INVESTIGATION OF THE TURBULENT SWIRL FLOWS IN A CONICAL DIFFUSER

Transcription

1 Benšek, M. et. al.: Investgaton of the turbulent swrl flows n a onal dffuser THERMAL SCIENCE: Vol. 14 (1), Suppl, pp.sxx Sxx INVESTIGATION OF THE TURBULENT SWIRL FLOWS IN A CONICAL DIFFUSER by Mroslav H. BENIŠEK, Dejan B. ILIĆ, Đorđe S. ČANTRAK, Ivan O. BOŽIĆ Faulty of Mehanal Engneerng Unversty of Belgrade Orgnal Sentf Paper UDC: DOI: Results of the theoretal and expermental nvestgatons of the turbulent mean swrl flows haratersts hange along straght onal dffuser of nompressble flud (ar) are presented n ths paper. The man swrl flow haratersts revew s gven. In addton: the spef swrl flow energy, the energy loss, the mean rulaton, the swrl flow parameter, the rato between the swrl and axal flow loss oeffents hange along the dffuser are presented. Among other values: the Boussnesq number, outlet Corols oeffent and swrl flow loss oeffent dependenes on nlet swrl flow parameter are also gven. The swrl flow spef energy and outlet Corols oeffent alulaton proedure are presented n ths paper, as well as expermental test bed and measurng proedures. The swrl flow felds were ndued by the axal fan mpeller. Varous swrl parameters were aheved by the mpeller openngs and rotatonal speeds. Key words: Swrl flow, swrl parameters, spef energy, loss oeffent, measurements. 1. Introduton Investgaton of the axal fan geometres, ther n bult and operatng haratersts and turbulent swrl flow generated followng the axal fan mpeller have been oupyng researhers attenton for years. Though most of the operatng haratersts have been leared out, stll fundaments of the generated swrl flud phenomena stay undsovered. Fous of ths paper s on ths very omplex physal phenomenon and reent tehnques n modelng modern blade geometres and revealng exstng ones. Swrl turbulent flow of the nompressble fluds n the straght onal dffusers oupes attenton of many researhes due to ts tehnal presene and spef flow phenomena hallenge. Suh knd of flow arses at the ext of bulb turbne runners, and also n the dffusers after axal pump mpellers, as well as n onal dffuser behnd the axal fan runners and n many other dffuser passages wth nternal swrl flow. Some aspets of swrl flow have been nvestgated n [1-11], but defnte answers of many questons have not been gven yet. One mportant task s to fnd good dffuser flow predton usng the reent CFD alulatons. In onneton wth ths s the problem of flow energy as well as the value of the Corols oeffent at the ext of dffuser, what represents the man objet of ths paper. The man reason for performng these measurements s the bulb turbne draft tube flow nvestgatons. The bulb turbne has the draft tube lke the straght onal dffuser. Turbne runner ndues swrl flow at ts nlet ross seton and t exsts tll the draft tube outlet. Draft tube has to reuperate the great amount of nlet knet energy wth as small as possble losses. Dependng on turbne s operatng pont, swrl flows at the nlet ross setons s less or more sgnfant. In workng regmes wth small flow rates, when runner blades are more losed, rumferental omponent of veloty at the ext of the runner beomes more sgnfant n relaton to axal omponent what results n greater losses n draft tube. Swrl at Correspondng author; e-mal: dl@mas.bg.a.rs

