- Email: [email protected]
Liquid Jet Ejector Efficiency Improvement
Available online at www.sciencedirect.com Available online at www.sciencedirect.com
ScienceDirect ScienceDirect
Available online at www.sciencedirect.com Procedia Engineering 00 (2017)000–000 Procedia Engineering 00 (2017)000–000
ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Procedia Engineering 206 (2017) 99–106
International Conference on Industrial Engineering, ICIE 2017 International Conference on Industrial Engineering, ICIE 2017
Liquid Jet Ejector Efficiency Improvement Liquid Jet Ejector Efficiency Improvement
A.R.Ismagilov, E.K.Spiridonov, O.V.Belkina* A.R.Ismagilov, E.K.Spiridonov, O.V.Belkina* South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, The Russian Federation South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, The Russian Federation
Abstract Abstract The issues of application of an agitator, a diffuser, and a vertical pipe in a liquid jet ejector are considered. Possible versions of an agitator as aofrotating nozzle with bladesaare recommended. A physical mathematical based on fundamental equations, The issues application of an agitator, diffuser, and a vertical pipe inand a liquid jet ejectormodel are considered. Possible versions of an which reflect the operating process of the device, is developed. The estimated dependencies and restrictive conditions of agitator as a rotating nozzle with blades are recommended. A physical and mathematical model based on fundamental equations, operation of thethe electrically rotating nozzle and is blades ejector are increase in the of application of which reflect operatingdriven process of the device, developed. Theprovided. estimatedThe dependencies andefficiency restrictive conditions of the agitator, diffusor, and driven verticalrotating pipe isnozzle numerically quantified by provided. means ofThe extreme characteristics. Thus, a maximum operation of the electrically and blades ejector are increase in the efficiency of application of efficiency gain of 37%and aftervertical agitatorpipe is installed; 13% when diffuser installed; 5% when vertical pipe Thus, is installed can be the agitator, diffusor, is numerically quantified by ismeans of extreme characteristics. a maximum reached. reflect relationship of maximum attainable and istheinstalled corresponding efficiencyThe gaincharacteristics of 37% after that agitator is the installed; 13% when diffuser is installed;operating 5% whenparameters vertical pipe can be values optimum relative nozzle area are Theofconstancy the optimum relative nozzle area a wide range of reached.ofThe characteristics that reflect the obtained. relationship maximumofattainable operating parameters andinthe corresponding operating while nozzle using the agitator alongside theconstancy diffuser and the vertical is revealed. Hence, the agitator is values of parameters, optimum relative area are obtained. The of the optimumpipe, relative nozzle area in aif wide range of applied, optimum while relativeusing nozzle is 0.29 ... 0.30,theif diffuser the diffusor and vertical vertical pipe, pipe is arerevealed. added, then – 0.40 ... agitator 0.41. The operatingthe parameters, the area agitator alongside and the Hence, if the is recommendations on the implementation of isthe0.29 obtained results arediffusor made. and vertical pipe are added, then – 0.40 ... 0.41. The applied, the optimum relative nozzle area ... 0.30, if the © 2017 The Authors. Published by Elsevier B.V. recommendations on the implementation of the results are made. © 2017 The under Authors. Published by Elsevier Ltd.obtained Peer-review responsibility of Elsevier the scientific committee of the International Conference on Industrial Engineering. © 2017 The Authors. Published by B.V. Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering Keywords: ejector; liquid jet; passive medium; agitator; diffuser; vertical pipe; efficiency. Peer-review underactive responsibility of the gas scientific committee of the International Conference on Industrial Engineering. Keywords: ejector; active liquid jet; passive gas medium; agitator; diffuser; vertical pipe; efficiency.
1. Introduction 1. Introduction The ejector is a device that is widely used as a pump, compressor, mixer, heater or transport device in many industries [1-3].is The research, improvement the ejector mixer, operating process, is continuous held The ejector a device that focused is widelyonused as a pump,ofcompressor, heater or transport device and in many throughout the world. Literaturefocused review on hasimprovement shown that the the liquidprocess, jet ejector can be improved via industries [1-3]. The research, of efficiency the ejectorofoperating is continuous and held additional on theLiterature active jetreview streamhas [4-7] and that / or the on the passiveofgas by liquid jet [8-10]. throughouteffect the world. shown efficiency themedium, liquid jetentrained ejector can be improved via Additional effect on the active passive[4-7] mediums to profiling of intake devices, also it additional effect active and jet stream and /can or be on geometrical the passive one gas due medium, entrained by liquid jet [8-10]. Additional effect on the active and passive mediums can be geometrical one due to profiling of intake devices, also it
* Corresponding author. Tel.: +7-351-267-9252. E-mail address:author. [email protected] * Corresponding Tel.: +7-351-267-9252.
E-mail address: [email protected] 1877-7058 © 2017 The Authors. Published by Elsevier B.V. Peer-review©under the scientific committee 1877-7058 2017responsibility The Authors. of Published by Elsevier B.V.of the International Conference on Industrial Engineering . Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering .
