KHOA HOC CdNG NGHE
THIET L A P PHUOIVG TRllXIH DOIXIG BIEIXI LUOIXIG TROMG LOIXIG DAIXI H O BAIXIG IXIGDYEIXI LY B A O TOAIXI DOIXIG LUOIVG
Hoang Nam Binh^'^ Nguyen Qudc H u / T6MTAT
Dong bi^n luong la mot trong nhung trudng hgp rieng cua vat the chuyen dong vdi khdi lirgng thay ddi.
Nam 1937, Konovalov I. M. da thidt lap phuong trinh mo phong chat long chuyen dong on dinh mdt chieu cd Imi lugng thay ddi doc theo chidu long din. Phuong trinh la td hpp su bien doi cua cot nude liru tdc trung binh mat cdt va ty le giua cdt nude luu tdc trung binh doan tinh toan vdi chieu dai doan do, cd xet den anh hudng cua hudng dong chay gia nhap hay phan tan. Phuong trinh duoc ung dung kha rong rai va duoc nhidu nha khoa hpc trich d&n trong cac nghien ciiu ve hien tirong thuy lire dac thii nay. Konovalov da thiet lap phirong trinh xuat phat tir nguyen ly bao toan nang lugng ddi vdi mdt chat diem co khdi lupng bien thien. Bai bao trinh bay mot each khac de thiet lap phuong trinh dong luc ddng bien luong dang Konovalov xuat phat tu nguyen ly bao toan dpng luong.
Tirkhda: Dong bien luong, dongluvng, mang tran ben, phmmg trinh Konovalov.
I.DATVANDE
Cac cdng trinh thao lu cd nhiem vu dam bao an toan cho cdng trinh dau mdi va ha luu. Cdng trinh duoc phan thanh 2 loai chinh la cdng trinh thao lu trong than dap va cdng trinh thao lu ngoai than dap.
Cac hinh thiic bd tri cdng trinh thao lu ngoai than dap thudng la tran doc, tran ngang hay gieng thao lu.
Tran ngang la loai dudng h-an hd, hudng nude chay vao gan nhu vuong gdc vdi ngudng ciia dudng thao.
Cac cdng trinh thuy lgi dau mdi thudng ap dung hinh thiic tran ngang khi dia hinh khu vuc xay dimg cdng trinh ddc, hep, sudn mii khdng cd vi tri thich hgp de bd ti-i tran doc hay cac hinh thiic thao lii khac [7].
Ngoai ra, tran ngang cdn cd the ap dung lam ti-an phu, tran su cd d cac cdng tiinh hd chua. Uu diem ciia ti-an ngang la bd tii ngudng ti-an dpc theo dirdng ddng miic, ngudng tran cd thd dugc keo dai ma khoi lugng cdng trinh tang khdng dang ke so vdi vide tiiay ddi kich thudc tran dge. Cdt nude tren ngudng ti-an thap nen cd the giam do cao cua d^p va giam dien tich ng|.p phia thucmg luu ho [2]. Cac bd phan cua
tran ngang gdm: kdnh dan vao tuydn dap (cd the cd), ngudng tran, mang tran ben va dudng thao ndi tiep sau mang [7]. Mang tran ben thudng cd mat cat ngang hinh chu nhat hoac hinh thang (Hinh 1). Day mang theo phuang dong chay cd the thang hoac cong vdi dp ddc nao dd phii hgp vdi tinh toan thuy luc. Che do thuy luc trong mang tran ben rat phiic tap [4]. Ddng chay trong mang cd Imi lupng thay doi dge theo chidu long dan. Su xao trpn manh vdi cau tnic xoay 3 chieu trong ddng bien lugng gay tdn tiiat nang lugng. Su tieu tan nang lugng nay la nhiing bien ddi CO ban trong qua trinh can bang nang lugng cua chuyen ddng. Ddng chay gia nhap hoac phan tan khdi khdi nude chuyen ddng hinh thanh nhieu gian doan lam tang miic do tieu nang.
