CC BY
14
Sharipov Kungrat Avezimbetovich, DSc., in technics, Rector of Turin Tashkent Polytechnic University, E-mail: K.sharipov@polito.uz Khalikova Nargiza Abduvalievna, Assistant, of the department "Tractors and cars" Tashkent Institute of Irrigation and Agricultural Mechanization
(Republic of Uzbekistan)
ESTABLISHING PATTERNS OF FLOW OF A VISCOUS FLUID ON THE LATERAL SURFACE OF THE ROTATING CONE
Abstract: The article considers the movement of the mixture - the motor oil and the acetone. The velocity distribution of the mixture, the densities in the analytical form in the constant temperature are also given.
Keywords: rotary drum, distribution plate, mixture, the interaction of particles, interpenetration of particles, viscosity, turbulent flow, laminar flow, repulsive particles
Introduction. In this paper, the problem of a cur- influence of centrifugal force moves along the lateral sur-rent of viscous liquid on the surface of a rotating cone is face, forming a liquid film thickness S(r) [2, 50, 51]. The
considered, dependences of a flow rate on technological parameters of tapered plates in a laminar and turbulent flow of liquid are established. The setup for receiving up to 83% of clarification of waste engine oil by a method of the selection clarification with acetone addition is developed. Regeneration of the used engine oil of farm vehicles is multi-stage process consisting of a filtration from different kind of impurity. Purification of the used oil can be carried out by manufacturer where the gathered liquid is obtained and at the small enterprises using small installations for cleaning. Quality of the cleared product and costs of process directly depend on a method and conditions of cleaning that should not be too complicated and high cost for realization of this process in the small enterprises. Therefore, the research of efficient ways of purification of the used oil is one of the urgent problems [1, 86, 88].
Results and discussion. In order to establish patterns of fluid flow we consider the flow of a viscous fluid on the surface ofthe rotating cone, simulating turning over a thin boundary layer of a viscous fluid. It is assumed that the flow axis of the symmetric and stationary, and the cone radius R0 - located perpendicular to the axis - OZ.
The flow of the liquid jet is incident on the vertex of the cone and spread over the surface of a rotating surface with a constant angular speed, which is under the
height of the cone is: h << Rg.
Then the equation of motion of the fluid in the border zone has the form:
^T + PfTG)2 = 0 (1)
dz
where, t - the shear stress oflaminar and turbulent viscosity of the mixture, which depend on the intensity of the flow coming from the surface roughness of the cone, and interaction forces dispersed phase mixture [3. 102,103]. pf - density of fluid and is the angular speed. The total shear stress of laminar or turbulent motion of the mixture can be written as:
(2)
T=T +Tt >
T =
dV
^ m
dZ
, T = Pml2
dVm
m
dZ
V
(3)
where /m - the dynamic viscosity ofthe dispersed mixture; Pm - the density of an incompressible fluid; l - the mixing length of turbulent flow; Vm - the average flow velocity of the particles. To determine the distribution of the axial velocity, we have the following boundary conditions, taking into account changes in the Reynolds number:
Re =
v
ESTABLISHING PATTERNS OF FLOW OF A VISCOUS FLUID ON THE LATERAL SURFACE OF THE ROTATING CONE
It should be noted that the flow can be incompressible laminar, turbulent-laminar (transition zone), and turbulent.
On a free surface at
z = 6(r), U = 0, uf (0) = 0, u (0) = 0. (4) dz f
For laminar flow at l = 0, we have the equation for
the velocity
dV 2 n
j—- + prrn = 0. dz
The solution to this problem with initial and boundary conditions (4) has the form
Vf = Pœ2
2
62 (z )--V ; 2
(5)
Consumption ofwater with dissolved mixtures in the border zone in the laminar regime is determined by the formula:
6 V 2nr2 a2 63 (r)
Q = 2n I udz =-—
J 3$
Hence, the expression is defined to determine the thickness of the boundary layer [1]:
8(r ) = ■
3SQ |2nR0V
• r
(6)
The case ofweak turbulized mode of motion between rotating propellers. The flow of the liquid jet is incident on the vertex of the cone and spread over the surface of a rotating surface with a constant angular velocity, which is under the influence of centrifugal force moves along the lateral surface, forming a liquid film thickness. The height of the cone h << R0.
