Investigation of Streamwise and Transverse Instabilities on Swept Cylinders and Implications for Turbine Blading

The starting point for this investigation was the observation of robust streamwise streaks in flow visualization on the suction surfaces of blades in a turbine cascade at subsonic and transonic speeds. The spanwise wavelength of an array of streamwise vortices had been predicted and is here confirmed experimentally. Observations of streaks on unswept turbine blades and on circular cylinders confirmed these earlier predictions, providing a firm basis for referencing the new measurements of vortical behavior. The observations made it clear that the boundary layers are highly three dimensional. In this paper observations of streamwise and transverse instabilities on swept circular cylinders, over a range of inclinations, are presented. The circular cylinder is a canonical case and observations relate the streamwise vorticity of the unswept case to the more aggressive crossflow instability at high sweep angles. Introducing sweep brings consideration of a wide range of instabilities. Prominent is crossflow instability resulting from the inflectional behavior of a three-dimensional boundary layer. [DOI: 10.1115/1.4007833]


Introduction
Turbine blades with subsonic inlet velocities usually have a leading edge that is quite blunt, and frequently circular.The result is that the flows in the leading edge region, and often well beyond, can be modeled quite well by the flow past the affine cylindrical body.The circular cylinder in crossflow is an important canonical case and it is difficult to imagine a solution for more complex geometries without the guidance of an understanding of the flow over a circular cylinder.
Fine scale organized and predictable streamwise vorticity has been shown to exist on both the pressure surface and the suction surface of turbine blades.For a turbine blade with a blunt leading edge, the stationary streamwise vorticity may persist on a timeaverage basis to influence the entire suction surface at the modest Reynolds numbers typical of aircraft cruise conditions.The lateral distance between streaks is likely to be an indicator of the extent of vortical activity from the surface and hence the strength of the associated vorticity.
Previous investigations have revealed streamwise vortices and "streaky structures" on flat plates [1] and on the suction surface of compressor blades [2,3].In surface flow visualization work at the National Research Council of Canada (NRC) Mahallati [4] observed strong and persistent streamwise vortices on the suction surface of a turbine blade in a planar cascade (Fig. 1).Halstead [5] observed fine-scale streaks on the suction surface of a turbine blade also in cascade (Fig. 2).These streaks continued to the trailing edge region and were insensitive to the state of the boundary layer.
In this paper, the designations of streaks, stationary structures and streamwise vortices are used interchangeably.The vorticity is considered implicit, while still requiring detailed experimental, computational and analytical characterization.Kestin and Wood [6] demonstrated the existence of streamwise vortices on an unswept cylinder.Poll [7] went on to examine the behavior of crossflow vortices on a highly swept cylinder.There has existed a gap between the investigations of Kestin and Wood [8], at zero sweep, and those of Poll [7], with 55 deg to 71 deg of sweep.The aim of the present investigation is to bridge that gap and to elucidate some implications for work on turbine blading.
The phenomenon of Go ¨rtler vorticity, well known to turbine blade designers, is thought to occur predominantly on the concave pressure surfaces of turbine blades.This organized vortex system makes the flow and heat transfer difficult to predict.It is often assumed that streamwise vorticity of this kind is confined to concave pressure surfaces.Examples of streamwise vorticity appearing on the convex surfaces of blades [9] and circular cylinders [10] have been observed both experimentally and computationally.The authors have observed streamwise vorticity on suction surfaces, both experimentally [4] and computationally [9].In this paper, examples of streamwise and crossflow vorticity on Fig. 1 Suction surface flow visualization of turbine blade at a discharge Mach number of 1.16 [4] convex surfaces will be considered.This behavior had been predicted and observed in low speed flows, with attendant theories for wavelength.For a predominantly convex surface, the behavior is consistent with the later predictions of Go ¨rtler [11] who postulated the existence of instability on a convex surface from the concave streamlines ahead of the leading edge stagnation region.The spanwise wavelength of the array of fine scale streamwise vortices was predicted theoretically and experimentally by Kestin and Wood [8], as confirmed experimentally in this paper.
For a turbine blade with a blunt leading edge, at Reynolds numbers typical of aircraft cruise conditions, the streamwise vorticity may persist, on a time-average basis, to influence the entire suction surface.The physics of this streamwise vorticity imposes severe requirements on the temporal and spatial resolution of both experimental and computational methods.Temporal resolution is required to capture the flow complexity, often involving traveling instabilities, that is fundamental for an understanding of the physical behavior of the laminar boundary layer and its separation and transition.Stationary vortex structures can be stronger but may only appear in an organized fashion after extensive timeaveraging.This combination of instantaneous and long duration mapping presents a strong challenge for both instrumentation and computational resources.
