step. J.N. Fernando, J. Kriegseis and D.E. Rival

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1 On the eparated region behind a confined backward-facing tep J.N. Fernando, J. Kriegei and D.E. Rival Department of Mechanical and Manufacturing Engineering, Univerity of Calgary, Calgary, AB, Canada T2N N4 jnfernan@ucalgary.ca ABSTRACT The eparated flow behind a three-dimenional backward-facing tep (BFS) i examined uing numerical and experimental technique. Thi i accomplihed through Reynold-Averaged Navier-Stoke (RANS) imulation and time-averaged particle image velocimetry (PIV) meaurement. Vortical tructure behind the contrained backward-facing tep are characterized uing each approach and the reattachment line downtream of the tep i determined through the numerical imulation. Thi reult i compared to data available in the literature for further validation. Topological difference are found to exit between timeaveraged olution of each approach. However, imilar vortical tructure are preent in both olution. Thee tructure are only viible in the PIV data through image equence proceing and are found to be highly unteady. The preence of thi obviou unteadine in the flow demontrate the limited validity of implementing time-averaged cheme for the prediction of three-dimenional tructure behind the backwardfacing tep. INTRODUCTION Flow eparation reulting from a trong advere preure gradient due to a udden expanion in geometry, uch a a backward-facing tep, occur in a large array of engineering application. Many tudie on eparated flow over the lat few decade have focued on the two-dimenional, backward-facing tep geometry, a a mean of undertanding hear-layer behavior and reattachment propertie [ 3]. Although the geometry i imple, the flow immediately downtream of the tep contain vortical tructure and complicated topology. Inide the recirculation zone the flow i characterized by flow reveral and vortical tructure [2 7]. Specifically, the flow phenomenon reponible for vortical tructure in the hear layer reult from Kelvin- Helmholtz intabilitie and i caued by the interaction between the hear layer and re-circulating flow near the tep wall [3]. In addition to the Reynold number, the key variable aociated with the backward-facing tep problem are the expanion and apect ratio, defined a the ratio of downtream to uptream channel height and channel width to tep height, repectively. In contrained (three-dimenional) channel, idewall effect produce complex flow tructure, and for the cae of laminar flow, thee tructure are found to intenify for increaing relative tep height and Reynold number at the channel lower wall for expanion and apect ratio of 2 and 2, repectively [4, 5]. In the preent tudy, the invetigation of the idewall effect are to be tudied in a turbulent flow. The major objective of the current tudy i to demontrate how vorticity and coherent tructure develop in the flow through both numerical and experimental technique. Furthermore, the limitation of time-averaged approache for the backward-facing tep problem will be dicued. 2 GEOMETRY The geometry ued in thi tudy i hown in Figure. The channel dimenion are h =.35 m, H =.45 m, =.35 m, L R =.78 m, L S = 2.22 m and c=.387 m. The inflow and outflow channel height are given by h and H, repectively. L R and L S are correponding tep and downtream channel length, i the tep height and c i the channel width. The expan-

2 h L R tep flow H LS c Figure : Schematic of tet geometry, containing a decription of relevant dimenion of the confined, backward-facing tep. ion ratio i defined a ER=H/h () and i equal to.4. Similarly, the apect ratio, defined a AR=c/, (2) i equal to The origin of the coordinate ytem i placed at the left-hand corner of the backward-facing tep bae (Figure 2). y x Figure 2: Cloe-up view of meh refinement in the region urrounding the backward-facing tep. 3 NUMERICAL SET-UP The complete water-tunnel plenum and channel geometry were modeled in ICEM CFD and then imported into ANSYS CFX. After meh refinement along the channel boundarie, o a to reolve the vicou ub-layer, the number of node in the model totaled 2,97,5. The Reynold-averaged Navier- Stoke (RANS) equation were olved together with the k ε turbulence model uing the ANSYS CFX commercial package. Figure 2 how a cloe-up view of the meh refinement in the region of interet. h Figure 3: Domain ued for numerical imulation. The inlet boundary condition i located by the arrow. Simulation were performed at a tep height of.35 m. The Reynold number, baed on the tep height wa evaluated to be approximately 6,. Velocity at the inlet of the contraction (ee Figure 3) wa et at.5 m/, with an eddy length cale of.45 m, and turbulence intenity of Tu = %. Two other imulation were alo performed, varying both turbulence intenity from % to % and velocity from.5 m/ to.25 m/ o a to determine their contribution (if any) to the flow. Thee etting were applied a a boundary condition at the inlet cro ection, a hown in Figure 3. In thi enitivity tudy, it wa found that although light change were oberved in magnitude contour of velocity and vorticity - the two variable of greatet interet - neither the turbulent intenity nor the free-tream velocity changed the overall flow topology. 4 EXPERIMENTAL METHOD The experiment were performed on a cloed-loop water tunnel, a hown in Figure 4. Water wa pumped to a main plenum chamber and through four conditioning unit (one honeycomb and three fine creen), before being accelerated into the tet ection through a ix-toone ratio contraction. The channel ended with a reervoir, which facilitated the recirculation of water back to the plenum through the pump. To validate the reult from the numerical imulation, PIV experiment were performed in the XZ-plane near the tep geometry. The experimental et-up conited of a New Wave Nd:YAG laer (λ=532 nm) and PCO CCD Camera (28 x 24 pixel, 4fp) equipped with a Nikon len (f = 2mm/2.8). For the data et preented in thi paper, 25 image pair ( t = 24 m) were pot-proceed uing the tandard LaViion multi-pa cro-correlation cheme.