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering. 10.1016/j.proeng.2017.10.444
100 2
A.R.Ismagilov et al. / Procedia Engineering 206 (2017) 99–106 A.R. Ismagilov et al. / Procedia Engineering 00 (2017) 000–000
can be hydrodynamic one – due to application of agitator units (AU). AU installation presupposes transfer of additional energy to passive flow which is necessary for the mixing process of active and passive mediums in the mixing chamber with minimal energy losses. This article refers to agitator application in a liquid jet ejector. Nomenclature ml, mg, mmix Tl, Tg pi psv ρgi, ρmixi Rg Qvgi, Ql, Qgi p͞i Uli, Umixi, Ugi di ζ10, ζ34, ζdif, ζ56 φ τ34 λ34 A34 L34, L56 kvi αg2 ψ Nsup ηnb ε42 ε52max ε12 kt nsup Г
mass flow rates of liquid, gas and gas-liquid mixture absolute temperatures of liquid and gas absolute static pressure of medium in the i-th section pressure of the saturated liquid vapor densities of gas and mixture in the i-th section gas constant volume flow rates of saturated gas-vapor mixture, liquid and gas in the i-th section absolute total pressure in the i-th section velocities of liquid, mixture and gas in the i-th section diameter of the i-th section resistance coefficients of the nozzle channel, the mixing chamber, the diffuser and the vertical pipe nozzle velocity ratio averaged (per length) wall-adjacent shear stress coefficient of hydraulic friction in the mixing chamber surface area of the mixing chamber length of the mixing chamber and the vertical pipe correction factor for pressure of saturated liquid vapor in i-th section volumetric coefficient of gas ejection in the suction chamber factor of phase slipping supplied power efficiency of the electric driver and the nozzle device ratio of backpressure of the mixing chamber and suction pressure maximum attainable ratio of gas compression degree of pressure reduction in the nozzle device correction factor for temperature difference between liquid and gas specific power for acceleration of passive gas flow jet dynamic parameter
2. Possible versions of an agitator unit Liquid-gas ejector (LGE) can include a gas accelerator or a rotating nozzle with blades used as an agitator. Fig. 1 shows a schematic diagram of LGE with rotating nozzle and blades (NB). Unlike the conventional ejector design, there is a rotating nozzle with blades 1 in the suction chamber 3. It should be noted that the nozzle and blades are of rigid construction. The blades have a shape similar to the shape of the axial fan blades [11]. A straightener 2 is installed just after the blades.
Fig. 1. Schematic diagram of LGE with rotating nozzle and blades driven by fluid energy: 1 – rotating nozzle with blades; 2 – straightener; 3 – suction chamber; 4 – mixing chamber.
A.R.Ismagilov et al. / Procedia Engineering 206 (2017) 99–106 A.R. Ismagilov et al. / Procedia Engineering 00 (2017) 000–000
101 3
Acceleration of ejected passive flow occurs due to energy transfer from the rotating blades, which in turn receive rotary motion from the impact of the active liquid flow on the nozzle. Conversion of the part of fluid power of the liquid flow into mechanical energy of rotating nozzle 1 is carried out by profiling of the inner surface of the nozzle 1 in the form of spiral converging ducts [12]. To exclude the swirl of passive flow at the inlet of the mixing chamber 5, the straightener 2 is used. Rotary motion NB 1 can be performed by additional driving device, for instance, electric driver (position 1 in Fig. 2). In this case, rotation will be transmitted via the rod 2 fixed to the inner side of the nozzle 4 through the ribs (not shown in Fig. 2).
Fig. 2. Schematic diagram of LGE with electrically driven rotating blade wheel and nozzle device: 1 – electric driver; 2 – rod; 3 – nozzle with blades; 4 – straightener; 5 – suction chamber; 6 – mixing chamber.
In all cases, additional increase in operating process efficiency is possible due to gas gradual compression by diffuser and / or vertical cylindrical pipe (VP) [13]. The diffuser allows to convert excess kinetic energy of mixture into potential energy. The vertical pipe reduces static pressure at the outlet of the ejector by column weight of gasliquid mixture. 3. Physical-mathematical model To estimate the potential use of agitator units, we construct the physical-mathematical model for LGE with electrically driven rotating nozzle (see. Fig. 2). The physical-mathematical model of device operating process is based on the following assumptions: 1) distribution of liquid and gas velocities in control sections is uniform; 2) flow of mediums in the suction chamber is isobaric; 3) dry gas is passive medium. Initial equations that reflect the stages of the ejector operating process are: the continuity equation
mmix ml mg
(1)
Bernoulli equation for the nozzle area between sections 1-1 and 0-0 [14] (see. Fig. 2)
p 1 p2
l U l 0 2
2
1 10
l U l 0
2
2 2
(2)
the momentum equation for the area between sections 3-3 and 4-4 (see. Fig. 2) ( ml mg ) U mix 4 ml U l 3 mg U g 3 ( p3 p4 ) (d 3 ) 2 / 4 – 34 A34
isothermal state equation of gas-liquid mixture [15]
(3)
A.R.Ismagilov al. / Procedia Engineering 206000–000 (2017) 99–106 A.R. Ismagilov et al. / et Procedia Engineering 00 (2017)
102 4
Rg Tl mixi mg mg 1 l 1 l pgi ml ml
1
(4)
Let’s calculate energy transfer from the electric motor to the passive gas medium through the supplied power. As net capacity we take capacity of gas medium as the product of dynamic pressure ρg2 ·Ug22 / 2 by volumetric gas discharge in the suction chamber Qg2. Then the supplied power will be equal to
g 2 U g22 Qg 2 ; 2 nb
Nsup
(5)
While making following calculations let’s assume ηnb = 0,85. When installing the diffuser and / or the vertical pipe we use additional equations: flow equation of liquid-gas mixture in the diffuser p4
mg Rg Tl ln( p4 ) l ml
mg Rg Tl ln ml
kv 5 l kv 4
l U mix4
dif
2
mg Rg Tl ln( p5 ) l l U mix5 p5 2 ml
2
l U mix4
2
2
(6)
2
Bernoulli equation for the flow of liquid-gas mixture in the vertical pipe L56
p5 U 25 p6 U2 U2 m m 6 56 m 6 2 g m5 g 2 g m6 g 2 g
(7)
Here density of the mixture is determined by the expression [16]
mixi
1 Q
Q
ml 1 mg ml Ql
vgi
(8)
l
volume flow rate of the saturated gas-vapor mixture in the 3rd section Qvg 3
mg Rg Tl p3 – psv
;
(9)
nozzle velocity ratio 1 / 1 10
(10)
Averaged (per length) wall-adjacent shear stress [17] τ 34 λ 34 ρ mix4 U mix4 / 8 2
correction factor for the pressure of the saturated liquid vapor psv in i-th section
(11)
A.R.Ismagilov al. / Procedia Engineering 206 (2017) 99–106 A.R. Ismagilov et al.et/ Procedia Engineering 00 (2017) 000–000
psv pi
kvi 1 –
1035
(12)
In Fig. 2 the sections 0-0, 1-1, 2-2, 3-3, 4-4 are illustrated. The section 5-5 takes place in the outlet section of the diffuser. The section 6-6 takes place in the outlet section of the vertical pipe (not shown in Fig. 2). While assessing the potential use of the agitator device, it is necessary to consider restrictive condition on limit structure of the liquid-gas flow [18]. This is described by the inequality which limits ejection coefficient αg2:
g 2 0, 43 42 ;
(13)
g 2 2,33 42 .
