîñòè æèäêèì ìåòàëëîì è îáðàçîâàíèå òâåðäîãî ñëîÿ ïðîèñõîäèò íà òåïëîîáìåííûõ òðóáàõ. Íà ðèñ. 5à ïîêàçàíà äèíàìèêà òåìïåðàòóð íà âõîäå è âûõîäå àâàðèéíîãî ÏÃ:, ïåðâîãî êîíòóðà; 3, 4 âòîðîãî êîíòóðà. Êðèâûì íà ðèñ. 5á ñîîòâåòñòâóþò ñëåäóþùèå îòíîñèòåëüíûå âåëè èíû: òîëùèíà òâåðäîãî ñëîÿ íà òåïëîîáìåííûõ 74

òðóáàõ; ïåðåêðûòèå ïðîõîäíîãî ñå åíèÿ òâåðäîé ôàçîé íà âûõîäå ÏÃ; 3 ðàñõîä ñâèíöîâîãî òåïëîíîñèòåëÿ. Êðèâàÿ èìååò õàðàêòåðíûé ðàçðûâ ïðîèçâîäíîé ïðè t 0 ñ, ñâÿçàííûé ñ ñîåäèíåíèåì ñëîåâ çàòâåðäåâøåãî ñâèíöà íà ñîñåäíèõ òðóáàõ. Ñ ýòîãî ìîìåíòà ïðîöåññ ïåðåêðûòèÿ ñå åíèÿ çíà èòåëüíî óñêîðÿåòñÿ (ñì. (4), (5)). Â ìîìåíò t 6 ñ ïðîèñõîäèò ïîëíîå ïåðåêðûòèå ïðîõîäíîãî ñå åíèÿ è ïðåêðàùåíèå ðàñõîäà ñâèíöîâîãî òåïëîíîñèòåëÿ â ÏÃ. T, C 500 400 300 4 00 00 3 f i 0 00 0 0 0 30 40 50 t, c à) 80 60 40 0 3 Ïðè îòñóòñòâèè êîíâåêòèâíîãî òåïëîïîäâîäà ïðîöåññ îáðàçîâàíèÿ òâåðäîé ôàçû áûñòðî ðàñïðîñòðàíÿåòñÿ ïî âûñîòå òåïëîîáìåííîãî ó àñòêà ÏÃ. Íà ðèñ. 6 ïîêàçàíà äèíàìèêà ðàñïðîñòðàíåíèÿ òâåðäîé ôàçû ïî âûñîòå ïåðâîãî êîíòóðà ÏÃ. Íîðìèðîâêà ïðîèçâîäèòñÿ íà ìàêñèìàëüíîå çíà åíèå δ * (ñì. (4)). Ìîæíî âèäåòü, òî ê ìîìåíòó t 40 ñ òâåðäîé ôàçîé çàïîëíåíà áîëüøàÿ àñòü îáúåìà ïåðâîãî êîíòóðà ÏÃ. δ/δ *,0 0,8 0,6 0 5 0 5 0 5 t, c á) Ðèñ. 5 0,4 0, t = 40 c t = 30 c t = 0 c t = 0 c 0 3 4 5 6 z, ì Ðèñ. 6 75

Äèíàìèêà ïðè íàëè èè îêñèäíîãî ñëîÿ íà êîíòàêòíîé ïîâåðõíîñòè. Îêñèäíûé ñëîé îáåñïå èâàåò íåñìà èâàåìîñòü ïîâåðõíîñòè æèäêèì ìåòàëëîì, òî ïðåïÿòñòâóåò îáðàçîâàíèþ íà íåé öåíòðîâ êðèñòàëëèçàöèè. Ïîòîê ñâèíöîâîãî òåïëîíîñèòåëÿ ñóùåñòâóåò ëèáî â ðàâíîâåñíîì äâóõôàçíîì ñîñòîÿíèè â âèäå æèäêîìåòàëëè åñêîé ñóñïåíçèè, ëèáî â ïåðåîõëàæäåííîì ñîñòîÿíèè. Íà ðèñ. 7 ïîêàçàí ïåðåõîäíûé ïðîöåññ ïðè âûíîñå òâåðäîé ôàçû èç ÏÃ è íàêîïëåíèè åå â íèæíåé àñòè âõîäíîé êàìåðû ÃÖÍ. Íóìåðàöèÿ êðèâûõ íà ðèñ. 7à òàêàÿ æå, êàê íà ðèñ. 5à. T, C 500 400 300 4 00 00 3 0 0 0 30 t, c à) f i 0 00 80 60 40 0 3 0 0 0 30 t, c á) Ðèñ. 7 Ñðàâíèâàÿ ïåðåõîäíûå ïðîöåññû â àâàðèéíîì ÏÃ ïðè íàëè èè (ñì. ðèñ. 7) è îòñóòñòâèè (ñì. ðèñ. 5) îêñèäíîãî ñëîÿ íà êîíòàêòíîé ïîâåðõíîñòè, ìîæíî âèäåòü, òî çàòâåðäåâàíèå ñâèíöà íà ñòåíêå ïðèâîäèò ê áîëåå áûñòðîìó ïåðåêðûòèþ ñå åíèÿ íà âûõîäå ÏÃ. Ýòî ñâÿçàíî ñ óìåíüøåíèåì ðàñõîäà, âûçâàííûì ðîñòîì ãèäðàâëè åñêîãî ñîïðîòèâëåíèÿ â ñóæàþùåìñÿ ïîòîêå. Êðèâàÿ íà ðèñ. 7á ïîêàçûâàåò äèíàìèêó íàêîïëåíèÿ òâåðäîé ôàçû â ïîëóñôåðè åñêîé ïîëîñòè íà âûõîäå ÏÃ: t () ϕ G V = dt, V ρ t0 ãäå ϕ () îáúåìíîå ñîäåðæàíèå òâåðäîé ôàçû íà âûõîäå ÏÃ (ðèñ. 7á, êðèâàÿ ); V îáúåì