VOL. 19, NO. 9, SEPTEMBER 1981 AIAA JOURNAL 1093

AIAA 80-1438R

A Review of Research on Subsonic Turbulent Flow ReattachmentJ. K. Eaton and J. P. Johnston

Stanford University, Stanford, Calif.

Nomenclatureh = step heightRee = momentum thickness Reynolds numberu = streamwise velocityU = mean streamwise velocityu' = u-UU0 = freestream velocity at separationv' = fluctuating component of cross-stream velocityx = streamwise coordinateXR = reattachment pointx =(x — xR)/hy = cross-stream coordinate5S = boundary-layer thickness at separation6 = momentum thickness at separation

Introduction

THE reattachment of a turbulent shear layer is an im-portant process in a large number of practical engineering

configurations, including diffusers, airfoils with separationbubbles, buildings, and combustors. In order to predict thesecomplicated flows, we must understand and be able to predictthe behavior of reattaching shear layers. However, ourcurrent understanding of the reattachment process is poor, afact demonstrated by our inability to predict simple reat-taching flows over a wide range of parameters. In fact, acomplete list of the parameters that affect reattachment hasyet to be formulated.

Among two-dimensional flows, the backward-facing step isthe simplest reattaching flow. The separation line is straightand fixed at the edge of the step, and there is only oneseparated zone instead of two, as seen in the flow over a fenceor obstacle. In addition, the streamlines are nearly parallel tothe wall at the separation point, so significant upstream in-fluence occurs only downstream of separation. Although theyare not always stated explicitly, these are the reasons whymost of the research on reattachment has been done inbackward-facing step flows. The backward-facing step is alsoused as a building block flow for workers developing tur-bulence models.1 Therefore, it is important to supply datawhich can be used to test codes and information that may aidthe development of future codes.

Bradshaw and Wong2 reviewed the experimental data forreattaching flows in 1972. Since that time there has been aproliferation of new research in the area, particularly since the

advent of the laser anemometer and the pulsed-wireanemometer. This research has been conducted by a numberof independent groups, and therefore the net result issomewhat disorganized. Very little systematic study has beendone on the effect of the governing parameters on reat-tachment. In addition, most of the experiments, when viewedseparately, have failed to cast any new light on the underlyingphysics of the reattachment process.

The purpose of this paper is twofold. The primary purposeis to review the available data for turbulent flows overbackward-facing steps, including some new data of our ownand other previously unpublished data. Second, we suggestseveral areas of research that we feel could lead to im-provements in our ability to predict flows with separationbubbles. Several physical mechanisms will be proposed toexplain some of the phenomena that have been observed. It isour hope that these suggestions will provoke further thought,comment, and research.

The review covers subsonic flows over backward-facingsteps in which the Reynolds number is high enough to insurethat the separated shear layer is fully turbulent. Importantwork on laminar and transitional reattaching shear layers hasbeen performed by Goldstein et al.3 and Armaly et al.4 butwill not be referred to here. Primary emphasis is on planarflows, but some data from axisymmetric flows will beutilized. Double-sided, sudden expansion flows in which theflow is asymmetric are not considered here, because theseflows are even more complicated than flows with a singleseparation bubble.

A companion paper5 examines the uncertainty of theavailable data in more detail. It also assesses the usefulness ofthe various data sets as test cases for computationalprocedures.

General Features of the Backward-Facing Step FlowAlthough the backward-facing step is the simplest reat-

taching flow, the flowfield is still very complex. Figure 1illustrates some of the complexities. The upstream boundarylayer separates at the sharp corner forming a free-shear layer.If the boundary layer is laminar, transition begins soon afterseparation, unless the Reynolds number is very low.

The separated shear layer appears to be much like an or-dinary plane-mixing layer through the first half of theseparated flow region. The dividing streamline is only slightlycurved, and the shear layer is thin enough that it is not af-

John K. Eaton is an Assistant Professor of Mechanical Engineering at Stanford University. He received hisPh.D. from Stanford and joined the faculty in 1980. Professor Eaton's research is primarily concerned with flowand heat transfer in separated and reattaching flows, and the development of advanced instrumentationtechniques for the measurement of near-wall turbulence. He is also interested in the application of small com-puters to fluid mechanics research.

James P. Johnston has been a member of the Department of Mechanical Engineering at Stanford Universitysince 1961. After he received his Sc.D. in 1957 from the Massachusetts Institute of Technology, he worked as anengineer with Ingersol-Rand Co. The fluid mechanics of internal flows with emphasis on three-dimensionalcurved and rotating turbulent flows, and the processes of flow separation in diffusers have been his primaryinterests. He has also worked on radial flow turbomachinery, aeroacoustics, and research instrumentation.Professor Johnston holds membership in AIAA and ASME. He has served on several committees of the ASMEFluids Engineering Division and as an Associate Editor of the Journal of Fluids Engineering.

