485
Tuyen tap cdng trinh Hdi nghj Cff hoc todn qudc Ky niem 30 nam Vien Cff hoc vd 30 niim Tap chi Cff hoc Hd Ndi, ngay 8-9/4/2009
Nghien ciiu hien tuo'ng dan hoi canh duoi tac dung ciia luc khi dong
Hoang Thj Bich Ngoc*, Dinh Van Phong*, Nguyen Hong Son**
Dai hoc Bdch khoa Hd Ndi*, Dgi hoc Cdng nghiep Hd Ndi**
Tom tat: Cdnh mdy bay dugc xem Id mot kit cdu ngdm vdo thdn mdy mdy. Khi may bay bay, canh may bay phdi chiu luc ndng khi ddng rdt lan, lan han todn bd trong luang ciia mdy bay di ndng mdy bay ehuyin ddng trong khdng trung Dudi tdc ddng ciia luc ndng khi ddng, cdnh mdy bay bi biin dgng udn venh len vd bi xodn. Luc khi ddng Id mot luc phdn bd thay ddi theo van tdc bay, gdc tdi vd diiu kien mdi trudng khi qiiyin. Luc khi ddng 3D tdc dung tin cdnh dicac tinh todn bdng lap trinh theo phuang phdp cdc diim ki di 3D vd cdc phdn mim Fluent, Ansys. Luc kM ddng phdn bd ndy duac ehuyin true tiep trong Ansys de tinh todn biin dgng vd ung sudt ciia kit cdu cdnh.
1. Dat van d e
Chiing ta cd the coi hien tugng "dan hdi khi ddng" canh la irng xir eiia ket cau canh dudi tac dung ciia luc khi ddng. Trong khudn khd bao cao nay, chiing tdi gidi ban nghien ciru d hien tugng dan hdi tTnh. Neu quan tam nhieu hon den quy luat bien doi eiia luc khi ddng khi ket cau da bj bien dang dan hdi, chiing ta cd the ggi dd la bai toan "khi dgng dan hdi" Dii ket qua xet cudi cimg la bien dang va irng suat eiia vat ran, hay quy luat phan bd lai luc khi ddng sau khi vat ran bj bien dang, thi tinh toan lire khi dgng eua tuong tac khi - ran van la dieu kien can. Dac thii cua luc khi ddng la loai lire phan bd cd quy luat thay ddi vdi mgi bien ddi eiia moi trudng khi quyen, tdc do chuyen ddng cua vat ran va gdc tdi eiia van tdc. Phan bd ap lue khi ddng dugc xac dinh bang viec giai he phuang trinh vi phan dao ham rieng md ta chuyen dgng eiia chat long (khi, thiiy). Tiiy theo tiing yeu cau cu the can thiet dua vao cae gia thiet de he phuong trinh chuyen ddng cd dang don gian hon. De xet hien tugng xoan canh, ap lue khi dgng phan bd tren canh can ed gia trj dugc biet dudi dang ba chieu. Luc tac ddng lam canh bien dang chii yeu la luc nang khi ddng, vi vay, bai toan tinh lire khi dgng 3D d day gidi ban ddi vdi ddng ly tudng dudi am. Lire nang khi dgng ed gia tri rat Idn, Idn hon tdng trgng lugng ciia toan may bay dl nang may bay chuyen dgng trong khdng gian, vi vay viec tinh toan luc khi dgng ddng vai trd rk quan trgng ddi vdi mgi tinh toan lien quan. Trong cdng trinh nay, tinh toan luc khi dgng dugc thuc hien theo ba phugng phap: lap trinh theo phuong phap ky dj 3D; diing phan mlm Fluent;
dimg phan mem Ansys. Chuong trinh lap trinh tinh luc khi dgng 3D da dugc so sanh kiim chii'ng dam bao do chinh xac cAn thiet. Viec tinh toan lire khi ddng 3D theo phin mlm Fluent va Ansys dugc so sanh vdi ket qua lap trinh de dam bao do chinh xac trong mien iing dung. Ket qua luc khi dgng tinh tii' ph4n mem Ansys dugc chuyen true tiep trong chuang trinh Ansys d l tinh img xir eua kit eau canh dudi tac dung eua lire khi dgng.
