Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 150 (2016) 753 – 760
International Conference on Industrial Engineering, ICIE 2016
Calculation of the Average Velocity of the Liquid in the StreamFilm Contact Devices O.S. Dmitrieva, A.V. Dmitriev*, L.V. Kruglov Kazan State Power Engineering University, 51, Krasnoselskaya str., Kazan, 420066, Russia
Abstract One of the most effective ways of energy saving is to upgrade the existing heat-mass transfer devices. To increase the efficiency of mass-transfer apparatus, a stream-film (bubble) contact device is suggested. The paper considers the prospects of using streamfilm contact devices for heat-mass transfer apparatus. The distinctive feature of the developed device is an intensive countercurrent contact between the gas and liquid in each element. Dependences of the volume flow rate of gas involving turbulence in the flow volume at different design parameters are set. © 2016 2016The TheAuthors. Authors. Published by Elsevier © Published by Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the organizing committee of ICIE 2016. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICIE 2016 Keywords: stream; contact device; velocity; heat-mass transfer
1. Introduction The research of hydrodynamic flow patterns in existing designs of heat-mass transfer devices shows the uneven distribution of liquid and gas phases in the cross section of the working area, which significantly reduces the efficiency of heat-mass transfer process. A well-known constructions of contact devices are characterized by low throughput capacity or high cost. According to the analysis of the most promising designs of contact devices in the last few years, each new design gives a slight gain of efficiency. Generally, constructions are becoming more complicated. When the gas is supplied to the unit, the irregularity ratios of the flow rate over its cross section is observed, which requires the installation of additional distribution systems. Walls, beams and other elements of the contact devices influence upon the gas flow [1-3].
* Corresponding author. Tel.: +7-904-663-16-96. E-mail address:
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1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICIE 2016
doi:10.1016/j.proeng.2016.07.101
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The development of new contact devices can increase the efficiency of heat-mass transfer processes, which helps to reduce the operation costs for electricity. Using new technologies in the field of engineering and technology may solve this problem. This way is very promising, because it often allows to achieve a significant energy costs reduction per unit of the output production with low capital costs and short deadlines [4,5]. 2. Description of the contact device The research of intensification of heat-mass transfer processes in the gas–liquid conditions led to the development of innovative devices for stream-bubble contact devices [6]. The stream-bubble contact device (Fig. 1) consists of a box with vertical walls, necessary to maintain the liquid level inside it. Boxes in each row are interconnected by means of rods to open its upper end, and the bottom is provided with a certain set of holes, required for liquid to drain below the box. Scheme of the gas and liquid flows interaction in the proposed streambubble contact device is shown in Fig. 2.
Fig. 1. Top view of the stream-bubble contact device.
Designed by the authors of this article, stream-bubble contact device operates as follows. Formed in the bottom of the box, fluid through a plurality of holes is dispersed in the form of streams, positioned at the lower box. Thus in one of the above-mentioned boxes fluid level is maintained by the presence of the vertical walls of the box. Boxes, placed chequerwise horizontally, are forming the plate. And the plate, located below, has an offset of glasses, forming their chequerwise vertical location. For this reason, gas, coming from underneath the plate, gets a zigzag motion (Fig. 2). The decomposition of the liquid streams and the formation of numerous drops take place during their motion. Striking the surface inside the box, the liquid sprays scatter in different directions. Thus, a constantly updated extensive surface contact between the phases is defined by the presence of relatively small gas bubbles in a liquid layer and drops departing from the surface. In addition, the upward gas stream is in contact with the falling drops or streams of liquid, forming a second contact zone of gas and liquid. Keeping the distance between the boxes at the same level, equal to the width of the boxes provides strength balance for the gas passage, reducing the hydraulic resistance for the proposed stream-bubble contact devices. To ensure maximum efficiency of the heat-mass transfer processes the cross section of the box has the square shape. Thus, the initial organization of the interaction between gas and liquid allows to intensify heat-mass transfer processes both in liquid and in gas phases with relatively simple device design.
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Fig. 2. Scheme of the gas and liquid flows interaction in the stream-bubble contact device: 1 – box; 2 – the gas flow; 3 – holes; 4 – droplets formed by a perforated device; 5 – droplets emitted from the liquid; 6 – bubbles.
