Определение границы устойчивости лопаточных венцов к дозвуковому флаттеру при больших углах атаки
This paper presents an experimental-numerical method for determination of the subsonic flutter stability boundary of blade rows at large angles of incident flow. The aerodynamic test rig for determining the unsteady aerodynamic loads is described. The test results are presented for a straight cascad...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
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| Cite this: | Определение границы устойчивости лопаточных венцов к дозвуковому флаттеру при больших углах атаки / С.Н. Кабанник, А.П. Зиньковский, А.Л. Стельмах // Проблемы прочности. — 2018. — № 2. — С. 27-37. — Бібліогр.: 14 назв. — рос. |
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nasplib_isofts_kiev_ua-123456789-1738752025-02-09T23:28:43Z Определение границы устойчивости лопаточных венцов к дозвуковому флаттеру при больших углах атаки Determination of the Subsonic Flutter Stability Boundary of Blade Rows at Large Angles of Attack Кабанник, С.Н. Зиньковский, А.П. Стельмах, А.Л. Научно-технический раздел This paper presents an experimental-numerical method for determination of the subsonic flutter stability boundary of blade rows at large angles of incident flow. The aerodynamic test rig for determining the unsteady aerodynamic loads is described. The test results are presented for a straight cascade of airfoils in a wide range of variation in the angle of attack and reduced vibration frequency, based on which the regularities in the effect of the angle of attack on the subsonic flutter stability boundary of blading are established. Изложена методика экспериментально-расчетного определения границы устойчивости лопаточных венцов к дозвуковому флаттеру при больших углах натекания потока. Описан аэродинамический стенд для определения нестационарных аэродинамических нагрузок. Приведены результаты испытаний плоской решетки лопаточных профилей в широком диапазоне изменения угла атаки и приведенной частоты колебаний, с использованием которых установлены закономерности влияния угла атаки на границу устойчивости лопаточных венцов к дозвуковому флаттеру. Викладено методику експериментально-розрахункового визначення границі стійкості лопаткового вінця до дозвукового флатера при великих кутах натікання потоку. Описано аеродинамічний стенд для визначення нестаціонарних аеродинамічних навантажень. Наведено результати випробувань плоскої решітки лопаткових профілів у широкому діапазоні зміни кута атаки і зведеної частоти коливань, із використанням яких установлено закономірності впливу кута атаки на границю стійкості лопаткових вінців до дозвукового флатера. 2018 Article Определение границы устойчивости лопаточных венцов к дозвуковому флаттеру при больших углах атаки / С.Н. Кабанник, А.П. Зиньковский, А.Л. Стельмах // Проблемы прочности. — 2018. — № 2. — С. 27-37. — Бібліогр.: 14 назв. — рос. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/173875 621.515/62-752 ru Проблемы прочности application/pdf Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
Russian |
| topic |
Научно-технический раздел Научно-технический раздел |
| spellingShingle |
Научно-технический раздел Научно-технический раздел Кабанник, С.Н. Зиньковский, А.П. Стельмах, А.Л. Определение границы устойчивости лопаточных венцов к дозвуковому флаттеру при больших углах атаки Проблемы прочности |
| description |
This paper presents an experimental-numerical method for determination of the subsonic flutter stability boundary of blade rows at large angles of incident flow. The aerodynamic test rig for determining the unsteady aerodynamic loads is described. The test results are presented for a straight cascade of airfoils in a wide range of variation in the angle of attack and reduced vibration frequency, based on which the regularities in the effect of the angle of attack on the subsonic flutter stability boundary of blading are established. |
| format |
Article |
| author |
Кабанник, С.Н. Зиньковский, А.П. Стельмах, А.Л. |
| author_facet |
Кабанник, С.Н. Зиньковский, А.П. Стельмах, А.Л. |
| author_sort |
Кабанник, С.Н. |
| title |
Определение границы устойчивости лопаточных венцов к дозвуковому флаттеру при больших углах атаки |
| title_short |
Определение границы устойчивости лопаточных венцов к дозвуковому флаттеру при больших углах атаки |
| title_full |
Определение границы устойчивости лопаточных венцов к дозвуковому флаттеру при больших углах атаки |
| title_fullStr |
Определение границы устойчивости лопаточных венцов к дозвуковому флаттеру при больших углах атаки |
| title_full_unstemmed |
Определение границы устойчивости лопаточных венцов к дозвуковому флаттеру при больших углах атаки |
| title_sort |
определение границы устойчивости лопаточных венцов к дозвуковому флаттеру при больших углах атаки |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| publishDate |
2018 |
| topic_facet |
Научно-технический раздел |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/173875 |
| citation_txt |
Определение границы устойчивости лопаточных венцов к дозвуковому флаттеру при больших углах атаки / С.Н. Кабанник, А.П. Зиньковский, А.Л. Стельмах // Проблемы прочности. — 2018. — № 2. — С. 27-37. — Бібліогр.: 14 назв. — рос. |
| series |
Проблемы прочности |
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2025-12-01T18:29:15Z |
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2025-12-01T18:29:15Z |
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1850331635354959872 |
| fulltext |
ÓÄÊ 621.515/62-752
Îïðåäåëåíèå ãðàíèöû óñòîé÷èâîñòè ëîïàòî÷íûõ âåíöîâ ê äîçâóêîâîìó
ôëàòòåðó ïðè áîëüøèõ óãëàõ àòàêè
Ñ. Í. Êàáàííèê, À. Ï. Çèíüêîâñêèé, À. Ë. Ñòåëüìàõ
Èíñòèòóò ïðîáëåì ïðî÷íîñòè èì. Ã. Ñ. Ïèñàðåíêî ÍÀÍ Óêðàèíû, Êèåâ, Óêðàèíà
Èçëîæåíà ìåòîäèêà ýêñïåðèìåíòàëüíî-ðàñ÷åòíîãî îïðåäåëåíèÿ ãðàíèöû óñòîé÷èâîñòè ëîïà-
òî÷íûõ âåíöîâ ê äîçâóêîâîìó ôëàòòåðó ïðè áîëüøèõ óãëàõ íàòåêàíèÿ ïîòîêà. Îïèñàí
àýðîäèíàìè÷åñêèé ñòåíä äëÿ îïðåäåëåíèÿ íåñòàöèîíàðíûõ àýðîäèíàìè÷åñêèõ íàãðóçîê. Ïðèâå-
äåíû ðåçóëüòàòû èñïûòàíèé ïëîñêîé ðåøåòêè ëîïàòî÷íûõ ïðîôèëåé â øèðîêîì äèàïàçîíå
èçìåíåíèÿ óãëà àòàêè è ïðèâåäåííîé ÷àñòîòû êîëåáàíèé, ñ èñïîëüçîâàíèåì êîòîðûõ óñòà-
íîâëåíû çàêîíîìåðíîñòè âëèÿíèÿ óãëà àòàêè íà ãðàíèöó óñòîé÷èâîñòè ëîïàòî÷íûõ âåíöîâ ê
äîçâóêîâîìó ôëàòòåðó.