486 Hodng Thi Bich Ngoc, Dinh Vdn Phong, Nguyin Hdng San
2. Tinh toan luc khi dong
2.1. Tinh todn luc khi dpng bang phirong phdp cdc diem ky di 3D
Trong phuong phap ki di ba chieu, eae ky dj su dung la he eae xoay vdng cd cudng do F , ngudn cudng do c- va xoay mong ngira cudng do y, bd tri tren tam canh va inat canh [1]. Chi so i theo chieu profil, ehi sd j theo chieu sai canh. Van tdc cam ung ciia cac ki dj ddi vdi phan tl n duge tinh:
•V = v + v ' ' ' + v''^'+v<^-'
vdi V'^' V'^' V'^"' la van tdc sinh ra til'ngudn, xoay vdng va xoay mdng ngua.
MxN N M N M N
V/^' = I Vj^'a^ = X I V „ , a , , ; V„'^' = ^ r . I V „ , r ^ V„-'' = X y , V , (T^)
fc=l j=l i=l j = l 1=1
Cac dieu kien bien trugt tai phan td (n) dugc viet: V^.ii„ = 0 (V^(s) + v/T) + v/''"').n„ =-V^.ii„ vdi n = U ( N x M )
j = i
(2.1)
(2.2)
(2.3) Dieu kien Joukovski tai mep ra dugc xac djnh bang dieu kien bien trugt tren mat phan giac ra khdi mep ra: V^ .iip^ = 0 vdi m = 1 ^ N
GOC CANH
Hinh 2.1. Ludi canh trong phuong phap cac diim ki dj 3D
Ludi canh duge chia theo quy luat (1-cosa) theo phuong ehuyin ddng dam bao ludi chia mjn d mep vao va mep ra ciia profil canh. Theo phuang sai canh, ludi dugc chia dIu vdi do day phu thude vao ty sd sai canh va day cung canh b/e.
2.2. Tinh todn luc khi dpng bang phan mim Fluent vd Ansys
Fluent la phan mem chuyen doi vdi chat Idng, cdn Ansys la phSn mlm tinh toan doi vdi chat ran va ed mot mang eho tinh toan eh4t Idng (CFX). Vi vay kit qua tinh toan eiia hai phlin mem so sanh vdi nhau cung la mdt su nghiem chirng. Tuy nhien, day la nhOng ph§n mlm khdng do chinh ban than lap trinh nen viec thao tac dilu chinh se thilu chii ddng. PhSn mem co the cho nhiing ket qua "hdi tu" ve nhQng gia trj khdng diing, tiiy thude vao ludi va eae tieu chuan hdi tu.
Dae biet trong trudng hgp tinh lue khi dgng 3D, viec thao tac xir ly cae phan mlm co san rat phire tap. Du cdng viec xir ly phan mlm r§t tdn thdi gian, nhung thdng thudng chiing toi ehi xem cac ket qua khi dgng tir nhung phan mlm nhu vay mang tinh ch§t so sanh hd trg.
Nghiin cim hien tuong dan hdi cdnh dudi tdc dung ciia luc khi ddng 487
2.3. Kit qud khi dpng 3D - So sdnh kit qud cda cdc phuang phdp
Tren hinh 2.2 trinh bay ket qua phan bd he sd ap suat Cp tren canh ehu' nhat (b/e=4) prqfil Naca 0012, gdc tdi 4 do, sd Mach vd ciing M , = 0.5 vdi su so sanh ket qua tinh toan tir chuong trinh lap trinh bang phuang phap eae diem ky dj 3D, tinh theo phan mem Fluent va CFX. Dd thj phan bd Cp dang ba chieu tren 11 dai tii' gdc canh den miit canh eiia 3 phuong phap ed dang tuang tu nhau. Tren mat cat gdc canh (b/c=0) va mat eat giQa canh (b/c=0.5), phan bd ap suat phia bung canh cua 3 phuong phap gan nhu trung nhau hoan toan toan. Cdn phia lung canh, ket qua cua 3 phuong phap cung tuong tu nhau, ehi ed gia trj diem pie tai mep vao, hai phuong phap phan mem Fluent va CFX chua dat tdi gia tri thuc te. Tuy nhien diem pic nay cd gia trj rat nhay cam vdi cdng nghe gia cdng be mat chi tiet va ve mat tich phan luc, no khdng cd anh hudng Idn. Ket qua so sanh tren hinh 2.3 ddi vdi canh ed profil Naca 2312, gdc tdi 0 do, sd Mach M„ = 0.5 cung cho thay sir gidng nhau giua 3 phuong phap.