ïîëîñòè íåïîñðåäñòâåííî ïîä êîðïóñîì ÏÃ. Ïðè çàïîëíåíèè âñåãî îáúåìà òâåðäîé ôàçîé ( V = 00% ) âûõîäíîå ñå åíèå ïåðâîãî êîíòóðà ÏÃ ïåðåêðûâàåòñÿ, è öèðêóëÿöèÿ ñâèíöà â àâàðèéíîé ïåòëå ïðåêðàùàåòñÿ (ðèñ. 7á, êðèâàÿ 3). Ïðåäñòàâëåííûå ìîäåëè îöåíèâàþò äèíàìèêó îáðàçîâàíèÿ òâåðäîé ôàçû â äâóõ êà åñòâåííî ðàçëè íûõ ñëó àÿõ. Íà ïðàêòèêå ìîæåò ðåàëèçîâàòüñÿ íåêîòîðûé ïðîìåæóòî íûé âàðèàíò, ñî åòàþùèé îáðàçîâàíèå òâåðäîãî ñëîÿ íà òðóáàõ ÏÃ ñ çàòâåðäåâàíèåì òåïëîíîñèòåëÿ â îáúåìå íà âûõîäå ÏÃ. 76

Âûâîäû Ðàçðàáîòàíà ìåòîäèêà èñëåííîãî ìîäåëèðîâàíèÿ äèíàìèêè ïðîöåññà êðèñòàëëèçàöèè â ïàðîãåíåðàòîðå ñ æèäêîìåòàëëè åñêèì òåïëîíîñèòåëåì, êîòîðàÿ ïîçâîëÿåò ó èòûâàòü íåîïðåäåëåííîñòü, ñâÿçàííóþ ñ ñîñòîÿíèåì êîíòàêòíîé ïîâåðõíîñòè. Íà åå îñíîâå ïðîâåäåíî èñëåííîå èññëåäîâàíèå ïðîöåññà êðèñòàëëèçàöèè ñâèíöîâîãî òåïëîíîñèòåëÿ â ïàðîãåíåðàòîðå ðåàêòîðíîé óñòàíîâêè òèïà ÁÐÅÑÒ-ÎÄ-300, âîçíèêàþùåãî â ðåçóëüòàòå ðàçãåðìåòèçàöèè âûõîäíîãî ïàðîïðîâîäà. Ïðè íåñðàáàòûâàíèè çàïîðíî-ðåãóëèðóþùåé àðìàòóðû ïî ïèòàòåëüíîé âîäå ïðîèñõîäèò ïîëíîå ïåðåêðûòèå ïðîõîäíîãî ñå åíèÿ àâàðèéíîãî ïàðîãåíåðàòîðà òâåðäîé ôàçîé. Â çàâèñèìîñòè îò ñîñòîÿíèÿ çàùèòíîãî îêñèäíîãî ñëîÿ òåïëîîáìåííîé ïîâåðõíîñòè çàòâåðäåâàíèå ñâèíöîâîãî òåïëîíîñèòåëÿ ïðîèñõîäèò ëèáî íà òåïëîîáìåííûõ òðóáàõ, ëèáî â íèæíåé àñòè øàõòû ïàðîãåíåðàòîðà. Â îáîèõ ñëó àÿõ âîçíèêàåò óãðîçà ïðåêðàùåíèÿ öèðêóëÿöèè â àâàðèéíîé ïåòëå, òî òðåáóåò äàëüíåéøåãî äåòàëüíîãî èññëåäîâàíèÿ àâàðèé äàííîãî êëàññà. Ñïèñîê ëèòåðàòóðû. Ïðîåêò «Ïðîðûâ» îñòàåòñÿ ïðèîðèòåòíûì äëÿ Ðîñàòîìà [Ýëåêòðîííûé ðåñóðñ]. Ðåæèì äîñòóïà: http: //www.rosatom.ru/journalist/news/proekt-proryv-ostaetsya-prioritetnym-dlyarosatoma (Äàòà îáðàùåíèÿ:.09.07).. Äðàãóíîâ Þ.Ã., Ëåìåõîâ Â.Â., Ñìèðíîâ Â.Ñ., åðíåöîâ Í.Ã. Òåõíè åñêèå ðåøåíèÿ è ýòàïû ðàçðàáîòêè ðåàêòîðíîé óñòàíîâêè ÁÐÅÑÒ-ÎÄ-300. Àòîìíàÿ ýíåðãèÿ. 0. Ò. 3. Âûï.. Ñ. 58 65. 3. Ôèëèí À.È., Öèêóíîâ Â.Ñ., Ïîïîâ Ñ.Â., Íåñòåðîâ Þ.Â., Øâàðö À.Ë., Êîëáàñíèêîâ À.Â., Øìóêëåð Á.È., Ãîìáîëåâñêèé Â.È., Ðàäèí Þ.À., Âàõðóøèí Ì.Ï. Ðàçðàáîòêà ñõåì, îáîðóäîâàíèÿ è ðåæèìîâ ðàáîòû âòîðîãî êîíòóðà ïåðñïåêòèâíîé ÀÝÑ. Òåïëîýíåðãåòèêà. 00. ¹6. Ñ. 7 3. 4. Íåñòåðîâ Þ.Â., Ëèñÿíñêèé À.Ñ., Ìàêàðîâà Å.È., Áàëüâà Ë.ß., Ïðèõîäüêî Ï.Þ. Òåïëîâàÿ ñõåìà è îáîðóäîâàíèå II êîíòóðà ýíåðãîáëîêà ÀÝÑ ñ ðåàêòîðíîé óñòàíîâêîé ÁÐÅÑÒ- ÎÄ-300. Òåïëîýíåðãåòèêà. 0. ¹6. Ñ. 3 36. 5. Äèäîðèí Ä.Â., Êîãóò Â.À., Ìóðàòîâ À.Ã., Òþêîâ Â.Â., Ìîèñååâ À.