(14)
Here volumetric coefficient of gas ejection in the suction chamber α g 2 Qg 2 / Ql ;
(15)
ratio of backpressure of the mixing chamber and suction pressure
ε 42 p4 / p2
(16)
Inequality (13) is used when there is mixing shock [19], and (14) – when mixing shock is absent. If there is no agitator device in the ejector, then there should be considered restrictive condition on limiting factor of phase slipping ψ, which is equal to the ratio of gas velocity Ug3 and liquid velocity Ul3 at the inlet of the mixing chamber [20]. The restrictive condition is characterized by the fact that the liquid jet can impart velocity to concurrent passive flow which does not exceed the velocity of active jet. The condition is described by the inequality
*
(17)
Limiting factor of phase slipping equals ψ* = 0,84…0,91 [21]. Efficiency of ejector with the agitator device is calculated by formula
η
max α max g 2 ln ε 52
kt ε12 ε
max 52
nsup
;
(18)
Here maximum attainable ratio of gas compression max ε 52 p5 / p2min ;
(19)
degree of pressure reduction in the nozzle device ε12 p1 / p2 ;
(20)
correction factor for temperature difference between liquid and gas kt Tg /Tl ;
(21)
A.R.Ismagilov et al. / Procedia Engineering 206 (2017) 99–106 A.R. Ismagilov et al. / Procedia Engineering 00 (2017) 000–000
104 6
specific power for acceleration of passive gas flow x N sup ρ g 3 α ma g2 nsup p2min Ql min 2 p2 ηsb
ψ
p2min ρl
2
(22)
jet dynamic parameter Г ρl (U l 0 ) 2 / p2
(23)
The physical and mathematical model is closed one and allows to calculate the most important characteristics of liquid-gas ejector with electrically driven rotating nozzle. 4. Results
The potential use of ejectors is defined by their extreme characteristics that establish relationship between the maximum attainable operating parameters of the device: efficiency η, ratio of gas compression ε52max, ejection coefficient αg2max, optimum relative nozzle area Ω03opt = (d0/d3)2 and degree of pressure reduction in the nozzle device ε12. Comparison of extreme characteristics of the ejector within conventional operating process and those ones of the ejector with an agitator, reveals the expected efficiency gain of the device η due to the use of the agitator. Dimensionless graphs (Fig. 3-5) were obtained by numerical study of extreme characteristics [8] of conventional water-air ejector (without the agitator, diffuser and vertical pipe), as well as the water-air ejector with the agitator, diffuser and vertical pipe with regard to restrictive conditions (13), (14) and (17). The calculations assumed constant pressure at the outlet of the ejector as equal to 105 kPa; water absolute temperature Tl = 283 K and gas absolute temperature Tg = 293 K; resistance coefficient of the mixing chamber ζ34 = 0,4 and resistance coefficient of diffuser ζ45 = 0,1; divergence ratio of diffuser Ω54 = 4 [22]; length of vertical pipe VP L56 = 2,5 m.
Fig. 3. Efficiency dependence of pressure reduction degree in the nozzle device: 1 – conventional ejector; 2 – ejector with agitator units; 3 – ejector with agitator and diffuser; 4 – ejector with agitator, diffuser and vertical pipe.
Analysis of the curves (see. Fig. 3) shows a possible efficiency gain due to the application of the agitator, diffuser and vertical pipe. When installing the agitator AU, it is possible to get the maximum efficiency gain with the degrees ε12 equal to 150 ... 300. In this case, the efficiency will grow by 37 %. When installing the diffuser, maximum efficiency gain amounts to 13 % or more with ε12 = 25 ... 110; and when installing the vertical pipe, efficiency gain
A.R.Ismagilov et al. / Procedia Engineering 206 (2017) 99–106 A.R. Ismagilov et al. / Procedia Engineering 00 (2017) 000–000
105 7
can be increased by 5%. Thus, the overall efficiency gain compared to the conventional device will be 51.9 % with ε12 = 200. The graph (see. Fig. 4) shows the dependence of maximum attainable ratio of compression ε52max of pressure reduction degree in the nozzle device ε12. It can be seen that maximum ratio of compression ε52max continuously grows with ε12 increase, if the agitator AU and diffuser are installed. Installation of the vertical pipe does not affect ε52max value. However, in [23] it is noted that there is reduction of fluid intake if the vertical pipe is available. Installation of the agitator unit and the diffuser will increase the maximum attainable ratio of gas compression ε52max.
Fig. 4. Dependence of maximum compression ratio of the degree of pressure reduction in the nozzle device: 1 – conventional ejector; 2 – ejector with agitator units; 3 – ejector with agitator and diffuser; 4 – ejector with agitator, diffuser and vertical pipe.
Fig. 5. Dependence of optimum relative nozzle area and ejection limiting factor of degree of pressure reduction in the nozzle device: 1 – conventional ejector; 2 – ejector with agitator units; 3 – ejector with agitator and diffuser; 4 – ejector with agitator, diffuser and vertical pipe.