Phan bo he so ap suat 30 (Cp)
a.
to zn
<
o
UJ X
•'\
NAC;a£012. C'OC TOI 4 do, M=0.5
——CT»CTX
jTidt dienIgofc cdnh; 1 1
1 ^ * . J ^ * ^ ' » • . « < •
J : : ! ! : ! • : :
S i a.3 aa o > HJi QB n.r
DAY CUMO PROFIL CANH
P P & - di 3D Sai caab
0 2 0 4 0 6 0,8 NAC.flC012. C-OC T 0 I 4 do, M=0.5
tiet'di^^ri giih) cejnh;
' ^^,-0.^--\--\
a Q' 0 2 a% DA 0 3 OB a.r 03
OAYCUN© PROFIL C/INH X/C
.A.NSYS /
0 4 O f *•* 1 1 •* i *
F L U E N T .
! f < ;i> s? )6
Hinh 2.2. He so ap suat 3D tren canh - So sanh ket qua lap trinh. Fluent va Ansys (Naea0012, a=4°, M«,=0.5)
488 Hodng Thi Bich Ngoc, Dinh Vdn Phong, Nguyen Hdng San
NACA2312, GOC TOI 0 do, IVI=0.5
o
<
•1 CO
n. <
O
w m X
04 0 2 0 .P7 -04 -0.6 -0.8
• — PP CFX
\ — • - PPFIuen!
Tiet dien goc o.e, . + 0.4
NACA2312, GOC TOI 0 do, IV1=0.5
; I + PPKydiYo"
- - - • . . . p p r p x
Tiet dien giOa carih
0 2 0,3 0 4 0,5 0,6 0.7 0,8
DAY CUNG PROFIL CANH X/C
0.2 0.3 0 4 0,5 0,6 0,7 0,8
DAY CUNG PROFIL CANH X/C
Hinh 2.3. Phan bd Cp tren canh ehu nhat - profil Naca 2312, a=0°, M„=0.5, tai tiet dien gdc canh va giua canh (so sanh ket qua lap trinh, Fluent va Ansys)
Hinh 2.4 la sir thay ddi cua phan bd he sd ap khi gdc tdi thay doi : a = 0° a = 4° a = 6°
doi vdi canh ehu nhat profil Naca 0012, sd Mach vd eiing M, = 0.5 (ket qua tai tiet dien goc canh, ed the doi chieu vdi [3]). KJii gdc tdi a = 0°, lire nang khi dgng bang khdng. Tai goc tdi
a = 6° lire day tir phia bung sang phia lung Idn hon nhieu so vdi trudng hgp gdc tdi a = 4°
Cp NACA0012, Mach = 0.5, Goc toi 0, 4, 6 do
O ro
13 CI.
ro o
to
o
0,5
0
.0,5
Day cung canh x/C
Hinh 2.4. Su thay ddi eiia phan bd ap suat theo gdc tdi (Profil Naca 0012, M„=0.5) Anh hudng eiia sd Mach tdi phan bd ap suk tren canh duge tbiy tren hinh 2.5. Ciing la canh CO profil Naca 2312, gdc tdi 4 do, nhung vdi so M=0.7 do chenh ap suat phia bung va phia lung rat Idn, do chinh la hieu irng qua do am lam gian doan ddng tren canh [4].
Nghiin cini hiin tuang dan hdi cdnh dudi tdc dung ciia luc khi dpng 489
Cp NACA2312, 4 do, Mach = 0.4, 0.6, 0.7
0,2 0.4 0.6
Day cung canh x/C
Hinh 2.5. Su thay ddi eiia phan bo ap suit theo so Mach (Profil Naca 2312 , ^-A°) 3. Tmh toan dan hoi khi dong
Ap suat tren canh
.A5SYSCEX
-Giai bai 10311 chit long -Giai bai ioiiicbkian
Tren ca sd phan bd lire khi ddng tren canh da dugc xac djnh vdi tirng trudng hop khac nhau eua kieh thude, van tdc chuyen ddng va goc tdi, ket qua bai toan dan hdi duge xac dinh bang each sir dung phan mem Ansys iing vdi mdi ket cau (hinh 3.1). Trong tinh toan luc khi dgng, kieh thude su dung trong tinh toan la kich thude bao phu phia ngoai va ludi dugc phat trien ra mien khdng khi den vd cimg. Cdn trong tinh toan dan hdi, cung vdi kich thude bao bien dang vat ran, can thiet xet den tinh chat ket cau va vat lieu ben trong vat the va ludi duge phat
trien vao phia trong vat the. Cung nhu bai toan khi dgng, trong bai toan dan hdi, viec chia ludi cung anh hudng den ket qua bai toan nhat la ddi vdi nhung kit eSu phii'c tap.
