CC BY
11
UDC 532.527
R. R. Usmanova, G. E. Zaikov DETERMINATION OF THE DYNAMIC AND INTEGRAL CHARACTERISTICS SCRUBBER WITH GENERATION OF MODELS IN THE PROGRAM ANSYS
Keywords: lines of current, gas cleaning, scrubber, hydrodynamic model, pressure drop, swirling flow.
Been developed and analyzed hydrodynamic model swirled flows of gas. The algorithm of the calculation of hydraulic resistance, it takes into account specific features of the device. Conducted researches provide an opportunity to predict aerohydrodynamic characteristics of the device at the design stage. This will provide an opportunity to provide constructive solutions to these individual units of the apparatus, which will lead to a significant increase in the efficiency of gas cleaning.
Ключевые слова: линии тока, газоочистка, скруббер, гидродинамическая модель, потери давления, закрутка потока.
Разработан алгоритм расчета гидравлического сопротивления, учитывающий специфические особенности газопромывателя. Проведенные исследования позволят спрогнозировать аэрогидродинамические характеристики устройства еще на стадии проектирования. Это даст возможность предусмотреть такие конструктивные решения отдельных узлов аппарата, которые приведут к значительному повышению эффективности газоочистки.
1. Current state of a problem
Vortex gas flow is a complex form of movement is entirely dependent on the design parameters are tightening devices. These devices determine the aerodynamic characteristics and flow chambers: the degree of twist, hydraulic resistance, structure and uneven speed, features recirculation zones, injection capacity, turbulence intensity. Possibility of a tangential inlet gas into the unit and the formation of internal swirling flows are extremely diverse. However, despite the differences of known devices in design, size and purpose, formed in these gas streams have common patterns.
Currently used mathematical models of gas purification formed on simplified theoretical concepts of gas flow. They are not sufficiently take into account the operational and design parameters of gas cleaning devices, as well as aero-hydrodynamic properties of gas-dispersed flows. These models can not be used to search for the best options of integrated gas cleaning systems, as they show the properties of objects in a narrow range of parameters. We need more complete and appropriate mathematical models based on the study of the aerodynamics of gas and taking place in these events.
The use of computer technology and software to compute the hydrodynamic characteristics of eddy currents during the development and design of industrial devices. This avoids the need for costly field tests of gas purification apparatus.
Software suite is a modern ANSYS-14/CFX-modeling tool, based on the numerical solution of the equations of hydrodynamics [1, 2]. Hydrodynamic calculation makes it possible to determine the flow resistance of the device and to predict the efficiency of the separation process in the design stage.
2. Statement of the problem
Mathematical modeling is always based on some physical hypothesis that simplifies considered real objects. At this stage of the development of mathematics is possible not only to describe the physical model in the form of equations and additional conditions, but also to solve. For the formulation of the problem of modeling and
the subsequent investigation of the processes occurring in the vortex of centrifugal machines, you need to define the relationship between the parameters of the device is twisted and formed them flow.
In studies of vortex centrifugal devices primarily include spatial flow. Similarly it is conducted in models based on the hypothesis of a plane vortex. Motion of the gas is described by the Navier-Stokes equations. The equation is introduced with the closure of the fluctuating components of the hypothesis on the path of displacement. The values of the tangential and radial velocity are taken close to each other. Axial velocity is very small. Exclusion from consideration of the axial movement of the gas is greatly reduced, the (idealized). This is not consistent with the physical picture, in which a large place occupied by forward and backward axial currents. The results of these studies are of interest to determine the effects of the vortex flow asymmetry with respect to the axis of the camera.
Numerical analysis of the gas inside the dynamic scrubber reduces to solving the Navier-Stokes equations [3]. For the solution of equations of Navier-Stokes equations with a standard (k-e)-tuibulence model. To find the scalar parameters k and e are two additional model equations containing empirical constants [4, 5, 6]. The computational grid was built in the grid generator ANSYS ICEM CFD. The grid consists of 1247 542 elements. The grid was constructed on a uniform and non-uniform radius along the axial coordinate. Unevenness wondered law exponentially decreasing to the exhaust pipe and increasing the bottom unit. Denominators geometric progressions were chosen so that in the high-velocity gradient mesh was thick as possible. On solid walls slip conditions from which is vorticity. On the input and output sections of laws of changing the current function, on the axis of the unit gradient target variable - constant. Conical part determine the boundary conditions and restrictions on the size of the computational grid, ie the reduction of radius corresponds to a decrease of the boundary node.