Â. Àíàëèç áåçîïàñíîñòè ÐÓ ÁÐÅÑÒ-ÎÄ-300 ïðè íàðóøåíèè óñëîâèé íîðìàëüíîé ýêñïëóàòàöèè. Èííîâàöèîííûå ïðîåêòû è òåõíîëîãèè ÿäåðíîé ýíåðãåòèêè: Òðóäû Ìåæäóíàð. íàó íî-òåõí. êîíô. ÎÀÎ «ÍÈÊÈÝÒ», Ìîñêâà. 7 0 îêòÿáðÿ 04 ã. [Ýëåêòðîííûé ðåñóðñ]. Ðåæèì äîñòóïà: http:// www.nikiet.ru/images/stories/nikiet/publications/conf/mntk_nikiet_04/i-3_rus.pdf (Äàòà îáðàùåíèÿ:.09.07). 6. Alemberti A. European lead fast reactor ELSY. Nuclear Engineering and Design. 0. Vol. 4. Iss. 9. P. 3470 3480. 7. èñòîâ À.Ñ., Ñàâèõèí Î.Ã., Îâ èííèêîâ Â.Ô., Íèêîëàåâ Ì.ß. Ìàòåìàòè åñêàÿ ìîäåëü íåñòàöèîíàðíîãî òåïëîìàññîïåðåíîñà â êàíàëå ñ æèäêîìåòàëëè åñêèì òåïëîíîñèòåëåì ñ ó åòîì ïðîöåññà êðèñòàëëèçàöèè-ïëàâëåíèÿ. Ïðîáëåìû ïðî íîñòè è ïëàñòè íîñòè. 06. Ò. 78. ¹4. Ñ. 368 377. 8. Áåçíîñîâ À.Â., Ìîëîäöîâ À.À., Íàçàðîâ À.Â., Ñàâèíîâ Ñ.Þ., Êóäðèí Î.Î. Èññëåäîâàíèå òåïëîîòäà è îò ñâèíöîâîãî òåïëîíîñèòåëÿ ê ïðîäîëüíîîáòåêàåìîé òðóáå. Òåïëîôèçèêà è àýðîìåõàíèêà. 007. Ò. 4. ¹3. Ñ. 49 436. 9. Ìàõîâ Ê.À. Èññëåäîâàíèå ñòðóêòóðû è òðèáîòåõíè åñêèõ õàðàêòåðèñòèê ïðèñòåííîãî ñëîÿ â ïîòîêå ÒÆÌÒ ïðèìåíèòåëüíî ê ýëåìåíòàì êîíòóðîâ ñ ðåàêòîðàìè íà áûñòðûõ íåéòðîíàõ, îõëàæäàåìûìè ÒÆÌÒ: Äèñ. êàíä. òåõí. íàóê. Í. Íîâãîðîä. ÍÃÒÓ èì. Ð.Å. Àëåêñååâà, 05. 64 ñ. 0. Áóäíèêîâ Â.È., Ñàâèõèí Î.Ã., èñòîâ À.Ñ. Ðàñ åòíîå èññëåäîâàíèå äèíàìèêè çàìîðàæèâàíèÿ ñâèíöîâîãî òåïëîíîñèòåëÿ ïðè ðàçðûâå ïàðîïðîâîäà ÐÓ ñ ðåàêòîðîì ÁÐÅÑÒ- 77

ÎÄ-300. Íàó íàÿ ñåññèÿ ÌÈÔÈ-00. Íàó íî-èííîâàöèîííîå ñîòðóäíè åñòâî: Ñáîðíèê òðóäîâ íàó íî-òåõí. êîíô... Ì.: ÌÈÔÈ, 00. Ñ. 64 65.. Áóäíèêîâ Â.È., Ñàâèõèí Î.Ã., èñòîâ À.Ñ. Ðàñ åòíûé àíàëèç ïðîáëåì áåçîïàñíîñòè, âîçíèêàþùèõ ïðè ðàçãåðìåòèçàöèè êîíòóðîâ öèðêóëÿöèè â ÐÓ ñ ðåàêòîðàìè òèïà ÂÂÝÐ è ÁÐÅÑÒ. Íèæåãîðîäñêèé óíèâåðñèòåò èì. Í.È. Ëîáà åâñêîãî. Âàæíåéøèå íàó íûå ðåçóëüòàòû. Íèæíèé Íîâãîðîä: Èçä-âî ÍÍÃÓ, 004. Ñ. 63 64.. Edwards A.R., O'Brien F.P. Studies of phenomena connected with the depressurization of water reactors. Journal of the British Nuclear Energy Society. 970. Vol. 9. P. 5 35. 3. Ìåéðìàíîâ À.Ì. Çàäà à Ñòåôàíà. Íîâîñèáèðñê: Íàóêà, 986. 39 ñ. 4. ÁÐÅÑÒ: áûñòðûé ðåàêòîð ñî ñâèíöîâûì òåïëîíîñèòåëåì è ïðèñòàíöèîííûì òîïëèâíûì öèêëîì [Ýëåêòðîííûé ðåñóðñ]. Ðåæèì äîñòóïà: http://www.atomic-energy.ru/technology/ 36000. (Äàòà îáðàùåíèÿ:.09.07). 5. Ñåì åíêîâ À.À., åêîâ Ì.Å., Âàñèëüåâ Ñ.Â., Êóçüìèíîâ Þ.Â. Ïàðîãåíåðàòîð ÐÓ ÁÐÅÑÒ-ÎÄ-300: ðàñ åòíî-ýêñïåðèìåíòàëüíîå îáîñíîâàíèå. Âîïðîñû àòîìíîé íàóêè è òåõíèêè. Ñåðèÿ: Îáåñïå åíèå áåçîïàñíîñòè ÀÝÑ. 06. ¹36. Ñ. 33 37. 6. Áóäíèêîâ Â.È., Ñàâèõèí Î.Ã., èñòîâ À.