Trong thuc te, ngoai hien tu'png dong chay trong mang tran bdn cua dudng tran ngang d cac ho chiia thuy lgi thi he thdng mang thu nude mua trdn mai nha, mang thoat nude tran cua be boi hay ranh bien (Hinh 2), ranh dinh, muong cat ddc [2] cung la nhiing iing dung cua hidn tugng ddng chay cd luu lugng tang din dge theo chieu long dan.
' Khoa Cdng trinh, Tnrdng Dai hoc Giao thong Van tai
^ NCS Vien Khoa hoc Thuy lgi Viet Nam 'Trudng Cao d^ng Co dien va Xay dung Bac Ninh Email: [email protected]
NONG NGHIEP VA PHAT TRIEN NONG THON - KY 1 - THANG 8/2020 59
KHOA HOC CONG NGHE
Hinh 1. Mang bdn cua cdng trinh hd chiia Bau IJm, tinh Binh Phudc Cac nha khoa hgc nghien ciiu vd hien tugng thuy luc dac thii nay cho den nay da dua ra dugc nhieu dang phuong trinh ddng luc cua ddng bidn lugng mpt chieu chuyen ddng dn dinh nhir Hinds J.
(1926), Favre H. (1933), Meyer - Peter (1934), Beij H. (1934), Camp (1940), De Marchi G. (1941), Keulegan G. H. (1952), Yen et al. (1971) (dugc hich dan bdi 0), dac bidt la Konovalov I. M. (1937) (dugc trinh dan bdi: [1], [2], [4], [6]. Phuong hinh la to hgp str bidn doi cua cdt nude luu tdc trung binh mat cat va ty 16 giua cdt nude luu toe trung binh doan tinh toan vdi chieu dai doan dd. Phuong trinh co xet ddn anh hudng cua hudng ddng chay gia nhap hay phan tan.
dx (1)
1 - F / -
Trong dd: h - chidu sau ddng chay tai mat cat tinh toan (m); x - tga dg mang theo phuong ddng chay (m); So - dd ddc day mang [-1; Sj - dd ddc thuy luc [-]; Q - luu luong dong chay (mVs); g - gia tdc trpng trudng (g = 9,81m/s^ ; A - dien tich mat cat udt (m^; Fr^ thdng sd ddng hoc ddng chay;
Fr • he sd hidu chinh ddng nang (he sd Conolis) [-]; B - chidu rpng mat thoang (m); ky - he sd xet den anh hirdng cua hudng ddng chay gia nhap hoac phan tan, ki, = 1 + a - n,,; no- ty sd giua hinh chidu cua luu tdc toan phan cua khdi gia nhap hoac phan tan d canh ben len phirong chuyen ddng (v(0 va luu tdc long dan chinh (v).
Phuong trinh (1) dugc gidi thieu trong tai heu Konovalov 1. M. Phuong tiinh chuyen ddng cua chat long cd luu luong thay ddi, Ky ydu cua LHVT (1937).
tap 8. trang 114-192 (Ban tidng Nga) (KoHOBanoB M.
M. VpaBHeHne flBM>KeHMfl >KHAKOCTH nepeMeHHOti Maccbt. Tpyflbi JlMMBTa (1937). Bbin. 8, C. 114-192).
Hinh 2. Ranh bidn thoat nude ven dudng Tai heu nay dugc nhieu tac gia trich din nhu tai lieu tham khao CTLTK) so 28 trong nghien ciiu ciia Lagereva E. A., Lagerev A. V. (2005) [8], TLTK sd 37 cua Anton Pavlovich Akpasov (2018) [9] hay TLTK sd 111 cua Novikova E. A. (2013) [10] va nhidu nghidn cuu khac. Phirong trinh (1) cung dugc gidi thieu trong cudn Sd tay tinh toan thuy luc ciia Kiselev K. G. va nnk. (1984) (ban tidng Viet) [4]
trong phdn hudng din thidt ke thuy lire mang han ben. Cac nghidn cuu hay cac so tay va hudng dan tinh toan thuy luc mang tran hen ti-ong nude hien nay su dung phuong trinh (1) deu trich din tu Kiselev K.