Presented as Paper 80-1438 at the AIAA 13th Fluid and Plasma Dynamics Conference, Snowmass, Colo., July 14-16, 1980; submitted Sept. 24,1980; revision received March 2, 1981. Copyright © American Institute of Aeronautics and Astronautics, Inc., 1980. All rights reserved.

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1094 J. K. EATON AND J. P. JOHNSTON AIAA JOURNAL

fected by the presence of the wall. However, the reattachingshear layer differs from the plane-mixing layer in one im-portant aspect; the flow on the low-speed side of the shearlayer is highly turbulent, as opposed to the low turbulence-level stream in a typical plane-mixing layer experiment. Someauthors, including Chandrsuda6 and Chandrsuda et al.7 havesuggested that the turbulent recirculating flow causes thereattaching shear layer to be substantially different from aplane-mixing layer. This question will be more fully discussedlater.

The separated shear layer curves sharply downward in thereattachment zone and impinges on the wall. Part of theshear-layer fluid is deflected upstream into the recirculatingflow by a strong adverse pressure gradient. The shear layer issubjected to the effects of stabilizing curvature, adversepressure gradient, and strong interaction with the wall in thereattachment zone. One or more of these mechanisms cause(s)a rapid decay of Reynolds normal and shear stresses withinthe reattachment zone. The flow in this zone is very unsteady.Very large turbulence structures with length scales at least aslarge as the step height are passing through the reattachmentregion. In addition, flow visualization by Abbott and Kline8

and Kirn et al.9 showed that the length of the separationregion fluctuated so that the impingement point of the shearlayer moved up and downstream. Quantitative measurementsby Eaton and Johnston10 confirmed this conclusion.

The recirculating flow region below the shear layer cannotbe characterized as a dead air zone. The maximum measuredbackflow velocity is usually over 20% of the freestreamvelocity, and negative skin-friction coefficients as large asCf= -0.0012 (based on the freestream velocity) have beenmeasured.6'10

Downstream of reattachment, the Reynolds stressescontinue to decay rapidly for a distance of several stepheights. Simultaneously, a new sub-boundary layer begins togrow up through the reattached shear layer. Themeasurements of Bradshaw and Wong2 and more recentmeasurements by Smyth11 have shown that the outer part ofthe reattached shear layer still has most of the characteristicsof a free-shear layer as much as 50 step heights downstream ofreattachment. This observation demonstrates the remarkablepersistence of the large-scale eddies that are developed in theseparated free-shear layer.

Until recently, the measurement of turbulence data in thebackward:facing step flow was very difficult. The flow ishighly turbulent, and frequent flow reversals occur, par-ticularly in the reattachment zone, one of the most importantareas in the flow. Hot-wire anemometers are not suitable foruse in reversing flows, a fact that has severely restricted thequality of available data. The current generation of tur-bulence models suffers from a lack of experimental inputbecause of this problem. Since the introduction of the laser-Doppler anemometer and the pulsed-wire anemometer, thequality of available data has slowly begun to improve.

Summary of Experimental ResultsAt the time of Bradshaw and Wong's2 review, very few

reliable data for reattaching flows were available. Only a fewsets of hot-wire turbulence data were available,12'14 andmeasurements in the reattachment zone were lacking.Bradshaw and Wong2 concluded that the ratio of theboundary-layer thickness at separation to the step height wasan important parameter characterizing the downstream flow.On the basis of the available turbulence data, they concludedthat the shear stress (- zT7*/) in the reattaching layer is muchlarger than the shear stress in an ordinary plane-mixing layer.They also pointed out that the shear stress decreases rapidlynear reattachment, despite the fact that there is very littlechange in the mean-velocity gradient (dU/dy).

Since the time of Bradshaw and Wong's2 review, severaldata sets have been taken in the two-dimensional, backward-

DIVIDING STREAMLINE

uX REATTACHMENT ZONE

Fig. 1 Backward-facing step flowfield.

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facing-step flow using hot-wire anemometers,6'9'15'16 pulsed-wire anemometers,10'17'18 laser anemometers,11'19'24 and flowvisualization.25'26 These data sets are summarized in Table 1.