2 Benšek, M. et. al.: Investgaton of the turbulent swrl flows n a onal dffuser THERMAL SCIENCE: Vol. 14 (1), Suppl, pp.sxx Sxx the ext of the draft tube does not dsappear n a large doman of turbne operaton. Corols oeffents are, as a onsequene, hgher at the ext than n the ase for pure axal flow. All values, suh as energy loss and Corols, depends on the swrl non-dmensonal parameters. There are several swrl non-dmensonal parameters whh are ntrodued by varous authors. These swrl parameters onsderatons follows.. Expermental and theoretal nvestgaton of swrl flow haratersts n the straght onal dffuser The expermental researh was performed wth the ar test bed presented n fg. 1. Straght onal dffuser () s plaed n the reservor (1). Swrl flow was produed by the axal fan mpeller (3). The test bed s equpped wth flow meter (4), honey-omb (6) and booster fan (5). Fgure 1. Test bed for expermental dffuser flow researh. The man dmensons of the onal dffusers are gven at the fg.. Veloty and pressure felds were measured at ten ross setons (numbered from to 9) by the ombned Prandtl probe [1] and Conrad probe [13, 14]. The followng values were measured:, z, u, r, pt ( pt pt pa) and ps ( ps ps pa), where r z. The measurements were performed for twenty two measurng seres A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U and V, haraterzed by varous swrl parameters or S and Re numbers. Fgure. The man dmensons of the onal dffuser. On the bass of the measurng results ( ps, pt, u and z ) obtaned at every dffuser ross seton ( to 9) along ther dameters for all measurng seres (A to V) the next onlusons an be stated. The rapd hange of stream and total pressure as well as veloty omponents s evdent along the dffuser. The profle of total pressure (energy) beomes more unform. Total pressure s almost onstant n the dffuser outlet. Stream pressure s the hghest on the wall, whle t s the lowest n the vortex ore, where the value of ps an be negatve. Axal veloty omponents have small values n the vortex ore and, also, n some ases reverse flow ourred [1]. The dffuser effet nfluenes on the flow unformty. Crumferental veloty omponents hange ther profle along the dffuser ross seton wth tendeny to form sold body profle on the dffuser outlet. The bulk swrl flow haratersts n the ross setons (,1,,...9 ) of the onal dffuser are:

3 Benšek, M. et. al.: Investgaton of the turbulent swrl flows n a onal dffuser THERMAL SCIENCE: Vol. 14 (1), Suppl, pp.sxx Sxx Flow dsharge R Q π r dr, m = ρq, (1) z Mean rulaton R 4π r u z Q dr, () Spef energy of the rotatonal flow R 1 u 1 u m m R u z A zm e d rdr, (3) Spef energy of the axal flow R 1 1 z 3 z m m z R A zm e d rdr, 4) Mean axal veloty Q, (5) zm πr Moment of momentum for tangental flow R M d πρ d u u u z A m r m r r, (6) π Moment of axal flow R K d π d β K z z m zr r zm A, (7) Moment of mean axal veloty K πρ R, (8) zm zm Boussnesq number [15] β K K z zm, (9) Swrl flow ntensty e θ e R ruz u R z 3 rzd dr, 1) r Swrl flow parameter [16] z R r u z R r dr Q Ω, (11) R R dr

4 Benšek, M. et. al.: Investgaton of the turbulent swrl flows n a onal dffuser THERMAL SCIENCE: Vol. 14 (1), Suppl, pp.sxx Sxx Swrl ntensty [17] Swrl number [18] Swrl ntensty [19] Ω R d M u r u z 3 zm zm R m R R R z u z u u R 3 β R z zm R rr z d r, (1) rdr rdr M S, (13) RK R R πρ d d M u z u z u 3 zm zm zm r r r r I. (14) K D D πρ R R Followng relatons for Ω, Ω, S and I exst: Ω 1, 1 1 I Ω, 15) Ω 4Ω 1 Ω S, Ω I S, (16) β β β For Rankn swrl flow, where r onst and onst, next relatons exst: Reynolds number For z : u z 1 Ω S, S Ω, (17) Re Re Ω Ω I, (18) 4 R zm. (19) R zm. () Above mentoned onsderatons offer varous forms for swrl parameter defnton and relatons between them. It s deded, here, to use parameter Ω as the most onvenent one for alulaton n turbomahnery. It an be easly determned on the runner (mpeller) outlet,.e. at dffuser (draft tube) nlet, knowng the flow dsharge and spef flow energy of mahne. Defnton of parameter S demands determned axal veloty profle at the dffuser nlet, what s Boussnesq number. It s, n ths way, more omplated. Spef swrl flow energy n eah dffuser ross seton s R π es rp t zdr (1) ρq for =, 1,, 9. Spef energy swrl flow losses along the straght onal dffuser from to -th ross setons are e e e. () s s s