Êëþ÷åâûå ñëîâà: ëîïàòî÷íûé âåíåö, äîçâóêîâîé ôëàòòåð, ãðàíèöà äèíàìè÷åñêîé
óñòîé÷èâîñòè, ðåøåòêà ëîïàòî÷íûõ ïðîôèëåé, ïðèâåäåííàÿ ÷àñòîòà êîëåáàíèé, óãîë
àòàêè.
Ââåäåíèå. Õàðàêòåðíîé îñîáåííîñòüþ ñîâðåìåííûõ àâèàöèîííûõ ãàçîòóðáèí-
íûõ äâèãàòåëåé (ÀÃÒÄ) ÿâëÿåòñÿ áîëüøàÿ âåðîÿòíîñòü âîçíèêíîâåíèÿ äîçâóêîâîãî
ðåøåòî÷íîãî ôëàòòåðà êîìïðåññîðíûõ, â òîì ÷èñëå è âåíòèëÿòîðíûõ, ëîïàòî÷íûõ
âåíöîâ. Ñòðåìèòåëüíîå ïîâûøåíèå àìïëèòóä òàêèõ êîëåáàíèé ëîïàòîê ìîæåò ïðè-
âåñòè åñëè íå ê âíåçàïíîìó îòêàçó äâèãàòåëÿ, òî ê çíà÷èòåëüíîìó ñîêðàùåíèþ åãî
ðåñóðñà äàæå ïðè êðàòêîâðåìåííîé ýêñïëóàòàöèè çà ãðàíèöåé äèíàìè÷åñêîé óñòîé-
÷èâîñòè. Îñîáåííî ýòî îòíîñèòñÿ ê ïðèìåíÿåìûì â íàñòîÿùåå âðåìÿ êîíñòðóêöèÿì
îáëåã÷åííûõ ëîïàòîê ñ áîëüøèì óäëèíåíèåì, ÷òî îáúÿñíÿåòñÿ ñòðåìëåíèåì êîíñò-
ðóêòîðîâ ê îáåñïå÷åíèþ ìåíüøåãî îñåâîãî ðàçìåðà è ñíèæåíèþ óäåëüíîãî âåñà
äâèãàòåëÿ.
Àâèàöèîííûå ãàçîòóðáèííûå äâèãàòåëè ýêñïëóàòèðóþòñÿ íà ðàçëè÷íûõ ðåæè-
ìàõ. Ïðè ýòîì, êàê ïðàâèëî, ñ öåëüþ ïîëó÷åíèÿ ìàêñèìàëüíîé ýôôåêòèâíîñòè
áîëüøóþ ÷àñòü âðåìåíè îíè ðàáîòàþò íà íåáîëüøèõ óãëàõ àòàêè, áëèçêèõ ê íîìè-
íàëüíûì. Îäíàêî óñëîâèÿ èõ ðàáîòû ìîãóò èçìåíÿòüñÿ, âñëåäñòâèå ÷åãî âûõîä íà
íåðàñ÷åòíûé ðåæèì íåèçáåæåí. Ýòî ïðèâîäèò ê èçìåíåíèþ ðàñïðåäåëåíèÿ îñåâûõ
ñêîðîñòåé âîçäóõà ïî òðàêòó äâèãàòåëÿ, à ñëåäîâàòåëüíî, è óãëîâ àòàêè íàáåãàþùåãî
íà ðàáî÷èå ëîïàòêè ïîòîêà.  òàêîì ñëó÷àå íàñòóïàåò ðàññîãëàñîâàíèå ñòóïåíåé,
îòêëîíåíèå îò ðàñ÷åòíûõ ðåæèìîâ ýêñïëóàòàöèè. Ïðè ýòîì ëîïàòêè ìîãóò ïîä-
âåðãàòüñÿ îáòåêàíèþ ïîòîêîì ïîä áîëüøèì óãëîì àòàêè. Âñå ýòî ìîæåò ïðèâåñòè ê
äèíàìè÷åñêîé íåóñòîé÷èâîñòè ëîïàòîê è, êàê ñëåäñòâèå, ê ïîòåðå çíà÷èòåëüíîé ÷àñòè
èõ ðåñóðñà èëè äàæå ðàçðóøåíèþ. Èìåííî ýòî îáñòîÿòåëüñòâî îáóñëîâëèâàåò íåîáõî-
äèìîñòü çíàíèÿ óæå íà ñòàäèè ïðîåêòèðîâàíèÿ ÀÃÒÄ ãðàíèöû óñòîé÷èâîñòè ëîïà-
òî÷íîãî âåíöà ê äîçâóêîâîìó ôëàòòåðó â øèðîêîì äèàïàçîíå èçìåíåíèÿ óãëà àòàêè.
Äëÿ îïðåäåëåíèÿ ãðàíèöû äèíàìè÷åñêîé óñòîé÷èâîñòè ëîïàòî÷íûõ âåíöîâ ñ
ó÷åòîì ñòðåìèòåëüíîãî ïðîãðåññà â ðàçâèòèè âû÷èñëèòåëüíîé òåõíèêè âñå áîëüøå
èñïîëüçóþòñÿ ÷èñëåííûå ìåòîäû, áàçèðóþùèåñÿ íà ðåøåíèè íåñòàöèîíàðíûõ óðàâ-
íåíèé Íàâüå–Ñòîêñà [1, 2]. Ïðè èõ èñïîëüçîâàíèè ïðèíèìàåòñÿ äîïóùåíèå, ÷òî îíè
àäåêâàòíî îïèñûâàþò íå òîëüêî ëàìèíàðíûå, íî è òóðáóëåíòíûå òå÷åíèÿ [3]. Õàðàê-
òåðèñòèêè âÿçêîñòè îáòåêàþùåãî ïîòîêà, íåîáõîäèìûå ïðè ðåøåíèè äàííûõ óðàâíå-
íèé, ó÷èòûâàþòñÿ ñ ïîìîùüþ ðàçëè÷íûõ ïîëóýìïèðè÷åñêèõ ìîäåëåé òóðáóëåíò-
íîñòè, êîòîðûå îïèñûâàþò êîíêðåòíîå òå÷åíèå. Ïðè èçìåíåíèè ïàðàìåòðîâ ïîòîêà,
© Ñ. Í. ÊÀÁÀÍÍÈÊ, À. Ï. ÇÈÍÜÊÎÂÑÊÈÉ, À. Ë. ÑÒÅËÜÌÀÕ, 2018
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2018, ¹ 2 27
íàïðèìåð óãëà àòàêè, íåîáõîäèìî âíîñèòü ðÿä äîïîëíèòåëüíûõ ïîïðàâîê, ó÷èòû-
âàþùèõ ýôôåêòû ñæèìàåìîñòè, âîçâðàò ïîòîêà, íåëèíåéíîñòü è ò.ä. Ýòî ìîæåò
ïðèâåñòè ê óâåëè÷åíèþ âû÷èñëèòåëüíûõ çàòðàò è óõóäøèòü ðåçóëüòàòû ñõîäèìîñòè
ðåøåíèé óêàçàííûõ óðàâíåíèé [4]. Îòðûâ ïîòîêà ñ ïåðà ëîïàòîê, êîòîðûé âîçíèêàåò ñ
ðîñòîì óãëà àòàêè, îáóñëîâëèâàåò íåîáõîäèìîñòü ïðèìåíåíèÿ î÷åíü ìåëêèõ ñåòîê ïðè
ìîäåëèðîâàíèè ëîïàòîê, ÷òî òàêæå òðåáóåò ÷ðåçâû÷àéíî áîëüøèõ âû÷èñëèòåëüíûõ
çàòðàò. Èìåííî ýòèì, ïî-âèäèìîìó, îáúÿñíÿåòñÿ ñóùåñòâåííûé ðàçáðîñ â ðåçóëüòàòàõ
÷èñëåííîãî ïðîãíîçèðîâàíèÿ âîçíèêíîâåíèÿ ôëàòòåðà ëîïàòî÷íûõ âåíöîâ. Îá ýòîì
ñâèäåòåëüñòâóþò ïðèâåäåííûå â [5] äàííûå èçó÷åíèÿ óñòîé÷èâîñòè îäíîãî è òîãî æå
âåíöà, âûïîëíåííîãî íåçàâèñèìî ðàçëè÷íûìè èññëåäîâàòåëÿìè, ê ôëàòòåðó. Áûëè
ïîëó÷åíû ñîâåðøåííî ïðîòèâîïîëîæíûå âûâîäû î âîçìîæíîñòè âîçíèêíîâåíèÿ
ôëàòòåðà ëîïàòîê èññëåäóåìîãî âåíöà.
