Analysis of Flow in Cylindrical Mixing Chamber

Transcription

1 Intenational Jounal of Mechanical, Aeosace, Industial, Mechatonic and Manufactuing Engineeing Vol:7, No:7, 013 Analysis of Flow in Cylindical Miing Chambe Václav Dvořák Intenational Science Inde, Mechanical and Mechatonics Engineeing Vol:7, No:7, 013 waset.og/publication/16569 Abstact The aticle deals with numeical investigation of aisymmetic subsonic ai to ai ejecto. An analysis of flow and miing ocesses in cylindical miing chambe ae made. Seveal modes with diffeent velocity and ejection atio ae esented. The miing ocesses ae descibed and diffeences between flow in the initial egion of miing and the main egion of miing ae descibed. The lengths of both egions ae evaluated. Tansition oint and oint whee the miing ocesses ae finished ae identified. It was found that the length of the initial egion of miing is stongly deendent on the velocity atio, while the length of the main egion of miing is deendent on velocity atio only slightly. T Keywods Ai ejecto, miing chambe, CFD. I. INTRODUCTION HE aticle deals with numeical investigation into the flow in a subsonic ai-symmetic ai to ai ejecto with constant aea miing. Quite a numbe of eseaches wee concened with ejectos and a geat numbe of ublications have been oduced. Fo eamle, Sun and Eames [1] named ove 100 citations in thei oveview fom In a eview caied out by Bonnington and King [], 413 efeences dating io 1976 wee cited. Pote and Squyes [3] comiled a list of moe than 1600 efeences elating to ejecto theoy and efomances. Fist methods of ejecto design wee based on eeience. The fist analysis of miing was made by Keenan and Neumann [4]. They conside only the simlest fom of ejecto, a constant aea miing chambe without diffuse. They calculated the efomance of an ejecto using the onedimensional continuity momentum and enegy equations. Although the analysis was simlified, the esults wee consistent and comaed well with eeimental esults. Late Keenan, Neumann and Lustwek [5] in a follow u to thei ealie wok, consideed miing at constant essue. This wok oduced the fist comehensive theoetical and eeimental analysis of the ejecto oblem, and is the basis of much of what has taken lace since. The constant essue design method is used in the majoity of ejecto alications, and has caused the most oblems fo eseaches. The main eason fo this is the comle natue of the flow stuctue in the constant essue miing section. Also the detemination of the miing chambe geomety to ensue constant essue miing and best miing is oblematic. Only few authos wee concened with otimization of This oject was ealized with financial suot by the Czech Science Foundation, gant no. P101/10/1709. Vaclav Dvoak is with the Deatment of Powe Engineeing Equiment, Faculty of Mechanical Engineeing, Technical Univesity of Libeec, Studentska, Libeec, Czech Reublic (hone: ; vaclav.dvoak@tul.cz). ejectos. Dvořák in wok [6] otimized an ejecto with the hel of Fluent and veified a manufactued ejecto eeimentally. The ejecto was otimized by using tubulence model ealizable k-ε with enhanced wall teatment. Model ealizable k-ε seemed to be the most suitable fo ai-symmetic miing oblems accoding the esults in wok of Dvořák [7] also many eseaches use it, e.g. Rusly, Aye, Chates and Ooi [8], while e.g. Batosiewicz, Aidoun, Desevau and Mecadie used tubulence model SST k-ω to simulate the flow in suesonic ejectos in wok [9]. Šimák [10] studied numeically flow in a two-dimensional suesonic ejecto by seveal tubulence models and found that tubulence model k- ω is sufficient to catue all imotant infomation about the flow. Howeve, it was found in wok [6] that all numeical esults fo vaious tubulence models vaied as comaed with eeiments. This study follows wok made by Dvořák et al. [11] in which PIV and CTA methods wee used to investigate flow in cylindical miing chambe. Comle eeimental data of fou vaious ejecto egimes wee obtained and velocity contous and vectos fo them wee esented. The aim of this study is to analyze the flow in cylindical miing chambe. A. Dimensions of the Ejecto II. METHODS The dimensions of the configuation of the nozzle and the miing chambe ae in Fig. 1. Fo numeical investigation, the ejecto had the same dimensions. We used imay nozzle with diamete of d = 19. (mm) and miing chambe of diamete D = 40 (mm), i.e. the inlet aea atio of nozzles was µ = A1 A = 0.3. The length of the miing chambe was L = 9 D = 360 (mm), the diffuse had divegence angle of 6 and enlagement atio of the diffuse was µ = A A B. Numeical Investigation D 4 3 = Fo numeical calculation we used commecial softwae Ansys - Fluent 14. On the base of knowledge obtained in woks [6] and [7], we used tubulence model ealizable k- ε with enhanced wall teatment. This tubulence model is suitable fo ai-symmetic oblems and oved the best convegence fo this kind of oblem. The model was twodimensional and had the same geomety as it is esented in the Fig. 1. The fluid was ai consideed as ideal gas. Pessue inlets, i.e. total essues and total temeatues, wee used fo definition of inlet bounday conditions, essue outlet, which is back-essue, was used at the ejecto eit. Values of temeatues and essues on boundaies wee taken fom eeiments in wok [11]. The oveessue of imay ai Intenational Scholaly and Scientific Reseach & Innovation 7(7)