Biendangcauli
Hinh 3.1: Sa dd tdng quan ket noi giua CFX va Multiphysies
Mep vao
VAN T o r i
Hinh 3.2. Md hinh hinh hge va ludi canh trong tinh toan dan hdi (profil Naca 0012)
490 Hodng Thi Bich Ngoc, Dinh Vdn Phong, Nguyin Hdng Son
Vdi mot kit eau ed do ciing chdng udn va chdng xoan biet trudc theo phuang sai canh, khi xac djnh dugc lire khi ddng phan bd tren canh cd the lap trinh xac dinh biin dang ciia canh theo cae he thuc sau [2]:
u = | -M(y)
E.I(y) dy (3.1)
trong dd, u la chuyen vi udn, M(y) la mdmen eiia lue khi ddng ddi vdi true dan hdi, duge s6 hoa nhu sau :
M(j) = £m_(i,j)
m x o . n ( ' J ) = [ P b u n g ( i J ) - P l u n g ( i J ) J * A S ( i , j ) * X ( i ) - X ^
(3.2)
(3.3) vdi AS(i,j) = [x(i-t-l)-x(i)]*Ay la dien tich phan td (ij); Pb„„g(i,j) va P|„„^(i,j) ap suit phia bung va lung cua phan td (i j).
Neu cho (E.I) va (G.J) cd quy luat phan bd bac nhat tii' gdc canh den miit canh vdi cac gia tri tai gdc la 2e5 Nm^ va 2.5e6 Nm"; luc khi dgng phan bo tren canh ehu nhat b/c=5m/lm, profil Naca 0006 , sd Mach 0.4, gdc tdi 4 do, vj tri tam xoan 0.285c, thi ket qua chuyen vj udn co the so sanh giua tinh toan theo (3.1) [2] va ket qua tinh theo Ansys duge thSy tren hinh 3.3.
NACA 0006, Mach=0.4, Goc toi 4 do
E 12
en B
• — K Q Ansys
—-KQnnhtQan[2]
1
j^^srss , ^
y^
/ '^
^
1 —
r
'D 1 2 3 Chieu sal canh
Hinh 3.3. Chuyin vi udn - canh ehu nhat profil Naca 0006, M^=0.4, a=4°
(so sanh ket qua tinh toan va Ansys)
a. Xet trudng hop cdnh chie nhdt profil Naca 0012, gdc tai 3°, van tdc thay ddi
Tren hinh 3.4 la kit qua phan bd ap suit 3D tren canh chO nhat cd ty sd dan dai cua canh b/e=10/4, profil Naca 0012, gdc tdi 3 do ung vdi cac van tdc chuyen dgng khac nhau - sd Mach vd cimg M„ = 0.3, M„ = 0.4 , M„ = 0.6 . Ket qua cho thdy phan bd lire khi dpng thay ddi ro ret khi thay ddi toe do chuyen dgng. Do chenh ap suit khi dgng tren bung canh va lung canh eua trudng hgp van toe Idn M„ = 0.6 Idn hon xk nhieu so vdi trudng hgp M„ = 0.4 va M„ = 0.3.
Theo phuang sai canh, lire khf dgng Idn nhSt d gdc canh va giam dSn din mut canh. Theo phuang chuyin ddng, lire khi dgng Idn nSm d vj tri nua ph§n trudc ciia canh tir mep vac.