Effect of System Parameters on ReattachmentThe experiments just listed have covered a wide range of

initial and boundary conditons, so some measure of the effectof various parameters on the flow can be seen by examiningthe data in Table 1. The most important dependent parametercharacterizing the individual flowfield is the reattachmentlength which varies from 4.9 to 8.2 step heights for the ex-periments in Table 1. Comparison of the reattachment lengthfrom various experiments provides insight into the effects ofvarying the following five principal independent parameters:1) initial boundary-layer state, 2) the initial boundary-layerthickness, 3) freestream turbulence, 4) pressure gradient, and5) aspect ratio. We shall consider each effect separatelybelow.

1) The effect of changing the state (laminar/turbulent) ofthe separation boundary layer has been systematically studiedby Eaton et al.17 and Eaton and Johnston.10 This parameterwas found to have a significant influence on the reattachmentlength (see Fig. 2). The flow apparently becomes independentof the Reynolds number when the boundary layer is fullyturbulent. Furthermore, the results in Fig. 2 agreequalitatively with the results of Bradshaw,27 who found thatlayers originating from laminar boundary layers initially growmore rapidly than those originating from turbulent boundarylayers.

2) The data of Narayanan et al.28 show a weak effect of theboundary-layer thickness on the reattachment length (Fig. 3).However, by using four data sets with different values of 5Sbut similar values of other parameters, we see a somewhatstronger effect of <55 on the reattachment length (Fig. 3).Further systematic study is needed to resolve this issue.

3) The effect of freestream turbulence on the reattachmentlength has never been studied systematically. However, threeof the data sets in Table 1 (Etheridge and Kemp, Hsu, and

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1096 J. K. EATON AND J. P. JOHNSTON AIAA JOURNAL

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Tropea and Durst) had fairly high levels (>1%) of thefreestream turbulence. An examination of Figs. 3 and 4suggests that high levels of the freestream turbulence decreasethe reattachment length. This result is in qualitativeagreement with the measurements of Patel29 in a plane-mixing layer. He found that plane-mixing layer growth rateswere increased by increasing the freestream turbulence level.The sensitivity to freestream turbulence is surprising since,according to most authors, the separated shear layer is alreadystrongly affected by the turbulence in the recirculating flow.The magnitude of the effect of freestream turbulence is likelyto be dependent on a) the initial conditions of the free-shearlayer and b) the spectrum of the freestream turbulence.Further investigation into the effect of freestream turbulenceon free-shear layers definitely is needed.

4) The effect of changing the streamwise pressure gradientin the reattachment zone has not been studied systematically.This pressure gradient is in part controlled by the overallsystem geometry. Kuehn30 pointed out that a plot of reat-tachment length vs area expansion ratio for sudden expansionflows shows a very substantial effect of the pressure gradienton the reattachment length. In Fig. 4, reattachment lengthshave been plotted vs expansion ratio for flows in which theboundary layer is fully turbulent at separation. There is aconsiderable amount of scatter, but a trend of increasingreattachment length with increasing expansion ratio is ap-parent. Kuehn and Seegmiller24 are proceeding with furtherinvestigation of this question.

5) The aspect ratio of the flow apparatus (channelwidth/step height) can also have an effect on the reattachmentlength. This effect was systematically studied by de Brederode

and Bradshaw,31 who found that the effect was negligible foraspect ratios greater than ten. For aspect ratios less than ten,the reattachment length increases if the boundary layer atseparation is laminar and decreases if it is turbulent, deBrederode and Bradshaw31 attributed this difference todifferences in details of the corner flow.

Turbulence MeasurementsTurbulence quantities have been measured for most of the

experiments in Table 1. There is a substantial variationbetween experiments in the peak values of the turbulenceintensity and shear stress (see Table 1). The variation isprobably caused as much by experimental uncertainty as byreal differences in the flows. Many of the turbulencemeasurements were done with jc-wire hot-wire probes, whichare inadequate for use in highly turbulent flows (see Tutu andChevray32). The local turbulence intensity near the center ofthe reattaching shear layer exceeds 30%, so the .x-wires areexpected to undermeasure turbulence quantities (particularlythe shear stress) in this region. In addition, the turbulence-intensity measurements can be affected strongly by low-frequency motions of the shear layer that are certainly presentin some of the experiments, but may not be present in all ofthem.