2 Intenational Jounal of Mechanical, Aeosace, Industial, Mechatonic and Manufactuing Engineeing Vol:7, No:7, 013 Intenational Science Inde, Mechanical and Mechatonics Engineeing Vol:7, No:7, 013 waset.og/publication/16569 steam was 1000 (Pa) = C. Theoetical Aoach We will comae obtained data with method esented by Tyle and Williamson in wok [1]. They divided the miing ocesses in the miing chambe into two egions: The initial egion and the main egion. They efomed a seies of eeiments fo vaious velocity atios and coss section atios. Accoding them, the momentum equation fo constant aea miing chambe has fom C = β 4 f X, (1) whee f is aveaged fiction coefficient, is coection of fiction fo initial egion and X = / D is elative aial coodinate. β is momentum coefficient defined by elation A v da ( A) β = β, () T ( v da) ( A) whee A eesents coss section, v velocity and β T 1. 0 is momentum coefficient fo fully develoed tubulent flow. is static essue coefficient defined by atio C C =, (3) ρ c whee (Pa) is static essue ise fom the beginning of 1 the miing chambe and the denominato eesents dynamic essue (Pa) of esulting flow. The total essue coefficient is similaly defined by elationshi. C 0 ( ) = (4) ρ c whee ( ) is total essue at the entance of the miing 0 1 chambe. Eeimental data was comiled and authos used coelation technic to obtain elation fo length of the initial egion of miing n C0 1 µ l 0 = 1, (5) 1 z 1 ω 1+ µ whee ω = v v is velocity atio and 1 µ = A 1 A is aea atio of nozzles. Constants obtained by Tyle and Williamson in wok [1] by coelation of eeimental data ae C 0 = 4. and n = 0 1. III. RESULTS AND DISCUSSION Results fo ejecto mode Γ = m / m1 = 0 and fo velocity atio ω = 0 ae lotted in Fig.. It is theefoe the mode with zeo seconday mass flow ate m = 0 and with vey high back essue. As it is seen fom contous of aial velocity c, a seaation zone with evesal flow occued, see gay aea. As it will be shown late, the tansition between the initial and main egions is usually in the lace, whee the shea laye intefees with the wall of the miing chambe, esectively, with the bounday laye on it. It seems in Fig. that it is not valid fo egimes with evesal flows. Similaly, the tansition oint is unclea when comaing contous of tubulent kinetic enegy k and dissiation ε. As will be shown on the contous of adial velocity c, the tansition can be most easily identified as a lace whee the adial velocity changes its diection, i.e. c = 0. Fig. 1 Dimensions of ejecto ats and ositions of static essue tas of the ai ejecto, investigated eeimentally by PIV and CTA methods by Dvořák et al. [11] Intenational Scholaly and Scientific Reseach & Innovation 7(7)

3 Intenational Jounal of Mechanical, Aeosace, Industial, Mechatonic and Manufactuing Engineeing Vol:7, No:7, 013 Intenational Science Inde, Mechanical and Mechatonics Engineeing Vol:7, No:7, 013 waset.og/publication/16569 Fig. Ejecto mode with ejection atio Γ = m / m1 = 0 and velocity atio ω = 0. Contous of aial velocity c, adial velocity c, tubulent kinetic enegy k, tubulent dissiation ε, couses of static essue, total essue, tubulent kinetic enegy, momentum coefficient β, static essue coefficient C and total essue coefficient C Intenational Scholaly and Scientific Reseach & Innovation 7(7)