Nghiin cini hiin tuong dan hoi cdnh dudi tdc dung ciia luc khi ddng 491
Ap suat NACA C012. fioc toi 3 do, M=0,3 Ap suat MACA 0012, goc toi 3 <fo, M=0.4 Ap sua! NACA 0012, goc loi 3 (Jo, M=0,6
m. V
^ 4 ( o ; - •-
V
\
r^
N
\ NN
'
Hinh 3.4. Ap suat khi ddng phan bd tren canh - profil Naca 0012, a=3°
M„=0.3 , Moo=0.4 , M«,=0.6
Ket cau canh cd dang hai dam nhu tren hinh 3.2. Sai canh va day cung b/c=5, profil Naca0012, kieh thude cae dam chir I nhu trong bang 3.1. Vat lieu ed md dun dan hdi
E = 7.10'°N/m' ; v = 0.3.
Bang 3.1. Thdng so ket cau dam canh
Dam trudc Dam sau
H 0.1 0.0425
C 0.0625 0.0375
t 0.01 0.0075
d 0.01 0.0075
v////y///y'/////////^
^ t
'^///////3//////////).
J
Tren hinh 3.5 la kit qua ehuyin vi khdng gian ciia canh ehu' nhat profil Naca 0012, gdc tdi 3 do, van tdc chuyin dgng Ma,=0.4. Chuyin vj udn ciia hai canh mep vao va mep ra trong 3 trudng hgp van tdc M„=0.3, M„=0.4, M„=0.6 dugc trinh bay tren binh 3.6. Trong trudng hgp van tdc Idn nbSt Maa=0.6 ehuyin vi tai mut canh cung Idn uhk va do chenh vl chuyen vi giua mep vao va mep ra ciing Idn nhat. Chinh do uon khdng dIu tir mep vao din mep ra la nguyen nhan gay nen su xoSn canh. Ket qua do xoan canh tren hinh 3.7 eho thiy trudng hgp chenh lech do udn canh giua mep vao va mep ra Idn nhat thi do xoan canh cung Idn nhat tirong iing vdi sd Mach vd cimg Moo=0.6. Gdc xoSn canh nhd nhat tuong iing vdi so Mach M„,=0.3. Trong ea ba trudng hgp van toe ehuyin ddng khac nhau, iing suit tdng hgp Von Mises Idn nhSt tai gdc canh
492 Hodng Thi Bich Ngoc, Dinh Vdn Phong, Nguyin Hdng San
ngam vao than, vdi tga do gan dam trudc, iing suat nen cue dai d phia tren lung canh va ung su§t keo cue dai d phia bung canh (hinh 3.8). Ket qua so sanh iing suat cue dai trong ba trudng hgp van toe khac nhau dugc trinh bay trong bang 3.2.
0 01224 \ b x
oox-:c-i
0UO5-1:- 0 OCHOfas
-J n on2o°6i 3 0Se 5\lin
M=0.4v
4
Hinh 3.5. Chuyin vj eua canh profil Naca 0012, a=3°, M„=0.4
BD uon mep vao, mep ra (NACA0012, Goc toi 3 do) po thi goc xoan tren tung sai, NACA0012, 3 do
4 6
Chieu sai canh
Hinh 3.6. Chuyin vj uon canh tai mep vao va mep ra (Naca 0012, a=3'')
2 4 6 8 Chieu sai canh z{m)
Hinh 3.7. Gdc xoan canh (Naca 0012, a=3'', M„=0.; 0.4; 0.6) Bang 3.2. Ung suat cue dai vdi gdc tdi 3 do
a=3°
M=0.3 M=0.4 M=0.6
Sx nen max (N/m-) 0.738E7 0.135E8 0.356E8
Sznen max 0.820E7 0.150E8 0.394E8
Sx keo max 0.707E7 0.129E8 0.338E8
Sz keo max 0.802E7 0.150E8 0.397E8
Nghiin cieu hiin tuang ddn hoi cdnh dual tdc dung ciia liec khi dpng 493
S, nen max S,. nen max
Hinh 3.8. Ung suat Von Mises
b. Xet trudng hgp cdnh chie nhdt profil Naca 0012, gdc tdi 5", van tdc thay ddi
Xet canh cd kieh thude cung gidng trudng hgp a, van tdc thay ddi vdi ba gia trj M„=0.3, M„=0.4, Mco=0.6, nhung hudng ciia van tdc tao vdi profil mdt gdc tdi 5° (Idn ban trudng hgp a 2 do). Ket qua ve iing suat cue dai tai gdc canh duge trinh bay trong bang 3.3.
