Hydrodynamic Characteristics of Staggered Ribbed Backward Facing Step Flow with Inclined Impinging Jet

Transcription

1 Internatonal Journal of Engneerng and Tecnology Volume 2 No. 5, May, 2012 Hydrodynamc Caracterstcs of Staggered Rbbed Backward Facng Step Flow wt Inclned Impngng Jet Kudeyer S. Musatet College of Engneerng, Tqar Unversty Nassrya, Iraq ABSTRACT In ts paper, A numercal study as been conducted to predct te ydrodynamc caracterstcs of te staggered rbbed backward facng step flow wt nclned mpngng et. Te mpngng et flow was nclned towards te man cross flow and te angle of nclnaton s ranged from 30 to 90. Te rbs were n staggered arrangement and algned after te slot et n normal drecton to te man cross flow. Te effect of angle of nclnaton and contracton rato on ydrodynamc caracterstcs was nvestgated for et and cannel Reynolds number of and respectvely. Te am of te present study s to verfy ow addng staggered rbs wt nclned et flow to te problem of backward facng can affect te ydrodynamc caracterstcs. Te contnuty, Naver-Stockes and energy equatons was dscretsed on non-unform staggered grd by usng fnte volume metod. Te resulted algebrac equatons were solved by usng a bult ome computer program based on smple algortm. Te obtaned computed results verfed tat te recrculaton regons and te turbulent knetc energy s ncreased as rbs egt and wdt ncrease. It was observed tat te turbulent knetc energy s ncreased as angle of nclnaton ncreases. Keywords: backward facng step, rbbed cannel, mpngng et B slot et wdt, m G generaton term, Kg/m.sec 3 H egt of te cannel, m k turbulent knetc energy, m 2 /s 2 L lengt of te cannel, m p ptc, m P pressure, N/m 2 Pr Prandtl number, - Re Reynolds number,- s step egt, m SR contracton rato (s/h),- U velocty at a cannel nlet n velocty at a slot et nlet U Greek symbols: є turbulence dsspaton rate, m 2 /s 3 µ dynamc vscosty, N.s/m 2 µ t turbulent vscosty, N.s/m 2 ρ ar densty, Kg/m 3 Γ eff effectve excange coeffcent, kg/m.s σ k ; σ Є turbulent Scmdt numbers, - NOMENCLATURE 1. INTRODUCTION Te separaton and reattacment penomena are spread n multple engneerng and tecnologcal applcatons suc as coolng of turbne blades and electronc devces. In recent years, te backward facng step flow became one of te target topcs for many researcers and t s classfed as one of complex flows snce t ncludes a mxng of g and low flud momentums bend te facng step. Tere are attempts from researcers to ncrease separaton and reattacment n ts knds of flows. However tese attempts need more work. Many researcers studed te problem of backward facng step flow. Ravlkant and Rcard [1] nvestgated numercally te turbulent flow and eat transfer past a backward facng step. A large eddy smulaton metod wt fully collocated grd tecnque was used. In ter study, tey demonstrated tat te Stanton number profles ndcated a strkng smlarty wt fluctuatng frcton profles. It was observed tat te vscous sub-layer played a crtcal role n controllng te eat transfer. Te effect of a step egt on te separated flow and eat transfer for a convectve flow adacent to a backward facng step was studed numercally by Ne and Armaly [2] and Tangam and Kngt [3]. Te turbulent flow adacent to a backward facng step was nvestgated by Wang et al. [4] for Reynolds number up to It was observed tat 844