The turbulence-intensity measurements do show a con-sistent pattern when the maximum intensity in a given profileis plotted as a function of streamwise distance (Figs. 5 and 6).In almost all cases, the turbulence intensity reaches a peakvalue approximately one step height upstream of reat-tachment, then decays rapidly. Many of the data sets have ashort plateau of constant turbulence intensity followed by

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SEPTEMBER 1981 RESEARCH ON SUBSONIC TURBULENT FLOW REATTACHMENT 1097

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another region of rapid decay (Fig. 6). The locus of points(normal to the wall) where turbulence intensity is a maximumdips toward the wall in the reattachment zone and then movesback out away from the wall downstream of reattachment.The point of maximum turbulence intensity dips closer to thewall the shorter the reattachment length, as shown in Fig. 7.Only three data sets are shown in Fig. 7 for clarity, but thepattern illustrated is almost universal for backward-facing-step experiments. Despite the rapid decay of the peak value ofturbulence intensity which occurs away from the wall, theturbulence intensity decays_very slowly near the wall.9>10)23

The shear stress (-IT7!/) measurements show the samegeneral pattern observed in the turbulence-intensitymeasurements (Fig. 8). Some of these data sets18>23 also have aplateau in the reattachment region. Lines of "acceptabledata" are shown in Fig. 8. In the authors' estimation, the twoexperiments outside these bounds must have encounteredsome unrecognized measurement problem. The large dif-ference between data sets far upstream of reattachment iscaused by two factors: 1) the scaling of the x coordinate usedhere is not appropriate to this region, and 2) differences ininitial conditons cause large differences in the earlydevelopment of the shear layer. The collapse of the data isbetter in the reattachment region and much better down-stream of reattachment. The variation within the reat-tachment zone is caused largely by instrumentation problems.

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The values measured with hot-wire arrays are consistentlylower than those measured with laser anemometers. Based onthe information in Fig. 7, the peak value of the shear stress formost_experiments is estimated to be in the neighborhood of

Chandrsuda6 has made the only measurements of higher-order turbulence quantities in the reattachment zone. Un-fortunately, the measurements were made with hot wires, andthe accuracy of the measurements is therefore questionable.However, Chandrsuda and Bradshaw33 felt that themeasurements at least could be used qualitatively. Theyconcluded that the triple products in the outer part of theshear layer decrease at roughly the same rate as the Reynoldsstresses, but decay much more rapidly than the Reynoldsstresses near the wall. They felt that this was primarily due tothe imposition in the reattachment region of the wall con-straint on the normal velocity (v = Q at y = Q). This resultindicates the gradient diffusivity of the Reynolds stresses isnot an adequate model for the triple products in the reat-tachment region. Further measurements of the triple productsusing laser-anemometer techniques are needed to verify theseconclusions.

Comparison of Profiles Near ReattachmentIt is difficult to compare mean velocity and Reynolds stress

profiles from different experiments due to the effects ofdifferent initial and boundary conditions. Much of the ap-parent differences between profiles from different ex-periments is caused by differences in the reattachment length.One possible way to compare profiles from various ex-periments is to renormalize the streamwise coordinate asx = (x — xR)/h. In this way, features of the reattachment zonemay be examined independent of experiment-to-experimentvariation in the reattachment length. Mean-velocity profiles atx = 0 have been compared for the experiment of Etheridge andKemp19 and two experiments from Eaton and Johnston.10

The initial conditions for these experiments ranged from avery thick (ds/h = 2) turbulent boundary layer to a thin

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(ds//z = 0.2) laminar boundary layer. The reattachmentlengths ranged from 5 to 7.9 step heights. The velocity profilesare in excellent agreement in the inner layer (Fig. 9). Thedifferences in the outer layer are caused by differences in theboundary geometry among the three experiments. _____

A similar comparison was made of shear stress (-zT7*/)profiles. In this case, the data are taken from the experimentsof Kirn et al.,9 Chandrsuda,6 and Baker.18 All three of theprofiles were measured with *-wire hot-wire probes. Theprofiles (Fig. 10) are again quite similar despite large dif-ferences in the initial conditions (see Table 1). The profile ofKim et al. is shifted up because the reattachment length issubstantially longer than in the other two experiments.

The agreement of the profiles in Figs. 9 and 10 shows thatthe effect of initial conditions has been overwhelmed by thetime the shear layer reattaches. Therefore, it appears that thecriterion for an overwhelming perturbation of the shear layercan be extended out to a value of 55//z<2, a considerableincrease compared to ds/h< 1, as suggested by Bradshaw andWong.2 In fact, this criterion may be further extended to evenhigher 5s/h with more research.

Large-Eddy Structure in the Reattaching Shear LayerThe large-eddy structure in the reattaching shear layer is an

area of much current interest. Brown and Roshko34 andWinant and Browand35 observed two-dimensional, spanwisevortices in plane-mixing layers. They suggested that thespanwise vortices are the dominant structure in plane-mixinglayers and are responsible for most of the growth and en-trainment of the shear layer. They showed that plane-mixinglayers grow by successive amalgamations (pairings) of thespanwise vortices. In more recent years this has been an areaof much interest and controversy. However, very little workhas been done on structure in reattaching shear layers.Chandrsuda et al.7 claim that the spanwise vortices would notform if the boundary layer at separation were turbulent. Theyalso suggested that, if these structures were formed in abackward-facing-step flow, they would be broken downquickly by three-dimensional disturbances introduced by thefluctuations in the recirculating flow. They did not supportthis latter conclusion experimentally, and there remainsconsiderable controversy on this question.