3 A B C D E F A B C D E F G G plenum conditioning unit 6: contraction tet ection tet ection 2 recirculation chamber return line and pump in previouly by Nie and Armaly [6], and erve a the main verification meaure of the preent tudy. Reult for the reattachment line from Nie and Armaly [6] were plotted againt the finding from numerical imulation in thi tudy. Figure 6 how thee data et compared with one another. 2 Figure 4: Schematic of water tunnel ued for PIV experiment. The pump, located at the bae of the plenum, drive water through the contraction into the tet ection and recirculation chamber. The et-up can be een in Figure 5, which depict PIV data acquiition for a lice in the XZ-plane. Prior to data acquiition, the PIV ytem wa ued to carefully adjut the mean tunnel peed with that from the CFD o a to match the operating Reynold number. Similarly, turbulence intenity of the mean flow in the tet ection near the tep wa meaured. It wa found that the turbulence intenity wa approximately 3%. At the ame poition in the CFD imulation, the average turbulence intenity had an average value of 5%. The enitivity analyi that wa performed a part of the numerical tudy uggeted that thi inconitency would not reult in any topological dicrepancie between the numerical and experimental imulation. Nd:YAG laer c flow y/ field-of-view (FOV) CCD camera Figure 5: Detailed ketch of the tep including the global origin located at the bottom-left corner of the tep; PIV etup and field of view are added for the ake of clarity. 5 RESULTS AND DISCUSSION One of the main flow feature reulting from eparated flow off a confined backward-facing tep i the primary recirculation reattachment line. Thi line ha been quantified both numerically and experimentally ER = 2.5, Nie & Armaly [6] ER = 2., Nie & Armaly [6] 2 ER =.67, Nie & Armaly [6] ER =.4, preent work Figure 6: Reattachment line for three expanion ratio in the laminar regime (Nie and Armaly [6]), and preent work evaluated for an expanion ratio of ER=.4 in the turbulent regime. Although there are clear difference between the reattachment line contour from each tudy, at leat the predicted length of the eparated region i in good agreement. The flow topology for the confined backward-facing tep in thi tudy ugget a much more unteady and vorticity-driven flow, a jutified by the large difference in the operating Reynold number between the two tudie. Although the precie flow topology for thi problem ha not yet been fullyquantified, a better undertanding of the preence of vorticity within the flow will play an important role in undertanding the phyic of the reattachment length. Accurately determining the reattachment line for thi problem may warrant meh-refinement in the treamwie direction to reduce exceive numerical diffuion. It i alo expected that replacement of the two-equation model with more accurate Reynold-tre model in the numerical olver will improve accuracy of the (panwie) reattachment length ditribution. However, thee effort are beyond the cope of the preent tudy. Two et of PIV meaurement were taken uing the tunnel centerline a the dividing line between data et, which provided the mot advantageou field-of-view (FOV) for direct comparion with the CFD. PIV data wa taken in the XZ-plane at the location y/ =.5. A comparion of velocity contour in thi region i hown in Figure 7. Velocity magnitude i of the ame order but with ignificant variation in ditribution. Topological differ-