Ñ. èñëåííîå ìîäåëèðîâàíèå íåñòàöèîíàðíûõ òåïëîãèäðàâëè åñêèõ ïðîöåññîâ â êîíòóðàõ öèðêóëÿöèè âîäÿíîãî òåïëîíîñèòåëÿ ïåðñïåêòèâíîé ÀÝÑ. Âåñòíèê Íèæåãîðîäñêîãî ãîñóäàðñòâåííîãî óíèâåðñèòåòà èì. Í.È. Ëîáà åâñêîãî. 03. ¹ (). Ñ. 58 63. 7. Êèðèëëîâ Ï.Ë., Þðüåâ Þ.Ñ., Áîáêîâ Â.Ï. Ñïðàâî íèê ïî òåïëîãèäðàâëè åñêèì ðàñ- åòàì (ÿäåðíûå ðåàêòîðû, òåïëîîáìåííèêè, ïàðîãåíåðàòîðû). Ì.: Ýíåðãîàòîìèçäàò, 990. 359 ñ. 8. Îâ èííèêîâ Ô.ß., Ñåìåíîâ Â.Â. Ýêñïëóàòàöèîííûå ðåæèìû âîäî-âîäÿíûõ ýíåðãåòè åñêèõ ðåàêòîðîâ. Ì.: Ýíåðãîàòîìèçäàò, 988. 359 ñ. 9. Iida T., Guthrie R.I.L. The Physical Properties of Liquid Metals. Oxford, UK: Clarendon Press, 988. 85 p. 0. Ñàâèõèí Î.Ã., Ëèííèê Ñ.Â., Ñàâèõèí À.Î. Àïïðîêñèìàöèÿ ïðîèçâîäíûõ òåðìîäèíàìè åñêèõ ôóíêöèé äëÿ âîäû, ïàðà è ïàðîâîäÿíîé ñìåñè. Âåñòíèê Íèæåãîðîäñêîãî ãîñóäàðñòâåííîãî óíèâåðñèòåòà èì. Í.È. Ëîáà åâñêîãî. 0. ¹4 (3). Ñ. 090 09. References. Proekt Proryv ostaetsya prioritetnym dlya Rosatoma [The PRORYV Project Remains a Priority for Rosatom] Electronic resource. Access mode: http: //www.rosatom.ru/journalist/news/ proekt-proryv-ostaetsya-prioritetnym-dlya-rosatoma (Date of application:.09.07) (In Russian).. Dragunov Yu.G., Lemekhov V.V., Smirnov V.S., Chernetsov N.G. Technical solutions and development stages for the BREST-OD-300 reactor unit. Atomic Energy. 0. Vol. 3. Iss.. P. 70 77. DOI: 0.007/s05-0-9597-3. 3. Filin A.I., Tsikunov V.S., Popov S.V., Nesterov Yu.V., Shvarts A.L., Kolbasnikov A.V., Shmukler B.I., Gombolevskii V.I., Radin Yu.A., Vakhrushin M.P. Development of the thermal schemes, equipment and operating regimes of the second circuit of a promising nuclear power station. Thermal Engineering. 00. No 6. P. 458 463. 4. Nesterov Y.V., Lisyanskii A.S., Makarova E.I., Bal'va L.Ya., Prikhod'ko P.Yu. The thermal process diagram and equipment of the secondary coolant circuit of a nuclear power station unit based on the BREST-OD-300 reactor installation for subcritical steam conditions. Thermal Engineering. 0. Vol. 58. Iss. 6. P. 438 48. DOI: 0.34/S004060506003. 5. Didorin D.V., Kogut V.A., Muratov A.G., Tyukov V.V., Moiseev A.V. Analysis of BREST- OD-300 safety during anticipated operational occurrences. Innovative Projects and Technologies of Nuclear Power: Digest of International Scientific and Technical Conference. Moscow. October 7 0, 04. Electronic resource. Access mode: http://www.nikiet.ru/images/stories/nikiet/ Publications/Conf/mntk_nikiet_04/I-3_rus.pdf (Date of application:.09.07) (In Russian). 6. Alemberti A. European lead fast reactor ELSY. Nuclear Engineering and Design. 0. Vol. 4. Iss. 9. P. 3470 3480. 7. Chistov A.S., Savikhin O.G., Ovchinnikov V.F., Nikolaev M.Ya. Matematicheskaya model nestatsionarnogo teplomassoperenosa v kanale s zhidkometallicheskim teplonositelem s uchetom 78