5 Benšek, M. et. al.: Investgaton of the turbulent swrl flows n a onal dffuser THERMAL SCIENCE: Vol. 14 (1), Suppl, pp.sxx Sxx Next expresson follows for the onal dffuser flow usng the nfluened values 1 s zm f e,r,,δ,ρ,,,,n, (3) where area rato s defned as n A /A. On the bass of dmensonal analyss the formula for spef swrl flow an be expressed as zm zm e f,re,ω,,n ζ, (4) s S where δ Δ/R, Ω - dffuser nlet swrl flow parameter Ω =Q /RΓ and ζs - dffuser swrl flow energy loss oeffent. Loss oeffent ζs an be represented as. (5) ζ f δ,re,ω,,n f δ,re,,n f Ω For pure axal dffuser flow spef energy loss [] s S 3 zm zm ea ζa f(δ,re 3,,n ), (6) where ζa s the axal flow oeffent of the dffuser axal flow spef energy [18]. (7) ζa f3 δ,re,,n From eq. (5) and (7) follows next relaton ζ ζ S A f Ω. (8) As swrl flow parameter at the dffuser nlet s onstant for one measurng seres t means that value ζ S /ζ A s also onstant along the gven dffuser. Corols oeffent at the dffuser outlet s R9 1 S z z9 R9πzm R 9 9 zm9. (9) α da r dr All relatons whh depend on the swrl flow parameter Ω an be presented as the funton of Boussnesq number β and swrl number S usng the dependene (16). 3. Some expermental results of the swrl flow n onal dffuser Numerous measurng seres were performed on the test bed (fg. 1) n the dffuser (fg. ). Measurements are marked by the A, B,... and V. Eah seres s haraterzed by the parameters, S, Re and β. These values are spefed n the table 1. Table 1. Charaterst dffuser swrl flow values Seres Re 1-5 S S / A A 1, 3,3,,356 1,15 3,36 B 1,19 4,7,3,367 1,14 3,3 C 1, 3,7,85,431 1,16 4,95 D 1,4 5,4,55,416 1,16 4,8 E 1,16,9,7,373 1,15 3,7 F 1,8 3,6,5,41 1,16 4,56 G,5 1,3 1,4 1,455 1,38 6,37

6 Benšek, M. et. al.: Investgaton of the turbulent swrl flows n a onal dffuser THERMAL SCIENCE: Vol. 14 (1), Suppl, pp.sxx Sxx H,9,6 34, 1,587 3,5 84,84 I,5 4,13,45,193 1,15,1 J 1,57 3,58 1,99,78 1,14,87 K 3,98 3,13 1,31,114 1,1 1,3 L,85,97,5,51 1,15 6,3 M,17 1,51 18,8 1,59 1,85 113,7 N,3 1,13 13,5 1,55 1,4 5,9 O,5 1,61 11,15 1,538 1,3 76,6 P,67 3, 3,99,635 1,17 8,75 Q,47,35 6,5,95 1,18 14, R,1 1,16 15,15 1,536 1,55 59, S,19 1,3 17,1 1,548 1,7 19, T,34 3, 9,5 1,176 1,5 9,14 U,37,64 8,1 1,16 1, 4,6 V 1,96 4,6 1,56,1 1,15,1 Corols oeffent values at the dffuser outlet S9 and rato (ζ S /ζ A ) 9 are presented. Many mportant values of the swrl flow are determned on the bass of the measured values ps, pt,, u and z n the numerous ponts of dffuser ross setons (, 1,...9). In the next fgures some haraterst values of swrl flow n dffuser are presented. Fgure 3. Swrl flow spef energy es along the dffuser ( z= z/l) for the measurng seres: A to I.

