Hydraulic parameters of flow bilaterally constrained by transverse floodplain dams in the region of its spreading Текст научной статьи по специальности «Физика»

Hydraulic parameters of flow bilaterally constrained by transverse floodplain dams in the region of its spreading

The obtained relationships include relative velocity along the left bank mn, value that changes from 0 to 1. From the experimental research data we introduce the relationship to describe the character of these changes with the following equation

(17)

U , x 42 m = — = (—)

" и X

gradual approximation. It is known that these values between the section lines K,-K, and K-K, decrease from U , U , U to

11 2 2 PK\ ' HHKi

, V , V" .

po ' HTi ' nn

Knowing this we must give values for mra or mnn and using equation (14,15) determine mnn or mm and further determine Up

with equation (12).

From the obtained values using discharge conservation equation (11) we equate the left and the right parts of the equation. In case if the condition is not satisfied, the calculation is carried out again.

Conclusions:

The analysis of the obtained relationships show, that in this case the task also remains undefined at some degree. There are three unknowns Up, Um, Unn in two equations (12) и (14,15) три

неизвестных величин Up, Um, Uпп, therefore the task is solved by

References:

1. Абрамович Г. Н. Теория турбулентных струй. - М., Физматгиз, - 1960, - 716 с.

2. Барышников Н. Б. Морфология, гидрология и гидравлика пойм. - Л., Гидрометеоиздат, - 1984, - 280 с.

3. Михалев М. А. Гидравлический расчет потоков с водоворотами. Л., Энергия, Ленинград. отд., - 1971, - 184 с.

4. Rajaratnam N., Ahmadi R. Hydraulics of channels with flood-plains. Journal ofhydraulic research. - Voc. 9, - 1981, - No. 1. - P. 43-60.

5. Бакиев М. Р. Совершенствование конструкций, методов расчетного обоснования и проектирование регуляционных сооружений. Автореферат. докт.диссер. - М., - 1992, - 57 с.

DOI: http://dx.doi.org/10.20534/ESR-17-1.2-195-199

Kahhorov Uktam Abdurahimovich, enior teacher at the department «Hydrotechnical construction and engineering structures» Tashkent institute of irrigation and melioration (TIIM), Uzbekistan.

E-mail: [email protected] Bakiev Masharif Ruzmetovich, Professor in the department «Hydrotechnical constructionand engineering structures», Tashkent institute of irrigation and melioration (TIIM), Uzbekistan.

E-mail: [email protected]

Hydraulic parameters of flow bilaterally constrained by transverse floodplain dams in the region of its spreading

Abstract: Using main equations of hydro mechanics, equation of momentum conservation and discharge conservation specifically, the authors of the article introduce design relationships for determining main parameters of flow bilaterally constrained by transverse floodplain dams in the region of its spreading.

The task differs from previous ones by the presence of bilateral floodplain, two zones of interaction between channel and floodplain flows, different roughness at floodplain and in the channel.

Keywords: floodplain, channel, transverse blank dams, interaction zone of floodplain and channel flow, turbulent mixing zone, region of flow spreading, traction forces, velocity in channel, velocity at floodplain, length of region of flow spreading.

The role of floodplains for national economy has grown significantly in recent years. First of all, it is determined by their agricultural use and also by urban development in floodplains. Floodplains can give high yields due to their close location to riverbanks. Exploitation of flood-plains is often carried out by using transverse solid dams as protection, and these dams are built of the same soil from the floodplain.

Designing transverse dams in rivers with floodplain has its special features as complex morphology, kinematic and dynamic interaction of riverbank and floodplain flows [1]. The work[2] discusses design issues for transverse dams in rivers with single-side floodplain and the influence ofpartial land use between dams [3] under one sided obstruction.

The given work discusses design issues for transverse dams, symmetrically obstructing flow. The task differs from the previous works by the presence of bilateral floodplain, two zones of inter-

action between riverbank and floodplain flows, various roughness measures at the right and left floodplains, differing from those in riverbank.

The experiments have been held in schematic riverbanks with bilateral symmetrical floodplains. The experiments showed that when the flow fills the whole floodplain, the riverbank roughness, the roughness of the left and the right floodplain differ from each other.