2 te partcle beavor depends eavly on te local flud turbulence along ts pat. Web et al. [5], Lo et al. [6], Hane and Park [7], Rau et al. [8], studed te turbulent flow n cannels rougened wt rbs. Ter nvestgatons were am to predct te termal feld and frcton factor. A tree dmensonal forced convecton flow over an nclned backward facng step n a rectangular duct was nvestgated by Cen et al.[ 9]. Ter nvestgaton ncluded examnng te effect of a step nclnaton angle on te flow and eat transfer dstrbuton. Kasag and Matsunaga [10] studed te turbulent flow n a cannel wt a backward facng step. Te partcle trackng velocmeter was used as a measurement tecnque. Tey verfed tat Reynolds normal and sear stresses ad te maxmum values upstream of te re-attacment. Jun-Yan San et al.[11] nvestgated expermentally Impngement eat transfer of crcular ets confned n a cannel. Te mpngement plate was exerted wt a constant surface eat flux. Te consdered et Reynolds number (Re) was exerted wt a constant surface eat flux. Te studed Reynolds number was n te range Tey sowed tat te Nusselt number ncreased lnearly wt et Reynolds number. An expermental study was conducted by Ozman[12] to predct te flow caracterstcs of te confned twn ets ssung from te lower surface and mpngng normally on te upper surface. It was observed tat tere s a relaton between te sub atmosperc regons and peaks n eat transfer coeffcent for low spacng n te mpngng ets. In ts work, a numercal study as been performed to predct te ydrodynamcs caracterstcs of te staggered rbbed backward facng step flow wt nclned mpngng et flow. To te best knowledge of te researcer tere s no study documented on ts new confguraton. A rectangular rbs are mounted along te bottom and upper wall n staggered arrangements wle a rectangular slot et s mposed on upper wall bend te facng step regon. Te et flow s nclned at dfferent angles as w 30 α 90. Te rbs wdt was ranged as1 3 and rbs egt as Te study s H performed at 0.35 CR and et and cannel Reynolds number of and Fg.1 sows te scematc dagram of te studed problem. Fg.1 Scematc dagram of te pyscal problem, H=0.05m, L=0.4m,x1=0.0492m, H/B=2, /H=0.38,W/=1 2. MATHEMATICAL MODEL AND NUMERICAL ANALYSIS Te governng partal dfferental equatons of contnuty, Naver-Stockes and energy are descrbed n tensor form as follows. Te workng flud s ar and constant termo pyscal propertes are assumed. x ( ) = 0 ρ (1) U U U UT P + U µ ρu u (2) = µ T ρu t Pr = Te turbulence wtn flud flow was modeled by usng a k-ε model [12]. Ts model ncludes two transport equatons, one for te turbulence energy and te oter for te dsspaton of turbulence energy. 2.1 Boundary condtons U n Re n =, U B Re =, ν ν 2 k =.05U, k =.05U n 0 n ε n = λh, ε = λb, λ = k n 1.5 k At te walls and rbs no slp condton was mposed. Te wall functon laws[14] were mposed to treat te large steep gradent near te walls and rbs. Te local Nusselt number on te ot wall s defned as: Nu = θ, T Tc θ =, Y = Y T T Te numercal computatons are done on non-unform staggered grd mes. A fnte volume tecnque (FVM) descrbed by Versteege [14] s adopted. Ts result n dscretsaton equatons wc means tat te system of fully ellptc partal dfferental equatons s transformed n to a system of algebrac equatons. Te soluton of tese algebrac equatons s performed by sem mplct lne by lne Guass elmnaton sceme. An ellptc fnte volume computer code s developed to obtan te results of te numercal procedure troug usng pressure-velocty couplng (SIMPLE algortm) [14]. To ensure tat te turbulent flud flow solutons are not sgnfcantly effected by te mes, te numercal smulatons are examned under dfferent grd szes rangng from untl control volumes. Any addtonal ncrease n grd ponts on does not sgnfcantly effect on te results. c y H (3) 845

3 3. RESULTS AND DISCUSSION In ts secton, te obtaned results for ydrodynamcs caracterstcs of staggered rbbed backward facng step flow wt nclned mpngng et are presented. Te et angle was vared from 30 to 90 wle te contracton rato, rbs egt and rbs wdt were vared as 0.35 CR 0.65, H respectvely. w, 1 3 Fgures 2-3 exbt te effect of et nclnaton angle on dstrbuton of velocty vectors and streamlnes for CR=0.5. It s observed tat te angle of nclnaton as an mportant mpact on controllng te sze and strengt of recrculaton regons bend te et, facng step and rbs turbulators. As a result, ts mpact ncludes te reattacment lengts. Te flow of mpngng et puses te man stream towards te bottom rbbed wall and ts flow affect te sze of recrculaton regon bend te steps and consequently te reattacment lengt. Te traectory of streamlnes clarfy ts trend. At angle 30, t can be observed tat a large amount of combned flow s pused towards te facng step and ts accelerates te flow and nbt te trend of facng step to make a complete recrculaton regon and consequently a an expected reattacment lengt. In addton, te presence of rbs mounted n staggered orentaton gave a dramatc cange for recrculaton regons on upper and lower walls. Tese rbs create recrculaton regons and ncrease te turbulence. However te sze of recrculaton regon bend te frst rb on upper wall s larger tan tat of te lower wall because of te effect of facng step and et flow consequently te reattacment lengt. Te mentoned pyscal explanaton s applcable for angles of nclnaton 60 and 90. At angle 60, te recrculaton regon bend te facng step becomes large and t s larger at angle 90 because wen te et nclnaton angle ncreases, te acceleraton of pused flow towards te facng step and bottom wall becomes less and tat permts te facng step to be a controllng factor at ts regon. Te acceleraton of te flow becomes lttle n downstream flow and consequently te recrculaton regons bend te oter two rbs become less strengt. Fg.4 sows te varaton of turbulent knetc energy near te bottom and upper wall for angle 90 and dfferent values of contracton ratos. For bottom wall, It s observed tat te turbulence energy s decreased as contracton rato ncreases but ts trend s reflected bend te facng step. Te maxmum values of te turbulent knetc energy are found bend te frst rb. Te effect of contracton rato s apparent bend te rbs. Te poston of maxmum and mnmum values of turbulence energy s canged for upper wall due to presence of et flow and absence of facng step effect. Te effect of et nclnaton angle on varaton of turbulent knetc energy near te upper wall for CR=0.5 s depcted n Fg.5. It s observed tat te maxmum values of turbulent knetc energy are found bend te facng step, te slot et and rbs. Tese values ncrease as angle of nclnaton ncreases because of ncrease of velocty gradents tat affects te stresses and consequently te turbulence energy. 846