protsessa kristallizatsii-plavleniya [Mathematical model of non-stationary heat and mass transfer in a channel with liquid-metal coolant taking into account the crystallization-melting process]. Problemy prochnosti i plastichnosti [Problems of Strength and Plasticity]. 06. Vol. 78. No 4. P. 368 377 (In Russian). 8. Beznosov A.V., Molodtsov A.A., Nazarov A.V., Savinov S.Y., Kudrin O.O. Investigation of heat transfer from a lead heat carrier to a tube streamlined longitudinally. Thermophysics and Aeromechanics. 007. Vol. 4. No 3. P. 4 48. 9. Makhov K.A. Issledovanie struktury i tribotekhnicheskikh kharakteristik pristennogo sloya v potoke TZhMT primenitel'no k elementam konturov s reaktorami na bystrykh neytronakh, okhlazhdaemymi TZhMT [The study of the structure and tribotechnical characteristics of boundarylayer flow HLMC in relation to the elements of the circuits with fast neutron reactors cooled HLMC]. Dis... kand. tekhn. nauk [Cand. Sci. (Engineering). Dissertation]. Nizhni Novgorod. NNSTU Publ. 05. 64 p. (In Russian). 0. Budnikov V.I., Savikhin O.G., Chistov A.S. Raschetnoe issledovanie dinamiki zamorazhivaniya svintsovogo teplonositelya pri razryve paroprovoda RU s reaktorom BREST-OD-300 [Numerical study of the lead coolant freezing dynamics at break of steam line of NPP with BREST- OD-300 reactor]. Nauchnaya sessiya MIFI-00. Nauchno-innovatsionnoe sotrudnichestvo: Sbornik trudov nauchno-tekhnicheskoy konferentsii. Ch.. [Scientific and Technical Conference Scientific-innovative Cooperation. Collection of Proceedinds]. Pt.. Moscow. MIFI Publ. 00. P. 64 65 (In Russian).. Budnikov V.I., Savikhin O.G., Chistov A.S. Raschetnyy analiz problem bezopasnosti, voznikayushchikh pri razgermetizatsii konturov tsirkulyatsii v RU s reaktorami tipa VVER i BREST [Computational analysis of security problems that occur when depressurization of nuclear power plan circuits with VVER and BREST type reactors]. Nizhegorodskiy universitet im. N.I. Lobachevskogo. Vazhneyshie nauchnye rezultaty [Lobachevsky State University of Nizhni Novgorod. The Most Important Scientific Results]. Nizhni Novgorod. UNN Publ. 004. P. 63 64 (In Russian).. Edwards A.R., O'Brien F.P. Studies of phenomena connected with the depressurization of water reactors. Journal of the British Nuclear Energy Society. 