The research result analyses show that there is significant deformation in flow depth and velocity regime, also formation of backwater takes place in head race, flow compression and spreading and natural flow restoration areas in the tailrace (pic.1.).

The velocities increase both in main riverbank and in floodplain area of flow. Flow spreading and restoration of natural flow restoration area form after compressed section.

Figure 1. Asymmetrical flow s2

Velocity distribution in the riverbank and floodplain flow interaction zones both for natural riverbank and for deformed flow depend on earlier obtained relationships [2]. Interaction zone width depend on relationship of depth for riverbank and floodplain [1;

2; 4; 5].

The velocity fields also undergo significant changes compared to natural flow. In the backwater area the velocities increase close to obstruction section. Behind the obstruction point there takes place planned and vertical flow compression. The velocity distribution by the flow width has significant transverse gradients exactly in compression area.

The velocities increase both in main riverbank and in floodplain area of flow. Flow spreading and restoration of natural flow restoration area form after compressed section.

Velocity distribution in the riverbank and floodplain flow interaction zones both for natural riverbank and for deformed flow depend on the following relationship:

U-U

_nx_

U -U

= (1 -n )

(1)

6 * — y

where tf =-*—; y - ordinate of the point where U is deter-

6*

mined;

U , U - velocities in channel and at floodplain;

px7 nx r '

6 - the width of interaction zone 6 = 6 + 6

P n

Interaction zone width comply with the relationship of depth for riverbank and floodplain [1; 2; 4; 5].

preading scheme for (n * nn)

distributed in confined space [6]. Therefore, the flow is considered as if it consists of hydraulically homogenous zones: a) weakly disturbed core in riverbank and floodplain with small transverse gradients; b) turbulent mixing with significant velocity gradients at both floodplain parts; c) interaction of riverbank and floodplain flows; d) back flow in protected banks.

Versatility of velocity fields in turbulent mixing zones, which depend on Shlihting-Abramovich relationship [6] has been proven experimentally. The distinctive feature of the problem is in formation of two zones of intensive turbulent mixing

— the first one forms between beams 0'-1 and 0'-2 with width

6;

— the second one forms between beams 0'-1 and 0'-2 with width 6'.

Velocity distribution in the first zone complies with the following relationship:

u -Us 3/A2 y - y.

—n-= (1 -n3/2) where n=-:

U -U V ' B

m- m-

in the second (right) zone: U -U

(5)

(l -n3/2) where n

y - K

(6)

B hp

— = 2,4 - 2,4 h h

.J. = 1,4 .-Z.

hnhn

n n

^=hp. -1 K h

1,4

(2)

(3)

(4)

The nature of flow velocity distribution beyond the obstructed section are close to those accepted in the theory of turbulent flow,

U -U e

nn nn

U , U - velocities at left and right floodplains;

m- ' nn Or-'

U , U - inverse velocities at floodplains.

Kn ' Hn L

Within the research (symmetrical obstruction and symmetrical floodplains) the following schemes are reviewed: a) when roughness of the right and left sides of the floodplain is the same, the flow spreads symmetrically; b) when the roughness differs, the flow spreads asymmetrically (pic.1).

In the second case the lengths of whirlpool zones are different and the velocity field restoration area generates there.

In both schemes laws for the velocity change in riverbank, floodplains, backflow, lengths of whirlpool zones should have been set.

In order to solve the task the equations for law of conservation of momentum, conservation of discharge, written for section lines C-C and X-X and some boundary conditions were used.

Hydraulic parameters of flow bilaterally constrained by transverse floodplain dams in the region of its spreading Momentum conservation equation

yi Bu

ph U'2 (B - e'- B - e ) + ph f Udy + ph U2 B + ph f Udy + ph f Udy +

r nnc nnc \ nn c annc n f r nnc J / r nnc nnc annc r nnc J / r pc J /

0

y«

+php Up e + php f U2dy + ph f U2dy + ph U2 e" + ph f U2dy +ph U"2 (B -

r pc pc xc ' pc i ' ' nnc J / r nnc nnc ann r nnc J / r nnc nnc \ nn

0 Bp y5

yi Bn

B - e" - e) = ph U2 (B - B-B - e) + ph J Udy +ph U B + ph J Udy + (7)

