Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 129 (2015) 446 – 450
International Conference on Industrial Engineering
Characteristics and Calculation of Cavitation Mixers Spiridonov E.K * South Ural State University, 76, Lenin Avenue, Chelyabinsk, 454080, Russian Federation
Abstract It is shown that one of the most efficient ways to obtain emulsion is cavitation treatment of the mixed stream in the jet boundary layer. The authors offer a model for calculating the operational process in the hydrodynamic mixer with multiple-jet nozzle as agitator of cavitation, based on hydrodynamic equations and data of experimental research on jet pumps. There has been considered and analyzed the characteristic of the cavitation mixer, which shows how relative loss of total stream pressure depends on relative nozzle square, and hydraulic resistance coefficient of flow-part elements. It is shown that gradual reduction of hydraulic resistance coefficient allows to decrease considerably the loss of total stream pressure. Besides, there exists the range of optimal relative square values where losses of total pressure are minimized. If the elements of the mixer flow-part are made hydraulically proper then the optimal values of the nozzle relative square are 0,66…0,76, whereas minimum losses of relative pressure don’t exceed 0,22. © 2015 The Authors. Published by Elsevier Ltd. © 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the organizing committee of the International Conference on Industrial Engineering (ICIE(http://creativecommons.org/licenses/by-nc-nd/4.0/). 2015). Peer-review under responsibility of the organizing committee of the International Conference on Industrial Engineering (ICIE-2015) Keywords: Type your keywords here, separated by semicolons ;
1. Introduction An urgent task of machine building, power engineering, chemical, oil and food manufacturing industries is to develop efficient and low-power mixer to prepare emulsions. For instance, in heat-power engineering burnout of diesel oil emulsion in steam boiler furnace units allows to reduce toxicity of stack gases, and if there is an optimum choice of parameters of fuel burnout and preparation of diesel oil emulsion, environmental and technical-andeconomic indexes of boilers will be increased [1]. However, application of high capacity mixers helps to prevent disposal of wastewater contaminated by petroleum products into environment.
* Corresponding author. E-mail address:
[email protected]
1877-7058 © 2015 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 the International Conference on Industrial Engineering (ICIE-2015)
doi:10.1016/j.proeng.2015.12.148
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E.K. Spiridonov / Procedia Engineering 129 (2015) 446 – 450
The quality of emulsion is characterized by structure homogeneity and dispersion degree of components. Consequently, operational efficiency of mixers, i.e. devices for emulsion preparation, significantly depends on the preparation method. Creation of highly-dispersive emulsion by means of traditional mechanical stimulation of flow components is rather complicated. Cavitation treatment of mix elements, which generates local energy concentration (pulsations and cavitation bubble collapse) enough for diffusion of medium components on the micro level, allows to obtain highly-dispersive product resistant to breaking. [2]. Literature review devoted to cavitation in jet pumps has shown that one of the most efficient ways to create emulsion is cavitation in the jet boundary layer [3]. At the same time to increase emulsion dispersion degree it is necessary to equally distribute cavitation points along the standard cross-section of the flow, and to enlarge their number when possible. One of such devices – agitators of cavitation is a multiple-jet nozzle with equally spaced holes which form several high velocity jets in a flow-part of a mixer. The goal of this research is to perform calculation and analysis of characteristics of the jet cavitation mixer. 2. The schematic diagram and calculation model, characteristics of the hydrodynamic mixer The schematic diagram of the jet mixer is shown in Figure 1. The mixer consists of a nozzle (1), the mixing chamber (2), and diffuser (3). The acceleration of a mixed stream and its dispersion into high-speed jets takes place in a multi-jet nozzle, where further in the jets’ boundary layers cavitation is initiated. Cavitation treatment of the flow results in the breakdown of jets and formation of highly dispersed medium. Due to equal distribution of cavitation points along the standard cross-section of the flow at a certain distance from the nozzle (1) vapor-liquid turbulent flow is formed in the mixing chamber (2) which further turns into low flow in the condensation shock. As a result emulsion is created near the outlet section of the mixing chamber. In a diffuser the part of kinetic energy of emulsion flow transforms into potential one. The pressure thus increases to the value smaller than before the mixer.
Fig.1. The schematic diagram of the hydrodynamic ejector.
