Microvortex generators in high-speed flow

Progress in Aerospace Sciences 53 (2012) 30–45

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Progress in Aerospace Sciences journal homepage: www.elsevier.com/locate/paerosci

Microvortex generators in high-speed flow Frank K. Lu a,n, Qin Li b, Chaoqun Liu b a b

Aerodynamics Research Center, Mechanical and Aerospace Engineering Department, University of Texas at Arlington, Arlington, TX 76019, USA Center for Numerical Simulation and Modeling, Mathematics Department, University of Texas at Arlington, Arlington, TX 76019, USA

a r t i c l e i n f o

a b s t r a c t

Available online 19 April 2012

A review of the state-of-the-knowledge of microvortex generators (MVGs) and their effect on separated shock/boundary-layer interactions is provided. The flowfield around and behind an MVG is discussed, paying attention on the major and minor vortical features. A detailed discussion is provided of the MVG wake where symmetry breaking and Kelvin–Helmholtz instability give rise to unsteadiness characterized by large, vortex ring structures. While MVGs are thought to be effective in reducing the separation zone, details of how they affect the separation zone remain to be understood properly. Ideas on how the MVG affects separated shock/boundary-layer interactions are reviewed. The review suggests that further optimization studies are needed to put MVGs to practice. In addition, performance metrics are proposed. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Microvortex generator Turbulent boundary layer Supersonic flow Flow control Shock/boundary-layer interaction

Contents 1. 2. 3.

4. 5.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Supersonic flow around an MVG. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Effect of MVGs on SBLI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.1. Transonic Mach numbers (normal shock) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.2. Supersonic Mach numbers (oblique incident shock or ramp-induced shock) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Some related concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

1. Introduction The desire to control the boundary layer so as to reduce or remove separation zones, to reduce drag and to improve flow quality is as old as the boundary layer concept itself. Practical requirements of flow control techniques, for example, robustness, ease of implementation, light weight and simplicity, tend to favor passive devices such as vortex generators, vanes and fences instead of active ones although active devices have their attractions [1–7]. Generally, for conventional aircraft applications, the incoming boundary layer is also turbulent. Controlling turbulence is itself a huge topic that lies outside the scope of this review. A boundary-layer flow control technique that has seen much recent interest is to distribute an array of microvortex generators (MVGs), also known as ‘‘low-profile’’ or ‘‘sub-boundary layer’’

n

Corresponding author. Tel.: þ1 8172722083. E-mail addresses: [email protected] (F.K. Lu), [email protected] (C. Liu).

0376-0421/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.paerosci.2012.03.003

vortex generators, whose height is less than the boundary-layer thickness, ahead of a region with adverse flow conditions. MVGs are also suggested as being able to improve the ‘‘health’’ of the boundary layer. As shown in Fig. 1 [8], there is more than one kind of MVG. (Of these, the backward-facing wedge is not covered in the review.) For flow control, such miniature, passive devices have obvious advantages of low-profile drag, lack of intrusiveness and robustness. These devices, being passive, have no need for actuation systems with their associated complications. While likely not as effective as their conventional counterparts, MVGs are still able to produce significant changes in the boundary layer to improve its capability to cope with adverse pressure gradients. Initial studies of MVGs for flow control were conducted at low speeds [8] with these devices proposed for practical configurations which are beyond the scope of this review. MVGs are thought to operate in the same manner as conventional vortex generators in energizing the boundary layer through entrainment of the freestream by trailing vortices although there are still open questions regarding the details of this process.

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Fig. 1. Types of MVGs, adapted from [8]. (a) Forward- and backward-facing wedge or ramp. (b) Counter- and co-rotating vane. (c) Wishbone and doublet type Wheeler vanes.

Lately, MVGs have been proposed as being able to alleviate or overcome the adverse effects of separated shock/boundary layer interactions (SBLIs) over transonic wings and supersonic inlets. As is well-known, SBLIs can significantly reduce the quality of the flowfield by inducing large-scale separation, causing total pressure loss, flow distortions, localized peak heating and pressures, and unsteadiness, the consequences being to degrade the performance of the wing or engine [1,9]. These high-speed studies generally were conducted with an impinging shock [10–25]. Numerical simulations have been made on MVGs for comparative studies with experiment and to support applications, using RANS, hybrid RANS/LES and monotone integrated large eddy simulations. As a sidenote, there have been few studies of conventional vortex generators in high speeds despite the utility of such devices at low speeds. A study by Mehta [26] placed a vortex generator in the form of a half delta wing ahead of a bump on a cylindrical body at freestream Mach numbers of 0.7–0.86 covering a range of pre- to post-critical conditions. Surface oil-flow visualizations appear similar to those obtained with micro-vanes. A further discussion will be provided later in Section 3.1. At about the same time, a theoretical study by Inger and Siebersma [27] suggested that a vortex generator row reduces the boundarylayer shape factor. This reduction produces favorable effects on the overall and local flow properties of transonic SBLI. However, this study found that the vortex generators promote earlier incipient separation of the interaction. Later, McCormick [10] performed a pioneering study of MVGs and compared its ability to control SBLI against that of a cavity at Mach 1.56–1.65. This study found that MVGs can suppress SBLI and improve the downstream boundary-layer flow. In another study, various conventional vortex generators were placed ahead of a variety of shock generators in a Mach 5 flow

