TURBULENT WALL JET OVER A FORWARD-BACKWARD FACING STEP PAIR

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1 Nnth Internatonal Conference on Computatonal Flud Dynamcs (ICCFD9), Istanbul, Turkey, July -5, ICCFD9-xxxx TURBULENT WALL JET OVER A FORWARD-BACKWARD FACING STEP PAIR Kabache Malka & Mataou Amna Unversty of M'Hamed Bouguerra, Boumerdes Theoretcal and appled laboratory of flud mechancs Faculty of physcs, Unversty of Scence and technology HouarBoumedenne, Algers, Algera mkabache@yahoo.com, mataou_amna@yahoo.fr.introducton Abstract. Ths study nvestgates the wall et outer layer effect on flow structure over obstacle. Indeed, two nlet flow confguratons are tested; a turbulent wall et whch has a partcular structure wth two sources of turbulence producton (the frst s due to the shear flow assocated to the nner layer characterzed by small scale and second one s of the free shear et flow wth large turbulence scales) and a free boundary layer flow. The nner regon of these two flows s smlar, but ther external regons are extremely dfferent. The flow structure manly depends manly on the momentum of the ncomng flow. The secondary eddy of the backward facng step corner appears only n the case of the boundary layer ncomng flow. For the two confguraton of ncomng flow (Boundary layer or Wall et), the dstrbuton of mean Nusselt number s correlated accordng wth some problem parameters. Keywords: Separated flow ; Heat transfer ; CFD ; Obstacle, Turbulence Turbulent flow over obstacles s a challengng task n heat exchangers, electronc equpments, nuclear reactors and other thermal devces. The channel flow or boundary layer over sold obstacle has been used for these applcatons by many researchers n the past. Wall et over obstacle s often found n multprocessor electronc components. Hence t s mportant to understand ths type of flow characterstcs. A small number of studes on the wall et flow over a separated flow are found n the lterature ([-]).These authors confrm that for the case of a wall et (b=h), the reattachment length s practcally halved compared to that of the boundary layer case. Ths dmnuton s explaned by the effect of the compresson of the external shear layer of the wall et. The reattachment length of BFS flow n the wall et case s reduced sgnfcantly compared to that of the boundary layer case and they confrmed through the knetc energy contours that the reducton s due to the turbulent external layer of the wall et effect on the recrculaton zone.the process of separaton and reattachment n a turbulent wall et flow over an obstacle s performed numercally.the effect nozzle thckness and et ext Reynolds number on the flow structure are nvestgated. A schematc dagram and parameters of the confguraton are shown n Fg..

2 Wall Wall 5 Y L/H= W/H= L W Nozzle U O Obstacle X b H Fgure.. The geometry of the confguraton Wall Wall Obstacle Wall Fgure. The geometry of the confguraton.methodology. Governng equatons The contnuty, Naver-Stokes and energy equatons for the steady state ncompressble flow are averaged as: U Contnuty: () x U Momentum: P U U uu x x x x where uu k t ( U, U, ) () Energy equaton: U T v T x x Pr x u () T where u t x Where U s the mean velocty component n x drecton; T s the mean temperature and u s the velocty fluctuaton component. s the temperature fluctuaton, P s the statc pressure and s the flud

3 k densty. uu are the Reynolds stress tensor components dependng on eddy vscosty t. The t quanttes u represent the turbulent heat flux depends on t Pr. NUMERICAL PROCEDURE The fnte volume method requres a transformaton of the equatons n conservatve form (Patankar S.V. []), to convecton, dffuson and source terms. The transport equatons are dscretzed on collocated meshes. The convecton and dffuson terms are nterpolated usng the POWER LAW scheme for all varables, exceptng for the pressure where the second order scheme s appled. The pressure velocty couplng s acheved by SIMPLE algorthm.. Boundary condtons The boundares condtons are sketched n Fgure ncludng nflow (Inlet), sold wall, symmetry and outlet condtons, as follows: - The nlet boundary condtons are chosen as follow: U=U, V=, I =k /U, ( k ) ε C, ω=, T=T. l m c μ k Where C µ s a turbulence model emprcal constant (C µ =.9 and l m s a length scale. For each wall, the non-slp condton s mposed (U=V=). The knetc energy (k) s set to zero and the specfc of dsspaton rate ω corresponds to the asymptotc value proposed by Wlcox [7]. The obstacle walls are mantaned at constant temperature (T w >T ). All other walls of the confguraton are adabatc. For the secton BC (see fgure ), the pressure nlet boundary s mposed for the wall et cases and velocty nlet for boundary layer ncomng flow case. At the free boundary, pressure outlet (fully developed) boundary condtons are used. The pressure at outlet boundary condtons s kept at the atmospherc value. At ths boundary, the temperature reaches the ambent value (T=T ). Symmetry condton s mposed for the case of boundary ncomng flow at the upper horzontal edge.. VALIDATION t Fgure (a) depcts the normalzed velocty U/U versus the dmensonless poston y/ at x=-h. A good agreement s obtaned between the present study and expermental data of Kleebanof []. The plane wall et s charactersed by two zones: The nner layer extendng from the wall to the secton of maxmum velocty; analogous to the boundary layer profle and the outer layer that extends from the secton of maxmum velocty at the outer edge; smlar to the free et profle (Erksson et al. [9]). Upstream of the obstacle, at x = -H, the dmensonless velocty (U/U max ) versus the normalsed dstance (y/y / ) profles are compared wth avalable expermental data of Erksson et al [9] (fgure (b)). A good agreement s observed between the two predctons. Furthermore, ths fgure confrms that the mpngng flow pattern upstream to the obstacle s a fully developed turbulent wall et.