7 Benšek, M. et. al.: Investgaton of the turbulent swrl flows n a onal dffuser THERMAL SCIENCE: Vol. 14 (1), Suppl, pp.sxx Sxx Fgure 4. Swrl flow spef energy loss es along the dffuser ( z= z/l) for the measurng seres: A to I. Fgure 5. Mean rulaton along the dffuser ( z= z/l) for the measurng seres: A to I. Fgure 6. Swrl flow parameter Ω along the dffuser ( z= z/l) for the measurng seres: A to I.

8 Benšek, M. et. al.: Investgaton of the turbulent swrl flows n a onal dffuser THERMAL SCIENCE: Vol. 14 (1), Suppl, pp.sxx Sxx Fgure 7. Rato ζ S /ζ A along the dffuser ( z= z/l) for the measurng seres: A to I. Fgure 8. Boussnesq number β dependene on swrl flow parameter Ω for measurng seres: A to V. Fgure 9. Rato S / A dependene on swrl flow parameter Ω for measurng seres: A to V.

9 Benšek, M. et. al.: Investgaton of the turbulent swrl flows n a onal dffuser THERMAL SCIENCE: Vol. 14 (1), Suppl, pp.sxx Sxx Fgure 1. Outlet Corols oeffent α S dependene on swrl flow parameter 9 Ω for measurng seres: A to V. On the bass of the obtaned results (fg. 3 to fg. 1) followng onlusons an be obtaned: Total spef energy of swrl flow es hange (fg. 3) along the dffuser has dereasng exponental harater n the form e S es exp( ωz ) for all seres ( e S - spef energy for z=, ω - dampng oeffent whh depends on Ω, Re and δ ), Spef energy loss ΔeS hange along the dffuser (fg. 4) has nreasng harater and depends on Ω, Re and δ, Mean rulaton dstrbuton (fg. 5) along the dffuser has dereasng lnear harater n the form γz 1 (γ/γ )z 1 a z for measurng seres A to I ( - mean rulaton for z=, γ - dampng oeffent whh depends on Ω, Re and δ ), Swrl flow parameter Ω hange (fg. 6) along the dffuser has dereasng harater n the form Ω Ω exp(1 1z +z ) for measurng seres A to I ( Ω - swrl flow parameter for z=, 1= Ltg R a onst, altg R a1 a onst, a = γ Γ, L and, fg. ), Rato ζ S /ζ A along the dffuser s onstant for any measurng seres that s for onstant swrl flow parameter Ω (fg. 7). Ths expermental results onfrms relaton (8), Boussnesq number dependene on swrl flow parameter Ω (eq. 16) shows that there are rapd hange n the regon Ω,5, but slowly tends toward β 1, n the regon Ω,5. It means that for the strong swrls at the dffuser nlet, when Ω s small and S s great, Boussnesq parameter s great and dfferene between these two parameters s also great. For the weak swrl the produton s Ω S β,4, On the bass of the results shown on fg. 7 and above mentoned fats the fg. 9 s drawn. It means that rato ζ S/ζ A depends only on Ω. Applyng method of least squares on expermental ganed ponts the next relaton an be derved ζ ζ k, (3) S 1 n A Ω where k=3,78 and n=1,839, Total spef energy loss ΔeS of swrl flow n onal dffuser an be now alulated on the bass of relatons (4) and (3) as Δe ζ ζ 1 zm k zm S S A n Ω, (31) Total spef energy at any ross seton an be alulated by the next relaton e e e, (3) S S S Corols oeffent (fg. 1) has a great value when the swrl flow parameter Ω s small. It means that the nlet mean rulaton s strong and dsharge s small. In the ase of great swrl parameter values Ω when the rulaton s weak and dsharge s greater the Corols oeffent dereases and tends to αa 1,58,