For any given flow regime various candidate instability modes exist.In unswept turbine blades and circular cylinders, streamwise vorticity may be associated with a high local disturbance level upstream of the leading edge.It is then stretched out into a lengthy vortical structure as it passes along the convex surface [9].It may well consist of weakly organized and meandering structures.After lengthy time averaging, these may settle into a clear stationary pattern.The experiments of Halstead [5] show that these stationary structures can persist through the turbulent boundary layer to the trailing edge.These fine-scale streaky structures are capable of persisting through laminar separation bubbles, the associated transition, and well into the turbulent layer.Some advanced computations are now showing the same thing.
Laminar separation is of interest for turbine blades and circular cylinders.Under the influence of an adverse pressure gradient, long wavelength disturbances are selectively amplified leading to a roll-up of streamwise vortices and their movement away from the surface.Filtering by shear sheltering [12] may cause the local coarsening of the spanwise wavelength on approach to laminar separation.This appears to be a local effect of the laminar separation bubble.The larger wavelength vortices lift off to give separation.Laminar separation is known [13] to be highly three dimensional.The fine scale turbulence towards the free stream plays a role in re-attaching the flow, but the sheltered long wavelengths persist, restoring the strength of the vorticity and hence the wavelength to its original level.
The introduction of sweep brings consideration of a wider range of instabilities.Crossflow instability is prominent, resulting from the inflectional behavior of the three-dimensional boundary layer.The Kestin and Wood theory may be regarded as the limiting case for zero sweep and it is interesting to work from that to consider stability of the flow over a wide range of sweep angles.Previous investigations of these vortical structures were conducted on an unswept (zero sweep) circular cylinder, by Kestin and Wood [8] and, on a swept circular cylinder, by Poll [7].The lowest sweep angle considered by Poll was 55 deg.There have been no previous published attempts to link the experimental data sets of Kestin and Wood [8] and of Poll [7].There are quite substantial differences between the streamwise vortices observed by Kestin and Wood [8] and the crossflow vortices observed by Poll [7].It has never been clear how, and where, the streamwise vorticity changes to crossflow vorticity.Nevertheless, the gap of 55 deg between the two sets of results has continued to exist and it was considered worthwhile and interesting to perform experiments over this unexplored region of parameter space.

Experimental Techniques
This paper has drawn on a wide range of results by different authors, using different facilities and covering a wide range of Reynolds number and Mach number.In particular, the work of Kestin and Wood [6] and Poll [7] has provided a framework.Experimental work by Ackerman [14] on a 37.26 mm diameter cylinder in the NRC 1.5 m trisonic tunnel is also incorporated.Nevertheless, the emphasis is on the new results provided from the testing of a 152 mm diameter circular cylinder with and without sweep.Tests on the near-surface flow over this circular cylinder were conducted in the Charles Wilson wind tunnel at the University of Leicester.
The Test Facility.This is a closed-loop, closed-section subsonic tunnel with an aerodynamic working section 0.85 m high, 1.145 m wide, and 4 m long.A downstream fan feeds the return leg of the wind tunnel circuit.The return flow is conditioned through three mesh screens and a honeycomb layer in the diffuser section and by a further screen upstream of the 4:1 area ratio converging test section inlet.This conditioning gives a free-stream turbulence level intensity of approximately 0.2% at 10 m/s.The wind speed in the test section is measured by a combined-head Pitot-static probe located along the test section centerline one cylinder diameter, D, above the wind tunnel floor and 3D upstream of the model anchoring point.The dynamic pressure is measured using a digital differential pressure manometer with a precision of 60.01 Pa.The free-stream turbulence intensity is measured by a single hot-wire probe mounted on the test section centerline 2.2D above the wind tunnel floor and 8D upstream of the cylinder.The hot-wire probe is connected to a constanttemperature TSI hot-wire anemometer.The hot-wire anemometer's time-averaged voltage gives a check on the free-stream velocity.