xnnc n / r nn nn \ nn xnn n / r mj / r nn nn nnnc r nn J / \ /

y20

Bn +Bp Bp Bp +Bn y6

+php J U2dy + pheU2A +phpJU2dy + phn J U2dy +pKU2nnB'nnn + phmJU2dy +

0 Bp ys

xBnn X XBP X xBnn X

phnnU": ( - B' - Bmn - Bn) + p J J ^dydx + p J J -nUdydx + p J J ^dydx

0 0 0 0 0 0

Discharge conservation equation

y B n Bn +er

h U (B - b'- B - B ) + h f Udy + h U B + h \Udy + h f Udy + hcUcB

nnc nnc V nn c 3nnc n / nn J / nnc nnc 3nnc nnc J / pc J ' pc pc 3'

r2 0 Bn

BP BP +Bn y,.

+hc f Udy +h f Udy + h U b" + h f Udy +h U" (B - b" - b" - b ) =

pc J / nnc J / nnc nnc 3nn nnc J / nnc nnc v nn c 3nnc nJ

0 Bn ys

yi B n Bn +BP

= h U (B -B-B -b ) + h fUdy + h U B + h fUdy + h f Udy + hUa +

nn nn \ nn 3nn n f nn j / nn nn 3nnc nn j S p J ' P P 3

(8)

y2

y,

+h f Udy + h f Udy + h U b" + h f Udy + h U"2 (B - b" - b" - b )

p J / n J / nn nn 3nn nn J / nn nn V nn 3nn n /

0 BP ys

Integration of equations (7, 8) are carried out by accounting (1,2,3,4,5,6) with condition UH = 0 [3, 5], and traction forces are computed by mean depth and velocities at flow spreading region

U + v U + V h = h ; h = h ; V* -^• V* =—nnc-^;

n nc ' p pc ' nn ^ nn ^

Upc + Vp, V' V*

17"* _ pc _P^ _ _nn f _ nn

v p — ; v nn — ; v nn —

We determine the velocity in channel from (7)

2 U Up

pc pc

Up _ |(0,416e'chnc + hncBxnnc)m2mc -e (hncKl + K2 -K3 -hncK4) + e,c ++(B'mnc + UPc ] (0,416? + Bn)hncm2m -e'(hnK5 + K6 -K7 -hncK8) + ~e„ +

+0,4167c)hncm2nnc - ^hncVi - U^v'1p - ^hncVi (9)

nnc222

+(e \nn + 0,416e ")hncm2nn

Jointly solving (7 and 8) we get equations for determining velocities — at the left floodplain

Am2 + Am + A = 0 (10)

1 nn 2 nn 3 ^ '

where

where

Aj = M.hncC - 0 2M 2 hnc; A2 = 2 Rhn£ mc 8 + 2 RfincC 7(b, - b C 9);

A3 = 2 ff1hncC8 (s. - e 'C 9)mnn - 0 2M}k«cm2n + ffjuncClml - 0 2Mt + - b "cj. - at the right floodplain

Am2 + Am + A = 0 (11)

4 nn 5 nn 6 V /

a4 = ff ¿lie 2 - 0 2M}hnc; a5 = 2 ffXcC 7c + 2 ffhncC S(B, + B c 9);

A6 = (ffXe -®2M2hncm + 2fflhncC7(~Bs -7c9)mm + -~e*C9)2 -®2Mi

= (0,416e'chnc + hncB^c)m2mc -b (hnCK1 + b K2 - K3 -hncKt) + b,c +

a p _ _^2 a O _*2 a p _ _*2

+(b \nnc + 0,416b "c )hncm2 —^hnV „ —^V p —^hncVnn

2 2 2

0 = (0,55b' c + B^nnc)hncmmc - b (hncK9 + b K10 -K11 -hncKl2) + b„c + (e"„„ + 0,55e"c)hnMnrw

M, = 8, - B\hnK5 + K6 - K7 - hKj; M2 = 0,416? + B„; M3 = 0,416^;i + Bm;

C7 = 0,55? + B «nn; C8 = 0,55e" + B; C9 = hncK9 + b'ri0 - R11 -hnCRu;

e

0

К = m +w,m2 ;

1 '1 '2 плс ' 3 плс'

К =w'+w'm +w[m2 ;

2 '1 '2 плс t 3 плс'