Ñ ó÷åòîì èçëîæåííîãî â íàñòîÿùåå âðåìÿ ïðè ðåøåíèè çàäà÷ ôëàòòåðà ëîïà-
òî÷íûõ âåíöîâ íàèáîëåå äîñòîâåðíûå ðåçóëüòàòû ìîãóò áûòü ïîëó÷åíû òîëüêî ñ
èñïîëüçîâàíèåì ýêñïåðèìåíòàëüíî-ðàñ÷åòíûõ ìåòîäîâ èññëåäîâàíèé, îñîáåííî ïðè
áîëüøèõ óãëàõ àòàêè èõ îáòåêàíèÿ ãàçîâûì ïîòîêîì.
 Èíñòèòóòå ïðîáëåì ïðî÷íîñòè èì. Ã. Ñ. Ïèñàðåíêî ÍÀÍ Óêðàèíû ðàçðàáîòàí
è èñïîëüçóåòñÿ ýêñïåðèìåíòàëüíî-ðàñ÷åòíûé ìåòîä ïðîãíîçèðîâàíèÿ óñòîé÷èâîñòè
ëîïàòî÷íûõ âåíöîâ ê äîçâóêîâîìó ôëàòòåðó [6]. Âàæíûìè ñîñòàâëÿþùèìè ýòîãî
ìåòîäà ÿâëÿþòñÿ ìåòîäèêà è ñòåíä äëÿ èçìåðåíèÿ íåñòàöèîíàðíûõ àýðîäèíàìè÷åñêèõ
íàãðóçîê íà ëîïàòî÷íûõ ïðîôèëÿõ. Îäíàêî âîçìîæíîñòè ñòåíäà îãðàíè÷åíû ïðè
èñïûòàíèÿõ íà áîëüøèõ óãëàõ àòàêè.
Öåëü ðàáîòû ñîñòîèò â èçó÷åíèè âëèÿíèÿ áîëüøèõ êàê ïîëîæèòåëüíûõ, òàê è
îòðèöàòåëüíûõ óãëîâ àòàêè íà ãðàíèöó äèíàìè÷åñêîé óñòîé÷èâîñòè ïðÿìîé êîìïðåñ-
ñîðíîé ðåøåòêè ëîïàòî÷íûõ ïðîôèëåé.
Îñíîâíûå ïîëîæåíèÿ ýêñïåðèìåíòàëüíî-ðàñ÷åòíîé ìåòîäèêè. Êîëåáàíèÿ ëî-
ïàòî÷íîãî âåíöà â ïîòîêå îïèñûâàþòñÿ ìàòðè÷íûì ëèíåàðèçîâàííûì óðàâíåíèåì [7,
8]
[ ]{��} [ ]{�} [ ]{ } [ ],M q C q K q Q� � � (1)
ãäå [ ],M [ ],C [ ]K – ìàòðèöû èíåðöèîííûõ, äèññèïàòèâíûõ è óïðóãèõ õàðàêòåðèñòèê
ëîïàòî÷íîãî âåíöà; [ ]Q – ìàòðèöà íåñòàöèîíàðíûõ àýðîäèíàìè÷åñêèõ íàãðóçîê, äåé-
ñòâóþùèõ íà ëîïàòêè â ïîòîêå; { }q – âåêòîð-ñòîëáåö ïåðåìåùåíèé.
Ïðè ðåøåíèè óðàâíåíèÿ (1) íåîáõîäèìî çíàòü àýðîäèíàìè÷åñêèå íàãðóçêè (ñèëû
è ìîìåíòû), äåéñòâóþùèå íà ëîïàòêè ïðè îáòåêàíèè ïîòîêîì âñëåäñòâèå èõ ïåðå-
ìåùåíèé. Äëÿ ðåøåíèÿ ýòîé çàäà÷è èñïîëüçóþòñÿ ïðÿìûå ðåøåòêè ëîïàòî÷íûõ
ïðîôèëåé, ìîäåëèðóþùèå ïåðèôåðèéíûå ñå÷åíèÿ âåíöà, ðàñïîëîæåííûå íà 0,75...
...0,95 âûñîòû h ïåðà ëîïàòîê. Ñõåìà òàêîé ðåøåòêè ñ óêàçàíèåì ïåðåìåùåíèé
ïðîôèëåé è äåéñòâóþùèõ íà íèõ íàãðóçîê ïðèâåäåíà íà ðèñ. 1, ãäå b – õîðäà
ïðîôèëÿ; t – øàã ðåøåòêè; � – óãîë âûíîñà; V1 – ñêîðîñòü íàáåãàþùåãî ïîòîêà; M A ,
LA , K A – àýðîäèíàìè÷åñêèå ìîìåíò è ñèëû ñîîòâåòñòâåííî; x, y – ïåðåìåùåíèÿ
ïðîôèëÿ ïðè åãî êîëåáàíèÿõ; � – óãîë ïîâîðîòà ïðîôèëÿ ïðè êîëåáàíèÿõ; n – íîìåð
ïðîôèëÿ â ðåøåòêå. Íåîáõîäèìî îòìåòèòü, ÷òî óêàçàíû ïîëîæèòåëüíûå íàïðàâëåíèÿ
íàãðóçîê è ïåðåìåùåíèé.