The Model.A 0.152-m diameter, 2.5-m long, hollow aluminum cylinder was tested in the forward region of the test section and is shown in Fig. 3.The model produces a blockage ratio of 5.6 and an aspect ratio of 7.5, based on the wind tunnel test section cross-section and on its length.The blockage will tend to present a stronger pressure gradient than would be expected in a larger tunnel.This could affect any loss measurements but is unlikely to have influenced the instability modes.The cylinder is mounted with its axis parallel to the wind tunnel floor at a constant vertical distance of 2.75D above the floor.The cylinder is pin-mounted on the tunnel far-side wall and simply supported through the near-side wall.This mounting arrangement allows the cylinder to be manually adjusted in fixed increments of sweep over the range 0 deg to 61 deg.At sweepback angles less than Surface Flow Visualization.The windward surface was prepared for flow visualization by hand polishing the surface to a uniform reflective finish over the arc of 6110 deg about the upstream stagnation line.The leeward side, left unpolished, is characterized by separated flow.The cylinder surface roughness is assumed not to substantially alter the wake flow.At the test section mid-span, a 0.4 m wide 0.226 mm thick sheet of UV stabilized clear PVC was tightly wrapped around the cylinder surface.The sheet was held in place by adhesive tape attached to the leeward side of the cylinder surface.The sheet creates a removable surface over which a flow visualization compound can be applied.Changing the sheet between tests builds a library of semipermanent flow records that can be analyzed and subsequently compared.The flow visualization compound is an oil mixture using titanium dioxide as the flow tracer.It consists of a suspension of 1 gm of desiccated titanium dioxide powder in a solution of 10 ml of paraffin oil, 0.84 ml of linseed oil, and three drops of polyoxyethylene 10 oleoyl ether.Before each application, the cylinder span was wetted by linseed oil using a soft cloth, to form a thin oil film that improves the dispersion of the compound.The latter was applied on the portion of the cylinder covered by the PVC sheet using a soft brush, stroking along the cylinder axis.The linseed oil on the wet cylinder facilitates the smearing of the brush strokes that become undetectable in the flow visualization results.After applying the compound, the cylinder is tested by running the tunnel at a constant Reynolds number for approximately forty minutes.The surface flow visualization pattern on the removable plastic sheet is analyzed by removing the sheet from the cylinder, placing it on an overhead projector, and projecting the pattern together with a reference grid onto a large white screen.The magnification from the optical projection facilitates the measurement of the oil flow visualization traces on the screen.

Streamwise Vorticity-The Benchmark
Blades in Cascade Without Sweep.The results of surface flow visualization [4] on the suction surface of a turbine blade tested in the NRC transonic planar cascade tunnel are presented in Fig. 1.For these high-speed flows, the blade was covered with a sheet of self-adhesive white vinyl; a mixture of linseed oil and powdered lampblack was applied in a very thin layer.After running for 5 min, the blade was removed and photographed.The large numbers on the scale represent percentage axial chord.Suction surface flow visualization was performed at three speeds, displaying coherent streamwise vorticity extending to the trailing edge.Figure 1 represents a discharge Mach number of 1.16, following strong acceleration through the blade passage from an inlet Mach number of 0.118.In this case, the shock impingement and separation regions were in the vicinity of 70% axial chord.Coherent fine-scale streamwise streaks cover the entire surface.An average spanwise wavelength, k, of 0.55 mm was measured from Fig. 1 and this value was used in the subsequent comparison.Once established, the streaks appear to retain that spanwise wavelength as far as the trailing edge.
Surface flow visualization photographs have been analyzed from a number of published experiments on blading.When examined in the same way as the surface flow visualization from the NRC cascade [4], three further results from turbine blading (Benner et al. [15], Hodson and Dominy [16], and Halstead [5]) were accessible.
Flow visualization was performed independently by the different authors using different facilities.The techniques and materials used were different in each case.There exist cases in which two completely different visualization techniques have been used for the same model, giving an identical final result.This would seem to eliminate any suggestion that factors such as surface tension variations or gravity effects might influence the observations.The results of Halstead [5] (Fig. 2) were particularly useful as they covered a wide range of Reynolds numbers and free-stream turbulence levels.Results with boundary layer trips were also given.Turbulence levels above 4% and trips were not encompassed by the predictions [8]; visualizations of such cases were therefore not examined.Another very helpful feature of the Halstead experiments is that surface film gauge signals were made available alongside the surface flow visualization.Features such as flow separation and relaminarization were clearly indicated by the surface film traces.The streamwise streaks observed on the NRC cascade and on the cascade tested by Halstead [5] were by no means confined to attached laminar layers.Streaks from a turbine blade in the cascade tested by Hodson and Dominy [16] appear to be limited to the laminar boundary layer.This also appears to be the case in the visualization of Benner [15].All four examples exhibit similar overall features of laminar separation and strong secondary vorticity.