[28,29]. Barter and Dolling [28] found that Wheeler doublet vortex generators placed upstream of a two-dimensional, rampinduced separation produce significant three-dimensionality, reduce the upstream influence and the length of the region of separation shock motion. These generators decrease the maximum rms value of wall pressure unsteadiness and shift the fluctuations to higher frequency with the overall maximum zero crossing frequency being 2.33 kHz, a 171% increase from the undisturbed interaction. These authors attribute the effects to be due to a fuller boundary-layer profile, a weaker separation shock1 and increased turbulence in the boundary layer, the last causing increased separation shock jitter. Subsequently, Barter and Dolling [29] noted that the vortex generators reduce the pressure loads on SBLIs induced by moderately swept compression ramps but not those induced by blunt fins. The authors concluded that SBLIs which are sensitive to the incoming boundary-layer properties are favorably influenced by vortex generators. By extension, these studies point to the possibility of using MVGs for mitigating separation of certain classes of SBLIs. MVGs are claimed to reduce the size of the separation zone although the evidence shows a more confused situation, as will be discussed later. It appears that no satisfactory explanation of how the MVGs affect the separation zone has been offered thus far. There are claims that MVGs work in a similar fashion as conventional vortex generators. It should be noted here that conventional, vane-shaped vortex generators are well established. These function by producing tip vortices which entrain freestream fluid, thereby energizing the boundary layer although even this

1

The present authors consider that this may be a three-dimensional effect.

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conventional wisdom has lately been called into question, with evidence suggesting the convection of transverse, ring vortex structures [30–32]. In high-speed flow, conventional vortex generators have seen application in diffusers and are visible on the wings of many types of transonic aircraft. Conventional vortex generators have apparently not been deployed in high-speed inlets to mitigate the adverse effects of SBLIs and there appears to be only limited studies into such applications. Perhaps a serious consideration with high-speed applications is the possible adverse effects of wave drag from the vortex generators themselves, conventional or micro, that mitigate their advantages [33]. Following Lin’s review on low-speed MVGs [8], numerous studies have been conducted at different institutions, both experimentally and numerically, on MVGs in supersonic flow such as to warrant another review of the state-of-the-knowledge. The emphasis of this review is on the flow physics around the MVG and on the effect of the MVG wake on separated SBLIs. The review is organized as follows: Section 2 reviews the flowfield around MVGs, followed by Section 3 which reviews the effects of MVGs on SBLIs in the transonic and supersonic regime. As far as we are aware, there is thus far only one study of MVGs at a high Mach number of 5 [34]. The review ends with an outlook of what further work needs to be done to understand the physical mechanisms of MVGs and on other potential areas of interest.

2. Supersonic flow around an MVG MVG studies in supersonic flow have focused on wedge and vane types, especially the former, in view of their robustness. This review therefore emphasizes the wedge type. Surface flow visualizations are shown in Fig. 2(a) and (b) of similar MVGs with a 241 leading edge, at Mach 1.4 and 2.5. These figures show that a leading-edge separation bubble forms due to a localized, twodimensional SBLI, the evidence being an accumulation of oil shown as a bright zone in these figures. The LES results of Fig. 2(d) indicate separation more directly by the presence of surface streamlines directed upstream [19,21]. The initial observations of Babinsky et al. [14] led them to propose a model of the flow past an MVG in which the leading edge (corner) separation produces a pair of weak trailing vortices. A strong primary vortex pair is shed from the slant top edges of the MVG. A number of weak, secondary vortex pairs are also identified. The separation actually occurs below the incipient criterion as shown in Fig. 3. This can be understood by considering that the separation is induced by a local Mach number within the boundary layer that is lower than the freestream. In fact, as observed by Settles et al. [35], accepted two-dimensional incipient separation criteria depended on observations such as the incipient presence of a plateau (kink) in the surface pressure distribution or incipient accumulation of oil in surface oil-flow visualization [36]. These authors suggest that a separation bubble is always present, even a miniscule one in unseparated interactions. The present observations lend further support to this suggestion. This leading-edge flow separation, weak as it is, leads to the formation of a weak horseshoe vortex, similar to those of protuberances whose height is approximately that of the boundary-layer thickness [38]. Experimental evidence for the horseshoe vortex has apparently been provided only from interpreting surface flow visualization thus far while numerical evidence came from high-order LES albeit at a lower Reynolds number, also from surface topology; see Fig. 2(d). It may be interesting to note that the surface flow visualization displayed in Fig. 2(a) shows no visible interference between the MVGs in spite of their proximity. The horseshoe vortex system, identified as a secondary vortex