Îáîñíîâàííîñòü èñïîëüçîâàíèÿ ïðÿìîé ðåøåòêè ëîïàòî÷íûõ ïðîôèëåé êàê
îáúåêòà èñïûòàíèé îáóñëîâëåíà ñëåäóþùèì. Íà îñíîâå àíàëèçà ìíîãî÷èñëåííûõ
äàííûõ èñïûòàíèé óñòàíîâëåíî, ÷òî ïðè êîëåáàíèÿõ ëîïàòîê ïî íèçøèì (ïåðâûå
èçãèáíàÿ è êðóòèëüíàÿ) ôîðìàì, êàê íàèáîëåå îïàñíûì ñ òî÷êè çðåíèÿ âîçíèêíîâåíèÿ
ôëàòòåðà, ïðàêòè÷åñêè 80% ïîäâîäèìîé ðàáîòû îò ïîòîêà ïðèõîäèòñÿ íà ïåðèôåðèé-
íóþ ÷àñòü ïåðà ëîïàòîê, ñîñòàâëÿþùóþ ïðèìåðíî 20% åãî âûñîòû, ÷òî â îñíîâíîì è
ïðåäîïðåäåëÿåò óñòîé÷èâîñòü âñåãî âåíöà [9]. Ïîýòîìó êðèòè÷åñêèå ïàðàìåòðû êîëå-
áàíèé ïðîôèëÿ, ñîîòâåòñòâóþùèå âûáðàííîìó ïåðèôåðèéíîìó ñå÷åíèþ ïåðà ëîïàòîê
Ñ. Í. Êàáàííèê, À. Ï. Çèíüêîâñêèé, À. Ë. Ñòåëüìàõ
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è õàðàêòåðèçóþùèå óñòîé÷èâîñòü ê äîçâóêîâîìó ôëàòòåðó ðåøåòêè ïðîôèëåé, ñ
áîëüøîé ñòåïåíüþ âåðîÿòíîñòè áóäóò îïðåäåëÿòü è óñòîé÷èâîñòü âåíöà ïðè êîëå-
áàíèÿõ ëîïàòîê ïî óêàçàííûì ôîðìàì.
Ñîãëàñíî [6] äëÿ ðàñ÷åòà ãðàíèöû äèíàìè÷åñêîé óñòîé÷èâîñòè ëîïàòî÷íîãî
âåíöà ïðàêòè÷íåå èñïîëüçîâàòü áåçðàçìåðíûå àýðîäèíàìè÷åñêèå êîýôôèöèåíòû âëèÿ-
íèÿ (ÀÊÂ), êîòîðûå îïðåäåëÿþòñÿ êàê îòíîøåíèå èçìåðåííûõ íåñòàöèîíàðíûõ àýðî-
äèíàìè÷åñêèõ ñèë è ìîìåíòîâ íà êîëåáëþùèõñÿ ïðîôèëÿõ ðåøåòêè ê ñîîòâåòñò-
âóþùèì èõ ïåðåìåùåíèÿì, ñêîðîñòíîìó íàïîðó è ïàðàìåòðàì ëîïàòî÷íîãî ïðîôèëÿ.
Ýòî îáóñëîâëåíî òåì, ÷òî, çíàÿ ÀÊÂ, ìîæíî ðàññ÷èòàòü ðàáîòó âåíöà äëÿ ðàçëè÷íûõ
ôîðì êîëåáàíèé ëîïàòîê áåç äîïîëíèòåëüíûõ ýêñïåðèìåíòàëüíûõ èññëåäîâàíèé.
Ðàññìàòðèâàþòñÿ òàêæå ÀÊÂ n-ãî ïðîôèëÿ èññëåäóåìîé ðåøåòêè: lny , ln� è
mny , mn� – ÀÊÂ ñèë è ìîìåíòîâ, âûçâàííûõ ïîñòóïàòåëüíûìè yn è óãëîâûìè �n
ïåðåìåùåíèÿìè ñîîòâåòñòâåííî,
l
L
V y h
ny
ny
n
�
1
2 1
2�
; l
L
V bh
n
n
n
�
�
� �
�
1
2 1
2
; m
M
V y bh
ny
ny
n
�
1
2 1
2�
; m
M
V b h
n
n
n
�
�
� �
�
1
2 1
2 2
, (2)
ãäå
1
2 1
2�V – ñêîðîñòíîé íàïîð.
Ìîäåðíèçàöèÿ àýðîäèíàìè÷åñêîãî ñòåíäà. Èñïûòàíèÿ ïðÿìûõ ðåøåòîê ëîïà-
òî÷íûõ ïðîôèëåé ïðè èõ äîçâóêîâîì îáòåêàíèè ãàçîâûì ïîòîêîì ïðîâîäèëè íà àýðî-
äèíàìè÷åñêîì ñòåíäå, ñîçäàííîì â Èíñòèòóòå ïðîáëåì ïðî÷íîñòè èì. Ã. Ñ. Ïèñàðåí-
êî ÍÀÍ Óêðàèíû (ðèñ. 2) [6] è ïîçâîëÿþùåì ýôôåêòèâíî îïðåäåëÿòü íåñòàöèîíàð-
íûå àýðîäèíàìè÷åñêèå íàãðóçêè íà êîëåáëþùèõñÿ ïðîôèëÿõ. Îäíàêî äëÿ ðåøåíèÿ
ïîñòàâëåííîé çàäà÷è âîçíèêëà íåîáõîäèìîñòü åãî äîðàáîòêè, â ïåðâóþ î÷åðåäü
ñîïëà.
 èñõîäíîì ñîñòîÿíèè ñòåíä ñîñòîèò èç ðàçãîííîãî (îáåñïå÷èâàåò âåðòèêàëüíûé
ïîäæèì ñ ïîìîùüþ äâóõñèíóñíîãî ïðîôèëèðîâàíèÿ ñòåíîê) è óïðàâëÿåìîãî (ãîðè-
çîíòàëüíûé ïîäæèì ïî óïðîùåííûì îáâîäàì) ñîïåë [10, 11]. Ýòî îáóñëîâèëî âîçíèê-
íîâåíèå ëîêàëüíûõ çîí óâåëè÷åííîé ñêîðîñòè ïîòîêà íà âûïóêëûõ ó÷àñòêàõ ñòåíäà ñ
ïîñëåäóþùèì óñëîæíåíèåì íàñòðîéêè ïðîñòðàíñòâåííîé ïåðèîäè÷íîñòè îáòåêàíèÿ
Îïðåäåëåíèå ãðàíèöû óñòîé÷èâîñòè ëîïàòî÷íûõ âåíöîâ ...
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2018, ¹ 2 29
Ðèñ. 1. Ñõåìà ïðÿìîé ðåøåòêè ëîïàòî÷íûõ ïðîôèëåé.
ïðîôèëåé. Äëÿ ïðåäîòâðàùåíèÿ ýòèõ ïðîáëåì ëåìíèñêàòíûé âõîä óïðàâëÿåìîãî
ñîïëà áûë ïðîäëåí â îáëàñòü íèçêèõ ñêîðîñòåé [12]. Òàêèì îáðàçîì, äâà ðàçãîííûõ
ñîïëà áûëè îáúåäèíåíû â îäíî ðåãóëèðóåìîå. Ðåçóëüòàòû ðàñ÷åòîâ ïîëåé ñêîðîñòåé ñ
ìîäåðíèçèðîâàííûì ñîïëîì ïðèâåäåíû íà ðèñ. 3,à. Âèäíî, ÷òî èç-çà áîëüøîãî
ïîäæàòèÿ íåðàâíîìåðíîñòü ïîòîêà èñ÷åçàåò, è ïåðåä ðåøåòêîé èìååò ìåñòî ðàâíî-
ìåðíîå ïîëå ñêîðîñòåé.
