CC BY
3
Section 7. Technical sciences
Arifjanov Aybek, Doctor of Technical Sciences, Professor Rakhimov Qudratjon, senior teacher, Abduraimova Dilbar, Assistant of professor Tashkent Institute of Irrigation and Agricultural Mechanization Engineers
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HYDRAULIC PARAMETERS OF THE VEINSING FLOW IN HYDRO TRANSPORT
Abstract: In article offers the New methods of the determination hydraulic parameter and critical velocity alluvium flow.
Keyword: Hydra transport. Alluvium flow. Concentration hydraulic friction factor. Hydraulic dimensions critical velocity.
Hydro-transport is characterized by a joint movement of liquid and solid particles, which in the mixture form two or multiphase flows different in physical-mechanical properties. One of the main tasks of hydro-transport is to study the throughput capacity of pipelines, where taking into account the distribution of their concentration along the section of the pipeline formed under the action of gravitational force is of great importance in describing the nature of the two-phase flow.
The pressure-weighted flows in hydro-transport systems are usually characterized by high volumetric concentrations and wide ranges of particle sizes and densities. The weighted flows are more complex in structure than the turbulent flows of homogeneous liquids in the pipes. Therefore, the methods for calculating these flows are much more complicated than the usual methods of hydraulics for pressure flows of homogeneous liquids.
The differential equations of one-dimensional motion of a two-phase mixture in a cylindrical coordinate system can be written in this form [1; 2; 3]:
f dl = HJL d
J n
dz r r
fd-l = 0
J n ^
dr f® = 0
dp dp
rf^
n
r
J f dUn.
r2 n
+ K (U2n - Un ) + PnFn
(1)
dp
there —, — and — - pressure drop across the axes;
dr dç dz
unr, unv and unz - components of the vector velocity of each phase;
f - distribution of the concentration of each phase; xn - viscosity coefficient of the phases;
F„,, Frv, Fnz - projections of mass forces;
K - coefficient force of interaction between phases. From the last two equations (1) obtained:
dr
= 0,
= 0
According to this the pressure drop is a function of the z coordinate and it does not depend on r and f, ie:
dp _ dp dz dz
HYDRAULIC PARAMETERS OF THE VEINSING FLOW IN HYDRO TRANSPORT
To differential equations of motion (1) we add the relation concentrations of phases
f + f = 1 (2) boundary adherence conditions for r = R:
U=0 (3)
and the symmetry condition along the vertical axis (y), i. e. at f = 90 ° and
I S-J'l Î
(4)
pressed as [2; 5]:
KP^2_ P2 - P1 • Snd
„„„„ du, „ du2 (p= 270 —1 = 0, —2 = 0 dç dç
The distribution ofconcentration is exi
f2 = f20 eXP
3(Pr -P)g - 3 p
' 2 0PC0 Prui 2
s,w;
(R + rsinç) (5)
It is seen from the differential equation of motion (1) that the velocity of phase of the mixture depends on distribution of concentration^ and interaction coefficient K. At the same time these parameters depend on distribution of velocities of the mixture.
With using well-known methods of hydromechanics [1; 4; 5], with adding the equation (1) term by term for each phase, we obtain the equation of motion of the slurry, with those for concentration of the second phase being taken f2 = s.
With integrating all the parts of equation with cross-sectional area of the flow, for the steady-state flow in a one-dimensional formulation from Eq. (1), we have the following [1; 2; 4]:
2
(6)
dP _ . XmpQ2__
dz 2d©2 0
snd a
With generalizing equation of motion for the density and velocity of the slurry (dispersoid), the following value was adopted:
p= (1 - s)p! + sp2 (7)
& = (1 - S)Pl^l + p2 (g)
(1 - s)Pi + SP2
there: s - volume concentration of solid components; p1 u p2 - density of liquid and solid particles; Q - consumption slurry; a - area of cross-sectional pipeline; S1 and S2 - averaged velocities of the liquid and the solid particle over the cross section of the pipeline; i - slope of the stream; P - hydrodynamic pressure; x - perimeter of the pipeline; t0 - initial resistance of the mixture; - coefficient of hydraulic friction.
