EXPERIMENTAL INVESTIGATIONS OF THE TURBULENT SWIRL FLOW IN STRAIGHT CONICAL DIFFUSERS WITH VARIOUS ANGLES

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1 Ilć, D. B., et al.: Expermental Investgatons of the Turbulent Swrl Flow n THERMAL SCIENCE, Year 17, Vol. 1, Suppl. 3, pp. S75-S736 S75 EXPERIMENTAL INVESTIGATIONS OF THE TURBULENT SWIRL FLOW IN STRAIGHT CONICAL DIFFUSERS WITH VARIOUS ANGLES by Dejan B. ILIĆ, Mroslav H. BENIŠEK, and Djordje S. ČANTRAK Hydraulc Machnery and Energy Systems Department, Faculty of Mechancal Engneerng, Unversty of Belgrade, Belgrade, Serba Orgnal scentfc paper Results of expermental nvestgatons of the turbulent swrl flow n three straght concal dffusers wth varous dffuser total angles are presented n ths paper. All three dffusers have the nlet dameter.4 m and total dvergence angles 8.6, 1.5, and 1.6. The ncompressble swrl flow feld s generated by the axal fan mpeller, and for each dffuser several regmes were acheved by changng rotaton number. Orgnal classcal probes were used for measurements. The dstrbutons of the average man swrl flow characterstcs along the dffuser are shown. Dstrbutons of the nlet Boussnesq number, outlet Corols coeffcent, rato of the swrl and completely axal flow loss coeffcents at concal dffuser on the nlet swrl flow parameter are also presented. Key words: dffuser, turbulent swrl flow, loss coeffcent Introducton Turbulent swrl flow s a complex phenomenon. It s a three-dmensonal and ansotropc flow, wth ntensve dffuson processes, hgh dsspaton rate, etc. Ths flud flow has regons characterzed by hgh vortcty. They often occur n techncal practce and n nature as well. Turbulent swrl flow occurs at the ext of the turbomachnes, such as n the case of the flow at the dffuser nlet followng the axal pump and fan mpellers, or n the draft tubes followng bulb turbnes. These problems attract researches wth the dea to ncrease energy effcency,. e. to acheve better power parameters (characterstcs) of hydraulc turbomachnes and systems. An overvew of the turbulent flow expermental research n dffusers s presented n papers [1, ]. In the past two decades, research of the swrl flow n a concal dffuser s manly performed by CFD, whch s also upgraded wth flow smulatons n the turbne flow passages. It s also desrable, for good dffuser swrl flow predcton, to know the value of the Corols coeffcent at the dffuser ext, because t has hgher values than n the case for pure axal flow. The man am of ths paper s to provde the ntegral characterstcs of the turbulent swrl flow n straght dffusers wth crcular cross-secton whch are used wth bulb turbnes n hydropower plants. Study of the energy losses, whch drectly nfluence the hydraulc machnery effcency, has focus on: determnaton of the rato of swrl and pure axal flow * Correspondng author, e-mal: dlc@mas.bg.ac.rs