К = V» +W* m +w, m2

3 T 4 '5 ппс t 6 ппс

К =w[+w[m +w[m2 ;

4 '4 '5 ппс t 6 ппс'

К5 =Vi +V2m„, +V3ml;

К 6 =wl+v2mm +v3 <

K7 =v{ +v'5 mm т2^;

К 8 =wl +V'5 mnn +V'6

у = 1,5Е4 + 0,143Е7 -0,727Е5,5 - 1,6Е2,5 + Е; у2 = 1,454Е5,5 - 0,286Е7 -2,5Е4 + 1,6Е; у3 = 0,143Е7 -0,727Е5,5 + Е4; у4 = 1,5(Вр)4 - 1,6(Вр)2,5 -0,727(Вр)5,5 + 0,143(Вр)7 + Вр; у5 = 1,6(Вр)2,5 -2,5(Вр)4 + 1,454(Вр)5,5 -0,286(Вр)7; у = 0,143(ёр)7 + (вр)4 -0,727(вр)5'5; у7 = Е - 0,8Е2,5 + 0,25Е4; у8 = 0,8Е2,5 -0,25Е4;

— —2,5 — 4

= бр - 0,8бр + 0,25бр ;

— 2,5 — 4

у/10 = 0,8бр - 0,25бр ; £ = (l - еЛ; m = U U m = U /U-, m = U Uр; m = U U

\ / плс плс l рс' ппс ппс I рс' пл пл / р' пп пп/

At the end of large vortex zone

K 9 =w7 +v»m„c; Kio =v7+v'mn,c; Kii =w9 +Viomn„c;

К12 =¥1+<тппс' К13 = ¥' '

Ki4 =v'7+v'm„,; Кis =w9 +Viomn„; Ki6 =^'+^i'om»».

у' = 1,5(Вр)4 - 1,6(Вр)2,5 - 0,727(Вр)5,5 + 0,143(Вр)7 + Вр;

у/' = 1,6(Вр)2,5 -2,5(Вр)4 + 1,454(Вр)5,5 -0,286(Вр)7;

у' = 0,143(Вр)7 + (Вр)4 - 0,727(Вр)5'5;

у' = 1,5Е4 + 0,143Е7 -0,727Е5,5 - 1,6Е2,5 + Е;

у' = 1,454Е5,5 -0,286Е7 -2,5Е4 + 1,6Е2,5;

у' = 0,143Е7 -0,727Е5,5 + Е4;

= Bp - 0,8(Вр)2,5 + 0,25(Вр)4; у'= 0,8(Вр)2,5 - 0,25(Вр)4; у' = Е - 0,8Е2,5 + 0,25Е4; < = 0,8Е2,5 -0,25Е4;

„ й =

р „ h

X B KB'

-- -- . я =_Ш!_Ш . =

ь

ял. £ = j* .

h ' в'

L" —

U„ = Uo; U = V ; U = V ; — = = L" ; X = I";

p po ' nn nn' m. Wl ' ~ 8 ' 8 '

B0 80

K = K; ^p = ^p,; ^ = vJuPi; = vJut*; (n)

= h Jh ; e = 0 ; B = - 8 ; B = 0 ; e" = Bnn - B

n6 / pc ' am ' n ' Ann ' n

Taking into consideration boundary conditions and from the flow momentum conservation equation we get the relationship for determining the length of the large vortex zone

U2

L" = -

Д'__PLC

у2 10

a t

hnv: +

apV' ahm

(12)

-V "

where

C10 = 0,416(BM - Bn )hnml6 + b, -

-b' (HniK5 + K6 - K7 - HntKJ + 0,416(Bnn - Bn )hp(m2nni

= (0,416b'chnc + hncB„n,c)m2mc + b„c -

-b' (hncK1 + b'K2 - K3 - hncK4) + (b\nnc + 0,416b "c )hncm2nicc m = U /U-; m = U IUP .

mc mc j pc ' nnc nnc / pc

As seen from the obtained equations, there are three unknowns in them, mra, mnn, and Up, therefore the task stays undetermined to some extent.

In order to get over the difficulty, gradual approximation method is proposed to solve the task.

1) With the assumption, that both floodplains have the same roughness nm = nnn = nn velocity is determined at right plain (where roughness is smaller, pic 1) from the relationship (11).