The graph (see. Fig. 5) shows the dependence of optimum relative nozzle area Ω03opt and ejection limiting factor αg2 of the degree of pressure reduction in the nozzle device ε12. It can be seen that optimum relative nozzle area Ω03opt increases when additional elements are installed. Thereby, for the conventional ejector (curve 1, see. Fig. 5) the parameter Ω03opt decreases with increase of ε12, and when the agitator unit is installed, it remains substantially constant (see curve 2. Fig. 5) and equal to Ω03opt = 0,29…0,30. When the diffuser and vertical pipe are installed on max
106 8
A.R.Ismagilov et al. / Procedia Engineering 206 (2017) 99–106 A.R. Ismagilov et al. / Procedia Engineering 00 (2017) 000–000
the initial part of the curves 3, 4 (see. Fig. 5), parameter Ω03opt decreases and then becomes constant (Ω03opt = 0,40…0,41). Fig. 5 shows that the curves that characterize dependence of the ejection limiting factor αg2max of ε12 are substantially linear and rising. When agitator units are installed, αg2max parameter increases, but when additional diffuser and / or vertical pipe are installed, the ejection limiting factor αg2max reduces. 5. Сonclusions
There is a big scope for the potential use of liquid jet ejectors. Installation of the agitator unit will allow to gain efficiency η of the ejector and reduce fluid flow rate and power consumption for its operation. The agitation unit may be installed on existing ejectors, or may be designed to be included into a new device. The characteristics obtained demonstrate the effect of application of the agitator alongside diffuser and vertical pipe. For the ejector design by means of graphs in Fig. 3-5, the missing operating parameters, under which the ejector can operate with maximum efficiency, can be identified. Further, at the stage of the device design under certain operating conditions such as: suction pressure p2, supply pressure p1, back pressure p5; the graph in Fig. 5 makes it possible to select the optimum relative nozzle area Ω03opt and calculate the optimum geometrical dimensions, based on recommendations [1-3]. Acknowledgements
The work was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0011. References [1] E.Y. Sokolov, N.M. Zinger, Inkjet Devices, third ed., Energoatomisdat, Moscow, 1989. [2] V.G. Tsegelsky, Two-Phase Jet Devices, Publishing House at N.E. Bauman Moscow State Technical University, Moscow, 2003. [3] Y.N. Vasiliev, Theory of a Two-Phase Gas-Liquid Ejector with Cylindrical Mixing Chamber, Shoulder machines and inkjet devices. 5 (1971) 175–261. [4] Y.N. Vasiliev, Y.P. Gladkov, G.A. Gorshkova, Liquid-gas ejector, State Committee On Inventions and Discoveries Attached to USSR State Committee on Science and Technics, Author's Certificate №985462, 1982, Bul. №48. [5] V.O Alexandrova, I.V. Bredikhin, A.D. Griga et al, Jet Pump, Federal Service for Intellectual Property, Patents and Trademarks, Patent №2246642, 2005, Bul. №03. [6] R. Okudaira, Jet pump, Japanese patent №60173400, 1985. [7] R.L. Campbell, R. Budica, High Efficiency Steam Ejector for Desalination Applications, US Patent and Trademark Office, US Patent №16779, 2002. [8] E.K. Spiridonov, Industrial gas-liquid jet pumps, Heavy Engineering. 10 (2005) 6-10. [9] E.K. Spiridonov, A.V. Podzerko, S.I. Gustov et al, Liquid-Gas Ejector, Federal Service for Intellectual Property, Patents and Trademarks, Patent №2132003, 1999. [10] A.R. Ismagilov, E.K. Spiridonov, Towards The Issue of Water-Air Jet Pump Energy when Applied Inactive Stream Activator, Vestnik UGATU. Mechanical and Materials Engineering Series, 4(57) (2013) 70–75. [11] A.N. Sherstuk, Pumps, Ventilators, and Compressors: manual for technical students, Vysshaya Shkola, Moscow, 1972. [12] Y.N. Vasilyev, E.P. Gladkov, G.A. Gorshkova, Liquid-gas ejector, State Committee On Inventions and Discoveries Attached to USSR State Committee on Science and Technics, Author's Certificate №1038618, 1983, Bul. №32. [13] A.R. Ismagilov, E.K. Spiridonov, Ways to increase efficieny of the compressed gas in gas-liquid jet pump, Proceedings 3-rd International Rotating Equipment Conference. Compressors Users International Forum 2016. Session name Vacuum, technology - research. VDMA, 2016, pp. 73–83. [14] L.G. Loitsiansky, Fluid Mechanics, Nauka, Moscow, 1987. [15] S.V. Iordansky, Equations of Motion of Liquid Containing Gas Bubbles, Zh. Prikl. Mekh. Tekh. Fiz. 3 (1960) 102-110. [16] M.E. Deutsch, G.A. Filipov, Gas Dynamics of Two-Phase Media, second ed, Energoizdat, Moscow, 1981. [17] R.R. Chugaev, Hydraulics: textbook for higher educational institutions, fourth ed., Energoizdat, Leningrad, 1982. [18] E.K. Spiridonov, S.B. Shkolin, Research Operation Limiting Modes of Two-Phase Ejector, Vestnik SUSU. 11(144) (2009) 18–27. [19] J.H. Witte, Mixing Shocks in Two-Phase Flow, The Journal of Fluid Mechanics. 36(4) (1969) 639–655. [20] R.G. Cunningham, Gas Compression with the Liquid Jet Pump, Theory of Engineering Calculations. 3(1974) 112–128. [21] E.K. Spiridonov, V.K. Temnov, Research Extreme Performances of Water-Air Ejector, Dinamika Pnevmogidravlicheskih Sistem (Dynamic of air-overpneumatic systems), Chelyabinsk Polytechnic Institute, Chelyabinsk, 1983, pp. 62–75. [22] I.E. Idelchik, M.O. Steinberg, Handbook of Hydraulic Resistance, third ed., Machinostroenie, Moscow, 1992. [23] E.K. Spiridonov, A.R. Ismagilov, Energy and Resource Operating Water-Air Jet Pumps, Vestnik of SUSU. Engineering. 20(33) (2012) 13-20.