G. va nnk (1984) [4].
Theo Pham Hoai Thanh (1994) [5], Konovalov I.
M. da thiet lap phuong trinh chuyen dgng ddi vdi ddng chay thay ddi dan cua chat long cd luu luong bidn thien dge theo dudng dan tir nguyen ly bao toan nang lugng viet cho chat diem cd khdi lugng bien ddi. Phuong phap nay tuong tu phuong phap cua Metserski (1904) do Hoang Tu An va nnk (2004) trich din [1]. Bai bao trinh hay mdt each khac dd thiet lap phuong trinh ddng lire mdt chidu ciia ddng bidn lugng dn dinh xuat phat tir nguyen Iy bao toan ddng lugng de tir dd din ra phuong tiinh dang Konovalov (1).
2 . niSOAl LUC Vii PHUDNG TRINH BIEN THBU BONG LUDNG Phuong trinh vi phan chuyen ddng cua ddng chay dn dinh cd luu luong thay doi dge theo chieu long din CO tiie dugc thidt lap tir phuong trinh kinh dien cua Navier • Stocks vidt eho chat long Nevrton khdng nen dugc chuyen ddng trong tiudng trgng luc. Tuy nhidn, ti-ong thuc te cac phuang trinh chuyen ddng thudng dugc thidt lap tir nguyen Iy bao toan ddng luong.
Theo dinh luat II cua Newton phat bieu cho ddng luong thi bien thien ddng lugng ciia mpt vat theo thdi gian ty le vdi tong luc tac dung len vat va co hudng la hudng ciia tdng luc [3].
60 NONG NGHIEP VA PHAT TRIEN NONG THON - KY 1 - THANG ? 2020
KHOA HOC CdNG NGHE
2 . 1 . C ^ n g o ^ l u c ^ . 3v . . . . . . • ^ dan den the tich thay doi mot luong A — dtd\ ( ).
Xet mot khoi chat long theo phuong dong chay, ™ cac luc lac ddng len khdi chat long do chu yeu la ap trong khi do. dien tich mat cat uot bien d6i thanh:
luc, trong luc va luc ma saL ^^ ^ ^ ^ 3 ^ P
A A-t•—dt-^" dt = A-^-^dt-^v^dt(.T|
dt dx dt at dx '''^-f) 7 5 ^ 2 " *• *^'''^'^ Tu (*) va (7) nhan duoc su bien doi th^ tich kh6i
• — d x — - ^ chat long trong mpt khoang thai gian dt tren mot don vi chieu dai dx la:
y M' = \A + ^dt + v^dt + A^dt]dx(8) X +-dx
dwjA-l- „. , . .
Hinh 3. Mo hinh khoi c h i t long hinh tni trong he toa V ° ' ™ ""^
do Descartes -pai thoi diem t + dt. luu tdc ciia khdi chat long la:
Gia su ddng chay bien doi cham. ap luc P trdn 9v 3v dx 3v 3v mat est phia thugng luu bang ap suM tai tam p nhan '''*'" ~ *" ^ ^ ' ' ' ^ 3^^ ^ * "^ *" ^ ^ * ^ ' 3x^ * vdi didn tich mat cat ngang A cda phan tir chat long
(Hinh 3) 0)
Goi K la dong luxmg khoi chat long sinh ra khi chuyen ddng. tai thdi diem t. ddng luong cila p h ^ tir P,\^=pA = yhA (2)
Vdi T la ti-ong luong rieng cua chat long. (N/m^. '=''*' ' " " * '*'
Khai h-ien Taylor ddi vdi chudi mdt bidn ap dung '^. = """' = P'"™' = P'''^''-*' (1") cho (2). bd qua cac vi phan bac cao, nhan duoc tdng xai thdi didm t + dt, ddng luong ciia phin hi chat ap luc chat Idng tien mat cat phia ha luu la: 15jig i^.