A distinctive feature of the stream-bubble contact devices is an intensive countercurrent contact between the vapor and liquid in each contact element. Proposed contact devices have high mass-transfer coefficient, low hydraulic resistance and high efficiency of mass transfer processes. The goal of all numerical studies is to determine geometrical parameters of the contact device to intensify the mass transfer processes by increasing the contact duration between vapor and liquid. The stages of stream-bubble devices are formed from contact devices of the same size, the amount of which is determined by the productivity/capacity of the apparatus. This approach to the design eliminates the need of a largescale transition and allows to develop devices of any productivity without the efficiency reduction. 3. Solution Procedures Calculation of hydrodynamics, heat-mass transfer in the proposed design of the contact devices is complicated by the variety of forms of the contact phases, the complexity of the decay of streams into droplets and the necessity of taking into account the intensification of heat-mass transfer by falling droplets on a surface section of gas–liquid. Due to the fact that the efficiency of heat-mass transfer processes is mainly determined by the hydrodynamic structure of the interacting phases, the authors of this article made experimental studies of hydrodynamics of the bubble layer in the contact elements. Studies of air-entraining ability of axisymmetric turbulent streams have shown that it increases with the volumetric fluid flow increase (Fig. 3). A lot of previously obtained experimental data of the airflow dependence, that is involved by turbulent stream in its interaction with the surface of a liquid at rest, was generalized by criteria equation in this report [7]: GV LV
0, 055
We 0,33 Fr 0,08 § l · ¨ ¸ Re 0,23 © d ¹
0,66
,
(1)
where LV – volumetric fluid flow, m3/h, GV – volumetric gas flow, m3/h, d – diameter of the stream, m; l – the length of the collapse of the streams, m; We – the Weber number, Re – the Reynolds number; Fr – the Froude number. Froude number defined by the formula: Fr
U ɫɪ2 gd
,
(2)
where g – the gravity acceleration, m/s2; Ucp – speed with an average consumption of liquid outflow through the holes in the bottom, m/s.
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Fig. 3. The dependence of the volume flow rate of gas involving turbulence of the flow volume at different distances between the boxes 2(h+h1), mm: 1 – 50; 2 – 70; 3 – 120; continuous line – calculation, point – experiment.
Calculation of air-entraining ability of turbulent stream by the (Eq. 1) matches the experimental data of the volumetric gas flow, entrained by the streams in a stream-bubble contact elements. In this case, the calculated values are mostly overestimated. Firstly, due to the fact that for the bubble liquid layer the calculated l/d ratio is also too high, and it’s contribution in (Eq. 1) is very powerful. Secondly, part of gas bubbles, drawn into the flowing streams cannot be considered because of the short residence time in the contact elements. Experimental studies of the liquid and gas dispersion allow to estimate the area of interfacial interaction between gas and liquid contact zones in the proposed devices. Studies have shown that the use of stream-bubble contact devices will create energy-efficient heat-mass transfer devices with a wide range of stable operations for rectification and absorption processes, as well as maintaining an appropriate output and quality of the marketable products. In many heat-mass transfer processes in order to achieve sufficient heat-mass transfer efficiency there must be quite a long contact time of the gas and liquid phases. A very difficult task is to achieve this while maintaining uniformity of gas and liquid flows distribution through the cross section of the device, while ensuring reliable separation of phases after the contact, and lower energy costs for carrying out the process. When creating a mathematical description haven’t been taken into account the effect of the gas flow on the fluid flow. This is true for estimation calculations at relatively low gas flow rates. Increasing the gas flow rate will reduce the average velocity of the liquid dripping. An average fluid velocity Uzcp on the section of the apparatus can be determined from the law of conservation of momentum (Fig. 4): U zcp z mcp
n
c z meic , U z1 z m1 U z 2 z m2 U z 3 z m3 U zi z mi ¦ U zei
(3)
i 1
where mcp – average weight, kg; mi – the mass of the i-th flow per unit time, kg. If we divide equation by time interval ǻIJ, it is possible to obtain an equation:
U zcp z mcp
U z1 z m1
'IJ
'IJ
U z 2 z m2 'IJ
U z 3 z m3 'IJ
U zi z mi 'IJ
1 n ¦U zeic z meic . 'IJ i 1
(4)
After the transformation we obtain the following: U zcp z Lmcp
n
c z Lmei c , U z1 z Lm1 U z 2 z Lm 2 U z 3 z Lm 3 U zi z Lmi ¦ U zei i 1
where Lmcp, Lm1, Lm2, Lm3, Lmi, L'mei – mass flows of the relative flows, kg/s.