The Kestin and Wood [8] graph was derived for a circular cylinder and it is difficult to locate turbine blade cases on it.The leading edge of many turbine blades is virtually circular; subsequently, much of the suction surface retains a strong convex curvature over the forward portion and is quite flat further downstream.The rapid changes in curvature of the convex surface raise the question of what effective diameter should be applied if comparing with the Kestin and Wood [8] model.Studies of the wall flow visualization and passage geometry for the NRC blade resulted in the conclusion that the blade surface curvature at around the 10% true chord location was quite representative of the curvature of streamlines approaching the suction surface.The measured spanwise wavelength for this blade was 0.55 mm.This value is reported in Fig. 4, normalized by the osculating circle diameter.According to the theory, this is compatible with the surface curvature on the suction surface at around the 10% true chord location.Although this is somewhat arbitrary, it was found that if this was taken as a reference for turbine blades, then good and consistent agreement with the theory was obtained for all blades examined.With this significant assumption, the diameter of the osculating circle, at the 10% true chord location on the suction surface, was adopted as the value of D. This enables comparison with the Kestin and Wood theory [8] and the theory becomes the basis of a correlation for turbine blades.
Measurements of the spanwise wavelength of the array of vortices are compared with the predictions of Kestin and Wood [8] in Fig. 4. The four turbine blade cases all gave reasonable agreement with the theory and experiments of Kestin and Wood [8].Freestream turbulence levels for these cases were all in the range 0.2% Tu 4.0%.
Circular Cylinders Without Sweep.The cross-flow over a circular cylinder is a canonical problem.The existence of regular streaks on circular cylinders was originally investigated by Kestin and Wood [8] who, in 1970, published a stability analysis.They predicted a theoretical value of spanwise wavelength between vortex pairs, k 0 , for a cylinder of diameter, D, given by k 0 ¼ 1:79pD Re À0:5 (1) This result (Eq.( 1)) is represented by the Tu ¼ 0% line in Fig. 4. Kestin and Wood [8] also undertook experimental work on circular cylinders which provided the results for nonzero turbulence levels.
The suitability of the Kestin and Wood [8] theory was confirmed as a basis for examining more complex surface geometries, and variables such as sweep.Further experimental work on circular cylinders was undertaken in 2002 at NRC; Ackerman [14] performed surface flow visualization on a 37.26 mm diameter cylinder at a free stream Mach number of 0.5.Streamwise streaks were observed before and after a separation bubble.Application of the visualization medium upstream of separation had been nonuniform.Because the liquid medium collected in a pool in the bubble a more uniform dispersion of the medium was observed downstream of the bubble.In this region spanwise periodicity showed up clearly (Fig. 5), forming a viable basis for measuring the spanwise wavelength.This experiment, performed at the relatively high Reynolds number of 675,000, provided a point for comparison with the Kestin and Wood [8] prediction (Fig. 6).
More recently, testing was undertaken on a 152 mm diameter aluminum cylinder in the University of Leicester low speed tunnel at three Reynolds numbers.Surface flow visualization has provided a further three points on the Kestin and Wood [8] plot in Fig. 6.All four results are in reasonable agreement with the Kestin and Wood theory [8] and therefore provide further confirmation of this theory as a reference for the case of the normal flow over an unswept circular cylinder.

Effects of Sweep
Cross-Flow Instability.Sweep is encountered or employed widely in the natural and physical worlds.It can be used very deliberately on the wings of high speed aircraft and on the turbines and compressors of gas turbines.One familiar usage is the alleviation of adverse effects of shock waves.In low pressure turbines, the blades might be stacked in a purely radial direction but the through-flow streamlines themselves may have a strong radial component.The expansion of the working fluid dictates the required flow path area increase.This situation is locally presented as blade sweep or hade.Hade occurs in both gas and steam turbines and is the angle made by the casing with respect to the axis of rotation.Lewis and Hill [17] define the sweep angle, K, as the angle between the normal to the inflow and the blade axis.A circular cylinder is a canonical body that is being studied to gain an understanding of sweep effects.The effect of sweep on circular cylinders has not been fully investigated and there is work to be done experimentally and computationally before a thorough understanding may be claimed.Turbine blades inherently have a more complex geometry than cylindrical bodies but would benefit strongly from a more complete understanding of flows about a swept cylinder.