P,l^^_^=L + ^ d x y = j(h + ^dx]A (3) K„„=n,v„„=pv„„dW (11) Tdng hop ap lire phia thugng luu (1) va ha luu
(2) duac tdng ap lire don vi tac ddng len khdi vi phan fb-a/nv')
vdi p la khdi lugng ridng cua chit long, p = —, Y
chat long la:
dh dx
Thay (8) va (9) vao (11), thuc hien bien doi nhan P = P^ - P^ ^ ^yA^^ dx (4) duac:
Mat khac, tdng ti-ong luc va luc ma sat tac dgng K,,^ ^ p ^'A+\ A—-+2vA-^+v—-+v •— \dt \dx(X2)
ldn khdi chat long la: ^ '^
_ _ _ . / ^ _ (. \ , .c) Tir (10) va (12) nhan duoc phuong ti-inh bien 1 "^ \ 0 ! I thien ddng lugng cua mdt phan tu chat long khdng (vdi So la do doc day, Sf la do ddc ma sat). "en duoc chuyen ddng trong ti-udng ti-ong lire dugc , , , , .- 1 .. thidt lap theo dinh luat II eua Newton phat bieu cho Ket hop (4) va (5) nhan duoc tong ngoai luc tac ^.^^ ^^^^ ^^^^^^,
ddng len khdi chat long la:
:,, N dK r , 3 v ^ , dv dA i^A] , - | ) ^ x (6) -^^V^^'^'Tx^'^^'-Yxr ''''
3 . THIET LAP PHUONG TRINH 2.2. Phuong trinh bidn thidn dong luong
. . . . . . . Xet ddng chay mdt chieu hong mang ti-an ben Xet khdi chat long chuyen dong sau khoang thoi • . . - . . T^ i . ^ .
AciKiioi ciiai luiig Cl J . s 6 cua duong tian ngang. Dong chay tiong mang cd luu gian dt, luu tdc v se thay doi mot khoang j - U " ' " ' ' " 8 '^"S '^^ tide theo chi Su dai mang.
NONG NGHIEP VA PHAT TRIEN NONG THON - KY 1 - THANG 8/2020
KHOA HQC CONG N G H £
Ggi q dQ
' dx la luu lugng don vi gia nhap trdn mdi don vi chidu dai ddng chay dx. Ung vdi q se cd Iim toe gia nhap d canh ben vi, khi dd hmh chieu ciia V| len phuong dong chay trong mang ben se la v,^
(Hinh 4). Vdi thanh phan ddng gia nhap trdn moi don VI chieu dai canh ben se sinh ra thanh phan ddng lugng K,:
dK,
I 2 Hinh 4. So dd ddng chiy h-ong mang trin bdn
Vi hinh chieu vector luu tdc gia nhap cimg phuong va chieu vdi vector luu tdc trong mang ndn vector ddng lupng cua ddng gia nhap mang dau am.
Ggi Ksc la ddng lugng trong mang tran ben, hi (13) va (14) nhan dugc phuong trinh bien thien ddng lugng ciia ddng chay trong mang tran bdn nhu sau:
dt
I . dl' - . dv
dl v - - - v , , , | . * l ( 1 5 )
S /^ , ket hop (6) va (15) nhan duoc Tir dinh luat 11 ciia Newton phat bieu cho ddng luong
\dt phuong trinh:
{A^ 2 A ' ^ V — + V- —
\ dt dx dt dx Vfe?ldx = yAlSo-S.
(16) idx
Tich phan phuong trinh (16). chia 2 vd cho -yAva sap xep lai. nhan duoc phuong tiinh sau:
' ^ • ' ^ = 5 „ - S , + l ^ , ( 1 7 ) dli I3i- 2vai'
— + - t — T - - r — ^ • d\- g dl g dx gA dt gA dx
Mat khac. phuong trinh lien tiic viet cho ddng chay mpt chieu tiong long dan hd co luu luong gia nhap hoac phan tan tien mdt don vi chieu dai cd dang [31. [41:
dQ dx
dA (18)
dA dv dA Hay v^—+ A — + ^ ~ =
dx dx dt (19)
Nhan 2 ve cua (19) vm — nhan duoc:
(20) V" dA V d v V dA _ V gA dx g dx gA dt gA Thay (20) vao (17) nhan dupc phuong trinh:
dh \ dv V dv I Q
— + - — + - — = So --Sf - ( v d.v g dt gdx
(21) Phuang trinh (21) cd th^ dugfc cdi la phuong trinh dong luc ciia ddng khdng on dinh chuyen ddng mdt chidu cd luu luong tang dan doc theo chi^u dong chay duoc thiet lap tir nguyen ly bao toan ddng luong.