Colculating equation (6) with taking account of boundary conditions (for z=0 P=P1 and for z=L, P=P2) one can obtain:
2d©'
■Q ' =-
T +P&- «0 L ©
(9)
Flow rate is determined by the expression:
_ 2d©2 (p - P2 . snd \
Q --{kA^™ "^J (10)
There P - P2 =AP - pressure drop which created by the pumping system. For i = 0:
^ 2d©2 f AP snd
Q =4 TP fx- ©
(11)
The condition, which the mixture begins to move can write as:
P - P2 s
1 2 >-T
L R 0 (12)
Consequently, it is necessary to create a difference of
s
pressure AP, which would exceed the value —t0 .
With a suspended flow in pipelines with a negative slope i < 0, we have:
_ /2d©2 f p - P2 . snd )
Q = Ah—-pgi--T0 I (13)
PK L ©J
Thus the condition, which the mixture begins to move one can write as:
P - P2 . s
—-- > pgi + —t0
LR0
(14)
The maintance of the approach is that, here the influence of the slope of the pipeline is taken into account additionnaly to the main factors which characterizing the movement of the suspended flow:
Ap >pgi + sTo. (15)
R
The regularity of distribution of the concentration of solid particles along the vertical diameter of a cylindrical tube depends on average speed of flow.
With a gradual decreasing of this speed approaching the critical, the weighting capacity of a stream containing a predetermined amount of solid material decreases continuously, which leads to complete siltation of the pipelines, saturation ofthe lower layers ofthe stream with solid particles, and reaches an almost maximum value [1; 2].
In average spped of mudflow which less than UKp, the weighing capacity of the stream decreases accordingly, and the solid particles in the stream are gradually precipitate.
Thus, the critical regime of hydro-transportation - boundary regime of the movement of slurry
through pipes. In this regime must be satisfied, the maximum dynamic equilibrium between the mixture as a whole and the continuous flow of solid particles.
Consider the condition that determines the limiting dynamic equilibrium between the moving layer of solid particles and the flow as a whole on the basis of the following considerations: Let and be the average tangential stress on the bottom wall of the pipe and the voltage of the average frictional force of sliding of the solid material. With an increase in the average flow velocity above critical, an increasing number of solids are entrained in the flow and in these regimes always rl >ta . This corresponds to clearly stable
modes of hydrotransportation.
Thus, the only condition that defines the limit regime is as follows:
T0 =TM (16)
It expresses the ultimate dynamic equilibrium between the weighted flow as a whole and the continuous flow of solid particles moving in the pipeline.
Denoting through S2 the average velocity of the motion of the slurry, for t> we have:
T0 =Po
w
(17)
At certain speeds, it is possible to fully weigh solid particles of a certain size, which we call the optimum diameter. In the works [1; 2]. The following dependence was proposed for determining the optimum diameter as a function of the flow velocity:
d0 =
18-v
dP
Po g dz
g (Pi - Po)
(18)
From the analysis of works it is known, that existing average speed in the flow which particles of a given hydraulic size begin to be transported with the speed of carrier fluid.
Thus, | — ] the partial gradient ofpressure must be
V dz J:@
determined from the condition of a stable regime of movement of the slurry in the pipeline.
Then, according to (4), |
as follows:
there,
w = K
j
equation will define
(19)
d2 • gp2 -Pl) Pi
(20)
w - hydraulic size of suspended particles.
K- coefficient which depends to the regime of motion of a solid particle in the liquid flow and it determined by the formulas [2; 4].
Thus, with bringinging (5) and (3) to (7) for the determination of the critical speed, we obtain:
=
2gDw
p0 A
(21)
Thus, a new relationship is proposed for determining the critical speed of the slurry in the suction pipe. Differing from the equation (7) there are taken into account a number of factors which characterizing hydro-transport of river sediments. Analysis of this formula is significant and it can be recommended for practical use on the basis of specially set experiments.
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1. 2.
3.
4.
5.
6.
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Arifjanov A. M. Hydraulics. - Tashkent, - 2005. - 110 p.
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