4 Intenational Jounal of Mechanical, Aeosace, Industial, Mechatonic and Manufactuing Engineeing Vol:7, No:7, 013 Intenational Science Inde, Mechanical and Mechatonics Engineeing Vol:7, No:7, 013 waset.og/publication/16569 Fig. 3 Ejecto mode with ejection atio Γ = m / m1 = 0. 5 and velocity atio ω = Contous of aial velocity c, adial velocity c, tubulent kinetic enegy k, tubulent dissiation ε, couses of static essue, total essue, tubulent kinetic enegy, momentum coefficient β, static essue coefficient C and total essue coefficient C Intenational Scholaly and Scientific Reseach & Innovation 7(7)

5 Intenational Jounal of Mechanical, Aeosace, Industial, Mechatonic and Manufactuing Engineeing Vol:7, No:7, 013 Intenational Science Inde, Mechanical and Mechatonics Engineeing Vol:7, No:7, 013 waset.og/publication/16569 Fig. 4 Ejecto mode with ejection atio Γ = m / m1 = 1 and velocity atio ω = Contous of aial velocity c, adial velocity c, tubulent kinetic enegy k, tubulent dissiation ε, couses of static essue, total essue, tubulent kinetic enegy, momentum coefficient β, static essue coefficient C and total essue coefficient C The length of the initial miing egion fo this mode is l0 = 0. 9 D and the length of the miing zone is l m = 4. 5 D. The end of the main egion is consideed in the oint of maimal static essue. In the to of Fig., static essue distibution on the miing chambe wall, total 0 essue and kinetic enegy k, which ae evaluated 0 as mass aveaged values, ae lotted in the diagam. The couse of total essue is affected by the evesal flow fo this mode. Fo othe modes, the couse of the total essue fall is moe monotonic. The eistence of evese flow does not affect the couse of the static essue. Afte the maimal static essue, i.e. afte the finished miing, the static and the total essue ae deceasing similaly. It is caused by fully Intenational Scholaly and Scientific Reseach & Innovation 7(7)

6 Intenational Jounal of Mechanical, Aeosace, Industial, Mechatonic and Manufactuing Engineeing Vol:7, No:7, 013 Intenational Science Inde, Mechanical and Mechatonics Engineeing Vol:7, No:7, 013 waset.og/publication/16569 develoed velocity ofile. The maimal kinetic enegy is attained at aoimately /5 of the main egion length. Cuves of momentum coefficient β, static essue coefficient C and total essue coefficient C ae lotted in the bottom of Fig.. Fo this mode, the value C = is eached at the miing chambe outlet. Results fo mode with ejection atio Γ = 0. 5 and velocity atio ω = ae lotted in Fig. 3. In this mode, the evese flow was absent and the tansition between the initial and the main egion can be well evaluated. Again, the easiest and most ecisely on contous of the adial velocity at the oint, whee c = 0, but also on the contous of tubulent kinetic enegy k and dissiation ε, fom which it is clea that the tansition oint is at the same oint, whee the shea laye meets the miing chambe wall. It is obvious, fom aial velocity contous, that the tansition caused etension of the bounday laye. The length of the initial miing egion fo this mode is l0 = 1. 6 D and the length of the main miing zone is = 4. 8 D. l m It will be shown in the othe modes, the length of the initial miing egion deends moe on velocity atio than the length of the main egion. The maimum of tubulent kinetic enegy is again in aoimately /5 of the main miing egion. The decease of the total essue is much moe gadual than in evious case, slightly highe losses ae in the main miing egion. The esulting decease of the total essue is at the end of the miing is C =. 75. Simila emaks can be done in the net mode in Fig. 4 fo mode with ejection atio Γ = 1 and velocity atio ω = 0. 3, again without etun flow. Miing is aleady quite slow in this case, the length of the initial egion of miing inceased to l0 = 3 D and the length of the main miing zone is l m = 5 D. The last investigated mode was fo ejection atio Γ = 1. 5 and velocity atio ω = Fo this mode, which is not esented in the aticle, the length of the miing chambe was aleady insufficient, so only the length of the initial egion of miing could be evaluated as l0 = 4. D. The end of miing occued afte the miing chambe. The values obtained fo the vaious modes ae lotted in Table I. IV. DISCUSSION Let us now look in moe detail at each of the miing egion in geneal. The initial miing egion begins at the tailing edge of the imay nozzle. It is the aea in which thee is an unaffected seconday ai flow and its end is defined as a lace in which unaffected seconday ai flow vanishes, i.e., meet the two shea layes that enclose diven flow: fee shea laye (miing laye) between the imay and seconday flows fom one side and the bounday laye on the miing chambe wall fom the othe side. TABLE I EVALUATION OF NUMERICAL RESULTS FOR VARIOUS MODES Ejection atio Γ Velocity atio ω Length of the initial egion of miing l 0 D Length of main egion of miing l h D Static essue ise C Total essue do C Fo the initial miing egion, vey small incease in static essue is tyical. In some cases, fo high velocity atios, the static essue even falls due to fiction losses. Sometimes this case can be consideed as a fee jet flow. Small change in static essue is of couse due to a small change in momentum. It can be shown that the decease of momentum due to change of the velocity ofile between the beginning of the miing chambe and the end of initial miing egion is vey small. It tuns out, howeve, that the essue incease in the initial miing zone affects the flow in the miing chambe athe negatively. The incease in essue caused deceleation of the seconday ai flow, see contous of c, and etension of the bounday laye. As a esults, the seconday ai flow is ushed to the miing laye, see the contous of c. The aim of the miing is but oosite, i.e., the acceleation of the seconday steam and mass tansfe in the diection to the seconday steam. The main disadvantage of the constant aea miing chambe and the eason why it cannot be effective enough ae: At the beginning, the seconday steam is slowed down and the fluid is dislaced towad the imay steam, and only in the main egion of miing the seconday steam is acceleated and enegy begins to move into the seconday steam. Although the change of momentum in the initial egion of miing is small, the total essue dos by almost the same intensity as in the main egion of miing. Tubulent kinetic enegy inceases fom the beginning of the miing chambe as the miing laye eands. The length of the initial egion of miing is obviously vey stongly deendent on the velocity atio. Once the bounday laye on the miing chambe wall and the miing laye meet, the momentum falls and the static essue ises faste. At this oint, thee is the highest deceleation of fluid in the bounday laye, which is not yet acceleated by faste fluid fom the miing laye. The modes with small velocity atios, when the seconday steam is slow and the essue ise is eteme, a flow seaation can occu at this oint. The tansition between the initial and main aea is vey sha. Fom this oint, the momentum coefficient deceases aidly and it is the lace of the lagest gadient of the static essue. In the main egion of miing thee is no longe unaffected seconday steam, and if the coe of the imay Intenational Scholaly and Scientific Reseach & Innovation 7(7)