Khi ddng chay la dn dinh thi cac ham sd khong phu thudc vao thdi gian t ma chi phu thudc vao tga do. Nhu vay. phirong tiinh (21) tid thanh:
dh V dv „
dx g dx
"t
- ( ' ' - " / x ) - (22) Xet cho toan mat cM udt cua ddng chay tiong mang tian ben, khi dd:Q = v A v a d A . B d h
Vdi B la chidu rdng mat thoang va v la luu toe trung binh toan mat cdt.
Gia til luu toe V trung binh toan mat cat sai khac mot dai luong a so vdi luu toe ciia phan tu chat long, a la he so Conolis [3].
Thuc hien bien doi dai luong thijr 2 6 ve tiai ciia phuong tiinh (22), nhan duoc:
g dx (23)
gdx
Thay (23) vao (22) va bidn doi nhan duoc phuong trinh:
wdQ aQdA a-cQj^ dA g\dx g 4 - A gAdx gi dx
djl w^dQ aQ- dA dx gA dx gA' dx
^mc^_o(^^dh
dx gfi dx dx So-Sf
;;4 dx
62 N O N G NGHIEP VA PHAT TRIEN N O N G THON - KY 1 - THANG 8/2020
KHOA HOC CONG NGHE
gA' )dx ~So-Sf-(v-v,^ ydQ Oil dQ, gAdx gA dx
^^ S„-S,-(l + a ) i ^ + v,,-L^
3 = SAdx ''gAdx
dx 1 - F r ^
d ^ ^ '' ' gA^ dx gA dx
dx l-Fr'
dh_ ' ' gA^ dx gAv^dx
dx l-Fr^ (24)
Bat HQ = - ^ thay vao (24) nhan duoc:
dx'
dh_
dx'
I, . Q dQ V- dA cA dx gA dx
5 ^ - ( l + a - « „ ) ^ - ^ Q_dQ gA^ dx
\-Fr'
(25) Neu dat ko - 1 + a - no thi phuong trinh (25) tid thanh phuong trinh (1):
Q dQ dh ^ gA^ dx
dx 1 - Fr^ (1)
Phuong trinh (25)' la phuong trinh ddng luc cua ddng bien lugng on dinh ti-ong mang tran ben duoc thiet lap theo nguydn Iy bao toan dgng lugng.
4.KFrLUAN
Phuong trinh dong luc (25) eua ddng chay mpt chidu chuyen dgng on dinh cd luu luong tang dan theo chieu ddng chay ti-ong mang tran bdn ciia dudng tran ngang dugc Konovalov I. M. thiet lap nam 1937 da dugc ap dung va tiich din trong nhieu nghien ciru va tai lieu trong va ngoai nude. Viec thiet lap phirong trinh cd the thuc hien bang nhieu each khac nhau. Bai bao ap dung nguyen Iy bao toan ddng lugng da thuc hien tai lap phuong trinh nham lam sang td ngudn gdc cua phuong trinh ma cac tai heu
trong va ngoai nude hien nay chi ap dung hoac trich dan.
TAI UEU THAM KHAO
1. Hoang Tu An va nnk (2004). Dong chay khdng gian khdng on dinh trong he thdng kenh din hd cua tram thuy didn. Tap chi Thuy loi va Mdi trudng, sd 5.
2. Hoang Nam Binh (2019). Mot sd nghidn cuu tidu biSu v4 ddng bien luong va mang tran bdn. Tap chi Khoa hgc va Cdng nghe TTiuy Igi, sd 52.