4 U/Ue,,,, y / y / y (cm) Y (cm) Experment Erksson & al. (99) Present study b=h/ b=h b=h,, Present study - Re= Kleebanof,,,,,,,, y/ Fgure. Mean velocty profles (Re=) The valdaton case s performed wth the avalable expermental results of B.V. Mudgal and B.S. Pan [], for a turbulent wall et over a cube. The fgure, llustrates the numercal predctons based on the k- ω SST model of the velocty profles compared to ther correspondng expermental data of B.V. Mudgal and B.S. Pan []. The measurements are acheved by laser-doppler anemometer. Sxteen cross-sectons are consdered. Ths fgure shows an overall good agreement, confrmng that the present numercal technque and k-ω SST turbulence model are sutable for ths type of flow confguraton.,,,,,, U/U max x=-,, x=-, x=-,79 x=-, x= x=,7 x=, x=,5, x=, x=, x=5, x=,5 x=9, x=, x=5,9 x=,9,9,9,,,7,7,,,5,5,,,,,,,,, , U (m/s) U (m/s) Fgure. Velocty profle - Valdaton (H=cm, L=H, =.5, Re=) 5. RESULTS The Shear Stress Tensor k-ω one pont closure model s used n ths study ([5]). The numercal predctons based on fnte volume method are performed by ANSYS FLUENT. CFD code. The fnte volume method requres a transformaton of the equatons n conservatve form ([]).The convecton and dffuson terms are nterpolated usng the POWER LAW scheme for all varables, except for the pressure where the SECOND ORDER scheme s appled.the pressure velocty couplng s acheved by the SIMPLE algorthm. As shown n Fg. (a), the streamlnes of the two types of ncomng flow are dfferent. Ths Fgure hghlghts the nteracton of the et external shear layer wth the obstacle. Snce, for a gven Reynolds number, the momentum of the boundary ncomng flow sgnfcantly exceeds those of all wall et ncomng flows (Table ).

5 Table. Momentum of the ncomng flow b=h/ Wall et ncomng flow b=h JH/= UH Incomng flow momentum JH UH Boundary layer ncomng flow JBL= Uh where b=h JH= UH/ h>h To clarty, an enlargement n the obstacle area s performed n fgure (b). Around the obstacle flow develops three man recrculaton zones around the obstacle for each tested case (wall et (H/ b H) and boundary layer nlet flow). The nozzle wdth nfluences strongly the volume of eddes (Fg. (b)). For the Boundary layer ncomng flow, the frst eddy (forward facng step and the thrd eddy (backward facng step) have the largest sze; contrary to that of the second eddes (atop of the obstacle) whch s reduced n comparson to that of the wall et ncomng flow. The reattachment length of the frst and the thrd eddy ncrease when the nozzle thckness ncreases, the hghest value s obtaned for the boundary layer ncomng flow. Inversely to the second bubble, the reattachment length decreases when the nozzle thckness ncreases and the smallest length s obtaned for the boundary layer case. The secondary eddy of the backward facng step corner appears only n the case of the boundary layer ncomng flow. The flow structure manly depends on the ncomng flow parameters partcularly the momentum of the ncomng flow (Table ). Boundary layer for Re=5 Boundary layer for Re= Wall et (b=h) and Re=5 - Wall et (b=h) and Re=5 Wall et (b=h) and Re=5 - X /H Wall et (b=h/) and Re= X /H (a) Effect of ncomng flow confguraton wall et thckness (b) Effect of ncomng flow confguraton and Fgure. 5 Streamlnes contours (L/H= and W/H=) The turbulence knetc energy s found hgh around the nozzle cross secton where the shear layer attans the hgh deformaton (Fgure. ). An addtonal bubble s vsble for the cases of the wall et ncomng flow. An alternatve descrpton of the turbulent flow feld has been obtaned usng a frequency analyss of the flow nstead of measurng the correlaton functons. Ths approach allows a detaled pcture of the energy dstrbuton among eddes of dfferent szes. It plays a sgnfcant role n the reattachment process, compressng the eddes, nducng a smaller reattachment length. 5