7 Intenational Jounal of Mechanical, Aeosace, Industial, Mechatonic and Manufactuing Engineeing Vol:7, No:7, 013 Intenational Science Inde, Mechanical and Mechatonics Engineeing Vol:7, No:7, 013 waset.og/publication/16569 steam has disaeaed, the miing laye occuies the entie coss section of the miing chambe. The tubulent kinetic enegy inceases and eaches its maimum at aoimately /5 of the length of the main egion of miing. Obviously, the length of the main miing zone is only little deendent on the velocity atio, the main effect is may be caused only by the atio of coss sections. End of the main egion of miing is consideed by many eseaches as the oint of maimum static essue. Let's look at this in moe detail coss section. Accoding to Tyle and Williams [1] the end of miing is at the oint whee momentum coefficient falls to nomal value of fully develoed tubulent flow, but the eact value is not stict, and the size is diffeent fo each Reynolds numbe. Fom the analysis of the numeical calculations, the oint of the maimal static essue coesonds aoimately to the oint, whee the tubulent kinetic enegy has its maimal value in the cente of coss section of the miing chambe, while the maimal values ae bound to the miing laye in the beginning of miing. Afte this oint, the dissiation deceases and the total essue fall is caused mainly by fiction losses. Fig. 5 The lengths of initial miing egion l 0 and main miing egion l accoding [1] and obtained by numeical calculation with m tubulence model ealizable k-ε (Rke) As shown in Fig. 5, whee is a ediction of the length of the main egion of miing accoding to [1], the theoetical and numeical values does not agee vey well. The esults do not coesond to the values calculated using the model of tubulence Realizable k-ε no measued mainly fo highe velocity atio. Thee is of couse the question of the ole of initial conditions of the tubulence, Reynolds numbe, and moe. But it is clea that the method [1] based on emiical data coelation may not aly geneally to othe ejecto configuation than those used in [1]. Detemining of the coect coefficients fo ou case would equie similaly lagescale eeiments, which made mentioned authos, and also thee would be no univesal method. V. CONCLUSIONS The esence of the initial and the main miing egion wee confimed. In the initial miing egion, an unaffected seconday ai steam eists. It stats at the tailing edge of the imay nozzle and the end can be defined as a lace in which two shea layes enclosing seconday steam meet: fee shea laye (miing laye) between the imay and seconday steams fom one side and the bounday laye on the wall of the miing chambe fom the othe side. Vey small incease in static essue associated with a small decease in momentum is tyical fo the initial miing egion. The imay steam can be consideed as a fee steam. It tuns out that the essue incease in the initial egion effects the miing ocesses athe negatively. It deceleates the seconday steam and etends the bounday laye, which ushed the seconday steam towads the miing laye. The miing is but oosite, i.e. the acceleation of the seconday steam and the mass and momentum in the diection of the seconday steam. Having said that the main disadvantage of the constant aea miing chambe and the eason why it cannot be effective enough: At the beginning of the miing chambe, the seconday steam is slowed down and the fluid is dislaced towad the imay steam. Only in the main miing egion the seconday steam is acceleated and fluid begins to move into the seconday steam. Although only a small change of momentum occus in the initial egion, the stagnation essue dos by almost the same intensity as in the main egion. Length of initial miing zone is obviously vey stongly deendent on the elative velocity. Once the miing laye meets the edge of the bounday laye on the wall of the miing chambe, the momentum begins to fall faste and also the static essue ises faste. Thee is the geatest deceleation of fluid in the bounday laye, which is not yet acceleated by faste fluid fom the miing laye at this oint. A flow seaation and evesal flow occus at this oint fo ejecto modes with low velocity atios. The tansition between the initial and main aea is vey shot. Fom this oint, momentum coefficient deceases aidly and it is the lace of the highest gadient of static essue. Thee is no longe unaffected seconday steam in the main egion of miing. If the coe of the imay steam has disaeaed, the miing laye occuies the entie coss section of the miing chambe. Obviously, the length of the main miing zone is only little deendent on the velocity atio. Accoding to many eseaches, the end of miing laced in a osition of maimal static essue. It is aoimately the oint, whee the tubulent kinetic enegy has its maimal value in the ais of the miing chambe, while the maimal value is bound to the miing laye in the beginning of miing. REFERENCES [1] D.W. Sun, I.W. Eames, Recent Develoments in the Design Theoies and Alications of Ejectos a eview, Jounal of the Institute of Enegy, (1995) Intenational Scholaly and Scientific Reseach & Innovation 7(7)