Bang 3.3. Ung suat cue dai vdi gdc tdi 5 do a=5°
M=0.3 M=0.4 M=0.6
Sx nen max (N/m^) 0.135E8 0.246E8 0.656E8
Sz nen max
0.136E8 0.249E8 0.665E8
Sx keo max
0.135E8 0.246E8 0.660E8
Sz keo max
0.136E7 0.249E8 0.667E8
Hinh 3.9 la kit qua ve gdc xoan trong trudng hop luc khi ddng eiia ddng khi co van tdc vd ciing Moo=0.3, M«,=0.4, M„=0.6 qua canh profil Naca 0012, gdc tdi 5 do vdi irng xir cua kit eau canh dang profil 2 dim va kit eau dang tam. Chiing ta cd the thay trong trudng hgp kit eiu tam (thdng sd kit eiu dugc tich phan theo phuang chuyen ddng), do ciing cua kit eiu theo phuang chuyen dgng khdng ddi nen canh bj udn d mep vao rit Idn do lue khi ddng tap trung d mep vao Idn, vi vay canh bj xoin rit rd ret (gdc xoin Idn nhat 3.4°). Nhung vdi kit ciu canh profil Naca 0012, theo phuang chuyin ddng ket cau ed do ciing eao tai viing mep vao nen gdc xoin canh do chenh lech do udn giua mep vao va mep ra nhd hon trudng hgp ket cau tam nhieu.
494 Hodng Thi Bich Ngoc, Dinh Vdn Phong, Nguyen Hdng Son
Do 0.5
thi goc xoan tren tung sai, NACA0012, 5do Do thi goc xoan tren tung sai, NACA0012, 5do
, « 1 M g JTil^lllH II "
2 4 6 8 Ghieu sai canh z(m)
2 4 6 8 Chieu sai canh 2(m)
Hinh 3.9. Gdc xoan canh trudng hgp gdc tdi 5 do (So sanh kit ciu profil Naca 0012 va tam) 4. Nhan xet
Hieu iing dan hdi canh may bay dudi tac ddng cua lire khi ddng la mdt bai toan can thiet khdng the thieu doi vdi hang khdng, dac biet trong trudng hop may bay chuyen dgng vdi toe do Idn (M>0.7) lire khi ddng rat Idn, nen canh bj bien dang rat nguy hiem. Canh bj bien dang se gay nen su thay doi ciia quy luat phan bd luc khi ddng lam thay ddi tam day ciia may bay anh hudng true tiep den van de on djnh eila may bay. Bien dang dan hdi cua canh d day gidi ban trong phan tinh toan tmh, su bien dang tiep tuc dao ddng theo thdi gian gay nen nhting nguy co pha buy do dao dgng. Tinh toan dan hdi khi ddng trong phan nghien ciiu nay da dua dugc vao tinh toan dang kit cau canh ed mat cit ngang bien dang profil vdi do eiing thay doi theo phuong chuyin ddng va gia trj luc khi dgng phan bd tren canh dugc tinh true tiep bang eae phuong phap tinh toan khi dgng 3D (ehu khdng phai bai toan dan hdi eiia canh vdi gia thiet luc khi dgng la mdt gia trj bilt trudc nao do). Sau khi canh bj dan hdi, lue khi ddng bi thay ddi, do la mue tieu bai toan "khi ddng dan hdi" dugc trinh bay d cac cdng trinh khac [2].
Tai Heu tham khao
[1] Hoang Thi Bich Ngoc, Vu Manh Cudng, Nguyin Manh Hung (2004). "Chuong trinh tinh todn lire khi dgng AER03D tac dong len canh may bay dudi am" Tap chi Khoa hoc vd Cdng nghi, ISSN 0868-3980, s6 48-49, trang 119-123.
[2] Hoang Thj Bich Ngoc (2007). "Tinh todn su thay d6i ciia lire khi dong sau dan hoi xoin canh xet vol canh CO canh dilu khiln". Tuyen tap Cdng trinh Hdi nghi khoa hoc todn qudc Ca hoc Thuy Khi todn
<7Moc,tr. 403-413.
[3] Riegels F. (1961). Aerofoil sections - Results from wind-tunnel. Butterworths, London.
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