6 Y/ H Y / H Y / H Y / H Boundary layer and Re= Wall et (b=h) for Re= Wall et (b=h) and Re=5 - - Wallet (b=h/) forre=5 - - kmax Fg.. Contours of knetc energy -knetc-energy: In order to predct the heat transfer rate along the heated walls composng the obstacle, the local Nusselt number s deduced from the temperature dstrbuton. It s defned by Eq. : L T Nu T T n Where n s the perpendcular drecton to the correspondng wall and L s the length w The average Nusselt number along the heated wall s deduced from Eq. 5: Lwall Nu Nu dl wall L (5) wall The mean Nusselt number along the walls that form the obstacle s deduced from eq. The weghtng factor of each term s proportonal to each wall length L such as: () Nu mean L Nu L Nu L Nu Nu Nu Nu ( L L L ) wall wall wall wall wall wall () Where L, L andl are the length of the heated wall (L = L =H and L =H). Fg. reflects the effect of the nozzle thckness of the wall et ncomng flow, on heat transfer va the value of average Nusselt number of the obstacle. Based on Fg., the mean Nusselt number over the obstacle s correlated accordng the parameters of ths study, for each ncomng flow confguraton:.7 Boundary layer flow: Numean. Re (7) Wall et flow: b.7 Numean..5( ) Re H () Fgure.7 evdences the effect of the ncomng flow confguraton on heat transfer va the value of mean Nusselt number. Ths could be used from an engneerng vewpont for the purpose of heat transfer enhancement. The wall ets thckness s set for varous values and t emerges that the thnnest exhbts the hgher heat transfer on each wall of the obstacle and for the entre surface of the obstacle. The boundary

7 layer case exhbts the hgher heat transfer the wall et cases, because the correspondng momentum of the nlet flow over the obstacle s hghest. The convectve heat transfer depends manly on the momentum of the flow. Wall et Correlatons (,-,5*(b/H))*Re,7 Boundary layer,*re.7 Nu mean Computatons Boundary layer Wall et (b=h/) Wall et (b=h) Wall et (b=h) Fg. 7. Mean Nusselt number - Correlatons. CONCLUSION Ths paper examnes a separated reattachng flow over a rectangular obstacle. Turbulent eddyng zones were dentfed and controlled by dfferent sources of turbulence: two man shear producton sources located on each sde of the et axs and a mnor one due to reverse flow nsde the recrculaton bubble. The reattachment length of the frst and the thrd eddy ncrease when the nozzle thckness ncreases, the hghest value s obtaned for the boundary layer ncomng flow. Inversely to the second bubble, the reattachment length decreases when the nozzle thckness ncreases and the smallest length s obtaned for the boundary layer case. 5. References. [] Badr Kusuma, M. S. (99). Etude expérmentale d'un écoulement turbulent en aval d'une marche descendante: cas d'un et parétal et de la couche lmte (Doctoral dssertaton). [] Arous, M., Mataou, A., & Bouahmed, Z. (). Influence of upstream flow characterstcs on the reattachment phenomenon n shallow cavtes. Thermal scence, 5(), 7-7. [] Mad Arous, F., Mataou, A., Terfous, A., & Ghenam, A. (). Jet cavty nteracton: effect of the cavty depth. Progress n Computatonal Flud Dynamcs, an Internatonal Journal, (5), -. [] Nat Bouda, N., Schestel, R., Mataou, A., Rey, C., and Benabd (9). Influence of ncomng flow structure on reattachment over a backward facng step. Modellng, Measurement and Control;B Mechancs and Thermcs AMSE ournal ; Vol. 7 Issue. [5] Menter, F. R. (99). Two-equaton eddy-vscosty turbulence models for engneerng applcatons. AIAA ournal, (), [] Patankar, S.V. 9. Numercal heat transfer and flud flow, Seres n computatonal methods n mechancs and thermal scences, hemsphere Publshng Corporaton. [7] D. C. Wlcox. Turbulence Modellng for CFD, DCW Industres Inc, La Canada, CA, 99. [] Klebanoff, P. S., & Dehl, Z. W. (95). Some features of artfcally thckened fully developed turbulent boundary layers wth zero pressure gradent. [9] Erksson, J. G., Karlsson, R. I., & Persson, J. (99). An expermental study of a two-dmensonal plane turbulent wall et. Experments n fluds, 5(), 5-. [] Mudgal, B. V., & Pan, B. S. (99). Flow around obstacles n plane turbulent wall ets. Journal of Wnd Engneerng and Industral Aerodynamcs, 7(), 9-. 7