970. Vol. 9. P. 5 35. 3. Meyrmanov A.M. Zadacha Stefana [The Stefan Problem]. Novosibirsk. Nauka Publ. 986. 39 p. (In Russian). 4. BREST: bystryy reaktor so svintsovym teplonositelem i pristantsionnym toplivnym tsiklom [BREST: Fast Reactor with Lead Coolant and On-site Fuel Cycle]. Electronic resource. Access mode: http://www.atomic-energy.ru/technology/36000 (Date of application:.09.07) (In Russian). 5. Semchenkov A.A., Chekov M.E., Vasilyev S.V., Kuzminov Y.V. Parogenerator RU BREST- OD-300: raschetno-eksperimentalnoe obosnovanie [Steam generator RU BREST-OD-300: calculation and experimental justification]. Voprosy atomnoy nauki i tekhniki. Seriya: Obespechenie bezopasnosti AES. [Questions of Atomic Science and Technology. Series: Ensuring the Safety of Nuclear Power Plants]. 06. No 36. P. 33 37 (In Russian). 6. Budnikov V.I., Savikhin O.G., Chistov A.S. Chislennoe modelirovanie nestatsionarnykh teplogidravlicheskikh protsessov v konturakh tsirkulyatsii vodyanogo teplonositelya perspektivnoy AES [Numerical simulation of non-stationary thermal-hydraulic processes in the water coolant circulation loops of an advanced nuclear power plant]. Vestnik Nizhegorodskogo gosudarstvennogo universiteta im. N.I. Lobachevskogo [Bulletin of UNN]. 03. No (). P. 58 63 (In Russian). 7. Kirillov P.L., Yur'yev Yu.S., Bobkov V.P. Spravochnik po teplogidravlicheskim raschetam (yadernye reaktory, teploobmenniki, parogeneratory) [A Handbook on Thermohydraulic Calculations (Nuclear Reactors, Heat Exchangers, Steam Generators)]. Moscow. Energoatomizdat Publ. 990. 359 p. (In Russian). 8. Ovchinnikov F.Y., Semenov V.V. Ekspluatatsionnye rezhimy vodo-vodyanykh energeticheskikh reaktorov [Operational Modes of Water-Water Power Reactors]. Moscow. Energoatomizdat Publ. 988. 359 p. (In Russian). 9. Iida T., Guthrie R.I.L. The Physical Properties of Liquid Metals. Oxford. UK. Clarendon Press. 988. 85 p. 0. Savikhin O.G., Linnik S.V., Savikhin A.O. Approksimatsiya proizvodnykh termodinamicheskikh funktsiy dlya vody, para i parovodyanoy smesi [Approximation of derivatives of thermo- 79