A few investigations of the large-eddy structure in reat-taching shear layers have been done. Rothe and Johnston26

observed spanwise vortices which grew by pairing in thereattaching shear layer. They found that three-dimensionalturbulence could be suppressed by rotating the test sectionabout a spanwise axis in the stabilizing direction. Thespanwise vortices, however, were not affected by the rotation.When the test section was rotated at a sufficient rate tocompletely suppress all three-dimensional turbulence, thereattachment length increased by only 8% over the reat-tachment length with no rotation. In contrast, when the testsection was rotated in the opposite direction, thus enhancingthe three-dimensional turbulence, the reattachment lengthdecreased by over 50%. This result indicates that the spanwisevortices are responsible for most of the entrainment from therecirculating flow in the zero-rotation case. Rothe andJohnston also concluded that the spanwise vortices areprimarily responsible for the region of unsteady reversingflow centered around the mean reattachment point.

Kasagi et al.36 used smoke-wire flow visualization toexamine the structure in a reattaching shear layer. Theirphotos showed that the turbulence structure becomes fullythree dimensional upstream of reattachment. The spanwiselength scale of the large eddies was of the order of one stepheight. Their work did not confirm or deny the existence ofspanwise vortices upstream of the reattachment region.McGuinness37 studied the large-eddy structure in a reat-taching shear layer behind an orifice at the entrance of a pipe.Spectra of streamwise velocity fluctuations and of the wallstatic pressure were used, along with flow visualization, to

infer the large-eddy structure. In addition, experiments wereconducted in which the lip of the orifice was vibrated slightly.This served to organize the large-eddy structure, allowingphase averages of velocity and pressure fluctuations.McGuinness concluded that the reattaching shear layer grewby a pairing mechanism until it approached the wall in thereattachment zone. He also tentatively concluded that some ofthe large eddies were swept upstream with the recirculatingflow, while others proceeded downstream. He attributed thedecay of turbulent stresses in the reattachment zone to thismechanism.

The latter conclusion is a matter of current controversy.Bradshaw and Wong2 believe that the eddies are torn roughlyin two in the neighborhood of the reattachment point. Otherworkers, including Chandrsuda6 and Kim et al.,9 agree withMcGuinness. Measurements by both Kim et al.9 andChandrsuda6 show that the intermittency is less than unitynear the wall just downstream of reattachment. This resultsupports the hypothesis that the eddies move alternately up-and downstream. Recent crude flow visualization in ourlaboratory showed no evidence of large eddies being sweptupstream. More careful flow visualization will, we hope,resolve this question in the near future.

Discussion: Comparison of the Reattaching Shear Layerto a Plane-Mixing Layer

Several authors have pointed out the similarity of thereattaching shear layer to a plane-mixing layer. Shear-layergrowth rates have .been calculated for the experiments ofBaker,18 Eaton and Johnston,10 Kim et al.,9 and McGuin-ness.37 In all of these cases, the growth rate was comparableto the plane-mixing layer growth rate. Baker18 and Eaton andJohnston10 have compared their mean-velocity profilesupstream of reattachment to plane-mixing layer profiles indetail. The profiles are nearly identical in the outer three-fourths of the layer but differ near the low-speed edge, as onemight expect.

It is somewhat more difficult to compare the Reynoldsstress measurements between the two types of shear layers.Turbulence measurements in plane-mixing layers typically arescaled by the total velocity difference across the shear layer.However, the velocity difference is not constant for a reat-taching shear layer; it changes from roughly 1.0 times thefreestream velocity just downstream of separation to about1.2 times the freestream velocity at a point roughly halfway toreattachment. Therefore, we can never expect a reattachingshear layer to reach a fully developed state, even if it startsfrom a very thin boundary layer. Nevertheless, approximatecomparisons of the two types of free-shear layers_can bemade. The peak values of the turbulence intensity (-tt7'2~/U2

0)are typically around 0.04 for data sets measured with laseranemometers or pulsed-wire anemometers. Guessing that theappropriate normalizing velocity difference is about 1.1 U0,we get zT7^At/2 =0.033. This value is 10-20% higher thantypical values measured in plane-mixing layers. We feel thatthis higher intensity level is due to a very low-frequencyvertical motion of the reattaching shear layer (flapping), butthere is not general agreement on this point.