2 S76 Ilć, D. B., et al.: Expermental Investgatons of the Turbulent Swrl Flow n THERMAL SCIENCE, Year 17, Vol. 1, Suppl. 3, pp. S75-S736 loss coeffcent n the straght concal dffusers, determnaton of the swrl flow coeffcents n the cross-sectons and the law of ther behavng along the dffuser, calculaton of the Corols coeffcent and Boussnesq number for the swrl flow n cross-sectons along dffuser and ther dependence on the swrl flow parameters. Paper [] presents part of the expermental results for dffuser II wth the angle 1.5. New expermental results for all three angles, ncludng the old one dffuser II, are revealed here. Two new steel dffusers are desgned and bult, wth a total dvergence expanson angles: dffuser I and dffuser III. Flud flow separaton for axal flow n dffusor could be presumed on the bass of the dffuser geometry (angle and area rato). Namely, n the case of the non-swrl flow, for dffusers whch are studed n ths paper, assumpton s that for total angles 8.6 and 1.5 separaton does not exst, whle wth angle 1.6 separaton should occur. Swrl flow relocates separaton pont downstream comparng to the non-swrl flow. The swrl flow gves more energy to the boundary flow, usng the centrfugal force, so that the separaton pont can be avod. Separaton does not exst for swrl flows n dffusers even wth angle 16, f moderate crcumferental flow s exerted at the dffuser nlet. It means that swrl flow n dffusers wth angle 1.6 wll not result wth flud flow separaton. Expermental test rg and methodology Expermental test rg s shown n fg. 1. The same test rg was used for the turbulent swrl flow researches n all three concal dffusers. Ths test rg s prmary use was for the axal fans expermental characterstcs determnaton after the nternatonal standard ISO 581. It was desgned and constructed by Prof. Dr.-Ing. Zoran D. Protć (19-1). Fgure 1. Test rg for expermental nvestgaton The ncompressble swrl flow feld s nduced (fg. 1) by the axal fan mpeller () wth rotatonal speed controlled motor (1). The man geometry characterstcs of the axal fan mpeller, model AP 4, Mnel, Serba, are gven n [3]. The axal fan s n-bult n the straght ppe secton wth a profled nlet nozzle (3). The mpeller s followed by the straght concal dffuser (4), whch s placed n the chamber (5). The test bed s equpped wth the honey-comb (6), flow meter (7), ppe (8), booster fan (9) and flow regulator (1). The man dmensons of the concal dffuser I, II and III are gven n tab. 1. The dffusers have the same nlet dameter D =.4 m and length L = 1.8 m. Velocty and pressure felds were measured at cross-sectons gven n tab. and fg., wth 39 measurng ponts along the dameter. The measurements are performed wth unque home-made combned Prandtl and angular probes [4, 5].

3 Ilć, D. B., et al.: Expermental Investgatons of the Turbulent Swrl Flow n THERMAL SCIENCE, Year 17, Vol. 1, Suppl. 3, pp. S75-S736 S77 Investgatons of the swrl flow performed wth Conrad probe [6] and LDA systems, n dffusers [7], showed that the radal velocty s much smaller than crcumferental and axal velocty c r «c z, c r «c u for the used axal fan mpeller. Furthermore, the assumpton of twodmensonal flow was ntroduced on the bass of ths. Also, the followng values were measured: α, Δp t (Δp t = p t - p a ), Δp (Δp = p - p a ), c {c = [(Δp t - Δp]/ρ) 1/ }, c z (c z = c cosα) and c u (c u = c snα). Table 1. Dmensons of the concal dffuser Dffuser D D 9 n 9 L α df [m] [m] [-] [m] [ ] I II III Table. Postons of the measurng sectons Measurng sectons () z [m] z* = z/l [-] * Fgure. Postons of the measurng sectons Each measurng seres,. e. regme, s characterzed by varous parameters: Ω - swrl flow parameter, Reynolds number and generated type of the swrl nflow profles (velocty, pressure and crculaton). The number of measurng seres for dffuser I s seven (A- G, tab. 3) and for dffuser III t s fve (A-E, tab. 3). Table 3. Measurng seres for dffuser Dffuser I (8.6 ) Dffuser III (1.6 ) Dffuser II (1.5 ) Seres Ω Re 1-5 Seres Ω Re 1-5 Seres Ω Re 1-5 A A.13.5 X B B Y C.1.53 C Z D D 3..7 E.73.7 E.9.83 F G For dffuser II measurements were performed for measurng seres (A-V), whch s presented n [], whle three new seres are added (X, Y and Z, tab. 3). These three new

4 S78 Ilć, D. B., et al.: Expermental Investgatons of the Turbulent Swrl Flow n THERMAL SCIENCE, Year 17, Vol. 1, Suppl. 3, pp. S75-S736 seres are added to complete the results of nvestgaton on dffuser II. Velocty and pressure felds n dffuser II at ten cross-sectons (from to 9, except *) were measured for all seres. Velocty and pressure felds were measured n dffusers I and III at certan cross-sectons. The same defntons of the swrl flow characterstcs [] are used for all three dffusers. These relatons for swrl flow characterstcs n the cross-sectons ( =, *, 1, 9) of the concal dffuser are presented heren. Flow dscharge s calculated as: Mean crculaton s gven as: whle specfc energy of the rotatonal flow s: R Q π rczdr, m = ρq (1) R 4π u z Q Γ r c c dr () R 1 cu 1 c d u u z m R A c zm e m c c rdr Specfc energy of the axal flow s calculated n the followng manner: (3) whle mean axal velocty s defned as: R 1 cz 1 d R A c zm 3 ec m czrdr z m Moment of the momentum for crcumferental flow: whle the moment of the axal flow s: c zm R c d πρ d u u u z A (4) Q πr (5) m Γ M rc m c c r r (6) π R c zd π z d z c zm A K c m c r r β K (7) Moment of the mean axal velocty s: whle the Boussnesq number [8] s defned as: K c π ρc R zm (8) zm