Input equations which describe operational process in a mixer are the equations of balance of consumption:
Q
vi Ai
const;
(1)
and specific energy of flow in the area between sections 1-1 and 4-4: __
p1
__
p4 ȗ ɋ
__ ȡ v 22 ȡv 32 ȗ Ʉ ȗ Ⱦ ǻ pP 2 2
Bernoulli equations for the mixed stream in the area between sections 1-1 and 2-2:
(2)
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E.K. Spiridonov / Procedia Engineering 129 (2015) 446 – 450
ȡ v 22 Į ɋ ȗ ɋ 2
__
p1
(3)
expression of the Euler number Eu which characterizes cavitation phenomena in the jet boundary layer: Eu
p2 p ɉ
(4)
ȡv 22 2
where ȡ - density of the mixture; pɩ - equilibrium vapor pressure of mixture component with minimum boiling point; Q - volume flow rate of the mixture; i – number of section on the schematic ; Ai, vi, pi – square of __ diagram; __ the normal cross section, average velocity and static pressure in «i»-th section, p1 , p 4 - total (static plus dynamic) pressure at the input (i=1) and output (i=4) mixer section; ȗs, ȗk, ȗd - coefficients of hydraulic resistance of the nozzle, mixing chamber and diffuser; Įɫ - the coefficient of kinetic energy of the mixed stream at the nozzle exit __ (i=2); ' p P - specific energy loss due to abrupt deceleration of the stream from the exhaust velocity v2 of liquid mixture from nozzle holes to velocity v3 of the emulsion in the mixing chamber upon its total filling. According to the theory of Borda-Carnot [4]: __
ǻ pP
ȡ
(v 2 v 3 ) 2 2
(5)
Simultaneous solution of these equations (1)-(5) results in the formula: __
ǻh
__
p1 p4 p1 p ɉ
ȗ ɋ ȗ Ʉ ȗ Ⱦ ȍ 2 (1 ȍ ) 2 Įɋ ȗ ɋ Eu
(6)
which is an expression of the basic characteristic of the hydrodynamic mixer, which establishes the relationship of the relative head flow loss ǻh of the relative square of the nozzle ȍ = A2 / A3, cavitation Euler number Eu, coefficient of hydraulic resistance of the flow-part elements. In the following works [5] an empirical formula of the relationship of the Euler cavitation Eu, and the relative square of the nozzle is proposed. Eu
0.07 1.36(1 ȍ)
With regard to the latter Figure 2 shows performance characteristics of the cavitation mixer with a kinetic energy coefficient Įɫ=1 and several values of hydraulic resistance coefficients. By comparing the lines, we can see that a steady decline in the hydraulic resistance coefficients of the flow-part elements allows to significantly reduce the losses of pressure in the mixer, and for each set of resistance coefficients there is a range of optimal values of the relative square of the nozzle, where the pressure losses are minimal. For example, with a resistance coefficient of the nozzle ȗs = 0.14, the mixing chamber and diffuser ȗk ȗd + = 0.4 minimum relative pressure losses are ǻhmin = 0,255 with relative square of the nozzle ȍopt = 0.6; and at ȗs = 0.06, + ȗk ȗd = 0,2 ǻhmin = 0,185 when relative square of the nozzle is ȍopt = 0.76.
(7)
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0,45
0,4
0,35 ǻh 0,3
3
2
0,25
1
0,2
0,15 0,4
0,5
0,6
0,7 ȍ
0,8
0,9
1
Fig. 2. Performance characteristics of the cavitation mixer when Įɫ=1: 1 – ȗɫ=0,06; ȗɤ+ȗɞ=0,2; 2 – ȗɫ=0,1; ȗɤ+ȗɞ=0,3; 3 – ȗɫ=0,14; ȗɤ+ȗɞ=0,4.
3.Conclusion Hydraulically perfect performance of the flow-part elements of the cavitation mixer and the optimum relationship between the nozzle square and the mixing chamber square are the basic requirements for the development of the cavitation mixer. References [1] V. Tausher, Technology of Static Mixing , J.Chemical and Petroleum Engineering. 3 (1996) 26–32. [2] V.I. Kormilitsyn, M.G. Lyskov, A.A. Rymunskiy, Integrated Biocompatible Compression Technology of Water-Oil Eemulsion and Natural Gas with the Addition of Waste Water. J. Teploenergetika. 9 (1996) 13-17. [3] N.V. Golub, Combustion Efficiency of Water-Oil Emulsion in Industrial CHP Plants, VTI, Moscow, 1985. [4] R.Y. Akchurin, Preparation of Fuel Oil for Burning in a Cavitation Reactor, J. Energetik. 9 (1986) 8–9. [5] A.I. Popov, N.V. Golub, V.I. Yerofeyev, Reducing Emissions from Water-Oil Emulsion Combustion, J. Energetik. 2 (1983) 11–14. [6] V.M. Ivanov, The Fuel Emulsion, Publishing House of the USSR Academy of Sciences, Moscow, 1962. [7] O.M. Yahno, N.N. Yaske, A.D. Koval, Features of Cavitation Technology of High Viscosity Fluids Mixing, J. Chemical and Petroleum Engineering. 3 (1996) 23–25. [8] M.A. Promtov, Prospects for Cavitation Technologies Use for Chemical-Engineering Processes Intensification, J. Vestnik TSTU. 4 (2008) 861–869. [9] R. Knapp, J. Daily, F. Hammitt, Cavitation, Mir, Moscow, 1974. [10] I. Peirsol, Cavitation, Mir, Moscow, 1975. [11] L.G. Podvidz, Cavitation Properties of Jet Pumps, J. Vestnik mashinostroeniya. 3 (1978) 17–20. [12] N.L. Sanger, A Jet Pump Cavitation Prediction Parameter, ASME Fluids Engineering Meeting, 1968 Cavitation Forum, Pamphlet Publication. (1968) 10-18. [13] V.K. Temnov, Basic Theory of Fluid Ejectors, ChPI, Chelyabinsk, 1971.
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