Çàòåì íåîáõîäèìî áûëî ðàçðàáîòàòü ýôôåêòèâíûå ýëåìåíòû óïðàâëåíèÿ ïåðèî-
äè÷íîñòüþ îáòåêàíèÿ ïðîôèëåé â ðåøåòêå ïðè áîëüøèõ óãëàõ àòàêè. Ýòî ìîæíî
îñóùåñòâèòü ñ ïîìîùüþ ïîâîðîòíûõ ñòâîðîê, êîòîðûå ïîçâîëÿþò ñîçäàòü äèôôó-
çîðíûå èëè êîíôóçîðíûå êðàéíèå êàíàëû ðåøåòêè. Â ðåçóëüòàòå óìåíüøàåòñÿ èëè
30 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2018, ¹ 2
Ñ. Í. Êàáàííèê, À. Ï. Çèíüêîâñêèé, À. Ë. Ñòåëüìàõ
a
á
Ðèñ. 2. Îáùàÿ ñõåìà àýðîäèíàìè÷åñêîãî ñòåíäà (à) è åãî ðàáî÷àÿ ÷àñòü â ðàçðåçå (á).
óâåëè÷èâàåòñÿ ðàñõîä âîçäóõà è äîñòèãàåòñÿ ïåðèîäè÷íîñòü îáòåêàíèÿ ëîïàòî÷íûõ
ïðîôèëåé, íà êîòîðûõ èçìåðÿþòñÿ àýðîäèíàìè÷åñêèå íàãðóçêè. Ïðè áîëüøèõ óãëàõ
àòàêè äëèíà êàíàëîâ, êîòîðàÿ îïðåäåëÿåòñÿ õîðäîé ëîïàòîê, íå âñåãäà îáåñïå÷èâàåò
ïåðèîäè÷íîñòü îáòåêàíèÿ. Ïîýòîìó íà êðàéíèõ ïðîôèëÿõ ê èõ çàäíèì êðîìêàì
äîïîëíèòåëüíî óñòàíàâëèâàëèñü ïëàñòèíû, à òàêæå ïåðåïðîôèëèðîâàëèñü ñòâîðêè
äëÿ ïëàâíîãî ïåðåõîäà îò áîêîâûõ ñòåíîê ñòåíäà ê åãî ðàáî÷åé ÷àñòè, ÷òî ïîçâîëèëî
äîáèòüñÿ ïåðèîäè÷íîãî îáòåêàíèÿ ïðîôèëåé ðåøåòêè. Ýòî íàãëÿäíî âèäíî èç ïðåä-
ñòàâëåííîãî íà ðèñ. 3,á ïîëÿ ñêîðîñòåé.
Äëÿ ïîäòâåðæäåíèÿ îáåñïå÷åíèÿ ïåðèîäè÷íîñòè îáòåêàíèÿ ëîïàòî÷íûõ ïðîôè-
ëåé ïðè áîëüøèõ óãëàõ àòàêè ìîäåðíèçàöèÿ àýðîäèíàìè÷åñêîãî ñòåíäà ïîçâîëèëà
ïðîèçâåñòè çàïèñü ñëåäîâ â ïîòîêå ïðè âàðüèðîâàíèè óãëà àòàêè. Ñ ýòîé öåëüþ
èñïîëüçîâàëè ïíåâìàòè÷åñêèé çîíä è êîîðäèíàòíîå óñòðîéñòâî äëÿ åãî ïåðåìåùåíèÿ
çà ðåøåòêîé.
 êà÷åñòâå ïðèìåðà íà ðèñ. 4 ïðèâåäåíû ñëåäû â ïîòîêå ïðè îáòåêàíèè ëîïà-
òî÷íûõ ïðîôèëåé ñî ñêîðîñòüþ V1 100� ì/ñ äëÿ òðåõ çíà÷åíèé óãëà àòàêè. Àíàëèç
ñëåäîâ ïîêàçûâàåò, ÷òî, âî-ïåðâûõ, ïðè óãëå àòàêè i� 0 (ðèñ. 4,à) ñëåäû, âîçíèêà-
þùèå â ïîòîêå çà ïðîôèëÿìè ðåøåòêè, ÿâëÿþòñÿ óçêèìè ñ ïðàâèëüíîé ôîðìîé è áåç
ðàçìûâà. Ýòî îçíà÷àåò, ÷òî ïðîôèëè êàê ñî ñòîðîíû ñïèíêè, òàê è êîðûòöà îáòå-
êàþòñÿ áåç ñðûâà ïîòîêà. Âî-âòîðûõ, â ñëó÷àå áîëüøèõ óãëàõ àòàêè ïðè ñîõðàíåíèè
ïåðèîäè÷íîñòè îáòåêàíèÿ íàáëþäàåòñÿ ñóùåñòâåííîå èçìåíåíèå õàðàêòåðà ñëåäîâ.
Òàê, ïðè i� �20 (ðèñ. 4,á) èìååò ìåñòî ñèëüíûé ðàçìûâ ÷àñòè ñëåäà ñî ñòîðîíû
ñïèíêè ïðîôèëÿ, ÷òî ñâèäåòåëüñòâóåò î ðàçâèòîì ñðûâå è èíòåíñèâíûõ ïóëüñàöèÿõ
ïîòîêà. Êðîìå òîãî, ñðûâ ïîòîêà îõâàòûâàåò ïðàêòè÷åñêè âåñü ìåæëîïàòî÷íûé êàíàë
ðåøåòêè. Îáòåêàíèå ðåøåòêè ïîòîêîì ñ òàêèì æå ïî âåëè÷èíå, íî îòðèöàòåëüíûì
óãëîì àòàêè, íàîáîðîò, îáóñëîâëèâàåò ðàçìûâ ÷àñòè ñëåäà òîëüêî ñî ñòîðîíû êîðûòöà
ïðîôèëÿ, ÷òî òàêæå ãîâîðèò î ðàçâèòîì ñðûâå è èíòåíñèâíûõ ïóëüñàöèÿõ ïîòîêà â
ìåæëîïàòî÷íîì êàíàëå ðåøåòêè (ðèñ. 4,â).
Ðåçóëüòàòû ýêñïåðèìåíòàëüíî-ðàñ÷åòíûõ èññëåäîâàíèé. Ðàññìîòðèì ðåçóëü-
òàòû èññëåäîâàíèé ïî îïðåäåëåíèþ âëèÿíèÿ óãëà àòàêè íà ãðàíèöó äèíàìè÷åñêîé
óñòîé÷èâîñòè ëîïàòî÷íûõ âåíöîâ ê äîçâóêîâîìó ôëàòòåðó íà ïðèìåðå âòîðîé ñòóïåíè
êîìïðåññîðà äâèãàòåëÿ ÀÃÒÄ ÒÂ3-117-ÑÁÌ1 ïðè ïåðâîé èçãèáíîé ôîðìå êîëåáàíèé
ëîïàòîê. Ïðîôèëè ðåøåòêè ñîîòâåòñòâóþò ñå÷åíèþ ëîïàòêè íà 0,9h åå âûñîòû. Â
ýòîì ñëó÷àå ãåîìåòðè÷åñêèå ïàðàìåòðû ðåøåòêè òàêèå: îòíîñèòåëüíûé øàã t b�
� 0 835, è óãîë âûíîñà �� �45 44, .