5 Ilć, D. B., et al.: Expermental Investgatons of the Turbulent Swrl Flow n THERMAL SCIENCE, Year 17, Vol. 1, Suppl. 3, pp. S75-S736 S79 K cz β K (9) czm Swrl flow ntensty s defned n the followng way: e θ e c u c z R R rc c dr u z rc dr Instead of prevously shown swrl flow parameters, another several swrl flow parameters are defned by varous authors []. These are: swrl flow parameter [9], swrl ntensty [1], swrl number [11] and swrl ntensty [1]. The relatons between them are obvous and are presented n tab. 4. Table 4. Swrl non-dmensonal parameters Swrl non-dmens parameters Formula Relatons 3 z (1) Swrl flow parameter Ω Q R Γ R R u z rc dr z R rccdr 1 Ω S β for Rankn swrl flow: 1 Ω S Swrl ntensty Ω * R ccrd u z M c u Rc m R c 3 zm zm r Ω * 1 Ω Swrl number Swrl ntensty R R z u z u ccrdr ccrdr M c u S RK β Rc R 3 cz zm R c rdr z R R π d d u z u z ρ ccr r ccr r M c u I K D Dπρc R R c 3 czm zm zm * Ω I S β β for Rankn swrl flow: S Ω * 1 1 * I Ω 4Ω for Rankn swrl flow: * Ω Ω I 4 The swrl flow parameter Ω s more convenent, because t can be easly determned on the runner (mpeller) outlet,. e. at dffuser (draft tube) nlet f the flow dscharge and the turbomachne specfc flow energy are known only. The swrl flow parameter [9] s defned as:

6 S73 Ilć, D. B., et al.: Expermental Investgatons of the Turbulent Swrl Flow n THERMAL SCIENCE, Year 17, Vol. 1, Suppl. 3, pp. S75-S736 Ω Q R Γ R rczdr R u zd R r c c r whle Reynolds number: czm R Re (1) In the case of the swrl flow, consderng the eqs. (5) and (11) Reynolds number s correlated to the swrl flow parameter n the defned cross-secton, wth the knematc vscosty and averaged crculaton: ΩΓ Re (13) π Introducng that the ar knematc vscosty s constant, t s obtaned for the dffuser nlet secton that Re = const Ω Γ. Specfc swrl flow energy n each dffuser cross-secton s: R (11) π es rptczdr ρq (14) Specfc energy swrl flow losses along the straght concal dffuser from to the -th cross-sectons are calculated as: e e e (15) S S S The swrl flow energy loss coeffcent s expressed as: ζ S e (16) c S zm The axal flow energy loss coeffcent of the dffuser s ntroduced from [13]: ζa f δ,re, df, n (17) where = Δ/R, Re = c zm R /ν, and n = A /A. The rato of swrl and pure axal flow loss coeffcent along the dffuser [] s: ζ ζ S A f Ω (18) where Ω s the dffuser nlet swrl flow parameter Ω = Q /R Γ. The Corols coeffcent at the dffuser outlet s then defned n the followng way:

