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Îïòèìèçàöèÿ ôîðìû ëîïàñòè ãèäðîòóðáèíû 191

Ðèñ. 5.14. Çàäà÷è

ZDT

(à),

ZDT

(á),

TNK

(â),

OSY

(ã)

DTLZ

(ä).

§ 5.8. ÐÅÇÓËÜÒÀÒÛ ÐÀÑ×ÅÒÎÂ

ÌÍÎÃÎÖÅËÅÂÎÉ ÎÏÒÈÌÈÇÀÖÈÈ

Â êà÷åñòâå îáúåêòà ìíîãîöåëåâîé îïòèìèçàöèè òàê æå, êàêèâñëó

÷àå îäíîöåëåâîé îïòèìèçàöèè, âûáðàíî ðàäèàëüíî-îñåâîå ðàáî÷åå êî

ëåñî ãèäðîòóðáèíû Áðàòñêîé ÃÝÑ. Äëÿ âàðèàöèè ôîðìû ëîïàñòè èñ

ïîëüçîâàëàñü òà æå ñàìàÿ ïàðàìåòðèçàöèÿ (ñì. § 5.2). Ðàñ÷åòû òå÷åíèÿ

äëÿ êàæäîãî èíäèâèäóóìà âûïîëíÿëèñü â íåâÿçêîì ïðèáëèæåíèè â

öèêëè÷åñêîé ïîñòàíîâêå. Èñïîëüçîâàëèñü öåëåâûå ôóíêöèîíàëû è îã

ðàíè÷åíèÿ, îïèñàííûå â § 5.3 è 5.4. Êàâèòàöèîííîå îãðàíè÷åíèå (5.5)

ïðè ïðîâåäåíèè ìíîãîöåëåâîé îïòèìèçàöèè áûëî íåñêîëüêî ìîäèôè

öèðîâàíî ñ öåëüþ èñïîëüçîâàíèÿ åãî íå òîëüêî äëÿ îãðàíè÷åíèÿ ðàçìå

ðà îáëàñòè êàâèòàöèè, íî è äëÿ åå ñìåùåíèÿ êàê ìîæíî áëèæå ê âûõîä

íîé êðîìêå ëîïàñòè. Äëÿ ýòîãî

cav

â (5.5) çàìåíÿëñÿ íà âûðàæåíèå

SwdS

cav

suc

∫

ãäå

cav

= 1

, åñëè âûïîëíÿåòñÿ óñëîâèå âîçíèêíîâåíèÿ êàâèòàöèè

(5.4), è

cav

= 0

, åñëè êàâèòàöèè íåò. Ôóíêöèÿ

wwl= ()

åñòü âåñîâàÿ

ôóíêöèÿ, âèä êîòîðîé èçîáðàæåí íà ðèñ. 5.15. Ïàðàìåòð

— íîðìè-

ðîâàííîå ðàññòîÿíèå îò âõîäíîé êðîìêè, èçìåðåííîå âäîëü ïîâåðõ-

íîñòè ëîïàñòè â íàïðàâëåíèè ïîòîêà.

5.8.1. Äâóõöåëåâàÿ îïòèìèçàöèÿ

Ïðîâåäåíà ìèíèìèçàöèÿ êèíåòè÷åñêîé ýíåðãèè íà âûõîäå èç

ðàáî÷åãî êîëåñà

(5.6) è îòêëîíåíèÿ ëèíèé òîêà îò “îñåñèììåòðè÷

íûõ”

(5.8) ïðè îãðàíè÷åíèÿõ

íà íàïîð â ðàáî÷åì êîëåñå è

íà ðàçìåð è ðàñïîëîæåíèå îá

ëàñòè êàâèòàöèè. Ïðè ïîèñêå

ôðîíòà Ïàðåòî èñïîëüçîâàëèñü

ñëåäóþùèå çíà÷åíèÿ ïàðàìåòðîâ

îïòèìèçàöèîííîãî àëãîðèòìà:

= 001,

Tr = 03,

d = 07,

m = 01,

100=

p = 70

. Ðàññ÷è

òàíî 80 ïîêîëåíèé, îäíàêî â

äàííîì ñëó÷àå ñõîäèìîñòü ê

192 Ãëàâà 5

Ðèñ. 5.15. Âèä âåñîâîé ôóíêöèè äëÿ

îãðàíè÷åíèÿ ïî êàâèòàöèè.

ôðîíòó Ïàðåòî äîñòèãíóòà çà 45 ïîêîëåíèé. Íà ðèñ. 5.16 â ïëîñêîñòè

ìèíèìèçèðóåìûõ ôóíêöèîíàëîâ èçîáðàæåíû ëó÷øèå èíäèâèäóóìû

0, 3, 5, 10, 20 è 80-ãî ïîêîëåíèé. Ðåøåíèå, ñîñòàâëÿþùåå ëó÷øèé

êîìïðîìèññ ìåæäó ôóíêöèîíàëàìè, îáîçíà÷åíî íà ðèñ. 5.16 êàê

ëîïàñòü Opt.