dynamic functions for water, steam and mixture]. Vestnik Nizhegorodskogo gosudarstvennogo universiteta im. N.I. Lobachevskogo [Bulletin of UNN]. 0. No 4 (3). P. 090 09 (In Russian). NUMERICAL SIMULATION OF HEAT AND MASS TRANSFER IN THE STEAM GENERATOR OF THE BREST TYPE REACTOR PLANT IN THE EVENT OF CRYSTALLIZATION OF LEAD COOLANT Chistov A.S., Savikhin O.G., Ovchinnikov V.F., Kiryushina E.V. Research Institute of Mechanics University of Nizhni Novgorod, Nizhni Novgorod, Russian Federation Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russian Federation The method of numerical simulation has been developed describing non-stationary heat and mass transfer and thermal conductivity in a steam generator with liquid metal coolant when there is a crystallization process. The method takes into account the differences of the process depending on the condition of the contact surfaces. On its basis the dynamics of solid phase formation in a lead-coolant of reactor plant BREST type during the accident with the steam generator steam line depressurization has been studied. The calculations are carried out with using of the RASPLAV software complex, which allows modeling the interconnected dynamics of thermal-hydraulic processes in the first and second circuits in terms of the one-dimensional equilibrium approximation. It is shown that at failure of feed water lock-regulatory armature there is a full closure of flow section of the emergency steam generator first circuit by solid phase. Depending on the condition of the protective oxide layer of the heat exchange surface the solidification of lead coolant takes place either on the heat exchanger tubes or in the lower part of the steam generator reservoir. In both cases, there is a threat of cessation of circulation in the emergency loop. A brief description of the mathematical model of the steam generator and the reactor plant circuit as a whole is given. A one-dimensional description of heat and mass transfer is used. A thermodynamic equilibrium of the phases at the boundary of phase transfer is postulated. The test results of the programmed numerical model are given. The calculation of the high pressure pipeline rupture is tested by comparison with the experimental data. The calculation of the solid layer formation dynamics on the surface of heat exchange tubes is tested by comparing the numerical solution with the analytical solution of the Stefan problem. The results of this research can be used for design of reactors with a lead coolant. Keywords: Stefan problem, stop valve, mathematical model, steam generator, reactor plant, lead coolant, surface wettability, mixing feedwater heater, crystallization process, phase transfer. 80