2) The velocity at the left floodplain is determined from (10).

3) From the discharge consistency condition (8) at constrained section and design section lines (the parity of right and left parts of the equation must be carried out), Ura is specified. It is obvious if n >n orX >X , then U <U or vice-versa n >n orX >

m nn m nn' nn nn nn m nn

X , then^ <U .

nn' nn nn

4) With the condition that n = n = n and from (12), ini' nn nn n \ / '

tially the length of the large vortex zone is determined for smaller value of X, and the length of small vortex zone is determined for the larger value of X.

5) The length of the large vortex zone is specified by (12).

Conclusion

1) The obtained relationships allow for determination of velocity fields, which lets to forecast possible channel and floodplain reformations after erecting structures.

2) Kinematic and geometric flow parameters depend on velocity fields in initial cross-section, relative velocities in floodplains, roughness, floodplain and riverbank morphometry, riverbank and flood-plain flow interaction zone parameters, transverse dam parameters.

3) Knowing the lengths of vortex zones, we can set distances between structure in the system.

References:

1. Барышников Н. Б. Морфология, гидрология и гидравлика пойм. Л., Гидрометеоиздат, - 1984, - 280 с.

2. Абдул Карим С. Ш. Закономерности растекания потока за поперечной дамбой на реках с щирокой поймой ТИИИМСХ. -Ташкент, - 1991.

The spectral characteristics of the new functional materials based on a single device spatial field

3. Бакиев М. Р., Хайитов Х. О растекании потока за глухой пойменной дамбой с учетом частичного освоения междамбного пространства. - № 3/4 ВестникТашИТТ. - 2007. - 34-39 с.

4. Rajaratnam N., Ahmadi R., Hydraulics of channels with flood-plains. Journalofhydraulicresearch. - Voc. 9, - 1981, - № 1. - P. 43-60.

5. Бакиев М. Р. Совершенствование конструкций, методов расчетного обоснования и проектирование регуляционных сооружений. Автореферат. докт.диссер. - М., - 1992, - 57 с.

6. Абрамович Г. Н. Теория турбулентных струй. - М., Физматгиз, - 1960, - 716 с.

DOI: http://dx.doi.org/10.20534/ESR-17-1.2-199-201

Kurbanov Janibek.Fayzullayevich, Tashkent Institute of Railway Transport Engineering Senior Research Fellow — Competitor of the Department "Electrical connection and radio", E-mail: [email protected]

The spectral characteristics of the new functional materials based on a single device spatial field

Abstract: This article is devoted to the theory of a single spatial field, the objective existence of which is established on the basis of the interaction of electrical, magnetic and gravitational forces has been developed multifunction installation of a single spatial field.

Keywords: devices, magnetic fields, electric fields, gravitational fields.

The aim of this work is the analysis of the experimental data on the basis of a single device of the spatial field (SDSF), and identifying opportunities for its use for new functional materials [1, 75].

Dispersion of solids (dry milling) into a special branch of science of technology. It deals with the mechanical strength required for the destruction of the structure and the structure of solids, as well as research and design of crushers, mills and similar facilities for rational grinding [2, 212].

Results grinding evaluate changes grading curve, an increase in the specific surface of the material.

The quality of these units is evaluated by comparing required to create new surface energy and operating costs. Resulting in the production of artificial stone, the quality of the structure of materials require optimal fineness.

Dispersion solids — of grinding to small particles is carried out

to enhance the rate of heterogeneous processes. In the process of dispersing discernible two main stages: the destruction of the particles by an external force and aggregation of particles such as spontaneous or caused by external compressive and tensile forces [3, 143].

Along with dispersing and aggregation during milling changes the crystal structure and energy state of the surface layers of particles. Their study presents grinding.

Due to the high cost and energy intensive fine grinding using the existing facilities have been designed with the device SDSF allowing dispersion material dispersion 500 microns to 1,5 microns.

The device is a single spatial field, based on the four fundamental interactions, and thus on the interactions of four types of fields: gravitational, electromagnetic, magnetostatic, electric (Fig.1).

External fields create compressive or tensile forces that result in fracture and particulate materials [4, 11].

Figure1. Industrial plant SDSF