ScienceDirect ScienceDirect
Available online at www.sciencedirect.com Procedia Engineering 00 (2017)000–000 Procedia Engineering 00 (2017)000–000
ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Procedia Engineering 206 (2017) 99–106
International Conference on Industrial Engineering, ICIE 2017 International Conference on Industrial Engineering, ICIE 2017
Liquid Jet Ejector Efficiency Improvement Liquid Jet Ejector Efficiency Improvement
A.R.Ismagilov, E.K.Spiridonov, O.V.Belkina* A.R.Ismagilov, E.K.Spiridonov, O.V.Belkina* South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, The Russian Federation South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, The Russian Federation
Abstract Abstract The issues of application of an agitator, a diffuser, and a vertical pipe in a liquid jet ejector are considered. Possible versions of an agitator as aofrotating nozzle with bladesaare recommended. A physical mathematical based on fundamental equations, The issues application of an agitator, diffuser, and a vertical pipe inand a liquid jet ejectormodel are considered. Possible versions of an which reflect the operating process of the device, is developed. The estimated dependencies and restrictive conditions of agitator as a rotating nozzle with blades are recommended. A physical and mathematical model based on fundamental equations, operation of thethe electrically rotating nozzle and is blades ejector are increase in the of application of which reflect operatingdriven process of the device, developed. Theprovided. estimatedThe dependencies andefficiency restrictive conditions of the agitator, diffusor, and driven verticalrotating pipe isnozzle numerically quantified by provided. means ofThe extreme characteristics. Thus, a maximum operation of the electrically and blades ejector are increase in the efficiency of application of efficiency gain of 37%and aftervertical agitatorpipe is installed; 13% when diffuser installed; 5% when vertical pipe Thus, is installed can be the agitator, diffusor, is numerically quantified by ismeans of extreme characteristics. a maximum reached. reflect relationship of maximum attainable and istheinstalled corresponding efficiencyThe gaincharacteristics of 37% after that agitator is the installed; 13% when diffuser is installed;operating 5% whenparameters vertical pipe can be values optimum relative nozzle area are Theofconstancy the optimum relative nozzle area a wide range of reached.ofThe characteristics that reflect the obtained. relationship maximumofattainable operating parameters andinthe corresponding operating while nozzle using the agitator alongside theconstancy diffuser and the vertical is revealed. Hence, the agitator is values of parameters, optimum relative area are obtained. The of the optimumpipe, relative nozzle area in aif wide range of applied, optimum while relativeusing nozzle is 0.29 ... 0.30,theif diffuser the diffusor and vertical vertical pipe, pipe is arerevealed. added, then – 0.40 ... agitator 0.41. The operatingthe parameters, the area agitator alongside and the Hence, if the is recommendations on the implementation of isthe0.29 obtained results arediffusor made. and vertical pipe are added, then – 0.40 ... 0.41. The applied, the optimum relative nozzle area ... 0.30, if the © 2017 The Authors. Published by Elsevier B.V. recommendations on the implementation of the results are made. © 2017 The under Authors. Published by Elsevier Ltd.obtained Peer-review responsibility of Elsevier the scientific committee of the International Conference on Industrial Engineering. © 2017 The Authors. Published by B.V. Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering Keywords: ejector; liquid jet; passive medium; agitator; diffuser; vertical pipe; efficiency. Peer-review underactive responsibility of the gas scientific committee of the International Conference on Industrial Engineering. Keywords: ejector; active liquid jet; passive gas medium; agitator; diffuser; vertical pipe; efficiency.
1. Introduction 1. Introduction The ejector is a device that is widely used as a pump, compressor, mixer, heater or transport device in many industries [1-3].is The research, improvement the ejector mixer, operating process, is continuous held The ejector a device that focused is widelyonused as a pump,ofcompressor, heater or transport device and in many throughout the world. Literaturefocused review on hasimprovement shown that the the liquidprocess, jet ejector can be improved via industries [1-3]. The research, of efficiency the ejectorofoperating is continuous and held additional on theLiterature active jetreview streamhas [4-7] and that / or the on the passiveofgas by liquid jet [8-10]. throughouteffect the world. shown efficiency themedium, liquid jetentrained ejector can be improved via Additional effect on the active passive[4-7] mediums to profiling of intake devices, also it additional effect active and jet stream and /can or be on geometrical the passive one gas due medium, entrained by liquid jet [8-10]. Additional effect on the active and passive mediums can be geometrical one due to profiling of intake devices, also it
* Corresponding author. Tel.: +7-351-267-9252. E-mail address:author. [email protected] * Corresponding Tel.: +7-351-267-9252.
E-mail address: [email protected] 1877-7058 © 2017 The Authors. Published by Elsevier B.V. Peer-review©under the scientific committee 1877-7058 2017responsibility The Authors. of Published by Elsevier B.V.of the International Conference on Industrial Engineering . Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering .