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2018, ¹ 2 31
Îïðåäåëåíèå ãðàíèöû óñòîé÷èâîñòè ëîïàòî÷íûõ âåíöîâ ...
a á
Ðèñ. 3. Ïîëå ñêîðîñòåé â îáúåäèíåííîì ñîïëå àýðîäèíàìè÷åñêîãî ñòåíäà (à) è â ðåøåòêå
ïðîôèëåé ëîïàòîê (á).
Èññëåäîâàíèÿ ïðîâîäèëèñü ïðè âàðüèðîâàíèè çíà÷åíèé óãëà àòàêè i â äèàïàçîíå
� �20 23... è ïðèâåäåííîé ÷àñòîòû êîëåáàíèé K b V� � 1 0 22 122, ... , , ãäå – óãëîâàÿ
÷àñòîòà êîëåáàíèé ïðîôèëÿ.
Äëÿ ðàñ÷åòíîãî àíàëèçà ãðàíèöû äèíàìè÷åñêîé óñòîé÷èâîñòè ðåøåòêè ëîïàòî÷-
íûõ ïðîôèëåé ïåðâîíà÷àëüíî ýêñïåðèìåíòàëüíî îïðåäåëÿëèñü íåñòàöèîíàðíûå àýðî-
äèíàìè÷åñêèå ñèëû è ìîìåíòû ñ ïîñëåäóþùèì ðàñ÷åòîì ÀÊ (2). Íà ðèñ. 5 ïðèâå-
äåíû çàâèñèìîñòè àáñîëþòíûõ âåëè÷èí ÀÊ îò óãëà àòàêè i äëÿ ïðèâåäåííîé
÷àñòîòû êîëåáàíèé K � 0 64, , íà ðèñ. 6 – òî æå îò ïðèâåäåííîé ÷àñòîòû êîëåáàíèé K
äëÿ óãëà àòàêè i� �20 . Óêàçàííûå çàâèñèìîñòè ïîëó÷åíû äëÿ ñëó÷àÿ îïðåäåëåíèÿ
àýðîäèíàìè÷åñêèõ íàãðóçîê íà òðåõ (n�
0 1; ) öåíòðàëüíûõ ïðîôèëÿõ ðåøåòêè. Ïðî-
ôèëü n� 0 ïîëàãàåì èñõîäíûì, à ïðîôèëè n�
1 – íèæå è âûøå ðàñïîëîæåííûìè
îòíîñèòåëüíî íåãî.
32 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2018, ¹ 2
Ñ. Í. Êàáàííèê, À. Ï. Çèíüêîâñêèé, À. Ë. Ñòåëüìàõ
a
á
â
Ðèñ. 4. Ñëåäû â ïîòîêå, âîçíèêàþùèå ïðè îáòåêàíèè ëîïàòî÷íûõ ïðîôèëåé ðåøåòêè ñî
ñêîðîñòüþ V1 100� ì/ñ äëÿ óãëà àòàêè 0 (à), 20 (á) è � �20 (â).
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Ðèñ. 5. Çàâèñèìîñòü àáñîëþòíûõ âåëè÷èí ÀÊ îò óãëà àòàêè i äëÿ ïðèâåäåííîé ÷àñòîòû
êîëåáàíèé K � 0 64, . (Çäåñü è íà ðèñ. 6: 1 – äëÿ êîëåáëþùåãîñÿ ëîïàòî÷íîãî ïðîôèëÿ; 2, 3 –
äëÿ íèæå è âûøå ñòîÿùèõ ëîïàòî÷íûõ ïðîôèëåé).
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Ðèñ. 6. Çàâèñèìîñòü àáñîëþòíûõ âåëè÷èí ÀÊ îò ïðèâåäåííîé ÷àñòîòû êîëåáàíèé K äëÿ óãëà
àòàêè i � �20 .
Íàèáîëüøåå âëèÿíèå êîëåáàíèé èñõîäíîãî ïðîôèëÿ íàáëþäàåòñÿ ïðè ÀÊÂ, îïðå-
äåëåííîì âûøå ñòîÿùåãî (n��1) ïðîôèëÿ ðåøåòêè.  ýòîì ñëó÷àå ïðè áîëüøèõ
óãëàõ àòàêè èç-çà ðàçâèòîãî ñðûâà àáñîëþòíûå âåëè÷èíû ÀÊ ïðåâûøàþò òàêîâûå
èñõîäíîãî.
Ïîëó÷åííûå ÀÊ ïîçâîëÿþò ðàññ÷èòàòü ðàáîòó ëîïàòî÷íîãî âåíöà (3) äëÿ
ëþáîãî ðåæèìà îáòåêàíèÿ ïðè ðàçëè÷íûõ êîìáèíàöèÿõ ïîñòóïàòåëüíûõ è óãëîâûõ
ïåðåìåùåíèé ïðîôèëåé. Ïðè ýòîì äëÿ èññëåäîâàíèÿ äèíàìè÷åñêîé óñòîé÷èâîñòè
ëîïàòî÷íîãî âåíöà äîñòàòî÷íî îïðåäåëèòü òîëüêî êîýôôèöèåíò ðàáîòû àýðîäèíàìè-
÷åñêèõ íàãðóçîê C A , êîòîðûé ñ ó÷åòîì âçàèìîäåéñòâèÿ òðåõ ïðîôèëåé âû÷èñëÿåòñÿ
ïî ôîðìóëå
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ãäå � – êîýôôèöèåíò èçãèáíî-êðóòèëüíîé ñâÿçàííîñòè, �� � �( ) ( )a a a ap z p z ;
a p , a z – àìïëèòóäû ïåðåìåùåíèé ïåðåäíåé è çàäíåé êðîìîê ïðîôèëÿ ñîîòâåòñò-
âåííî; � – ñäâèã ôàç ìåæäó èçãèáíûìè è êðóòèëüíûìè êîëåáàíèÿìè; � – ñäâèã ôàç
ìåæäó êîëåáàíèÿìè ñîñåäíèõ ïðîôèëåé; j – ìíèìàÿ åäèíèöà.
Äèíàìè÷åñêàÿ óñòîé÷èâîñòü ëîïàòî÷íîãî âåíöà îïðåäåëÿåòñÿ âåëè÷èíîé è çíà-
êîì êîýôôèöèåíòà C A (3).