7 Ilć, D. B., et al.: Expermental Investgatons of the Turbulent Swrl Flow n THERMAL SCIENCE, Year 17, Vol. 1, Suppl. 3, pp. S75-S736 S731 Expermental results and dscusson R9 1 S 3 9 z d z9 R9πczm R 9 9c zm9 (19) α cc A rcc dr Profles of the total and statc pressure become more unform along the dffusers I, II and III. Ths s also shown for measurements n the dffuser II []. The total pressure has the lowest value n the vortex core regon. Statc pressure s the hghest on the wall however t s the lowest n the vortex core regon, where the value of relatve statc pressure can be negatve. Axal velocty components have small values n the vortex core. In some cases, the reverse flow occurs. Crcumferental velocty profle transforms downstream wth the tendency to form a sold body profle on the dffuser outlet. Swrl flow characterstc values for dffusers I, II (three added seres) and III are calculated for each seres n the measurng poston = (z = ) and presented n tab. 5. The Corols coeffcent values and the rato of swrl and pure axal flow loss coeffcent at the dffuser outlet are also presented here. Table 5. Characterstc dffuser swrl flow values Dffuser I (8.6 ) Dffuser III (1.6 ) Ser. Ω α S9 θ β ζ S9 /ζ A9 Ser. Ω α S9 θ β ζ S9 /ζ A9 A A B B C C D D E E F Dffuser II (1.5 ) G Ser. Ω α S9 θ β ζ S9 /ζ A9 X Y Z It s notceable that the specfc swrl flow energy decreases exponentally, n the form e s = e s exp(-z*), along the dffusers I and III (fg. 3) for all measurng seres. Here, s the dampng coeffcent whch depends on Ω, Re and. Fgure 3. Swrl flow specfc energy e s along the dffuser (z* = z/l); I for the measurng seres A to G (left) and dffuser III for the measurng seres A to E (rght)

8 S73 Ilć, D. B., et al.: Expermental Investgatons of the Turbulent Swrl Flow n THERMAL SCIENCE, Year 17, Vol. 1, Suppl. 3, pp. S75-S736 Ths s also shown n the paper [] for dffuser II. Specfc energy flow losses have ncreasng character along the dffusers I and III for all measurng seres and depend on Ω, Re and (fg. 4). Fgure 4. Swrl flow specfc energy loss Δe s along the dffuser (z* = z/l); I for the measurng seres A to G (left) and dffuser III for the measurng seres A to E (rght) Mean crculaton dstrbutons along the dffusers I and III (fg. 5) decrease lnearly obeyng the functon Γ = Γ - z* = Γ (1 - (/Γ ) z*)= Γ (1 - a z*) for all measurng seres. Here, Γ s mean crculaton for z* = and s the dampng coeffcent whch depends on Ω, Re and. Fgure 5. Mean crculaton Γ along the dffuser (z* = z/l); I for the measurng seres A to G (left) and dffuser III for the measurng seres A to E (rght) Swrl flow parameter transformaton along the dffusers I and III (fg. 6) has the followng character Ω = Ω (1+c 1 z*-c z * ) -1 for all measurng seres (c 1 = Ltgα df /R - a, c = altgα df /R = ac 1 + a = const and a = /Γ ). Reynolds number nfluence on the dstrbuton of the presented parameters s gven through the nfluence of the swrl flow parameter and average crculaton. Dependence of the Re - number of Ω Γ for all operatng regmes of dffusers I and III, and some regmes of dffuser II s presented n fg. 7. Swrl flow characterstc values (β, ζ S9 / ζ A9 and α S9 ) dependences on the swrl flow parameter Ω, for dffusers I, II, and III, are presented n fgs. 8-1.

9 Ilć, D. B., et al.: Expermental Investgatons of the Turbulent Swrl Flow n THERMAL SCIENCE, Year 17, Vol. 1, Suppl. 3, pp. S75-S736 S733 These, the most mportant results, for three added and all other seres, for dffuser II, are presented because they nfluence on the coeffcent change reported n paper []. Ths s shown n tab. 6. Fgure 6. Swrl flow parameter Ω along the dffuser (z* = z/l); I for the measurng seres A to G (left) and dffuser III for the measurng seres A to E (rght) The Boussnesq number dependences on the swrl flow parameter Ω for dffusers I and III (fg. 8) show that there s a great gradent n the regon Ω <.5, but t slowly converges to β = 1. n the regon Ω.5. Ths s also shown for dffuser II []. Fgure 7. Reynolds number Re dependences of Ω Γ for dffusers; I (measurng seres A to G), II (measurng seres A to I, X, Y, Z) and III (measurng seres A to E) Fgure 8. Boussnesq number β dependences on swrl flow parameter Ω for dffusers; I (measurng seres A to G), II (measurng seres A to Z) and III (measurng seres A to E) The Boussnesq number dependence on swrl flow parameter, at the entrance of the dffuser, for each dffuser (fg. 8), can be approxmated by an exponental law: B β 1,1 p () Ω where the values of the coeffcents B and p are provded n tab. 6.