In the development of transonic and supersonic wings, usually having high Reynolds numbers, the early encounters with sweep invoked its role in causing early transition from the leading edge region.Much effort has gone into studying this aspect of sweep effects.In turbomachinery, the Reynolds numbers tend to be lower and the situation is less obvious.The frequent occurrence of laminar separation bubbles quite late on the blade (Figs. 1 and 2) shows that leading edge transition is not necessarily a factor.Until further clarification is achieved, it is prudent to assume that a number of stationary and traveling modes may be competing.
The results of Kestin and Wood [8] are a good starting point for a discussion of these effects.Although the work is related to unswept circular cylinders, it does provide an excellent benchmark for sweep effects on cylinders and blades.This was confirmed by the new experimental results of Fig. 6.These demonstrate that the formula of Eq. ( 1), for the lateral spacing of streamwise vortex pairs as a function of Reynolds number, gives a solid foundation from which other stability investigations may be viewed.The principal published collection of experimental results for high sweep angles is that of Poll [7] on a cylindrical model previously tested by Cumpsty [18] to study attachment line flows.Poll's [7] experiments covered the range 55 deg < K < 71 deg.No systematic surface flow visualization data have previously been published that cover a wider range of sweep angles.Data in the useful range of sweep up to 50 deg are virtually nonexistent, although the experiments of Takagi et al. [19], Dagenhart [20], and Kohama [21] are of interest.The former gives an experimental point and a theoretical point at 50 deg sweep.The latter publication gives an intriguing photograph showing two instability modes simultaneously.A possible interpretation is that one mode is the remnant of the type of streamwise vorticity observed by Kestin and Wood [8] at zero sweep, the other coarser mode being a vigorous cross-flow instability.The unknown flow regime for designers might be an understanding of when the crossflow instability mode is expected.Another paper by Kohama [22] points the way here.His liquid crystal work suggests that the cross-flow instability is first observed at around 40 deg sweep and becomes most strongly amplified at around 57 deg.
Kestin and Wood [8] had expressed reservations about the use of the swept Hiemenz flow model [23] for attachment line flows.The practice of superposing streamwise and cross-flow boundary layer profiles in turbomachinery is well established [24].Poll [7] was the first to distinguish between crossflow mechanisms and the instability mechanisms of the leading edge boundary layer.Hall et al. [25] added a spanwise component to a plane Hiemenz flow.Their swept Hiemenz flow shows that the sweep flow renders the flow potentially unstable.Obrist [26] has given a useful summary of more recent theoretical developments.
Analytical Approaches to Modeling.In an attempt to generalize Kestin and Wood's [8] prediction of vortex spacing (Eq.( 1)) to nonzero sweep angle, K, two alternative approaches have been taken.The first approach considers that, in the swept case, the projection of the cylinder surface on the streamwise plane is an ellipse, leading to a modification of the effective local diameter, D. The second approach considers the growth in boundary-layer thickness through the introduction of a flow component parallel to the leading edge of the cylinder.
Under the first approach, an expression for the local effective diameter D can be derived in terms of the sweep angle and used to modify Kestin and Wood's [8] original estimate.This is done by considering the local curvature at points on the notional ellipse formed by approaching the circular cylinder at an oblique angle.The resulting expression is given below, in terms of the sweep angle, the streamwise distance from the center of the notional ellipse, x, and the ellipse major axis, 2a: This modifies Kestin and Wood's [8] original estimate, k 0 , to a function of sweep that is parameterized by the location x/a at which the effective radius is taken: Treating x/a as a fitting parameter, the best fit to the experimental data is obtained for x/a ¼ 0, for which k/k 0 ¼ 1/cos K.This is indicated by the "Theory" curve in Fig. 7. x/a ¼ 0 corresponds to the 50% chord location on the cylinder, which is the position of maximum thickness of the ellipse.However, the applicability of Kestin and Wood's [8] underlying stability analysis at locations away from the leading edge is questionable, and careful consideration of the steady inner flow at each location is required to confirm this result.