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering. 10.1016/j.proeng.2017.10.444
100 2
A.R.Ismagilov et al. / Procedia Engineering 206 (2017) 99–106 A.R. Ismagilov et al. / Procedia Engineering 00 (2017) 000–000
can be hydrodynamic one – due to application of agitator units (AU). AU installation presupposes transfer of additional energy to passive flow which is necessary for the mixing process of active and passive mediums in the mixing chamber with minimal energy losses. This article refers to agitator application in a liquid jet ejector. Nomenclature ml, mg, mmix Tl, Tg pi psv ρgi, ρmixi Rg Qvgi, Ql, Qgi p͞i Uli, Umixi, Ugi di ζ10, ζ34, ζdif, ζ56 φ τ34 λ34 A34 L34, L56 kvi αg2 ψ Nsup ηnb ε42 ε52max ε12 kt nsup Г
mass flow rates of liquid, gas and gas-liquid mixture absolute temperatures of liquid and gas absolute static pressure of medium in the i-th section pressure of the saturated liquid vapor densities of gas and mixture in the i-th section gas constant volume flow rates of saturated gas-vapor mixture, liquid and gas in the i-th section absolute total pressure in the i-th section velocities of liquid, mixture and gas in the i-th section diameter of the i-th section resistance coefficients of the nozzle channel, the mixing chamber, the diffuser and the vertical pipe nozzle velocity ratio averaged (per length) wall-adjacent shear stress coefficient of hydraulic friction in the mixing chamber surface area of the mixing chamber length of the mixing chamber and the vertical pipe correction factor for pressure of saturated liquid vapor in i-th section volumetric coefficient of gas ejection in the suction chamber factor of phase slipping supplied power efficiency of the electric driver and the nozzle device ratio of backpressure of the mixing chamber and suction pressure maximum attainable ratio of gas compression degree of pressure reduction in the nozzle device correction factor for temperature difference between liquid and gas specific power for acceleration of passive gas flow jet dynamic parameter
2. Possible versions of an agitator unit Liquid-gas ejector (LGE) can include a gas accelerator or a rotating nozzle with blades used as an agitator. Fig. 1 shows a schematic diagram of LGE with rotating nozzle and blades (NB). Unlike the conventional ejector design, there is a rotating nozzle with blades 1 in the suction chamber 3. It should be noted that the nozzle and blades are of rigid construction. The blades have a shape similar to the shape of the axial fan blades [11]. A straightener 2 is installed just after the blades.
Fig. 1. Schematic diagram of LGE with rotating nozzle and blades driven by fluid energy: 1 – rotating nozzle with blades; 2 – straightener; 3 – suction chamber; 4 – mixing chamber.
A.R.Ismagilov et al. / Procedia Engineering 206 (2017) 99–106 A.R. Ismagilov et al. / Procedia Engineering 00 (2017) 000–000
101 3
Acceleration of ejected passive flow occurs due to energy transfer from the rotating blades, which in turn receive rotary motion from the impact of the active liquid flow on the nozzle. Conversion of the part of fluid power of the liquid flow into mechanical energy of rotating nozzle 1 is carried out by profiling of the inner surface of the nozzle 1 in the form of spiral converging ducts [12]. To exclude the swirl of passive flow at the inlet of the mixing chamber 5, the straightener 2 is used. Rotary motion NB 1 can be performed by additional driving device, for instance, electric driver (position 1 in Fig. 2). In this case, rotation will be transmitted via the rod 2 fixed to the inner side of the nozzle 4 through the ribs (not shown in Fig. 2).
Fig. 2. Schematic diagram of LGE with electrically driven rotating blade wheel and nozzle device: 1 – electric driver; 2 – rod; 3 – nozzle with blades; 4 – straightener; 5 – suction chamber; 6 – mixing chamber.
In all cases, additional increase in operating process efficiency is possible due to gas gradual compression by diffuser and / or vertical cylindrical pipe (VP) [13]. The diffuser allows to convert excess kinetic energy of mixture into potential energy. The vertical pipe reduces static pressure at the outlet of the ejector by column weight of gasliquid mixture. 3. Physical-mathematical model To estimate the potential use of agitator units, we construct the physical-mathematical model for LGE with electrically driven rotating nozzle (see. Fig. 2). The physical-mathematical model of device operating process is based on the following assumptions: 1) distribution of liquid and gas velocities in control sections is uniform; 2) flow of mediums in the suction chamber is isobaric; 3) dry gas is passive medium. Initial equations that reflect the stages of the ejector operating process are: the continuity equation
mmix ml mg
(1)
Bernoulli equation for the nozzle area between sections 1-1 and 0-0 [14] (see. Fig. 2)
p 1 p2
l U l 0 2
2
1 10
l U l 0
2
2 2
(2)
the momentum equation for the area between sections 3-3 and 4-4 (see. Fig. 2) ( ml mg ) U mix 4 ml U l 3 mg U g 3 ( p3 p4 ) (d 3 ) 2 / 4 – 34 A34
isothermal state equation of gas-liquid mixture [15]
(3)
A.R.Ismagilov al. / Procedia Engineering 206000–000 (2017) 99–106 A.R. Ismagilov et al. / et Procedia Engineering 00 (2017)
102 4
Rg Tl mixi mg mg 1 l 1 l pgi ml ml
1
(4)
Let’s calculate energy transfer from the electric motor to the passive gas medium through the supplied power. As net capacity we take capacity of gas medium as the product of dynamic pressure ρg2 ·Ug22 / 2 by volumetric gas discharge in the suction chamber Qg2. Then the supplied power will be equal to
g 2 U g22 Qg 2 ; 2 nb
Nsup
(5)
While making following calculations let’s assume ηnb = 0,85. When installing the diffuser and / or the vertical pipe we use additional equations: flow equation of liquid-gas mixture in the diffuser p4
mg Rg Tl ln( p4 ) l ml
mg Rg Tl ln ml
kv 5 l kv 4
l U mix4
dif
2
mg Rg Tl ln( p5 ) l l U mix5 p5 2 ml
2
l U mix4
2
2
(6)
2
Bernoulli equation for the flow of liquid-gas mixture in the vertical pipe L56
p5 U 25 p6 U2 U2 m m 6 56 m 6 2 g m5 g 2 g m6 g 2 g
(7)
Here density of the mixture is determined by the expression [16]
mixi
1 Q
Q
ml 1 mg ml Ql
vgi
(8)
l
volume flow rate of the saturated gas-vapor mixture in the 3rd section Qvg 3
mg Rg Tl p3 – psv
;
(9)
nozzle velocity ratio 1 / 1 10
(10)
Averaged (per length) wall-adjacent shear stress [17] τ 34 λ 34 ρ mix4 U mix4 / 8 2
correction factor for the pressure of the saturated liquid vapor psv in i-th section
(11)
A.R.Ismagilov al. / Procedia Engineering 206 (2017) 99–106 A.R. Ismagilov et al.et/ Procedia Engineering 00 (2017) 000–000
psv pi
kvi 1 –
1035
(12)
In Fig. 2 the sections 0-0, 1-1, 2-2, 3-3, 4-4 are illustrated. The section 5-5 takes place in the outlet section of the diffuser. The section 6-6 takes place in the outlet section of the vertical pipe (not shown in Fig. 2). While assessing the potential use of the agitator device, it is necessary to consider restrictive condition on limit structure of the liquid-gas flow [18]. This is described by the inequality which limits ejection coefficient αg2:
g 2 0, 43 42 ;
(13)
g 2 2,33 42 .