The peak value of the shear_s_tress in the reattaching layerwas estimated to be about - u7:v7/U2

0 = 1.25 x 1 0 ~ ~ 3 . Againchoosing 1.1 U0 as the appropriate normalizing velocitydifference, we get a value of -tPt^/Af/2 = 1.03x 10 ~ 3 , veryclose to the typical plane-mixing-layer value of about1 . 0 x l O ~ 3 . The low frequency motions of the shear layer,while having a substantial effect on w /T7 would not contributesignificantly to the shear stress.

The conclusion that can then be reached is that the reat-taching shear layer is indeed very similar to a plane-mixinglayer upstream of the reattachment zone. This conclusion issupported by observations of the large-eddy structuredescribed in the previous section. The implication is that theeffects of many parameters (such as freestream turbulence,

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Mach number, or upstream boundary-layer state) could bepredicted using plane-mixing-layer data. The data also in-dicate that turbulence models useful in plane-mixing layersshould be adequate for the reattaching shear layer, at leastupstream of the reattachment zone. Improved models may berequired closer to and downstream of reattachment.

Decay of Turbulence Quantities in theReattachment Zone

Perhaps the most poorly understood part of a reattachingflow is the rapid decrease of the Reynolds stresses in thereattachment zone. A correct understanding of this decrease isnecessary in order to correctly predict the redevelopment ofthe downstream boundary layer. However, as was pointed outearlier, the shear layer is subjected to several differentdistorting "forces" in the reattaching zone. In addition,detailed and accurate measurements are lacking for thereattachment zone.

Bradshaw and Wong2 first concluded that the impositionof the normal velocity constraint by the wall (v = 0) and thestrong streamwise pressure gradients cause the large eddies tobe torn in two in the reattachment zone. The rapid reductionin length scale would therefore be responsible for the decreasein the turbulence levels. However, the majority of otherworkers have disagreed that eddies are torn in two, andmeasurements far downstream of reattachment indicate thatthe free-shear-layer structure persists in the outer part of theboundary layer.

In many of the data sets, the decay of turbulence occurs intwo stages, as shown in Fig. 5. The initial decay usually beginsabout 1.5 step heights upstream of the mean-reattachmentpoint. This first stage of decay may be caused by stabilizingcurvature of the free-shear layer. Castro and Bradshaw38 andGillis and Johnston39 have shown that convex streamwisecurvature can cause rapid decay of shear-layer turbulence.The separated shear layer is only slightly curved until it beginsto curve sharply toward the wall about two step heightsupstream of reattachment. Just upstream of reattachment,the ratio of shear-layer thickness to radius of curvature ex-ceeds 0.1. Such strong curvature would be expected to reducerapidly the Reynolds stresses in the absence of other effects.However, the shear layer curvature cannot account for thecontinued decay of turbulence quantities downstream ofreattachment.

Summary and Recommendations for Future WorkWith this paper we have attempted to consolidate the

available experimental data for the subsonic backward-facing-step flow. We have also expressed some of our ownopinions about the nature of the flow. It is apparent that a lothas been learned about two-dimensional reattachment sincethe time of Bradshaw and Wong's2 review in 1972. Severaladditional experiments are needed before we can claim a goodunderstanding of the flowfield.

An accurate assessment of the effects of freestream tur-bulence and streamwise pressure gradient on the reattachmentlength is needed. This information may allow us to predictaccurately flows of engineering importance.

One or two complete sets of mean-velocity and turbulencedata are still needed for checking computer codes. Despite thelarge number of experiments on reattachment, none is fullysuited as a test case for computer codes (see Eaton andJohnston5). The experiment should be conducted in a large-scale, high Reynolds number facility with a fully turbulentboundary layer at separation. Laser anemometers should beused for most of the velocity measurements, but the resultsshould be checked with other instrumentation where possible.Measurements should include mean velocity, Reynolds stresscomponents, triple products, and an accurate measurement ofthe reattachment length.

Further experimentation is needed in the reattachmentzone. The vital phase of this experimentation should be flow

visualization to clarify our understanding of the large-eddystructure.

Finally, work is needed to understand the low-frequencymotions of the shear layer. Eaton and Johnston10 have ob-served very large-scale, low-frequency motions of theirreattaching shear layer, using a variety of techniques. On theother hand, Chandrsuda6 and Tani et al.12 found no evidenceof low-frequency motions in their experiments. These low-frequency motions could be very important in engineeringapplications. Therefore, it is important to understand thephysical circumstances under which they occur and developcriteria for prediction of their occurrence.