4 PIV CFD velocity [m/] Figure 7: Side-by-ide comparion of velocity magnitude and vector for both PIV (top) and CFD (bottom). ence were found to exit between time-averaged olution for both the imulation and experiment. In the numerical olution, two counter-rotating vortice, ymmetric about the center line, are evident in the flow. However, for the PIV only treamline curvature i noted, again ymmetric about the centerline. Thi dicrepancy in the flow pattern between PIV and CFD warrant a dicuion into the vorticity level preent in thi region of the flow. Figure 8 how a comparion between PIV and CFD reult uing treamline and vorticity contour intead. z/ PIV CFD S N N ω y,max PIV =.9 S ω y,max CFD = vorticity ω y /ω y,max Figure 8: Side-by-ide comparion of normalized vorticity and treamline between PIV (top) and CFD (bottom); topological ingularitie indicated a addle (S) and node (N). Although the region of greatet vorticity wa almot identical in both PIV and CFD, precie topological flow feature (a indicated by velocity vector), and vorticity magnitude, were found to differ to a ignificant extent. Furthermore, topological diimilarity wa noted between the time-averaged olution in both the imulation and experiment. Flow tructure variation i evident in Figure 8 through the location of topological ingularitie (ee Fo [8]) in the flow, uch a addle (S) and node (N) a well a through the region of peak vorticity. In the numerical imulation, the large-cale back-flow form a vortex in the XZ-plane. When the recirculating flow hit the tep, a pair of ymmetric node (counter-rotating vortice) i generated, and movement of the fluid in the vertical (y-direction) only occur at the node (N). In contrat, the flow topology of the PIV data ugget that the back-flow after hitting the tep i redirected toward the center plane, which lead to flow in the vertical direction in proximity of the center plane. Time-averaging the reult i reponible for the removal of alient feature in the flow, cauing unteady and coherent flow pattern to vanih. At certain time interval in the data et, the formation and ubequent diffuion of vortical tructure i viible, revealing imilar velocity and vorticity level a found in the CFD reult. Thi obervation i demontrated in Figure 9 where a equence of four PIV nap-hot i hown. Vortical tructure analogou to the CFD reult are viible in the PIV data, although uch occurrence are highly unteady (Figure 9). The preence of uch vortice in the flow, which hare order of magnitude agreement with numerical reult, demontrate the contribution of unteady flow feature to the overall velocity average. Thi inight furthermore emphaize the limited validity of implementing (timeaveraged) RANS imulation for the prediction of three-dimenional tructure in the region behind the backward-facing tep. 6 CONCLUSIONS We have invetigated the eparated region behind a confined backward-facing tep geometry for a Reynold number of approximately 6, and contant expanion and apect ratio of.4 and 2.67, repectively. The purpoe of thi tudy wa to gain an undertanding into the flow topology of the confined backward-facing tep geometry uing teadytate RANS cheme. Thi wa accomplihed through the ue of the tandard k ε turbulence model and time-averaged PIV data collection. It i apparent from thi tudy, however, that the flow i ubject to unteadine, epecially beneath the hear layer where the flow regime i not eaily determined. The direct comparion of the time-averaged reult (Reynold decompoition, ee Adrien et al. [9]) of PIV and CFD howed

5 t = 8. t 2 = 8.25 t 3 = 8.5 t 4 = N N 2 N 3 N 4..5 velocity [m/] vorticity ω y [/] Figure 9: Sequence of PIV naphot; (top) velocity magnitude and vector; (bottom) vorticity and treamline; the trajectory of the paing vortex tructure i indicated with N for the repective naphot. Note the increaed order of magnitude a compared with Figure 7 and 8. ignificant difference of the flow topology. Conequent analyi of the formation and diffuion of vortical tructure in the flow through PIV image equence proceing demontrated the preence of large-cale coherent flow pattern. Thi obervation retropectively implie that time-averaging the flow information (for both approache) i in fact a trong overimplification, at leat with repect to the flow feature within the recirculation zone. Therefore, upcoming analyi will involve the application of URANS imulation alongide time-reolved PIV experiment. Further pot-proceing by mean of proper orthogonal decompoition will provide inight into the preence and contribution of the unteady coherent pattern uperimpoed on the averaged flow field []. ACKNOWLEDGEMENTS The author gratefully acknowledge financial upport from Canadian Project Limited (CPL) and the Natural Science and Engineering Reearch Council (NSERC) for thi project. REFERENCES [] T. Lee and D. Mateecu: Experimental and numerical invetigation of 2-D backward-facing tep flow, J. Fluid and Structure, Vol. 2, (998). [2] H. Le, P. Moin and J. Kim: Direct numerical imulation of turbulent flow over a backward-facing tep, J. Fluid Mech., Vol. 33, (997). [3] H. P. Rani, T. W. H. Sheu, and E. S. F. Tai: Eddy Structure in a tranitional backward facing tep flow, J. Fluid Mechanic, Vol. 588, (27). [4] P. T. William and A. J. Baker: Numerical imulation of laminar flow over a 3D backward facing tep, International J. Numerical Method in Fluid, Vol. 24, (997). [5] N. Tylli, L. Kaikti and B. Ineichen: Sidewall effect in flow over a backward facing tep: Experiment and numerical imulation, Phyic of Fluid, Vol. 4, No., (22). [6] J. H. Nie and B. F. Armaly: Three-dimenional convective flow adjacent to backward facing tep - effect of tep height, International J. Heat and Ma Tranfer, Vol. 45, (22). [7] D. Barkley, M. Gabriella, M. Gome, R. O. Henderon: Three-dimenional intability in flow over a backward-facing tep, J. Fluid Mechanic, Vol. 473, 67-9 (22). [8] J. F. Fo: Surface election and topological contraint evaluation for flow field analye, Experiment in Fluid, Vol. 37, (24). [9] R. J. Adrian, K. T. Chritenen and Z.-C. Liu: Analyi and interpretation of intantaneou turbulent velocity field, Experiment in Fluid, Vol. 29, (2). [] J. Kota, J. Soria and M. S. Chong: A comparion between naphot POD analyi of PIV velocity and vorticity data, Experiment in Fluid, Vol. 38, 46-6 (25).