The k/k 0 ¼ 1/cos K relationship can also be derived from the second approach which follows the formulation outlined by Obrist [26] and is performed at the leading edge.The method is based on an asymptotic match between an outer potential flow region and an inner flow region at the leading edge.The outer region of the flow is characterized by a modified form of Kestin and Wood's [8] Reynolds number and by the potential flow around the cylinder.The inner region is the stagnation point flow at the leading edge of the cylinder, which is given by a swept Hiemenz flow.The thickening of the boundary layer with increased sweep can be determined and then used to modify Kestin and Wood's [8] estimate appropriately; this results in the k/k 0 ¼ 1/cos K relationship.Implicit in this approach is the assumption that the swept Hiemenz flow leads to the same wall shear rate as the unswept flow.Consideration of the swept flows studied by Obrist [26], for example, and the unswept flow of Kestin and Wood [8] implies this to be true.Schlichting's [27] numerical estimate of the wall shear is therefore expected to apply for all sweep angles and this simple modification to Kestin and Wood's [8] result can be made.
In spite of the restrictive assumptions underpinning either approach, the same relationship of k/k 0 ¼ 1/cos K is reached.This is also in agreement with the traditional Cosine Rule used to predict sweep effects on airfoils.Bursnall and Loftin [28] showed this approach to be only valid for subcritical flows and that the critical Reynolds number decreases with increasing sweep.It will be seen that k/k 0 ¼ 1/cos K is a reasonable first order descriptor of the measurements for subcritical flows over the sweep angle range 0 deg to 60.1 deg.It is now possible to use the generalization to plot the lateral vortex spacing, normalized by the unswept case.
Transverse Spacing.Testing was carried out in the University of Leicester wind tunnel over a range of Reynolds numbers from 132,000 to 175,000 and over the range of sweep angles from 0 deg to 60.1 deg.As described previously, the emphasis was on surface flow visualization.The Reynolds numbers available were relatively low.Poll [7] found that at a Reynolds number below 339,000, streaks were only visible quite late on the surface.In the current measurements, streaks were faint, but visible and consistent, much further forward.It was found that, if care was taken with the surface coating and the optical techniques, streaks were visible in all cases.Each count of streak spacings was performed at least three times and suitable average spacings were recorded.In all cases, it was possible to make consistent and repeatable measurements of streak spacings and angles.
Care was taken to check that the new wind tunnel results and the published results of Poll were quoted and normalized in the same way.Here they are both normalized using Eq. ( 1) as a reference.Equation ( 1) is used because Kestin and Wood's [8] theoretical result is widely accessible and represents very closely a regression line fit through our own experimental results for unswept cylinders.
In the previous section, two different approaches to generalizing Kestin and Wood's [8] prediction of vortex spacing (Eq.( 1)) to nonzero sweep angle were outlined.Both resulted in the same simple modification: Equation ( 4) is now used to plot the lateral vortex spacing, normalized by the unswept case.The results for the range of sweep angles have been referenced to the Kestin and Wood [8] results and are presented in Fig. 7.They appear to be self-consistent and compatible with the results obtained at higher Reynolds numbers by Poll [7] and the single result of Takagi et al. [19].The latter result was obtained from hot wire measurements above the surface.It measured a stationary mode, compatible with the new data and those of Poll [7], but since the relationship with the surface flow visualization streaks has not yet been rigorously demonstrated, it was omitted from the plot.The k/k 0 ¼ 1/cos K theoretical curve is also plotted and demonstrates reasonable agreement with both the Poll data and the new data.This agreement is tested further in Fig. 8 by normalizing by the theoretical result and plotting (k/k 0 ) cos K. Figure 8 would seem to reflect a significant additional Reynolds number effect beyond the first order correction.The new data are compatible with the data of Poll and Takagi et al [19].Poll's [7] data suggest a similar but even stronger additional Reynolds number effect at intermediate sweep angles.Although the maximum variation from unity of these results is no more than 20% the bulge in the region of 30 deg of sweep, and the sharp rise in Poll's [7] results as his sweep angle is reduced to 55 deg, suggest the potential for mode changes at intermediate sweep angles.Since the zero sweep results pertain to contrarotating vortex pairs and the Poll [7] results reflect the vigorous corotating vortex regime prevalent at high sweep angles such a change is anticipated.
Full data sets were obtained at 55 deg sweep, by Poll [7] and from the current tests.These are of particular value in determining consistency and the lateral sweep spacings are plotted as a function of Reynolds number in Fig. 9. Despite the large gap in the intermediate Reynolds number range, the results obtained from both investigations fall nicely onto a common relaxation line.This would seem to confirm that the present results are quite compatible with those of Poll [7].