10 S734 Ilć, D. B., et al.: Expermental Investgatons of the Turbulent Swrl Flow n THERMAL SCIENCE, Year 17, Vol. 1, Suppl. 3, pp. S75-S736 The rato of the swrl and pure axal flow loss coeffcents ζ S9 /ζ A9 dependence on the nlet swrl flow parameter along the dffuser, for each dffuser (fg. 9), can be also approxmated by the law: where the values of the coeffcents k and n are lsted n tab. 6. ζ ζ S9 A9 k 1 Ωn (1) Fgure 9. Rato ζ S9 /ζ A9 dependences on swrl flow parameter Ω for dffusers; I (measurng seres A to G), II ([]) and III (measurng seres A to E) Fgure 1. Outlet Corols coeffcent α S9 dependences on swrl flow parameter Ω for dffusers; I (meas. seres A to G), II (meas. seres A to Z) and III (meas. seres A to E) The outlet Corols coeffcent dependence on the nlet swrl flow parameter, for each dffuser (fg. 1), can be approxmated by an exponental law as follows: α () Ω A S 1 9 m where the values of the coeffcents A and m are gven n tab. 6. Table 6. Coeffcents Dffuser I (α df = 8.6 ) II (α df = 1.5 ) III (α df = 1.6 ) B p A m k n It s obvous that the outlet Corols coeffcent has a great value when the swrl flow parameter Ω s small (fg. 8). It means that the nlet mean crculaton s strong and dscharge

11 Ilć, D. B., et al.: Expermental Investgatons of the Turbulent Swrl Flow n THERMAL SCIENCE, Year 17, Vol. 1, Suppl. 3, pp. S75-S736 S735 s small. In the case of the great swrl parameter values Ω, when the crculaton s weak and dscharge s greater, the Corols coeffcent decreases and tends to value α A = Total specfc energy loss Δe s9 of the turbulent swrl flow n the concal dffuser can be now calculated as follows: c Δe ζ ζ 1 zm k zm S S 9 9 A9 Ωn The Corols coeffcent for swrl flow at the dffuser outlet α S9 s very mportant for determnaton of the real swrl flow specfc knetc energy loss at the dffuser outlet. The value of the real specfc knetc energy loss Δe K9 s: c (3) czm9 A czm 9 K 9 S 9 A m Ω Δe α α 1+ where c zm9 s the mean velocty axal component c zm9 =Q/A 9. (4) Conclusons Ths paper presents expermental nvestgatons performed for three dffuser geometres α df = 8.6, 1.5, and 1.6. Part of the expermental results for dffuser II s presented n []. Geometry of the dffuser wth α df = 1.5 s an adapted geometry of the draft tube of one bulb turbne. It s demonstrated that t s very practcal to use swrl number (Ω) for the case of the turbomachnes as one of ts characterstc parameters. A sgnfcant number of measurement seres, characterzed by the swrl flow parameters Ω, Re numbers and varous types of generated swrl nflow profles are presented here. The velocty and pressure expermental profles transform ntensvely along the dffuser for all three dffuser angles. The mean crculaton decreases lnearly downstream for all tested dffuser geometres. It s shown that ratos of the loss coeffcents for swrl and pure axal flow along the dffuser cross measurng sectons depend only on the nlet swrl parameter Ω. Ths s more ntense for lower values of the nlet swrl flow parameter Ω and t s also the case for the Boussnesq number β and outlet Corols coeffcent α S9. Obtaned laws ζ S9 / ζ A9 = f(ω ) for all dffusers are gven. Dependences β = f(ω ), α S9 = f(ω ) and ζ S9 / ζ A9 = f(ω ) for all three dffuser angles have smlar character, and t s not possble to derve ther practcal dependence. It could be concluded that dffuser I, wth the smallest angle, has lower values β and α S9, for the same Ω, comparng to other two dffusers wth wder angles. The Corols coeffcent, for the case of the turbulent swrl flow at the dffuser outlet, depends only on the nlet swrl flow parameter Ω. Value α S9 provdes the possblty to determne the real swrl flow specfc knetc energy loss at the dffuser outlet. Ths concluson s of great mportance for the effcency bulb turbne calculaton. Expermentally obtaned velocty profles for all seres and dffusers have shown that there s no wall flow separaton. The reason s the presence of the centrfugal forces whch occur n the swrl flow.