8 Intenational Jounal of Mechanical, Aeosace, Industial, Mechatonic and Manufactuing Engineeing Vol:7, No:7, 013 Intenational Science Inde, Mechanical and Mechatonics Engineeing Vol:7, No:7, 013 waset.og/publication/16569 [] S.T. Bonnington, A.L. King, Jet Pums and Ejectos, a State of the At; Review and bibliogahy (nd edn), BHRA Fluid Eng, Canfield, Bedfod UK (1976) [3] J.L. Pote, R.A. Squyes, A Summay/Oveview of Ejecto Augmento Theoy and Pefomance, ATC Reot No. R-91100/9CR-47A, Vought Con Advanced Technology C, Dallas, Teas (1981) [4] J.H. Keenan, E.P. Neumann, A Simle Ai Ejecto, J Alied Mechanics, Tans ASME 64, A75 - A81 (194) [5] J.H. Keenan, E.P. Neumann, F. Lustwek, An Investigation of Ejecto Design by Analysis and Eeiment, Jounal of Alied Mechanics, Tans ASME 7, (1950) [6] V. Dvořák, Otimized Ai-Symmetic Ejecto Eeimental and Numeical Investigation, Eeimental Fluid Mechanics 4 (1), (009) [7] V. Dvořák, Numeical Comutation of Efficiency Cuve of Ejecto, Confeence ANSYS, Pague, (007) [8] E. Rusly, Lu Aye, W.W.S. Chates, A. Ooi, CFD Analysis of Ejecto in a Combined Ejecto Cooling System, Intenational Jounal of Refigeation 8, (005) [9] Y. Batosiewicz, Z. Aidoun, P. Desevau, Y. Mecadie, Numeical and eeimental investigations on suesonic ejectos, Intenational Jounal of Heat and Fluid Flow 6, (005) [10] J. Šimák, Comutation of the Flow and Inteaction of Shock Waves in a D Suesonic Ejecto, Colloquium Fluid Dynamics 009, Institute of Themomechanics AS CR, v.v.i., Pague, Czech Reublic, Octobe 1-3, 009. [11] V. Dvořák, P. Novotný, P. Dančová, D. Jašíková, PIV and CTA Measuement of Constant Aea Miing in Subsonic Ai Ejecto, Eeimental Fluid Mechanics 7 (1), (01) [1] R. A. Tyle, R. G. Williamson, Confined miing of coaial flows, Aeonautical eot LR-60, NRC no (Division of Mechanical Engineeing, Ottawa, Canada 1980). Intenational Scholaly and Scientific Reseach & Innovation 7(7)