On the separated region behind a confined backward-facingstep

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

Department of Mechanical and Manufacturing Engineering, University of Calgary,Calgary, AB, Canada T2N 1N4

Email: jnfernan@ucalgary.ca

ABSTRACT

The separated flow behind a three-dimensionalbackward-facing step (BFS) is examined using nu-merical and experimental techniques. This is accom-plished through Reynolds-Averaged Navier-Stokes(RANS) simulations and time-averaged particle imagevelocimetry (PIV) measurements. Vortical structuresbehind the constrained backward-facing step are char-acterized using each approach and the reattachmentline downstream of the step is determined through thenumerical simulations. This result is compared to dataavailable in the literature for further validation. Topo-logical differences are found to exist between time-averaged solutions of each approach. However, similarvortical structures are present in both solutions. Thesestructures are only visible in the PIV data through im-age sequence processing and are found to be highlyunsteady. The presence of this obvious unsteadinessin the flow demonstrates the limited validity of im-plementing time-averaged schemes for the predictionof three-dimensional structures behind the backward-facing step.

1 INTRODUCTION

Flow separation resulting from a strong adverse pres-sure gradient due to a sudden expansion in geometry,such as a backward-facing step, occurs in a large arrayof engineering applications. Many studies on sepa-rated flows over the last few decades have focused onthe two-dimensional, backward-facing step geometry,as a means of understanding shear-layer behavior andreattachment properties [1–3]. Although the geometryis simple, the flow immediately downstream of thestep contains vortical structures and complicatedtopology.

Inside the recirculation zone the flow is character-ized by flow reversals and vortical structures [2–7].Specifically, the flow phenomenon responsible for vor-tical structures in the shear layer results from Kelvin-Helmholtz instabilities and is caused by the interactionbetween the shear layer and re-circulating flow nearthe step wall [3]. In addition to the Reynolds number,the key variables associated with the backward-facingstep problem are the expansion and aspect ratios, de-fined as the ratios of downstream to upstream channelheight and channel width to step height, respectively.In constrained (three-dimensional) channels, sidewalleffects produce complex flow structures, and for thecase of laminar flow, these structures are found to in-tensify for increasing relative step height and Reynoldsnumber at the channel lower wall for expansion and as-pect ratios of 2 and 20, respectively [4, 5].

In the present study, the investigations of the sidewalleffects are to be studied in a turbulent flow. The ma-jor objective of the current study is to demonstratehow vorticity and coherent structures develop in theflow through both numerical and experimental tech-niques. Furthermore, the limitations of time-averagedapproaches for the backward-facing step problem willbe discussed.

2 GEOMETRY

The geometry used in this study is shown in Figure 1.The channel dimensions areh = 0.315 m,H = 0.45m, s = 0.135 m, LR = 1.78 m, LS = 2.22 m andc = 0.387 m. The inflow and outflow channel heightsare given byh andH, respectively.LR andLS are cor-responding step and downstream channel lengths,s isthe step height andc is the channel width. The expan-

hs

LR

LS

H

c

flow

step

Figure 1: Schematic of test geometry, containing adescription of relevant dimensions of the confined,backward-facing step.

sion ratio is defined as

ER= H/h (1)

and is equal to 1.4. Similarly, the aspect ratio, definedas

AR = c/s, (2)

is equal to 2.67. The origin of the coordinate system isplaced at the left-hand corner of the backward-facingstep base (Figure 2).

h

sy

x

Figure 2: Close-up view of mesh refinement in the re-gion surrounding the backward-facing step.

3 NUMERICAL SET-UP

The complete water-tunnel plenum and channel ge-ometry were modeled in ICEM CFD and then im-ported into ANSYS CFX. After mesh refinement alongthe channel boundaries, so as to resolve the vis-cous sub-layer, the number of nodes in the modeltotaled 2,197,500. The Reynolds-averaged Navier-Stokes (RANS) equations were solved together withthe k − ε turbulence model using the ANSYS CFXcommercial package. Figure 2 shows a close-up viewof the mesh refinement in the region of interest.

Figure 3: Domain used for numerical simulations. Theinlet boundary condition is located by the arrows.

Simulations were performed at a step height of0.135 m. The Reynolds number, based on the stepheight s was evaluated to be approximately 60,000.Velocity at the inlet of the contraction (see Figure 3)was set at 0.05 m/s, with an eddy length scale of0.45 m, and turbulence intensity ofTu = 1%. Twoother simulations were also performed, varying bothturbulence intensity from 1% to 10% and velocity from0.05 m/s to 0.025 m/s so as to determine their contri-bution (if any) to the flow. These settings were appliedas a boundary condition at the inlet cross section, asshown in Figure 3. In this sensitivity study, it wasfound that although slight changes were observed inmagnitude contours of velocity and vorticity - the twovariables of greatest interest - neither the turbulent in-tensity nor the free-stream velocity changed the overallflow topology.