12 S736 Ilć, D. B., et al.: Expermental Investgatons of the Turbulent Swrl Flow n THERMAL SCIENCE, Year 17, Vol. 1, Suppl. 3, pp. S75-S736 Acknowledgment Ths work was funded by the grant from the Mnstry of Educaton, Scence and Technologcal Development, Republc of Serba (TR 3546), whch s gratefully acknowledged. Nomenclature c local velocty, [ms 1 ] Greek symbols c r radal velocty component, [ms 1 ] α flow angle, [ ] c u crcumferental velocty component, [ms 1 ] α df dffuser angle, [ ] c z axal velocty component, [ms 1 ] Δ roughness, [m] L dffuser length, [m] Δp relatve statc pressure, [Pa] n 9 area rato (=A 9 /A ) Δp t relatve total pressure, [Pa] p a ambent pressure, [Pa] relatve roughness R dffuser radus, [m] Ν knematc vscosty, [m s 1 ] z dstance from dffuser nlet to specfed ρ flud densty, [kgm 3 ] dffuser cross secton, [m] z* relatve dstance from dffuser nlet to specfed dffuser cross secton, [] References [1] Azad, R.S., Turbulent Flow n a Concal Dffuser: A Revew, Expermental Thermal and Flud Scence, 13 (1996), 4, pp [] Benšek, M. H., et al., Investgaton of the Turbulent Swrl Flows n a Concal Dffuser, Thermal Scence, 14 (1), Suppl., pp. S141 - S154 [3] Čantrak Dj., et al., Investgaton of the Turbulent Swrl Flow n Ppe Generated by Axal Fans Usng PIV and LDA Methods, Theoretcal and Appled Mechancs, 4 (15), 3, pp. 11- [4] Benšek, M., Investgaton of the Swrlng Flow n Long Lned Crcular Ppes (n Serban), Ph. D. thess, Faculty of Mechancal Engneerng, Unversty of Belgrade, Belgrade, 1979 [5] Benšek, M. H., et al., Aplcaton of New Classcal Probes n Swrl Flud Flow Measurements, Expermental Technques, 34 (1), 3, pp [6] Benšek, M., et al., Unversal Calbraton Characterstcs Conrad Probe for Measures 3D Velocty, Pressure and Total Pressure of Statonary Invscd Flud Flow, Proceedngs of Metrologsts, Yug. Cong., Nov Sad, Serba, [7] Ilć, D. B., Swrl Flow n Concal Dffusers, Ph. D. thess, Faculty of Mechancal Engneerng, Unversty of Belgrade, Belgrade, 13 [8] Čantrak, S. M., Hdrodnamka Izabrana poglavlja (Hydrodynamcs Selected Chapters n Serban), Ffth revsed edton, Faculty of Mechancal Engneerng, Unversty of Belgrade, Belgrade, 1 [9] Strscheletzky, M., Equlbrum Forms of the Axsymmetrc Flows wth Constant Swrl n Straght, Cylndrcal Rotaton Geometres (n German), Voth Forschung und Konstrukton, Heft 5 (1959), Aufsatz 1 [1] Ktoh, O., Expermental Study of Turbulent Swrl Flow n a Straght Ppe, J. Flud Mech., 5 (1991), pp [11] Mahmud, T., et al., Flow Characterzatons of Swrl Coaxal Jets from Dvergng Nozzles, J. Flud Eng., 19 (1987), pp [1] Baker, W., Sayre, C.L., Decay of Swrl Flow of Incompressble Fluds n Long Ppes, Flow: Its Meas. and Control n Sc. and Ind., Proc. Symp., Pt. 1, Pttsburgh, USA, 1971, l, pp [13] Povh, I.L., Аэродинамический эксперимент в машиностроении (Aerodynamc Experments n Mechancal Engneerng n Russan), Moscow, Lenngrad, SSSR, 1974 Paper submtted: February 5, 16 Paper revsed: March 3, 16 Paper accepted: Aprl 9, Socety of Thermal Engneers of Serba. Publshed by the Vnča Insttute of Nuclear Scences, Belgrade, Serba. Ths s an open access artcle dstrbuted under the CC BY-NC-ND 4. terms and condtons.