(5)
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Fig. 4. Scheme of flows in stream-bubble contact element: Uz1 – axis projection of the liquid velocity, coming from the holes, located in the bottom of the central element; Uz2 – axis projection of the liquid velocity, coming from the holes, located in the bottom of adjacent elements; Uz3 – axis projection of the liquid velocity, coming from the holes located in the wall at the bottom; Uzi – axis projection of the liquid velocity, coming from the holes, located in the wall at a distance hi from the bottom; Uze – axis projection of the liquid velocity in the elements.
Consequently, the average velocity of a flow can be determined: n
U zcp z
c z U 0cei f 0cei İ0c ei U z1 z U 01 f 01İ01 U z 2 z U 02 f 02 İ02 U z 3 z U 03 f 03 İ03 U zi z U 0i f 0i İ0i ¦ U zei i 1
n
, (6)
U 01 f 01İ01 U 02 f 02 İ02 U 03 f 03 İ03 U 0i f 0i İ0i ¦ U 0cei f 0cei İ0cei i 1
where f01, f02, f03, f0i, f´0ei – area of holes, m2; İ0i – the compression ratio of the i-th stream. Dependence of the velocity of z:
U z1 z
U 012 2 gz at 0 d z d h h1 ,
(7)
Uz2 z
U 022 2 g h h1 z at 0 d z d h h1 – h2 ,
(8)
U z2 z
0 at z ! h h1 h2 ,
(9)
U z3 z
2 gz at 0 d z d h h1 – h2 ,
(10)
U z3 z
0 at z ! h h1 – h2 ,
(11)
U zi z
2 g hi z at 0 d z d h h1 – h2 ,
(12)
U zi z
0 at z ! h h1 – h2 ,
(13)
U zei z
Lme at h h1 – h2 d z d h h1 – hi , ȡL b 2
(14)
where ȡL – density of the liquid, kg/m3; h – distance between adjacent boxes, mm; h1 – height of vertical walls of the boxes, mm; h2 – the liquid level in the box, m; b – width of the stream-bubble element (box), m.
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The average fluid velocity in the elements will change dramatically in height due to the flowing out of the walls streams. Mass flow on the liquid surface in the element is determined: n
Lme
Lm1 Lm 3 ¦ Lmi .
(15)
i 1
Thus an average fluid velocity in the element up to the level of the first stream expiry at h + h1 – h2 z h + h1 – hi is determined: n
U zei
Lm1 Lm 3 ¦ Lmi i 1
ȡL b 2
.
(16)
An average fluid velocity in the element from the level of the first stream expiry up to the level of the second stream expiry is determined: n
Lm1 Lm 3 Lmc 1 ¦ Lmi i 2
U zei 1
ȡL b 2
at h h1 – hi d z d h h1 – hi 1 ,
(17)
where Lmc 1 – mass fluid flow out of the upper hole, kg/s. The remaining values of an average velocity of a flow in the cell are determined by the same way. The velocity of liquid outflow from the hole and the mass flow can be determined by the formulas:
p2 p1 · 2g § ¨ h2 ¸, Įȗ © ȡL g ¹
U 01
Lm1
f 01İ01 ȡL
(18)
p2 p1 · 2g § ¨ h2 ¸, Įȗ © ȡL g ¹
(19)
where Į – Coriolis coefficient; ȗ – local resistance coefficient of the hole; İ01 – compression ratio of the stream; p1, p2 – gas pressure underneath and above the element, Pa. Feature Lm1U01 written: U z1 Lm1
f 01İ01 ȡL 2 g
· p2 p1 · § 1 § p2 p1 · 1 § ¨ h2 ¸ ¨¨ ¨ h2 ¸ z ¸¸ . ȡL g ¹ Įȗ © ȡL g ¹ © Į ȗ © ¹
(20)
If we assume the equality of all the values of the diameters of the holes and compression ratios, (Eq. 6) is simplified. Average height velocity of the fluid along the axis is determined: n
U zcp z
c ( z )U 0cei n0c ei U z1 ( z )U 01n01 U z 2 ( z )U 02 n02 U z 3 ( z )U 03 n03 U zi ( z )U 0i n0i ¦ U zei i 1
n
U 01n01 U 02 n02 U 03 n03 U 0i n0i ¦ U 0cei n0c ei i 1
,
(21)
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U zcp
1 h h1
h h1
³
U zcp z dz .