General view of the computational domain is shown in Figure 1.
<
Fig. 1 - General view of the computational domain
3. Analysis of the results
During the flow of gas and dust in a dynamic scrubber is complex. This is explained by the fact that in the central part of the device is vane swirler. Analysis of fluid flow and distribution of deposited particles in a dynamic scrubber showed that the presence of turbulent diffusion particles concentrate at the vessel wall is not a thick layer, and in the form of gas and dust loosened concentrated layer.
In this case, the dust is localized in the annular wall layer of a certain thickness in a spiral of dust accumulations in the form of bundles. Initiated the formation of helical bundles is dusty swirl vane. With the passage of dust in vane curved channel is the concentration of particles in the peripheral zone of the channel. Thus, after the passage of a uniform flow swirler vane is divided into a number of parallel streams with alternating then small, the large concentration of dust. The thickness and density of the boundary layer depends on the gas velocity, the angle of twist, the character input stream to a dynamic scrubber. Higher speeds may reduce the thickness of the boundary layer, in spite of increasing the role of turbulent diffusion (Figure 2).
Reducing the length of the inlet pipe reduces the eccentricity of the axis of rotation of the gas flow from the geometrical axis of the apparatus. Even in this case, the center of the rotational flow does not coincide completely with the geometric axis of the machine. There is some minor eccentricity, the value of which does not exceed 68% of the radius of the device. The presence of such eccentricity swirling flow, there are also researchers [8].
Fig. 2 - The flow pattern of gas and dust in the dynamic flow scrubber
Given that the eccentricity of the machine is small, and in its central part of the irrigation device, we consider for a gas flow as symmetric about the axis of the machine.
4. Output calculation formulas
Aerodynamics of the apparatus were conducted in the range of the Reynolds number changes from 3, 5' 104 to 15' 104. This corresponded to an average of 5 to 25 m/s. The degree of spin flow was constant at £=1,5.
A large study focused on determination of the resistance unit and study of the effect of dynamic geometry scrubber on the energy characteristics A P and 4 [7, 8]. Resistance scrubber is calculated by the total pressure drop at the entrance to the unit and to exit. In our case, we write the Bernoulli equation for incompressible gas in the form of:
P-
«kW2
2
+ Pi +PggZi =Pc
«Ä + P2 + AP 22
(1)
where z - the distance between the sections; Pi, P2 -Static pressure, Pa; W1, W2 - the average flow velocity in the annulus and in the exhaust pipe; a k - Coriolis coefficient taking into account the non-uniformity of the velocity distribution in the cross section. Ratio is the ratio of the true kinetic energy to kinetic energy of the flow, calculated at the average rate (for the turbulent regime of motion take a =1,05^1,10). Knowing AP, we can calculate the coefficient of hydraulic resistance, referred to the conditional mean in terms of the speed machine W0.
Co
2AP
(2)
Hydraulic resistance of centrifugal machines are generally viewed as the local resistance. Hydraulic resistance coefficient, pressure losses in the unit determined experimentally and are mainly as a function of the geometry and the Reynolds number [9].
In [10], an approach to the calculation of flow resistance as the sum of the individual parts of resistance tract. This approach helps to clarify the physical nature of the process, to evaluate different designs aerodynamic perfection swirlers.
Hydraulic resistance machines centrifugal type represented by the sum of the resistances of the cylindrical device, swirler and exhaust pipe. The resistance of the cylindrical part of the theoretically calculated for different distribution laws tangential velocity.
The processing of the experimental data suggested an empirical equation for calculating the coefficient of hydraulic resistance machines centrifugal type. Found that the flow resistance of the "dry" machine obeys the square of the velocity of the gas. With the increase in the coefficient of spin 4 down. This is due to the decreasing level of the tangential component of the gas velocity in the swirler. At some value of K, the coefficient of hydraulic resistance is almost independent of the flow scrubbing liquid. This is explained by the influence of two factors related to the supply of irrigating
fluid dynamic scrubber one hand - increasing 4 due to the increase of pressure loss of the gas stream to transport liquids; other hand - reducing 4 due to the decrease of the tangential velocity of the gas by the braking action of the liquid.
On this basis was constructed empirical mathematical model for calculating the coefficient of hydraulic resistance, including a formula to calculate 4 «dry» machine
v, -1 ( r - >K Kr(9i.
I (3)
empirical relationship for calculating the pressure drop in the gas transport liquid
ÇtT - 4.