4 EXPERIMENTAL M ETHOD

The experiments were performed on a closed-loop wa-ter tunnel, as shown in Figure 4. Water was pumped toa main plenum chamber and through four conditioningunits (one honeycomb and three fine screens), beforebeing accelerated into the test section through a six-to-one ratio contraction. The channel ended with a reser-voir, which facilitated the recirculation of water backto the plenum through the pump.

To validate the results from the numerical simulations,PIV experiments were performed in the XZ-plane nearthe step geometry. The experimental set-up consistedof a New Wave Nd:YAG laser (λ = 532 nm) and PCOCCD Camera (1280 x 1024 pixels, 4fps) equipped witha Nikon lens (f = 20mm/2.8). For the data set presentedin this paper, 2500 image pairs (∆t = 24 ms) werepost-processed using the standard LaVision multi-passcross-correlation scheme.

A

C D E F

G

B

plenumconditioning units6:1 contractiontest section 1test section 2recirculation chamberreturn line and pump

ABCDEFG

Figure 4: Schematic of water tunnel used for PIVexperiments. The pump, located at the base of theplenum, drives water through the contraction into thetest sections and recirculation chamber.

The set-up can be seen in Figure 5, which depicts PIVdata acquisition for a slice in the XZ-plane. Prior todata acquisition, the PIV system was used to carefullyadjust the mean tunnel speed with that from the CFDso as to match the operating Reynolds number. Simi-larly, turbulence intensity of the mean flow in the testsection near the step was measured. It was found thatthe turbulence intensity was approximately 3%. At thesame position in the CFD simulation, the average tur-bulence intensity had an average value of 5%. The sen-sitivity analysis that was performed as part of the nu-merical study suggested that this inconsistency wouldnot result in any topological discrepancies between thenumerical and experimental simulations.

Nd:YAG laser

CCD camera

y/s

x/sz/c

c

s

field-of-view(FOV)

flow

Figure 5: Detailed sketch of the step including theglobal origin located at the bottom-left corner of thestep; PIV setup and field of view are added for the sakeof clarity.

5 RESULTS AND DISCUSSION

One of the main flow features resulting from sepa-rated flow off a confined backward-facing step is theprimary recirculation reattachment line. This line hasbeen quantified both numerically and experimentally

in previously by Nie and Armaly [6], and serves asthe main verification measure of the present study. Re-sults for the reattachment line from Nie and Armaly [6]were plotted against the findings from numerical sim-ulations in this study. Figure 6 shows these data setscompared with one another.

0 0.1 0.2 0.3 0.4 0.50

2

4

6

8

10

12

z/cx/s

ER = 2.50, Nie & Armaly [6]

ER = 2.00, Nie & Armaly

ER = 1.67, Nie & Armaly [6]

ER = 1.40, present work

[6]

Figure 6: Reattachment line for three expansion ra-tios in the laminar regime (Nie and Armaly [6]), andpresent work evaluated for an expansion ratio of ER=

1.4 in the turbulent regime.

Although there are clear differences between the reat-tachment line contours from each study, at least thepredicted length of the separated region is in goodagreement. The flow topology for the confinedbackward-facing step in this study suggests a muchmore unsteady and vorticity-driven flow, as justified bythe large differences in the operating Reynolds num-bers between the two studies. Although the preciseflow topology for this problem has not yet been fully-quantified, a better understanding of the presence ofvorticity within the flow will play an important role inunderstanding the physics of the reattachment length.Accurately determining the reattachment line for thisproblem may warrant mesh-refinement in the stream-wise direction to reduce excessive numerical diffusion.It is also expected that replacement of the two-equationmodels with more accurate Reynolds-stress modelsin the numerical solver will improve accuracy of the(spanwise) reattachment length distribution. However,these efforts are beyond the scope of the present study.

Two sets of PIV measurements were taken using thetunnel centerline as the dividing line between data sets,which provided the most advantageous field-of-view(FOV) for direct comparison with the CFD. PIV datawas taken in the XZ-plane at the locationy/s = 0.5.A comparison of velocity contours in this region isshown in Figure 7.

Velocity magnitude is of the same order but with sig-nificant variation in distribution. Topological differ-

x/s

z/c

P

IVC

FD

|vel

ocity

| [m

/s]

0 0.5 1 1.5

0

0.2

0.4

0.6

0.8

1

0.01

0.02

0.03

0.01

0.02

0.03

Figure 7: Side-by-side comparison of velocity magni-tude and vectors for both PIV (top) and CFD (bottom).

ences were found to exist between time-averaged so-lutions for both the simulations and experiments. Inthe numerical solution, two counter-rotating vortices,symmetric about the center line, are evident in theflow. However, for the PIV only streamline curvatureis noted, again symmetric about the centerline.