3. Nguydn Canh Cam (2005). Thuy luc tap L NXB Ndng nghiep.
4. Kiselev K. G. va nnk. (1984). Sd tay tinh toan thuy luc (ban dich tidng Viet). NXB Ndng nghiep.
5. Pham Hoai Thanh (1994). Mdt sd bai toan ve van tai chat long nhdt - deo trong dng din, Luan an Phd tien si khoa hoc ky thuat, Tnrdng Dai hgc Bach khoa Ha Ndi.
6. Nguydn Vu Viet, Hoang Nam Binh (2019).
Cac dang phuong trinh ddng chay dn dinh cd luu luong thay ddi doc theo chieu Idng din. Tap chi Ngudi Xay dung, sd 5&6.
7. Vien Khoa hgc Thiiy lgi (2005). Sd tay Ky thuat tiiuy loi, Phin 2 - Cdng tiinh tiiuy lgi, T$p 2 - B.
Cdng tiinh thao Id, NXB Ndng nghiep.
8. Lagereva E. A., Lagerev A. V. (2005). Nghien ciiu tinh toan thuy luc dudng tran ngang, Moscow,3.
ISBN 5-94275-191-9. (Ban tieng Nga) (A. riarepeea, A. B. JlarepeB, MccneflOBaHMn H PacHeibi B0fl0C6p0C0B C BOKOBblM CriHBOM, MocKBa).
9. Anton Pavlovich Akpasov (2018). Cai tiiien hieu qua cdng cu tudi phun mua bang viec hieu chinh cac tiidng sd thidt ke vdi phun trong chuyen ddng trdn. Dai hgc Ndng nghiep Saratov (Ban tie'ng Nga) (Saratov. AKnacoB AHTOH FlaBnoBi/m, nOBblLUeHMe 34)4DeKTMBHOCTM flO)Kfleo6pa30BaHMfl c 06ocHOBaHiieM KoHCTpyKTWBHbix riapaMerpoB flec|3neKTopHbix HacaflOK KpyroBoro fleiicTBMfl, CapaTOBOKHM rocyAapCTBeHHbm arpapHbiki yHHaepCHieT HM. H . V\. BaBHJioBa, C a p a r o B ) .
10. Novikova E A (2013). Cai thien sir an toan ciia van chuyen bang tai ti-ong cac md khai thac than, Dnepropeti-ovsk, ISBN 978-966-350-421-6 (Ban tieng Nga) (E.A. HoBMKOBa, (loBbiujeHMe BeaonacHocTH KoHBewepHoro TpaHcnopia B fopHbix BbipaSoTKax YronbHbix UJaxi.flHenponeTpoBCK).
N O N G NGHIEP V A PHAT TRIEN N O N G THON - KY 1 - THANG 8/2020 63
KHOA HOC CdNG NGH|
ESTABUSHING THE KONOVALOVS DYNAMIC EQUATION FOR STEADY SPATIALLY VARIED FLOW BYTHE PRINCIPLE OF MOMENTUM CONSERVATION
Hoang Nam Binh, Nguyen Quoc Huy Summary
Spatially varied flow is a specific case of moPon for a vanable-mass system. In 1937, Konovalov I. M. had established the dynamic equation for steady spaUally varied How. The equation is a combinaUon of velocity pressure head and the ratio of average velocity presiire head on channel segment and length of this segment and consider the effect of the lateral flow directtons. Tlie equaPon is widely used and cited in many articles related to spatially varied flow phenomenon. Konovalov's equation had taken by energy conservaUon principle. This paper presents anodier way to establish the Konovalov's dynamic equaUon for steady spatially vaned flow by the principle of momentum conservaUon.
Keywords: SpaUally varied How, momentum, side-channel, konovalov's equation.
Ngudi phan bi§n: TS. Nguydn Nggc Nam Ngay n h ^ bjli: 22/5/2020
Ng^y thdng qua phan bidn: 23/6/2020 Ngiy duyet dang: 30/6/2020
NONG NGHIEP VA PHAT TRIEN NONG THON - KY 1 - THANG 5/2020