Íà ðèñ. 7 ïðèâåäåíû çàâèñèìîñòè êîýôôèöèåíòà ðàáîòû àýðîäèíàìè÷åñêèõ
íàãðóçîê C A îò ïðèâåäåííîé ÷àñòîòû êîëåáàíèé K äëÿ ðàçëè÷íûõ çíà÷åíèé óãëà
àòàêè i ïðè êîëåáàíèÿõ ëîïàòîê ïî ïåðâîé èçãèáíîé ôîðìå è �� 0135, . Òî÷êà
ïåðåñå÷åíèÿ ïîëó÷åííûõ çàâèñèìîñòåé ñ îñüþ àáñöèññ îïðåäåëÿåò êðèòè÷åñêèå çíà-
÷åíèÿ ïðèâåäåííîé ÷àñòîòû êîëåáàíèé K êð, êîòîðàÿ ñîîòâåòñòâóåò ãðàíèöå äèíàìè-
÷åñêîé óñòîé÷èâîñòè ëîïàòî÷íîãî âåíöà.
Ñ èñïîëüçîâàíèåì ðåçóëüòàòîâ ðàñ÷åòà êîýôôèöèåíòà ðàáîòû àýðîäèíàìè÷åñêèõ
íàãðóçîê Ñ À áûëà îïðåäåëåíà çàâèñèìîñòü êðèòè÷åñêîé ïðèâåäåííîé ÷àñòîòû êîëå-
áàíèé K êð îò óãëà àòàêè i (ðèñ. 8). Íà ðèñ. 8 ïðèâåäåíû òàêæå çàâèñèìîñòè,
ïîëó÷åííûå äëÿ èññëåäóåìîãî ëîïàòî÷íîãî âåíöà ïî äàííûì èñïûòàíèé íà èñõîäíîì
(íåìîäåðíèçèðîâàííîì) àýðîäèíàìè÷åñêîì ñòåíäå [13] è ñ ïîìîùüþ ýêñïðåññ-ìåòîäà
ïðîãíîçèðîâàíèÿ äèíàìè÷åñêîé óñòîé÷èâîñòè ëîïàòî÷íûõ âåíöîâ [14].
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Îïðåäåëåíèå ãðàíèöû óñòîé÷èâîñòè ëîïàòî÷íûõ âåíöîâ ...
Ðèñ. 7. Çàâèñèìîñòü êîýôôèöèåíòà ìíèìîé ÷àñòè ðàáîòû íåñòàöèîíàðíûõ àýðîäèíàìè÷åñêèõ
íàãðóçîê Ñ À îò ïðèâåäåííîé ÷àñòîòû êîëåáàíèé K äëÿ ðàçëè÷íûõ óãëîâ àòàêè: 1 – i �� �20 ;
2 – i �� �18 ; 3 – i � 0; 4 – i � �20 ; 5 – i � �23 .
Àíàëèç ïðåäñòàâëåííûõ äàííûõ ïîêàçûâàåò, ÷òî, âî-ïåðâûõ, ïîäòâåðæäàþòñÿ
âûâîäû î òîì, ÷òî ðåæèìû ðàáîòû äâèãàòåëÿ íàõîäÿòñÿ â óñòîé÷èâîé çîíå íà
çíà÷èòåëüíîì óäàëåíèè îò ãðàíèöû äèíàìè÷åñêîé óñòîé÷èâîñòè [13, 14]. Ïðè ýòîì
èìååòñÿ ñóùåñòâåííûé çàïàñ äèíàìè÷åñêîé óñòîé÷èâîñòè ëîïàòî÷íîãî âåíöà â øèðî-
êîì äèàïàçîíå èçìåíåíèÿ óãëîâ àòàêè. Âî-âòîðûõ, äëÿ ìàëûõ óãëîâ àòàêè óñòàíîâ-
ëåííàÿ ãðàíèöà äèíàìè÷åñêîé óñòîé÷èâîñòè õîðîøî ñîãëàñóåòñÿ ñ äàííûìè, ïîëó÷åí-
íûìè â [13, 14]. Â-òðåòüèõ, ïðè áîëüøèõ êàê îòðèöàòåëüíûõ, òàê è ïîëîæèòåëüíûõ
óãëàõ àòàêè ãðàíèöà äèíàìè÷åñêîé óñòîé÷èâîñòè ñìåùàåòñÿ â íàïðàâëåíèè áîëüøèõ
çíà÷åíèé ïðèâåäåííîé ÷àñòîòû êîëåáàíèé. Îñîáåííî åå ðîñò íàáëþäàåòñÿ ïî äîñòè-
æåíèè óãëà àòàêè 14�, ãäå âçàèìîñâÿçü ëîïàòîê ÷åðåç ïîòîê ïðîèñõîäèò â óñëîâèÿõ
áîëåå èíòåíñèâíîãî ñðûâà, êîòîðûé îõâàòûâàåò âåñü ìåæëîïàòî÷íûé êàíàë.
 û â î ä û
1. Ïî ðåçóëüòàòàì èñïûòàíèé ïðÿìîé êîìïðåññîðíîé ðåøåòêè â øèðîêîì äèàïà-
çîíå èçìåíåíèÿ óãëà àòàêè è ïðèâåäåííîé ÷àñòîòû êîëåáàíèé îïðåäåëåíû íåñòà-
öèîíàðíûå àýðîäèíàìè÷åñêèå íàãðóçêè, ñ èñïîëüçîâàíèåì êîòîðûõ ðàññ÷èòàíû àýðî-
äèíàìè÷åñêèå êîýôôèöèåíòû âëèÿíèÿ è óñòàíîâëåíî âëèÿíèå óãëà àòàêè è ïðèâåäåí-
íîé ÷àñòîòû êîëåáàíèé íà èõ âåëè÷èíó.
2. Îïðåäåëåíà çàêîíîìåðíîñòü èçìåíåíèÿ êðèòè÷åñêèõ çíà÷åíèé ïðèâåäåííîé
÷àñòîòû êîëåáàíèé â äèàïàçîíå óãëîâ àòàêè � �20 23... .
3. Ìîäåðíèçèðîâàí àýðîäèíàìè÷åñêèé ñòåíä, ÷òî ïîçâîëÿåò ïðîâîäèòü èñïû-
òàíèÿ ïðÿìûõ ðåøåòîê ëîïàòî÷íûõ ïðîôèëåé ïî îïðåäåëåíèþ àýðîäèíàìè÷åñêèõ
íàãðóçîê ïðè áîëüøèõ êàê ïîëîæèòåëüíûõ, òàê è îòðèöàòåëüíûõ óãëàõ àòàêè. Î
ðåçóëüòàòèâíîñòè ïðîâåäåííîé ìîäåðíèçàöèè ñòåíäà ñâèäåòåëüñòâóþò ðåçóëüòàòû
÷èñëåííîãî àíàëèçà òå÷åíèÿ ïîòîêà â ðåøåòêå è èçìåðåíèÿ ïîëÿ ñêîðîñòåé çà èñïû-
òóåìîé ðåøåòêîé ïðîôèëåé çîíäîì, ïåðåìåùàåìûì êîîðäèíàòíûì óñòðîéñòâîì.
Ð å ç þ ì å
Âèêëàäåíî ìåòîäèêó åêñïåðèìåíòàëüíî-ðîçðàõóíêîâîãî âèçíà÷åííÿ ãðàíèö³ ñò³éêîñò³
ëîïàòêîâîãî â³íöÿ äî äîçâóêîâîãî ôëàòåðà ïðè âåëèêèõ êóòàõ íàò³êàííÿ ïîòîêó.