10 Benšek, M. et. al.: Investgaton of the turbulent swrl flows n a onal dffuser THERMAL SCIENCE: Vol. 14 (1), Suppl, pp.sxx Sxx Corols oeffent at the dffuser outlet s presented n the fg. 1. Applyng the method of the last squares on expermentally ganed ponts the next relaton was obtaned: αs9 A 1, (33) m αa Ω where A=1,534 and m=1,353, Corols oeffent for swrl flow at the dffuser outlet α S9 s very mportant for determnaton of the real swrl flow spef knet energy loss at the dffusor outlet. The value of the real spef knet energy loss Δe K 9 s zm9 A zm9 K 9 S 9 A m Ω Δe α α 1+ where zm 9 s the mean veloty axal omponent zm Q/A 9 9., (34) 4. Conluson On the bass of nvestgatons, presented n ths paper n short, followng lams an be gven: All expermental nvestgatons were performed on one dffuser geometry, whh s adapted geometry of the draft tube of one bulb turbne, Several parameters for swrl flow defnton are ntrodued by varous authors. In ths paper are gven relatons between them. For the pratal use the most onvenent s Ω behnd the runner, whh an be smply alulated bulk swrl flow parameter knowng the spef hydraul energy of turbomahne, The measurements of veloty and pressure profles n varous ross setons along the dffuser show the rapd hange. Ext profles of energy, axal veloty and stream pressure beome nearly unform by the atvty of frton and dffuser effet, Many swrl flow measurement seres, haraterzed by swrl flow parameters Ω, Reynolds number Re and, also, for varous forms of veloty omponents and pressure profles were measured. These seres were hosen to over a wde range of dffuser operaton ponts, The hange of man rulaton along the dffuser has a dereasng lnear harater, Ratos ζ S/ζ A along the dffuser ross setons stay onstant for the onstant entrane swrl parameter Ω. It depends only on swrl parameter Ω. The nfluene of Re number on total energy swrl flow loss oeffent ζ S s taken nto aount by the oeffent pure axal flow loss oeffent ζ A whh depends only on Re number and δ for gven dffuser geometry. Dependene ζ S /ζ A f(ω ) s proved by numerous measurng results, Changes of the total spef energy loss Δe and the total spef energy e along the dffuser an be determned by knowng the relatons for ζ S, Corols oeffent α S9 at the ext of dffuser depends only on swrl flow parameter Ω. Knowng the value α S 9 gves the possblty for determng the real knet loss of flow at the dffuser outlet. Aknowledgment Ths work was funded by grants from the Mnstry of Sene and Tehnologal Development, Republ of Serba (TR 18). Nomenlature