Figure 10 is a visualization record of both upper and lower quadrants, from the leading edge to laminar separation.It gives an idea of the streak spacings and angles and also acts as a check on the symmetry of the two surfaces.It demonstrates that the two surfaces behave in a similar manner and are not noticeably influenced by gravitational effects.
Streak Angles.In addition to lateral spacing between streaks, Poll [7] presented some results on angular orientation of streaks, e o .For swept cylinders, the streaks are not linear from the leading edge, but follow a somewhat S-shaped trajectory.However, in most cases, it is reasonable to take them as linear as the apogee of the cylinder is approached.Poll made his measurements in that region, which approaches the laminar separation and boundary layer transition regions.For consistency, measurements from the new results are measured in the same way and are given in Fig. 11.Again, it can be said that there is generally good agreement between the present results and those of Poll [7].

Implications for Turbine Blading
In turbines, sweep is encountered as a result of hade, as the flowpath expands, and more locally in the blade end regions.An Transactions of the ASME excellent basis for the design of swept blading was set out by Smith and Yeh [29].The work of Lewis and Hill [17] has further helped in clarifying swept flow regimes.Subsequently, significant progress has been made in applying computational methods to produce the contemporary approach to the modeling of sweep that can lead to spectacular blade shapes and substantial performance improvement.This is not without a risk to performance, especially upon encountering adverse flow conditions in the end wall regions.This is where the best possible understanding of sweep effects is essential.
Although heat transfer has been considered to be beyond the scope of this work, experimental evidence [10] indicates that, for blunt leading edges, streamwise vorticity is accompanied by a significant local increase in heat transfer rate.The rotor blades of cooled High Pressure Turbines usually have little or no sweep, but they will be susceptible to pure streamwise vorticity.Upstream of this, the nozzle guide vanes tend to have a significant degree of localized sweep for which the main results of this paper could be relevant.The current work is more likely to be applicable to the Low Pressure Turbine, having a low Reynolds number at altitude cruise and inherently a high degree of sweep as the hot gases expand.It is also important to consider that the degree of sweep resulting from hade will vary along the height of the blade.
The increase in heat transfer rate applies especially to the laminar boundary layer region; however, there could also be commensurate increases where streamwise vorticity exists in a turbulent boundary layer.This is understood for concave pressure surfaces, but there is no general awareness of these fine scale streaks or vortical structures on convex suction surfaces.In any event, although further quantification is required, an implication of the current investigation is that heat transfer calculations that fail to account for streamwise vorticity are likely to under-predict heat transfer.
Other implications concern the fluid mechanics of convex suction surfaces.Turbine blades, especially low pressure turbines, have become more highly loaded.Low pressure turbines are vulnerable because of their relatively modest Reynolds numbers.They also often operate with substantial sweep and this is likely to increase as turbines operate in increasingly diverging flowpaths.
The available evidence suggests that instability modes change as the sweep angle increases, as with a swept wing.However, the investigation has not resulted in any particular degree of sweep beyond which crossflow instabilities result in a more aggressive environment.The changes appear to be more gradual than that, although Fig. 8 indicates an increase in lateral spacing of 16.2% for sweep increase from 0 to 11.6 deg.The measured results from flow visualization on cylinders suggest that conditions change markedly between 30 deg and 40 deg sweep where there is a significant departure from the Cosine Rule.This might be expected to be exacerbated at Reynolds numbers around and above critical.
The scope of this paper has been to demonstrate the existence of these vortical structures in flows over circular cylinders and turbine blades.Although indications of the strength and persistence are present in the measurements, it will take further detailed work to quantify the effects of the structures on boundary layer transition and laminar separation.The survival of the vortical structures in the unsteady environment created by wakes impinging from upstream is still unknown and is yet a further area for investigation.For low pressure turbine blades, the periodic effects of wakes from upstream on the calmed region [30] can be strong, but the effects of streamwise and crossflow vorticity on these remain to be studied.
In turbine applications, the lateral gap between structures is quite fine.It is asking too much of available computational methods to predict these structures routinely for design purposes and it is very difficult to measure them experimentally.This presents a challenge of resolution both computationally and experimentally which will need further diligent work.It should then be possible to attempt a quantification of the effects on heat transfer and blade losses.In a similar fashion to the effects of Go ¨rtler vorticity on pressure surfaces the effects are there and probably strong but not easy to quantify.