4 Fg. 5 Varaton of turbulent knetc energy near te upper wall at Re =20000, Re n =16000, H/B=2.5,/H=0.38 and CR=0.5. Fg.6 sows te effect of rbs egt on varaton of turbulent knetc energy near te upper and lower walls of te consdered problem. For lower wall, t s observed tat te turbulence energy s decreased as rbs egt ncreases and te maxmum values are found bend te rbs. For upper wall, ts trend s reflected were te turbulence energy s ncreased as rb egt ncreases. However ts trend s domnant for x and after ts range t s decreased. a. bottom wall b. upper wall Fg.7. varaton of turbulent knetc energy values of dmensonless rbs wdt, Re =20000, Re n =16000, H/b=2.5, /H=0.38 and CR=

5 Te effect of rbs wdt on varaton of turbulence energy near te upper and lower walls for CR=0.5 and angle 90 s demonstrated n Fg.7. It s evdent tat te turbulent knetc energy s ncreased as rbs wdt ncreases. However ts effect s clear at 0.15 <x. Te valdty of te present numercal code s tested troug comparson wt publsed expermental results of turbulent separated flows as sown n Fgs.8-9. It can observed tat an acceptable agreement between te present and publsed results as been obtaned. However some dscrepancy s observed. Ts s due to te use of k-ε model were ts model gves percentage of un predcton n some of re-crculatng flows. Te percentage of ts un predcton s about 10 Fg. 8 Comparson of te present results wt expermental publsed results of Kasag[10],Re=5540. Fg.9 Comparson between te present results and publsed expermental data of Lo et al.[6] 4. CONCLUSIONS A computatonal study for ydrodynamcs caracterstc of staggered rbs backward facng step flow wt nclned mpngng et as been performed. Te obtaned results sowed tat te et nclnaton angle and staggered rbs arrangement as been found to be a controllng factor on dstrbuton of ydrodynamc parameters n a cannel backward facng step flow. It was found tat te turbulence energy s ncreased as rbs wdt ncreases for lower wall and vce versa for upper wall wle t decreases as rbs egt ncreases. [2] J.H. Ne, Armaly, B.F., Tree Dmensonal Convectve Flow Adacent to a Backward Facng Step-Effects of Step Hegt, Int. J. Heat Mass Transfer, 45(2002), pp [3] S. Tangam, D. Kngt, Effect of Step Hegt on te Separated Flow Past a Backward Facng Step, Pys. Fluds, 3(1989), pp [4] B. Wang, H. Q. Zang, X. L. Wang large eddy smulaton of partcle response to turbulence along ts traectory n a backward facng step turbulent flow, Heat Mass Transfer, vol.49, pp ,2006. REFERENCES [1] V. R. Ravkant Avanc, H. Rcard Pletcer Large eddy smulaton of te turbulent flow past a backward-facng step wt eat transfer and property varatons, Heat and Flud Flow, vol.23, pp , [5] R.L. Webb, E.R.G. Eckert, and R.J. Goldsten, Heat transfer and frcton n tubes wt repeated rb rougness, Internatonal Journal of Heat and Mass, 14(1984), pp [6] T..M. Lo, G.G. Hwang and S.H. Cen, Smulaton and Measurements of Enanced Turbulent Heat Transfer n Cannels wt Perodc Rbs on One Prncpal Wall, Internatonal Journal of Heat Mass Transfer, 36(1997), pp

6 [7] Han, J.C. and Park, J.S., Developng Heat Transfer Troug Rectangular Cannels wt Rb Turbulators, Internatonal Journal of Heat mass Transfer, 31(1988), pp [8] G. Rau, M. Cakan, Moeller, D. and Arts, T.,Te Effect of Perodc Rbs on te Local Aerodynamcs and Heat Transfer Performance of a Stragt Coolng Cannel, ASME Journal of Turbo macnery, 120(1988), pp [9] Y.T. Cen, J.H Ne, H.T. Hse, L.J. Sun, Tree Dmensonal Convectve Flow Adacent to Inclned Backward Facng Step, Int. J. Heat and Mass Transfer, 49(2006), pp [10] Nobude Kasag, Ako Matsunaga, Tree- Dmensonal Partcle-Trackng- velocmetry measurement of Turbulence Statstcs and Energy Budget n a backward-facng Step Flow, Int. J. Heat and Flud Flow,16(1995), pp [11] Jung-Yang San, Y-Mng Tsou, Zeng-Ce Cen, 2007, Impngment eat transfer of staggered arrays of ar ets confned n a cannel, Int. J. Heat and Mass Transfer, 50, [12] Ozman, O., 2010, Confned mpngng twn ar ets at g Reynolds numbers, Expermental Termal and Flud Scence, n press. [13] W.P. Jones, B.E. Lunder, Te Predcton of Lamnarzaton wt a Two equaton Model of Turbulence, J. Heat and Mass Transfer, [14] H.K. Versteege, W. Malalasekera, An Introducton of Computatonal Flud Dynamcs, Hemsopere Publsng Corporaton,, Unted States of Amerca,