(22)
0
4. Results and discussion
The increase of the cell width of a contact device leads to the increased average velocity of a fluid flow (Fig. 5a), which is associated with increasing height of the land which has the greatest speed.
Fig. 5. The dependence of the liquid velocity flowing from the relative coordinate: 1 – Uzcp; 2 – Uz1; 3 – Uz2; 4 – Uz3; 5 – Uzi; (a) h2 = h1/2; hi = h2/2; b = 80 mm; (b) b = 80 mm; h2 = h1; hi = h2/2.
Changes of the liquid level in the elements leads to a shift of the profile jump of the average velocity. (Fig. 5b). With the increasing level usually the reducing average velocity of a flow takes place, because of the increasing height at which the average velocity of a fluid flow is minimum. The level, at which the holes are arranged in the wall of elements, does not affect the average velocity of a flow (Fig. 5b and Fig. 6a). This is due to the low fluid flow from the holes. Arrangement and number of the holes in the bottom part of the elements significantly affects the average velocity of the fluid flow. The absence of holes in the bottom significantly reduces the average velocity, because as the liquid flows through them with a maximum velocity (Fig. 6b).
Fig. 6. The dependence of the liquid velocity flowing from the width of box: (a) hi = h2/2; 1 - h2 = h1/4; 2 - h2 = h1/2; 3 - h2 = h1; (b) h2 = h1/2; hi = h2/2: 1 – drain through the holes; 2 – without holes in the bottom of the central element; 3 – without holes in wall beside the bottom; 4 – without holes in the wall at a distance from the bottom.
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5. Conclusion
Based on the performed research it is possible to draw the following conclusions: 1) the maximum velocity of the fluid is in the initial section; 2) with the increase of the width of elements the average velocity of a flow under any conditions increases. Calculations show that the proposed design can create the optimal conditions for a wide variety of heat-mass transfer processes while providing a sufficiently high efficiency and relatively low energy costs for the organization processes. Developed delivery devices use energy of the liquid, flowing downwards, which reduces the flow resistance for the vapor phase (gas phase). In addition, by reducing the separation space, we can also reduce the size of units/cells with the installed heat-mass transfer stream-bubble contact devices. Thus, the use of streambubble contact devices will increase the efficiency of the working units and reduce energy costs for heat-mass transfer processes in the energy, chemical and petrochemical industry.
Acknowledgements
The reported study was funded by RFBR, according to the research project No. 16-38-60081 mol_a_dk. References [1] A.A. Shagivaleev, A.A. Ovchinnikov, N.A. Nikolaev, Calculation of the efficiency of contact stages of distillation columns with cocurrent swirl contact devices, Theor. Found. Chem. En+ (TFCE). 39 (2005) 590–593. [2] I.N. Madyshev, O.S. Dmitrieva, A.V. Dmitriev, A.N. Nikolaev, Assessment of Change in Torque of Stream-Bubble Contact Mass Transfer Devices, Chem. Petr. Eng. 51 (2015) 383–387. [3] A.V. Dmitriev, O.S. Makusheva, K.V. Dmitrieva, A.N. Nikolaev, Contact mass exchanger to increase output of active tower units, Chem. Petr. Eng. 47 (2011) 319–323. [4] N. Kolev, B. Kravlev, D. Kolev, Gas side controlled mass transfer in a new packing with stamped horizontal lamellae operating at extremely low liquid loads, Chem. Eng. Proc.: Proc. Intens. 63 (2013) 44–49. [5] Z.J. Wei, Z.L. You, S.Q. Gui, Gas pressure drop and mass transfer characteristics in a cross-flow rotating packed bed with porous plate packing, Ind. Eng. Chem. Res. 49 (2010) 3732–3740. [6] A.V. Dmitriev, O.S. Dmitrieva, I.N. Madyshev, G.S. Sagdeeva, A.N. Nikolaev, Patent RU 156379. (2015). [7] Yu.M. Fetisov, Capturing the interaction of the air jet with a stationary liquid, Ph.D. Diss., MSUCE, Moscow, 1995. (in Russ.).