Íà ðèñ. 5.17 ïðèâåäåíû ìåðèäèîíàëüíûå ðàñïðåäåëåíèÿ

ñêîðîñòåé íà âûõîäå èç ðàáî÷åãî êîëåñà, à íà ðèñ. 5.18 — ëèíèè

ðàñòåêàíèÿ è ëèíèè òîêà íà ðàáî÷åé ñòîðîíå ëîïàñòè äëÿ íà÷àëü

íîé ëîïàñòè è ëîïàñòè Opt. Âèä

íî, ÷òî äëÿ ëîïàñòè Opt ïîëå ìå

ðèäèîíàëüíîé êîìïîíåíòû ñêî

ðîñòè áîëåå ðàâíîìåðíîå, à

ëèíèÿ ðàñòåêàíèÿ ïîëíîñòüþ

ñîâïàäàåò ñ âõîäíîé êðîìêîé

Îïòèìèçàöèÿ ôîðìû ëîïàñòè ãèäðîòóðáèíû 193

Ðèñ. 5.16. Ëó÷øèå èíäèâèäóóìû â ðàçëè÷íûõ ïîêîëåíèÿõ.

Ðèñ. 5.17. Ðàñïðåäåëåíèå ñêîðîñòè íà

âûõîäå èç ðàáî÷åãî êîëåñà.

à — íà÷àëüíàÿ; á — ëîïàñòü Opt.

ëîïàñòè. Îäíàêî íà îïòèìàëüíîé ëîïàñòè ïîÿâèëàñü çîíà êàâèòà

öèè, ñîñòàâëÿþùàÿ 5 % îò ïëîùàäè òûëüíîé ïîâåðõíîñòè ëîïà

ñòè (ðèñ. 5.19).

5.8.2. Òðåõöåëåâàÿ îïòèìèçàöèÿ

Ïîñêîëüêó ïðè îïòèìèçàöèè èñõîäíîé ëîïàñòè îòíîñèòåëüíî

êðèòåðèåâ

áûëè óõóäøåíû åå êàâèòàöèîííûå êà÷åñòâà, ïðî

âåëè îïòèìèçàöèîííûé ðàñ÷åò, íàïðàâëåííûé íà ìèíèìèçàöèþ

194 Ãëàâà 5

Ðèñ. 5.18. Ëèíèè ðàñòåêàíèÿ è ëèíèè òîêà íà ðàáî÷åé ñòîðîíå ëîïàñòè.

à — íà÷àëüíàÿ; á — ëîïàñòü Opt.

Ðèñ. 5.19. Ðàñïðåäåëåíèå äàâëåíèÿ è çîíà êàâèòàöèè íà òûëüíîé ñòîðîíå

ëîïàñòè.

à — íà÷àëüíàÿ (0 %); á — ëîïàñòü Opt (5 %).

Îïòèìèçàöèÿ ôîðìû ëîïàñòè ãèäðîòóðáèíû 195

Ðèñ. 5.20. Ïðîåêöèÿ ôðîíòà Ïàðåòî íà ïëîñêîñòü ôóíêöèîíàëîâ

Ðèñ. 5.21. Ëîïàñòü Opt1. Ðàñïðåäåëåíèå ñêîðîñòè íà âûõîäå èç ðàáî÷åãî êîëå

ñà (à); ëèíèÿ ðàñòåêàíèÿ (á) è ëèíèè òîêà (â) íà ðàáî÷åé ñòîðîíå ëîïàñòè.

òðåõ ôóíêöèîíàëîâ:

ïðè îãðàíè÷åíèè íà íàïîð. Ïðè ðå-

øåíèè äàííîé çàäà÷è ÷èñëî èíäèâèäóóìîâ â ïîïóëÿöèè

óâåëè÷è

ëè äî 100. Íà ðèñ. 5.20 èçîáðàæåíà ïðîåêöèÿ 3D ôðîíòà Ïàðåòî, ïî

ëó÷åííîãî ïîñëå ðàñ÷åòà 150 ïîêîëåíèé, íà ïëîñêîñòü ôóíêöèîíà

ëîâ

. Êðóæêàìè îáîçíà÷åíû ðåøåíèÿ çàäà÷è — ôðîíò

Ïàðåòî, ëèíèÿìè — ëèíèè óðîâíÿ ôóíêöèîíàëà

. Áåñêàâèòàöè

îííàÿ ëîïàñòü ñ ëèíèåé ðàñòåêàíèÿ, ñîâïàäàþùåé ñ âõîäíîé êðîì

êîé è èìåþùàÿ íàèáîëåå ðîâíîå ïîëå ñêîðîñòè íà âûõîäå èç ðàáî

÷åãî êîëåñà, îáîçíà÷åíà Opt 1. Íà ðèñ. 5.21–5.22 ïðåäñòàâëåíû äàí

íûå äëÿ ëîïàñòè Opt 1.

196 Ãëàâà 5

Ðèñ. 5.22. Îòêëîíåíèå ñðåäèííîé ïîâåðõíîñòè ëîïàñòè îò íà÷àëüíîé.

à — ëîïàñòü Opt; á — ëîïàñòü Opt 1. Ñâåòëûì ïîêàçàíà íà÷àëüíàÿ ñðåäèííàÿ ïîâåðõ-

íîñòü, òåìíûì — îïòèìèçèðîâàííàÿ.

Ê ÂÂÅÄÅÍÈÞ

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ÁÈÁËÈÎÃÐÀÔÈ×ÅÑÊÈÉ ÑÏÈÑÎÊ

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200 Áèáëèîãðàôè÷åñêèé ñïèñîê