This discrepancy in the flow pattern between PIV andCFD warrants a discussion into the vorticity levelspresent in this region of the flow. Figure 8 showsa comparison between PIV and CFD results usingstreamlines and vorticity contours instead.

x/s

z/s

PIV

CF

D

S

S

N

N|ω

y,max|PIV

= 0.19 s−1

|ωy,max

|CFD

= 1.10 s−1

vort

icity

|ωy/ω

y,m

ax |

0 0.5 1 1.5

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

−0

−0.2

−0.4

−0.6

−0.8

−1

Figure 8: Side-by-side comparison of normalized vor-ticity and streamlines between PIV (top) and CFD(bottom); topological singularities indicated as saddles(S) and nodes (N).

Although the region of greatest vorticity was almostidentical in both PIV and CFD, precise topologicalflow features (as indicated by velocity vectors), andvorticity magnitude, were found to differ to a signif-icant extent. Furthermore, topological dissimilaritywas noted between the time-averaged solutions in boththe simulations and experiments. Flow structure varia-

tion is evident in Figure 8 through the location of topo-logical singularities (see Foss [8]) in the flow, such assaddles (S) and nodes (N) as well as through the re-gions of peak vorticity.

In the numerical simulations, the large-scale back-flowforms a vortex in the XZ-plane. When the recircu-lating flow hits the step, a pair of symmetric nodes(counter-rotating vortices) is generated, and movementof the fluid in the vertical (y-direction) only occurs atthe node (N). In contrast, the flow topology of the PIVdata suggests that the back-flow after hitting the stepis redirected towards the center plane, which leads toflow in the vertical direction in proximity of the centerplane.

Time-averaging the results is responsible for the re-moval of salient features in the flow, causing unsteadyand coherent flow patterns to vanish. At certain timeintervals in the data set, the formation and subse-quent diffusion of vortical structures is visible, reveal-ing similar velocity and vorticity levels as found inthe CFD results. This observation is demonstrated inFigure 9 where a sequence of four PIV snap-shots isshown.

Vortical structures analogous to the CFD results arevisible in the PIV data, although such occurrencesare highly unsteady (Figure 9). The presence of suchvortices in the flow, which share order of magnitudeagreement with numerical results, demonstrates thecontribution of unsteady flow features to the over-all velocity average. This insight furthermore em-phasizes the limited validity of implementing (time-averaged) RANS simulations for the prediction ofthree-dimensional structures in the region behind thebackward-facing step.

6 CONCLUSIONS

We have investigated the separated region behinda confined backward-facing step geometry for aReynolds number of approximately 60,000 and con-stant expansion and aspect ratios of 1.4 and 2.67, re-spectively. The purpose of this study was to gainan understanding into the flow topology of the con-fined backward-facing step geometry using steady-state RANS schemes. This was accomplished throughthe use of the standardk − ε turbulence model andtime-averaged PIV data collection. It is apparent fromthis study, however, that the flow is subject to unsteadi-ness, especially beneath the shear layer where the flowregime is not easily determined. The direct compari-son of the time-averaged results (Reynolds decompo-sition, see Adrienet al. [9]) of PIV and CFD showed

x/s

z/c

0 0.5 1 1.5

0.1

0.2

0.3

0.4

0.5

x/s0 0.5 1 1.5

x/s0 0.5 1 1.5

x/s

0 0.5 1 1.5

vort

icity

ωy [1

/s]

−2

−1

0

1

2

3

z/c

t1 = 18.00 s

N1

N1

0.1

0.2

0.3

0.4

0.5

t2 = 18.25 s

N2

N2

t3 = 18.50 s

N3

N3

t4 = 18.75 s

N4

N4

|vel

ocity

| [m

/s]

0

0.05

0.1

Figure 9: Sequence of PIV snapshots; (top) velocity magnitude and vectors; (bottom) vorticity and streamlines;the trajectory of the passing vortex structure is indicatedwith N for the respective snapshots. Note the increasedorders of magnitude as compared with Figures 7 and 8.

significant differences of the flow topology. Conse-quent analysis of the formation and diffusion of vorti-cal structures in the flow through PIV image sequenceprocessing demonstrated the presence of large-scalecoherent flow patterns. This observation retrospec-tively implies that time-averaging the flow informa-tion (for both approaches) is in fact a strong oversim-plification, at least with respect to the flow featureswithin the recirculation zone. Therefore, upcominganalysis will involve the application of URANS simu-lations alongside time-resolved PIV experiments. Fur-ther post-processing by means of proper orthogonaldecomposition will provide insight into the presenceand contribution of the unsteady coherent patterns su-perimposed on the averaged flow field [10].

ACKNOWLEDGEMENTS

The authors gratefully acknowledge financial supportfrom Canadian Projects Limited (CPL) and the NaturalSciences and Engineering Research Council (NSERC)for this project.

REFERENCES

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