(14)
Here volumetric coefficient of gas ejection in the suction chamber α g 2 Qg 2 / Ql ;
(15)
ratio of backpressure of the mixing chamber and suction pressure
ε 42 p4 / p2
(16)
Inequality (13) is used when there is mixing shock [19], and (14) – when mixing shock is absent. If there is no agitator device in the ejector, then there should be considered restrictive condition on limiting factor of phase slipping ψ, which is equal to the ratio of gas velocity Ug3 and liquid velocity Ul3 at the inlet of the mixing chamber [20]. The restrictive condition is characterized by the fact that the liquid jet can impart velocity to concurrent passive flow which does not exceed the velocity of active jet. The condition is described by the inequality
*
(17)
Limiting factor of phase slipping equals ψ* = 0,84…0,91 [21]. Efficiency of ejector with the agitator device is calculated by formula
η
max α max g 2 ln ε 52
kt ε12 ε
max 52
nsup
;
(18)
Here maximum attainable ratio of gas compression max ε 52 p5 / p2min ;
(19)
degree of pressure reduction in the nozzle device ε12 p1 / p2 ;
(20)
correction factor for temperature difference between liquid and gas kt Tg /Tl ;
(21)
A.R.Ismagilov et al. / Procedia Engineering 206 (2017) 99–106 A.R. Ismagilov et al. / Procedia Engineering 00 (2017) 000–000
104 6
specific power for acceleration of passive gas flow x N sup ρ g 3 α ma g2 nsup p2min Ql min 2 p2 ηsb
ψ
p2min ρl
2
(22)
jet dynamic parameter Г ρl (U l 0 ) 2 / p2
(23)
The physical and mathematical model is closed one and allows to calculate the most important characteristics of liquid-gas ejector with electrically driven rotating nozzle. 4. Results
The potential use of ejectors is defined by their extreme characteristics that establish relationship between the maximum attainable operating parameters of the device: efficiency η, ratio of gas compression ε52max, ejection coefficient αg2max, optimum relative nozzle area Ω03opt = (d0/d3)2 and degree of pressure reduction in the nozzle device ε12. Comparison of extreme characteristics of the ejector within conventional operating process and those ones of the ejector with an agitator, reveals the expected efficiency gain of the device η due to the use of the agitator. Dimensionless graphs (Fig. 3-5) were obtained by numerical study of extreme characteristics [8] of conventional water-air ejector (without the agitator, diffuser and vertical pipe), as well as the water-air ejector with the agitator, diffuser and vertical pipe with regard to restrictive conditions (13), (14) and (17). The calculations assumed constant pressure at the outlet of the ejector as equal to 105 kPa; water absolute temperature Tl = 283 K and gas absolute temperature Tg = 293 K; resistance coefficient of the mixing chamber ζ34 = 0,4 and resistance coefficient of diffuser ζ45 = 0,1; divergence ratio of diffuser Ω54 = 4 [22]; length of vertical pipe VP L56 = 2,5 m.
Fig. 3. Efficiency dependence of pressure reduction degree in the nozzle device: 1 – conventional ejector; 2 – ejector with agitator units; 3 – ejector with agitator and diffuser; 4 – ejector with agitator, diffuser and vertical pipe.
Analysis of the curves (see. Fig. 3) shows a possible efficiency gain due to the application of the agitator, diffuser and vertical pipe. When installing the agitator AU, it is possible to get the maximum efficiency gain with the degrees ε12 equal to 150 ... 300. In this case, the efficiency will grow by 37 %. When installing the diffuser, maximum efficiency gain amounts to 13 % or more with ε12 = 25 ... 110; and when installing the vertical pipe, efficiency gain
A.R.Ismagilov et al. / Procedia Engineering 206 (2017) 99–106 A.R. Ismagilov et al. / Procedia Engineering 00 (2017) 000–000
105 7
can be increased by 5%. Thus, the overall efficiency gain compared to the conventional device will be 51.9 % with ε12 = 200. The graph (see. Fig. 4) shows the dependence of maximum attainable ratio of compression ε52max of pressure reduction degree in the nozzle device ε12. It can be seen that maximum ratio of compression ε52max continuously grows with ε12 increase, if the agitator AU and diffuser are installed. Installation of the vertical pipe does not affect ε52max value. However, in [23] it is noted that there is reduction of fluid intake if the vertical pipe is available. Installation of the agitator unit and the diffuser will increase the maximum attainable ratio of gas compression ε52max.
Fig. 4. Dependence of maximum compression ratio of the degree of pressure reduction in the nozzle device: 1 – conventional ejector; 2 – ejector with agitator units; 3 – ejector with agitator and diffuser; 4 – ejector with agitator, diffuser and vertical pipe.
Fig. 5. Dependence of optimum relative nozzle area and ejection limiting factor of degree of pressure reduction in the nozzle device: 1 – conventional ejector; 2 – ejector with agitator units; 3 – ejector with agitator and diffuser; 4 – ejector with agitator, diffuser and vertical pipe.