A correlation has been established for turbine blades that should assist prediction of the lateral extent of streaks and hence the strength of vortical structures on convex suction surfaces.The correlation might be of use running alongside existing design tools as a check on what might expected, especially when the use of high degrees of sweep is contemplated.
A key question that may be of immediate design impact is whether there is a critical sweep angle, beyond which the flow is adversely affected.It appears from the results that the critical sweep angle from this perspective is between 30 and 40 deg.The designer is advised to exercise caution as the sweep angle enters that range.It seems that the contrarotating streamwise vortices over the surface at zero sweep are relatively benign compared with the corotating crossflow vortical structures at higher sweep angles; however, it also seems likely that streamwise vortices may survive longer into turbulent boundary layer regions.
The thrust of this work is an appreciation that the flow over the convex suction surfaces of turbine blades cannot be assumed to be two dimensional.The three-dimensional effects, manifest here in streamwise and crossflow vortical structures, can be strong and potentially modify appreciation of any practical outcomes.Further research is therefore needed, firstly to quantify the strength and characteristics of the vortical structures, and then to quantify their impact on the losses, heat transfer and boundary layer characteristics of turbine blading.No evidence has been seen that transition is affected for zero sweep although some results would suggest that the strong vortical structures at higher sweep angles may well promote early transition.
The question raised, however, is more fundamental than that.It is not meaningful to ask how the vortical structures are affected, compared with a laminar boundary layer, but rather whether a two-dimensional laminar boundary layer can exist in flows over a blunt or cylindrical leading edge.The evidence suggests that in these circumstances a truly two-dimensional boundary layer does not exist.This question will become more compelling as further results from highly resolved computational studies of leading edge flows become available.

Conclusions
Experimental work has confirmed the suitability of the zerosweep Kestin and Wood theory [8] as a basis for predicting streamwise streaks and vortical structures on unswept circular cylinders and turbine blades.High-speed testing was undertaken on a normal 38 mm diameter cylinder and low-speed testing on a normal 152 mm diameter cylinder.The results confirm the theory for circular cylinders for which the Kestin and Wood theory [8] may be used directly.For the related shape of the many turbine blades that have a rounded leading edge, basing the prediction on the curvature of the blade at 10% chord provides a correlation that has been supported by test results from a number of investigators.
Although the Kestin and Wood work [8] is related to unswept circular cylinders, it can also provide an excellent benchmark for sweep effects on turbine blading.Experimental work, confirming the zero-sweep results, gives a reference for subsequent work over a wide range of sweep angles.Published data on streamwise and crossflow vortices in the useful sweep range of up to 55 deg have been virtually nonexistent.Testing on a circular cylinder has been undertaken by the authors over a range of sweep angles from zero to 61 deg giving results for lateral spacing and angular orientation of the vortical streaks.The new results cover the range between zero-sweep and the high sweep angles and at high-sweep angles the results are consistent with those of Poll [7].First order theories for circular cylinders predict the effects of sweep surprisingly well.It is the small discrepancies between theory and flow visualization that are likely to point to the occurrence of changes in the instability mode.
An outcome of these investigations is to establish that organized and systemic fine-scale streamwise vorticity may occur more frequently on convex surfaces, such as turbine blade suction surfaces, than hitherto appreciated.Both experimental work and computational predictions should be extended to encompass that possibility.
The observed streaks could be of particular concern for the thermal design of turbine blades.It is hoped to give designers confidence about the flow regimes they might anticipate for a given sweep angle and particularly of when and how the vigorous crossflow instability mode is likely to be encountered.This becomes particularly important as higher degrees of blade sweep are required.
It is clear that the conventional view of two-dimensional laminar boundary layers following blunt leading edges is not realistic.Such boundary layers need to be treated three-dimensionally, particularly when sweep is present.This requires a sufficiently fine spanwise spacing that streamwise vortical structures are resolved.Application of computational methods to these problems is likely to be expensive.It is hoped that until such computations become feasible for turbine design purposes the work reported here might be useful in correlation form.

Fig. 3
Fig. 3 Circular cylinder mounted in wind tunnel

Fig. 5 5 Fig. 6 Fig. 4
Fig. 5 Surface flow visualization downstream of separation bubble on circular cylinder in NRC tunnel at a Mach number of 0.5

Fig. 11
Fig.11Angle between streaks and normal to cylinder axis, for present results and those of Poll[7]