11 Benšek, M. et. al.: Investgaton of the turbulent swrl flows n a onal dffuser THERMAL SCIENCE: Vol. 14 (1), Suppl, pp.sxx Sxx - loal veloty, [ms-1] Greek letters r - radal veloty omponent, [ms-1] - dffuser angle, [ ] u - rumferental veloty omponent, [ms-1] - roughness, [m] z - axal veloty omponent, [ms-1] pt - relatve total pressure, [Pa] L - dffuser length, [m] ps - relatve stream pressure, [Pa] p a - ambent pressure, [Pa] δ - relatve roughness, [-] R - dffuser radus, [m] - knemat vsosty, [ms-1] z - dstane from dffuser nlet to spefed dffuser ross seton, [m] ρ - flud densty, [kgm-3] z - relatve dstane from dffuser nlet to spefed dffuser ross seton, [-] Referenes [1] Beler, M. G., Carolus, T.H., Computaton and Measurement of the Flow n Axal Flow Fans wth Skewed Blades, ASME J. of Turbomahnery, Vol. 11 (1999), pp [] Azad, R.S., Hummel, R.H., Measurement of the Intermtteny Fator n Dffuser-Flow, Canadan J. of Physs, Vol. 49 (1971), No. 3, pp [3] Čantrak, S., Expermental Investgaton of the Statstal Propertes of Swrl Flows n Ppes and Dffusers (n German), Ph.D. thess, Karlsruhe, Germany, 1981 [4] Čantrak, S., Benšek, M., Nedeljkovć, M., Lečć, M., Ansotrop Turbulene and Non-Loal Dffuson n Swrl Shear Flow (n German), PAMM, 3, pp [5] Čantrak, S., Felsh, K. O., Jungbluth, H., Turbulene Struture and Mehansm of the Transport Proess n Dffusor Swrl Flow (n German), ZAMM 65 (4), 1985, pp. T 189-T 191 [6] Neve, R.S., Wrasnghe, N.E.A., Changes n Conal Dffuser Performane by Swrl Addton, Aeronautal Quarterly, Vol. 9 (1978), pp [7] Okwuob, P.A.C., Azad, R.S., Turbulene n a Conal Dffuser wth Fully Developed Flow at Entry, J. Flud. Meh., Vol. 57 (1973), part 3, pp [8] Senoo, Y., Kawaguh, N., Nagata, T., Swrl Flow n Conal Dffusers, Bulletn JSME, Vol. 1 (1978), No. 151, pp [9] So, K.L., Vortex Phenomena n a Conal Dffuser, AIAA Journal, Vol. 5 (1967), No. 6, pp [1] Weske, J.R., Sturov, G.E., Expermental Investgaton of Turbulent Swrl Flow n a Cylndral Tube, Pro. Sberaton Sv. Aad. S., USSR, 197, Vol. 13, No. 3, p. 3-7 [11] Wggns, E.G., Measurement and Correlaton of Reynolds Stresses n a Conal Dffuser, Ph.D. thess, Purdue Unv., Lafayette, Ind., 1976 [1] Benšek, M., Investgaton of the Swrl Flow n Long Lned Crular Ppes (n Serban), Ph.D. thess, Faulty of Meh. Eng., Belgrade, 1979 [13] Benšek, M., Čantrak, S., Nedeljkovć, M., Lečć, M., Unversal Calbraton Charatersts Conrad Probe for Measures 3D Veloty, Pressure and Total Pressure of Statonary Invsd Flud Flow, Pro. of Metrologal, Yug. Cong., Nov Sad, [14] Benšek, M.H., Lečć, M.R., Ilć, D.B., Čantrak, Đ.S., Aplaton of New Classal Probes n Swrl Flud Flow Measurements, Expermental Tehnques, Vol. 34 (1), Issue 3, pp [15] Čantrak, S., Hydrodynams Seleted Chapters (n Serban), Faulty of Mehanal Engneerng, Belgrade, 1998 [16] Strsheletzky, M., Equlbrum Forms of the Axsymmetr Flows wth Constant Swrl n Straght, Cylndral Rotaton Geometres (n German), Voth Forshung und Konstrukton, Heft 5 (1959), Aufsatz 1 [17] Ktoh, O., Expermental Study of Turbulent Swrl Flow n a Straght Ppe, J. Flud Meh., Vol. 5 (1991), pp [18] Mahmud, T., Truelove, J.S., Wall, T.F., Flow Charaterzatons of Swrl Coaxal Jets from Dvergng Nozzels, J. Flud Eng.,Vol. 19 (1987), pp [19] Baker, W., Sayre, C.L., Deay of Swrl Flow of Inompressble Fluds n Long Ppes, Flow: Its Meas. And Control n S. And Ind., Pro. Symp., Vl. (1971) Pt. 1, Pttsburgh, pp [] Povh, I.L., Aerodynam Experments n Mehanal Engneerng (n Russan), Mosow, Lenngrad, 1974 Paper submtted: Jun. 3, 1 Paper revsed: Jul. 6, 1 Paper aepted: Jul. 7, 1