AcknowledgmentsWe gratefully acknowledge the support of the National

Science Foundation (Grant NSF-CME-78-02248), whichsupports our own reattachment research. We also thank theOrganizing Committee of the 1980/81 Stanford Conferenceson Complex Turbulent Flows, who helped support the data-review work. The willing cooperation of the entire communityof researchers interested in the backward-facing stepespecially was appreciated.

References!Marvin, J. G., "Turbulence Modeling for Compressible Flows,"

NASATMX-73, 188, 1977.2Bradshaw, P. and Wong, F. Y. F., "The Reattachment and

Relaxation of a Turbulent Shear Layer," Journal of Fluid Mechanics,Vol.52, Pt. 1, 1972, pp. 113-135.

3Goldstein, R. J., Eriksen, V. L., Olson, R. M., and Eckert, E. R.G., "Laminar Separation, Reattachment, and Transition of Flowover a Downstream-Facing Step," Transactions of the ASME,Journal of Basic Engineering, Vol. 92D, No. 4, 1970, pp. 732-741.

4Armaly, B. F., Durst, F., and Scheming, B., "Measurements andPredictions of Flow Downstream of a Two-Dimensional SingleBackward-Facing Step," Report SFB 80/ET/172, Karlsruhe Univ.,July 1980.

5Eaton, J. K. and Johnston, J. P., "An Evaluation of Data for theBackward-Facing Step Flow," Report prepared for the 1980/81Stanford Conferences on Complex Turbulent Flows, 1980.

6Chandrsuda, C., "A Reattaching Turbulent Shear Layer in In-compressible Flow," Ph.D. thesis, Dept. of Aeronautics, ImperialCollege of Science and Technology, 1975.

7Chandrsuda, C., Mehta, R. D., Weir, A. D., and Bradshaw, P.,"Effect of Free-Stream Turbulence on Large Structure in TurbulentMixing Layers," Journal of Fluid Mechanics, Vol. 85, Pt. 4, 1978, pp.693-704.

8Abbott, D. E. and Kline, S. J., "Experimental Investigation ofSubsonic Turbulent Flow over Single and Double Backward-FacingSteps," Transactions of the ASME, Journal of Basic Engineering,Vol. 84D, Ser. D, 1962, pp. 317-325.

9Kim, J., Kline, S. J., and Johnston, J. P., "Investigation ofSeparation and Reattachment of a Turbulent Shear Layer: Flow overa Backward-Facing Step," Thermosciences Div., Dept. of MechanicalEngineering, Stanford Univ., Rept. MD-37, 1978.

10Eaton, J. K. and Johnston, J. P., "Turbulent Flow Reat-tachment: An Experimental Study of the Flow and Structure Behind aBackward-Facing Step," Dept. of Mechanical Engineering, StanfordUniv., Rept. MD-39, 1980.

nSmyth, R., "Turbulent Flow over a Plane Symmetric SuddenExpansion," Transactions of the ASME, Journal of FluidsEngineering, Vol. 101, No. 3, 1979, pp. 348-353.

12Tani, I., luchi, M., and Komoda, H., "Experimental In-vestigation of Flow Separation Associated with a Step or Groove,"Aeronautical Research Institute, Univ. of Tokyo, Rept. 364, 1961.

13Hsu, H. C., "Characteristics of Mean Flow and Turbulence at anAbrupt Two-Dimensional Expansion," Ph.D. thesis, Dept. ofMechanics and Hydraulics, State Univ. of Iowa, 1950.

14Mueller, T. J. and Robertson, J. M., "A Study of Mean Motionand Turbulence Downstream of a Roughness Element," Proceedingsof the 1st Southeastern Conference on Theoretical and AppliedMechanics, Galinburg, Tenn., 1962, pp. 326-340.

15Ha Minh, H. and Chassaing, P., "Perturbations of TurbulentPipe Flow," Turbulent Shear Flows, I, edited by Durst et al.,Springer-Verlag, Berlin, 1977, pp. 178-197.

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16Seki, N., Fukusako, S., and Hirata, T., "Turbulent Fluctuationsand Heat Transfer for Separated Flow Associated with a Double Stepat Entrance to an Enlarged Flat Duct," Transactions of the ASME,Journal of Heat Transfer, Vol. 98, Nov. 1976, pp. 588-593.

17Eaton, J. K., Johnston, J. P., and Jeans, A. H., "Measurementsin a Reattaching Turbulent Shear Layer," Proceedings of the 2ndSymposium on Turbulent Shear Flows, London, 1979.

18Baker, S., "Regions of Recirculating Flow Associated with Two-Dimensional Steps," Ph.D. thesis, Dept. of Civil Engineering, Univ.of Surrey, 1977.