The graph (see. Fig. 5) shows the dependence of optimum relative nozzle area Ω03opt and ejection limiting factor αg2 of the degree of pressure reduction in the nozzle device ε12. It can be seen that optimum relative nozzle area Ω03opt increases when additional elements are installed. Thereby, for the conventional ejector (curve 1, see. Fig. 5) the parameter Ω03opt decreases with increase of ε12, and when the agitator unit is installed, it remains substantially constant (see curve 2. Fig. 5) and equal to Ω03opt = 0,29…0,30. When the diffuser and vertical pipe are installed on max
106 8
A.R.Ismagilov et al. / Procedia Engineering 206 (2017) 99–106 A.R. Ismagilov et al. / Procedia Engineering 00 (2017) 000–000
the initial part of the curves 3, 4 (see. Fig. 5), parameter Ω03opt decreases and then becomes constant (Ω03opt = 0,40…0,41). Fig. 5 shows that the curves that characterize dependence of the ejection limiting factor αg2max of ε12 are substantially linear and rising. When agitator units are installed, αg2max parameter increases, but when additional diffuser and / or vertical pipe are installed, the ejection limiting factor αg2max reduces. 5. Сonclusions
There is a big scope for the potential use of liquid jet ejectors. Installation of the agitator unit will allow to gain efficiency η of the ejector and reduce fluid flow rate and power consumption for its operation. The agitation unit may be installed on existing ejectors, or may be designed to be included into a new device. The characteristics obtained demonstrate the effect of application of the agitator alongside diffuser and vertical pipe. For the ejector design by means of graphs in Fig. 3-5, the missing operating parameters, under which the ejector can operate with maximum efficiency, can be identified. Further, at the stage of the device design under certain operating conditions such as: suction pressure p2, supply pressure p1, back pressure p5; the graph in Fig. 5 makes it possible to select the optimum relative nozzle area Ω03opt and calculate the optimum geometrical dimensions, based on recommendations [1-3]. Acknowledgements
The work was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0011. References [1] E.Y. Sokolov, N.M. Zinger, Inkjet Devices, third ed., Energoatomisdat, Moscow, 1989. [2] V.G. Tsegelsky, Two-Phase Jet Devices, Publishing House at N.E. Bauman Moscow State Technical University, Moscow, 2003. [3] Y.N. Vasiliev, Theory of a Two-Phase Gas-Liquid Ejector with Cylindrical Mixing Chamber, Shoulder machines and inkjet devices. 5 (1971) 175–261. [4] Y.N. Vasiliev, Y.P. Gladkov, G.A. Gorshkova, Liquid-gas ejector, State Committee On Inventions and Discoveries Attached to USSR State Committee on Science and Technics, Author's Certificate №985462, 1982, Bul. №48. [5] V.O Alexandrova, I.V. Bredikhin, A.D. Griga et al, Jet Pump, Federal Service for Intellectual Property, Patents and Trademarks, Patent №2246642, 2005, Bul. №03. [6] R. Okudaira, Jet pump, Japanese patent №60173400, 1985. [7] R.L. Campbell, R. Budica, High Efficiency Steam Ejector for Desalination Applications, US Patent and Trademark Office, US Patent №16779, 2002. [8] E.K. Spiridonov, Industrial gas-liquid jet pumps, Heavy Engineering. 10 (2005) 6-10. [9] E.K. Spiridonov, A.V. Podzerko, S.I. Gustov et al, Liquid-Gas Ejector, Federal Service for Intellectual Property, Patents and Trademarks, Patent №2132003, 1999. [10] A.R. Ismagilov, E.K. Spiridonov, Towards The Issue of Water-Air Jet Pump Energy when Applied Inactive Stream Activator, Vestnik UGATU. Mechanical and Materials Engineering Series, 4(57) (2013) 70–75. [11] A.N. Sherstuk, Pumps, Ventilators, and Compressors: manual for technical students, Vysshaya Shkola, Moscow, 1972. [12] Y.N. Vasilyev, E.P. Gladkov, G.A. Gorshkova, Liquid-gas ejector, State Committee On Inventions and Discoveries Attached to USSR State Committee on Science and Technics, Author's Certificate №1038618, 1983, Bul. №32. [13] A.R. Ismagilov, E.K. Spiridonov, Ways to increase efficieny of the compressed gas in gas-liquid jet pump, Proceedings 3-rd International Rotating Equipment Conference. Compressors Users International Forum 2016. Session name Vacuum, technology - research. VDMA, 2016, pp. 73–83. [14] L.G. Loitsiansky, Fluid Mechanics, Nauka, Moscow, 1987. [15] S.V. Iordansky, Equations of Motion of Liquid Containing Gas Bubbles, Zh. Prikl. Mekh. Tekh. Fiz. 3 (1960) 102-110. [16] M.E. Deutsch, G.A. Filipov, Gas Dynamics of Two-Phase Media, second ed, Energoizdat, Moscow, 1981. [17] R.R. Chugaev, Hydraulics: textbook for higher educational institutions, fourth ed., Energoizdat, Leningrad, 1982. [18] E.K. Spiridonov, S.B. Shkolin, Research Operation Limiting Modes of Two-Phase Ejector, Vestnik SUSU. 11(144) (2009) 18–27. [19] J.H. Witte, Mixing Shocks in Two-Phase Flow, The Journal of Fluid Mechanics. 36(4) (1969) 639–655. [20] R.G. Cunningham, Gas Compression with the Liquid Jet Pump, Theory of Engineering Calculations. 3(1974) 112–128. [21] E.K. Spiridonov, V.K. Temnov, Research Extreme Performances of Water-Air Ejector, Dinamika Pnevmogidravlicheskih Sistem (Dynamic of air-overpneumatic systems), Chelyabinsk Polytechnic Institute, Chelyabinsk, 1983, pp. 62–75. [22] I.E. Idelchik, M.O. Steinberg, Handbook of Hydraulic Resistance, third ed., Machinostroenie, Moscow, 1992. [23] E.K. Spiridonov, A.R. Ismagilov, Energy and Resource Operating Water-Air Jet Pumps, Vestnik of SUSU. Engineering. 20(33) (2012) 13-20.