(4)
: q 1 - *
and ultimate dependence for calculating % irrigation apparatus
^ -1 ((Rm)2n -l)+a-K,. n K2
l +PL
(5)
+ 4
l +-
K2
where 4 - coefficient of hydraulic resistance; Rm - radius of the cylindrical chamber, m; p„, pi - density of gas and liquid, kg / m3; uin - velocity of gas at the inlet and outlet of the unit, m/s; n, e - indicators vortex movement, K - factor twist swirler; Q, G - liquid and gas flow kg/m3; a - twist angle of the flow,
The resulting formula takes into account the presence of the dispersed phase and the partial loss of swirling flow.
4. Processing of results
Figure 3 shows that the swirl angle of the blades with a = 45 ° has the lowest power characteristics. However, the efficiency in the gas cleaning unit with swirler is reduced by 6^8% in comparison with the unit, where the blades are tilted at an angle a = 30 °. This can be explained by the decreasing flow swirling, which is characterized by a relative twist angle (90 ° ^ 45 °), and the lowest centrifugal forces.
1
—
A P
I
->
Fig. 3 - The impact of the angle a on the energy characteristics of dynamic scrubber
Therefore, from the point of view of increasing the efficiency of gas treatment, preference should be given with the greatest twist of swirled flow-30 °.
Fig. 4 - The dependence of the hydraulic resistance of the Reynolds number and the angle of the blades of the swirler
Study of hydrodynamic characteristics scrubber showed that the coefficient of hydraulic resistance depends strongly on the angle of the blade swirler a. It also depends on the movement of gas-dispersed medium defined by the Reynolds number Re=pDv/^. As seen in Figure 4, with increasing Reynolds number of 8-104 sets scaling of 4. The exception is with the swirl angle of blades 35, 5°, installation of which continues to increase hydraulic resistance.
Conclusions
1. The program ANSYS-14/CFX mathematical model of motion of polydispersed gas system. The character of the movement of dust particles under the influence of centrifugal force. This allowed to choose the desired hydrodynamic conditions and take into account of the design under various conditions of scrubber.
2. Experimental study of the hydrodynamic characteristics of the device to determine the empirical constants and test the adequacy of the hydrodynamic model.
3. The empirical relationships for determining the coefficient of hydraulic resistance scrubber. They take into account the diameter of the separation chamber, the gas density and the scrubbing liquid, the angle of the blades of the swirler. The dependences obtained are suitable for the calculation of centrifugal machines of any type.
References
1. Kaplun A.B. ANSYS in the hands of the engineer. A practical guide. 272. (2003).
2. Basow K.A. ANSYS and LMS Virtual Lab. 640. (2005).
3. Pat 2339435 RF. (2008).
4. Bulgakov V.K. Finite element scheme of the High-order for the Navier-Stokes equations. Modified by the SUPG-method . T. 1. 129-132. (2003).
5. Goncharov A.L. On the construction of monotone of difference schemes for the Navier-Stokes equations on devyatito of point patterns. 93. 14-16. (1986).
2
x
P
g
2
0,4
S
l
out
X
S
6. Goncharov A.L. Difference schemes on a nine-point template for the Navier-Stokes equations in velocity-pressure. 53.17. (1986).
7. Usmanovа R.R., A.K. Panov, K.S. Minsker. Increased efficiency in flue gas kilns Chemical industry today. 9, 43-46.(2003).
8.Sazhin B.S. Mathematical modeling of the gas in the separation zone of the once-through vortex apparatus based
on the model of turbulence. Theoretical Foundations of Chemical Engineering, V. 35. 5. 472 - 478.(2001).
9. Idelchik I.E. Hydraulic resistance of a (physical-mechanical basis). 316. (1954).
10.Tarasova L.A .Hydraulic calculation of the resistance of the vortex unit Chemical and Petroleum mechanical engineering. 2. 11-12.(2004).
© R. R. Usmanova - She is currently Associate Professor of the Chair of Strength of Materials at the Ufa State Technical University of Aviation in Ufa, Bashkortostan, Russia, regina.uu2012@yandex.ru; G. E. Zaikov - DSc, Professor of the Chair Plastics Technology Kazan National Research Technological University in Kazan, Tatarstan, Russia, chembio@sky.chph.ras.ru.
© Р. Р. Усманова - канд. техн. наук, доц. каф. СМ Уфимского госуд. авиационного технич. ун-та, regina.uu2012@yandex.ru; Г. Е. Заиков - д-р хим. наук, проф. каф. ТПМ КНИТУ, chembio@sky.chph.ras.ru.