19Etheridge, D. W. and Kemp, P. H., "Measurements of Tur-bulent Flow Downstream of a Rearward-Facing Step," Journal ofFluid Mechanics, Vol. 86, Pt. 3, 1978, pp. 545-566.

20Denham, M. K., "The Development of a Laser Anemometer forRecirculating Fluid-Flow Measurements," Ph.D. thesis, Exeter Univ.,1974.

21 Grant, I., Barnes, F. A., and Created, C. A., "VelocityMeasurements Using the Photon Correlation Technique in aSeparated Boundary Layer," AIAA Journal, Vol. 18, May 1975, pp.504-507.

22Pitz, R. W. and Daily, J. W., "Experimental Studies of Com-bustion in a 2-D Turbulent Free Shear Layer," Proceedings of the 2ndSymposium on Turbulent Shear Flows, London, July 1979.

23Tropea, C. and Durst, F., personal communication, Stanford,1980.

24Kuehn, D. M. and Seegmiller, H. L., personal communication,Stanford, 1980.

25Kasagi, N., Hirata, M., and Yokobari, S., "Visual Studies ofLarge Eddy Structures in Turbulent Shear Flows by Means of Smoke-Wire Method," Proceedings of the International Symposium on FlowVisualization, Tokyo, Oct. 1977, pp. 169-174.

26Rothe, P. H. and Johnston, J. P., "Free-Shear-Layer Behaviorin Rotating Systems," Journal of Fluids Engineering, Vol. 101,March 1979, pp. 117-119.

27Bradshaw, P., "The Effect of Initial Conditions on theDevelopment of a Free Shear Layer," Journal of Fluid Mechanics,Vol. 26, Pt. 2, 1966, pp. 225-236.

28Narayanan, M. A. B., Khadgi, Y. N., and Viswanath, P. R.,"Similarities in Pressure Distribution in Separated Flow behindBackward-Facing Steps," Aeronautical Quarterly, Vol. 25, Nov.1974, pp. 305-312.

29Patel, R. P., "Effects of Stream Turbulence on Free ShearFlows," Aeronautical Quarterly, Vol. 29, Pt. 1, 1978, p. 1-17.

30Kuehn, D. M., "Some Effects of Adverse Pressure Gradient onthe Incompressible Reattaching Flow over a Rearward-Facing Step,"AIAA Journal, Vol. 18, March 1980, pp. 343-344.

31 de Brederode, V. and Bradshaw, P., "Three-Dimensional Flowin Nominally Two-Dimensional Separation Bubbles. I. Flow Behind aRearward-Facing Step," Imperial College, Aeronautical Rept. 72-19,1972.

32Tutu, N. K. and Chevrey, R., "Cross-Wire Anemometry inHigh-Intensity Turbulence," Journal of Fluid Mechanics, Vol. 74, Pt.4, 1975, pp. 785-800.

33Chandrsuda, C. and Bradshaw, P., "Turbulence Structure of aReattaching Mixing Layer," paper submitted to Journal of FluidMechanics, 1980.

34Brown, G. and Roshko, A., "On Density Effects and LargeStructure in a Turbulent Mixing Layer," Journal of Fluid Mechanics,Vol. 64, July 1974, pp. 775-816.

35Winant, C. D. and Browand, F. K., "Vortex Pairing: TheMechanism of Turbulent Mixing-Layer Growth at Moderate ReynoldsNumber," Journal of Fluid Mechanics, Vol. 63, April 1974, pp. 237-256.

36Kasagi, N., Hirata, M., and Yokobori, S., "Visual Studies ofLarge-Eddy Structures in Turbulent Shear Flows by Means of Smoke-Wire Method," Proceedings of the 1st International Symposium onTurbulent Shear Flows, Pennsylvania State College, 1977.

37McGuinness, M., "Flow with a Separation Bubble—Steady andUnsteady Aspects," Ph.D. dissertation, Cambridge Univ., 1978.

38Castro, I. P. and Bradshaw, P., "The Turbulence Structure of aHighly Curved Mixing Layer," Journal of Fluid Mechanics, Vol. 73,Pt. 2, Jan. 1976, pp. 265-304.

39Gillis, J. C. and Johnston, J. P., "Experiments on the TurbulentBoundary Layer over Convex Walls and Its Recovery to Flat-WallConditions," Proceedings of the 2nd Symposium on Turbulent ShearFlows, London, 1979.

40Pronchick, S. and Kline, S. J., unpublished work in progress.41Rashed, M. I. I., El-Taher, R. M., and Ghazy, M. A., "Ex-

perimental Investigation of the Effect of Surface Discontinuity onStep-Backward Flow," Journal of Engineering Sciences, Vol. 4, No.2, Riyad University, Saudi Arabia, 1978.

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