Comparisons the numerical results of the turbulence model for the problem of rotating tubes inside a dynamic hydrocyclone

Scientific research results in pandemic conditions (COVID-19)

37

Nazarov Farrux. Institute of Mechanics and Seismic Stability of Structures

of the Republic of Uzbekistan.

Fardayev Jonibek, Navoi State Mining Institute of the Republic of

Uzbekistan.

COMPARISONS THE NUMERICAL RESULTS OF THE TURBULENCE MODEL

FOR THE PROBLEM OF ROTATING TUBES INSIDE A DYNAMIC

HYDROCYCLONE

F. Nazarov, J. Fardayev.

Abstract: The article provides a comparative analysis of turbulence

models by numerically simulating a swirling flow inside a rotatable pipe. To
solve this problem, the Reynolds averaged non-stationary Navier-Stokes
equations in a cylindrical coordinate system were used. To find the Reynolds
voltage, the turbulence model was used the most popular semi-empirical
turbulence model. Comparison is made between models of different
approaches to turbulence SSG / LRR-RSM-w2012 and νt-92. The numerical
results obtained on the basis of turbulence models are compared with the
well-known experimental results of Reich and Beer (1989).

Keywords: swirling flows, Reynolds averaged Navier-Stokes equations,

model SSG / LRR-RSM-w2012, model νt-92.

Introduction. Known as a multiphase separator with high separation

efficiency, small space requirement, and low energy consumption,
hydrocyclone is gradually replacing the conventional vessel separator in the
petroleum industry, and has been popularized to various fields [1].
However, the swirling flow in a conventional hydrocyclone is established by
a tangential inlet, so the swirl intensity is closely related to the inlet pressure
or flow rate. Thus the conventional hydrocyclone is handicapped by some
inherent limits such as the necessity to have a high pressure inlet to get
sufficient acceleration field and the loss of efficiency at low flow rate.
Considering these drawbacks of conventional hydrocyclones, dynamic
hydrocyclone (DH) was developed by TOTAL CFP and NEYRTEC [2]. The
structure diagram of oil-water DH is shown in Figure 1, the main difference
against static hydrocyclone is that fluid enters DH from an axial inlet, and is
rotated by synchronous rotating blades and pipe (separation chamber wall)
driven by a motor. Under the centrifugal force produced by swirling flow,
lighter phase migrates towards the centerline then exits from overflow
outlet and heavier phase moves towards the wall then exits from the
underflow outlet. The performance of DH has been investigated by several
researchers [3]. the results showed that DH can remove smaller oil droplets
from water and can operates efficiently at lower inlet pressures compared
with conventional hydrocyclones.

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38

Fig. 1: Diagram of dynamic hydrocyclone.
1 - Inlet; 2 - Motor; 3 - Mechanical seal; 4 - Bearing; 5 - Blades; 6-

Rotating pipe; 7 - Overflow outlet; 8 - Underflow outlet.

Statement of the problem. For numerical simulation of the turbulent

flow of an incompressible fluid, the Reynolds equations were used [4]:



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.

)

(

1

,

0

i

i

j

i

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j

i

i

i

i

i

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i

i

x

x

V

x

V

x

x

p

x

V

V

t

V

x

V









(1)

The system of Navier-Stokes equations averaged by Reynolds (1) is

open. For closure in methods, the linear and nonlinear Boussinesq
hypothesis is used.

Modeling turbulence. To describe the turbulent flow, the Reynolds-

Averaged Navier-Stokes Equations (RANS) averaged according to the
Reynolds equations are used. This system of equations is open, because It
contains additional unknown components, the so-called Reynolds stresses.
Therefore, all models that are aimed at closing this system are called RANS
turbulence models. There are two approaches to finding Reynolds stresses.
The first approach is linear (the Bussensk hypothesis is used). A striking
representative of such models can be considered the Secundov νt-92 model.





.

))

(

(

)

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)

(

)

(

0

1

0

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j

v

v

j

t

j

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x

C

C

x

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C

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P

x

u

t



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

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

















(2)

The remaining functions and constants are presented in [5].
This model uses one equation for turbulent viscosity. Therefore, it is

called a one-parameter model. The second nonlinear approach. A typical
representative of the nonlinear RANS model is the various Reynolds stress
models. The representative from this class of models is the SSG / LRR-RSM
model. This is a Reynolds stress model with a second moment of mixed SSG
/ LRR that uses the ω equation for a length scale equation. The second
moment Reynolds calculates each of the 6 Reynolds stresses directly (the
Reynolds stress tensor is symmetric, so there are 6 independent terms).

Scientific research results in pandemic conditions (COVID-19)

39

Each Reynolds stress has its own transport equation. There is also a seventh
transfer equation for the scale variable. This model is currently mainly used
where conventional RANS models are not able to describe complex
anisotropic turbulent flows.

































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













 









































.

1

2

,

2

j

j

d

k

k

kk

k

k

ij

ij

ij

ij

k

ij

k

ij

x

x

k

x

k

x

B

P

k

a

x

U

t

D

P

x

R

U

t

R































(3)

The remaining terms and constants are presented in the article [6].
The aim of this work is to test and compare their numerical results with

the linear RANS model νt-92 and the nonlinear SSG / LRR-RSM-w2012
model. To analyze

Fig. 2. Axial velocity profile in a rotating pipe
these models, the experimentally well-studied flow of a strongly

swirling turbulent flow in a channel with sudden expansion is considered.

Study results. The numerical result was compared with experimental

data [7]. In fig. 2-3, we compare the resulting axial and tangential velocity
profiles.

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40

Fig. 3. Tangential velocity profile in a rotating pipe

Conclusions. The results obtained and their comparison with

experimental data show that all the two approaches considered as a whole
show good results. However, the closest results were obtained using the SSG
/ LRR-RSM model. The results for the νt-92 model are slightly worse.
Therefore, given that it is a practical model, it can be recommended for use
in engineering tasks where strong rotation of the flow occurs.

References:

1.

Papoulias D., Lo, S. 2015, Advances in CFD Modelling of Multiphase

Flows in Cyclone Separators. Chemical Engineering Transactions, 43, 1603–
1608.

2.

Gay J.C., Triponey G., Bezard C., Schummer P., 1987, Rotary cyclone will

improve oily water treatment and reduce space requirement/weight on
offshore platforms, In Offshore Europe. Society of Petroleum Engineers,
Aberdeen, UK.

3.

Chen J.W., Hou J., Li G., Xu C., Zheng B., 2015, The Effect of Pressure

Parameters of a Novel Dynamic Hydrocyclone on the Separation Efficiency
and Split Ratio, Separation Science and Technology, 506, 781-787.

4.

Loytsyansky L.G. Fluid and gas mechanics // Maskva. Science, 1987.-

678 p.

5.

Shur, M., Strelets, M., Zaikov, L., Gulyaev, A., Kozlov, V., Secundov, A.,

"Comparative Numerical Testing of One- and Two-Equation Turbulence

Scientific research results in pandemic conditions (COVID-19)

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Models for Flows with Separation and Reattachment." // AIAA Paper 95-
0863, January 1995.

6.

Wallin S., Johansson А.V. An explicit algebraic Reynolds stress model

for incompressible and compressible turbulent flows // Journal of Fluid
Mechanics 2000 89-132.

7.

Reich G., Beer H., 1989, Fluid flow and heat transfer in an axially

rotating pipe-I. effect of rotation on turbulent pipe flow, International
Journal of Heat & Mass Transfer, 32, 551-562.