Îïèñàíî àåðîäèíàì³÷íèé ñòåíä äëÿ âèçíà÷åííÿ íåñòàö³îíàðíèõ àåðîäèíàì³÷íèõ íà-
âàíòàæåíü. Íàâåäåíî ðåçóëüòàòè âèïðîáóâàíü ïëîñêî¿ ðåø³òêè ëîïàòêîâèõ ïðîô³ë³â ó
36 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2018, ¹ 2
Ñ. Í. Êàáàííèê, À. Ï. Çèíüêîâñêèé, À. Ë. Ñòåëüìàõ
Ðèñ. 8. Çàâèñèìîñòü êðèòè÷åñêîé ïðèâåäåííîé ÷àñòîòû êîëåáàíèé ëîïàòî÷íîãî âåíöà K êð îò
óãëà àòàêè i (øòðèõîâàÿ ëèíèÿ). (Ïóíêòèðíàÿ ëèíèÿ – äàííûå [13], ñïëîøíàÿ – [14].)
øèðîêîìó ä³àïàçîí³ çì³íè êóòà àòàêè ³ çâåäåíî¿ ÷àñòîòè êîëèâàíü, ³ç âèêîðèñòàííÿì
ÿêèõ óñòàíîâëåíî çàêîíîì³ðíîñò³ âïëèâó êóòà àòàêè íà ãðàíèöþ ñò³éêîñò³ ëîïàòêîâèõ
â³íö³â äî äîçâóêîâîãî ôëàòåðà.
1. Vedeneev V. V., Kolotnikov M., and Makarov P. Numerical analysis of compressor
blade flutter in modern gas turbine engines. Proc. of the 10th Europ. Turbomachinery
Conf. 2013. P. 199–209.
2. Luengo A. S., Vogt D. M., Schmitt S., and Fransson T. H. Validation of linearized
navier-stokes based flutter prediction tool. Part 2. Quantification of the prediction
accuracy on a turbine test case. Proc. of the ASME Turbo Expo. 2012. P. 1581–1592.
3. Ãàðáàðóê À. Â., Ñòðåëåö Ì. Õ., Øóð Ì. Ë. Ìîäåëèðîâàíèå òóðáóëåíòíîñòè â
ðàñ÷åòàõ ñëîæíûõ òå÷åíèé. ÑÏá.: Èçä-âî Ïîëèòåõí. óí-òà, 2012. 88 ñ.
4. Ãàðáàðóê À. Â., Ñòðåëåö Ì. Õ., Òðàâèí À. Ê., Øóð Ì. Ë. Ñîâðåìåííûå ïîäõîäû
ê ìîäåëèðîâàíèþ òóðáóëåíòíîñòè. ÑÏá.: Èçä-âî Ïîëèòåõ. óí-òà, 2016. 234 ñ.
5. Vogt D. M. and Fransson T. H. Towards flutter-free turbomachinery blades. Eds.
D. Knörzer and J. Szodruch. Innovations for Sustainable Aviation in a Global
Environment. Amsterdam: IOS Press, 2012. P. 161–167.
6. dzíüêîâñüêèé À. Ï., Öèìáàëþê Â. À. Åêñïåðèìåíòàëüíî-ðîçðàõóíêîâèé êîìï-
ëåêñ ç ïðîãíîçóâàííÿ ñò³éêîñò³ äî äîçâóêîâîãî ôëàòåðà ëîïàòêîâèõ â³íö³â. Íàóêà
òà ³ííîâ. 2012. 8, ¹ 5. Ñ. 38–48.
7. Bendiksen O. and Friedmann P. Coupled bending-torsion flutter in cascades. AIAA J.
1980. 18, No. 2. P. 194–201.
8. Bendiksen O. O. Flutter of mistuned turbomachinery rotors. J. Eng. Gas Turb. Power.
1984. 106, No. 1. P. 25–33.
9. Ñòåëüìàõ À. Ë., Ñòåëüìàõ ß. À., Çèíüêîâñêèé À. Ï. Ìåòîäèêà ýêñïðåññ-îöåíêè
äèíàìè÷åñêîé óñòîé÷èâîñòè êîìïðåññîðíûõ ëîïàòîê ãàçîòóðáèííîãî äâèãàòåëÿ
ê äîçâóêîâîìó ðåøåòî÷íîìó ôëàòòåðó. Àâèàö.-êîñì. òåõíèêà è òåõíîëîãèÿ.
2003. ¹ 5 (40). Ñ. 71–75.
10. Luxa M., Jonáð P., and Ðafaøík P. Eintrittentwurf des Windkanals. Fluid Mechanics
and Thermodynamics (Proc. of Student’s Work in the Year 2001/2002, Prague). 2002.
P. 29–39.
11. Hanus D. Experimentální vzduchová trat pro výzkum proudìni v zakøivených
kanálech. Vnitøní Aerodynamika Lopatkových Strojù. Praha, 2001. S. 41–44.
12. Êàáàííèê Ñ. Ì., Öèìáàëþê Â. À. Àýðîäèíàìè÷åñêîå óñîâåðøåíñòâîâàíèå ñòåí-
äà äëÿ èññëåäîâàíèÿ ðåøåòîê ïðîôèëåé ïðè áîëüøèõ óãëàõ íàòåêàíèÿ äîçâó-
êîâîãî ïîòîêà. Âåñòí. äâèãàòåëåñòðîåíèÿ. 2015. ¹ 2. Ñ. 160–164.
13. Çèíüêîâñêèé À. Ï., Ñòåëüìàõ À. Ë., Öèìáàëþê Â. À. Ìåòîäû, ñðåäñòâà è
ðåçóëüòàòû îöåíêè óñòîé÷èâîñòè ðàáî÷èõ ëîïàòîê êîìïðåññîðîâ ê äîçâóêîâîìó
ôëàòòåðó. Ïðî÷íîñòü ìàòåðèàëîâ è ýëåìåíòîâ êîíñòðóêöèé: Òð. ìåæäóíàð.
íàó÷.-òåõí. êîíô. Êèåâ: Èí-ò ïðîáëåì ïðî÷íîñòè èì. Ã. Ñ. Ïèñàðåíêî ÍÀÍ
Óêðàèíû, 2011. Ñ. 35–49.
14. Êàáàííèê Ñ. Í. Ðåàëèçàöèÿ ìåòîäà ýêñïðåññ-îöåíêè óñòîé÷èâîñòè ê äîçâóêî-
âîìó ðåøåòî÷íîìó ôëàòòåðó äëÿ èçãèáíîé ôîðìû êîëåáàíèé ëîïàòî÷íûõ âåí-
öîâ îñåâûõ êîìïðåññîðîâ ÃÒÄ. Àâèàö.-êîñì. òåõíèêà è òåõíîëîãèÿ. 2015. ¹ 7.
Ñ. 90–93.
Ïîñòóïèëà 26. 12. 2017
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/ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /ConvertToCMYK
/DestinationProfileName ()
/DestinationProfileSelector /DocumentCMYK
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure false
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles false
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /DocumentCMYK
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /UseDocumentProfile
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|