Flowing along the lateral surface of the cone and the propellers stir the turbulent zone is created. The length of the mixing can be identified by the Prandtl formula as follows:
l = x(6(r)-z) (7)
where 6 (r) - the thickness of the border zone of the rotating cone
X - coefficient of Karman, and defined by the formula:
x = K0F0 where F0 =
l
fl + f % qi
fi + f2
Here q1,q2 - flow rate of incoming mixture into conical surface.
f1, f2 - the concentration of acetone and motor oil.
The equation of motion (1) taking into account the length of the mixing (7) can be written as.
d dz
Z (6(r)-z))
2 f dv_
dz
2
+ a> r = 0.
Integrating over and using the boundary conditions (4) we get:
dV
œ2r
1
dz \ %2 a/6(r) - z Hence we have an expression for the velocity distribution of fluid flow:
V = 2.
œ2n
6 (r )
- 2.
\m2r
(6 (r )-z )
(8)
V X \ X
We define a second flow rate within the border zone
with a thickness of b (r) from the equation:
6 (r )
Q = 2nr | Vdz
0
Using the expression for the velocity and calculating the integral, we find the flow of the liquid mixture in the film:
Q - 2ln Q -T\
(r6 (r )))
2nl v2R6
X
Q _ 2nla>R3 3Z
4r3Ö3(r); Q =
3
3Q
X
v 2nlo>Rl j
= r6 (r ).
Find the thickness of the carnival of film:
6 (r ) = -
r V
' 3QmX^% 2nla>R3 j
(9)
These expressions correspond to the transition zone from laminar to turbulent zone.
Consider a turbulent flow between the two propellers at high Reynolds numbers when Re > 105. The case of strong turbulized flow. Then, it is advisable to apply for a mixing-length formula L. A. Satkeevicha [3], ie:
K = xJz ( (r )-z ).
Then we have the following expression for the shear stress at a given formula (2):
r = PX2z (6(r)-z))
dV dz
2
And the equation of motion of the dispersed mixture will be:
d dz
p x2 z (6 (r)- z) dV
2
+ rn2r Px = 0.
Integrating with respect to the resulting equation with the boundary conditions (5) we obtain the expres-
sion for the velocity distribution in a strongly turbi lizovannoy area and we have:
■sir
Where z = — ; v =_ - the dimensionless pa
R
V0
rameters.
Also, integration by taking into account the boundary conditions we have:
y = 1 ^kjarctgl-^- (10)
n x (r)-z
Now we define a flow rate of the mixture in the border area for the consideration of turbulent models:
6 (r )
Q = 2nr J
(oRn
X
-arctg
6 (r )-
-z ■ dz =
2nR0air
4T6(P t J arctg
■ dz
x o i6(r)-z
Integrating the last equation by parts we obtain an expression for the mixture flow rate in the border zone:
^ 2nmRn Where Q =-0
X
r 32106 (r); rAe Io =n. (11)
How do we find the change in surface tension of the liquid in the form:
6(r)= XoQQF^ r (12)
4
The equations obtained in the border zone of the
surface at different flow regimes is the degree of compres-
_2/
sion of the surface tension in the form (12), 6 (r)« r /3 , in the transition zone, 6 (r)« r-1, and in much turbu-
lized zone surface tension has a value of: 6 (r)« r 32.
Calculations show that the laminar compression of the surface tension will be weaker than in the turbulent regime, so that the turbulence of the flow between the propellers significantly affects the process flow. Conclusion
One of methods of refining oil from oxidizing products on places of utilization is application of the selective methods that can be used in economic conditions and without requirement of composite cars and mechanisms. At the same time, it is possible to use an acetone, a methanol and furfurol as a solvent material.
The analysis of oil refining technology showed that for cleaning oil with the PU0M-100 setup the selective solvents can be used at the final stage of refining.
References:
1. 2.
3.
4.
Ahmad Jonidi Jafari, Malek Hassanpour, Resources, Conservation and Recycling, 103, October - 2015.- P. 179-191. Prudnikov A. P., Brichkov Yu. A., Marichev O. I. Integrals and series, Moscow, Nauka - 1985.- 800 p. Khamidov A. A. Plane axially symmetric problem of stream flow ideal uncompressed liquid.- Tashkent: Fan,-1978.
Khamidov A. A., Khudaykulov S. I. Stream theory of multiphase viscous fluid. Tashkent,- 2003.
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