Fig. 2. Experimental surface flow visualization and numerical surface streamlines from various investigators. (a) From Herges et al. [17] (M 1 ¼ 1:4). (b) From Babinsky et al. [14] (M 1 ¼ 2:5). (c) From Lu et al. (M 1 ¼ 2:5). (d) From Li and Liu [19,21] (M 1 ¼ 2:5).

pair skirting off the leading edge of the MVG in Fig. 4, is extremely weak as it arises from the extremely weak leading-edge separation; it does not appear to significantly affect the downstream flow. However, an envelope of separation [39] is associated with the horseshoe vortex which serves to isolate the flow around an MVG from its neighbors, thereby the aforestated observation of no interference between adjacent MVGs. Getting closer to an MVG, despite its geometrical simplicity, the flow topology is extremely complex as revealed by a detailed

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Fig. 3. Existence of separation ahead of MVG below the incipient separation threshold aI . The wedge’s leading-edge angle is indicated with each data point. Figure adapted from [37].

Fig. 5. Side views. (a) Experimental surface oil-flow visualization [40]. (b) Numerical surface streamlines [19,21,25].

Fig. 4. Flow model of multiple trailing vortices shed from an MVG [14].

analysis of data obtained from high-order LES [19,21,25], as well as of surface and off-surface flow visualization [40]. This complexity may not be unexpected as three-dimensional geometries produce rich topologies. The high-order LES results show for the first time eight detailed surface and off-surface topological features around and downstream of the MVG, namely, (i) surface spiral points connected to vortex filaments, (ii) surface separation topology, (iii) five pairs of vortex tubes around MVG, (iv) the source of momentum deficit in the downstream flow, (v) an inflection surface that gives rise to a (vi) Kelvin–Helmholtz instability and (vii) the generation of ring vortices, and (viii) a ring vortex/shock interaction and a proposed new mechanism for separation reduction [19,21,25]. The above features will be described further. The dominant vortex pair shed by the MVG is not the aforementioned horseshoe vortex system but arises from the flow separating off the slant sides. Fig. 2 and the side views of Fig. 5, together with video clips of the experimental visualizations, identify low and high shear regions on the MVG sides, and on the flat plate. These regions are indications of a large primary vortex. The surface streamline patterns reveal that the horseshoe vortex system confines the primary vortex pair to trail downstream and then clash behind the trailing edge as previously mentioned. Moreover, Fig. 5(b) reveals singularities along the MVG leading edge which apparently have not been observed if at all experimentally [19,21]. The high and low shear regions are reflected in the surface pressure distributions. Time-averaged, surface pressure distributions from high-order LES [19,21] show a high-pressure region lying ahead of the MVG, Fig. 6(a). This is a result of the localized shock/boundary layer interaction induced by the MVG leading edge. A slightly higher pressure is also present on either side of

Fig. 6. Surface pressure distribution around an MVG. (a) Surface pressure distribution [19,21]. (b) From Herges et al. [17].

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the MVG. However, extremely low pressures exist on the flat plate nearest to the MVG junction. This low pressure can be interpreted to be the result of the high-speed flow present in this region associated with an open, three-dimensional separation. The timeaveraged result also shows an asymmetry downstream especially of the trailing edge, whether in the LES or in the experimental result, Fig. 2. While the asymmetry may be an artifact from the simulation or the data processing, it may also be evidence of unsteadiness. A pair of swept, high-pressure regions exist downstream of the MVG. A simple construction of the inviscid wave pattern reveals that these high-pressure regions arise from a recompression shock as the flow is turned from the direction of the slant sides to an axial direction. Similar features of a high-pressure region at the MVG leading edge is evident in the experimental results of Herges et al. [17], Fig. 6(b). The low-pressure regions due to the rapid flow past the MVG is also evident and so are the highpressure regions downstream due to the recompression shock. A further analysis of the high and low shear regions identify these to be due to the presence of secondary vortices, namely, one each at the corner of the MVG and flat plate, and one each just off the sides at the top. The presence of these secondary vortices satisfy topological rules [39]. Further, it is thought that when either the opposing primary or secondary vortices impinge each other, symmetry breaking occurs [30,31,41,42] which contributes

to unsteadiness. These vortical interactions give rise to a large number of surface singularities as revealed by high-order LES, Fig. 7. Some of these singularities have subsequently been found experimentally. For example, Fig. 8 shows a pair of spiral points in both the LES and experimental results [43]. The experimental result was obtained through image processing of raw videos of surface flow visualizations. (It can be noted that a synergistic approach in combining computations and experiments can yield great benefit.) Finally, a detailed analysis of the numerical results with experimental support led to a five-pair vortex model for the near-field topology, Fig. 9 [25,43]. It remains unclear if these singularities exist in the mean flow or only in instantaneous snapshots. The fact that they are absent in slow or time-averaged experimental observations may point to the latter. In addition, a new visualization technique revealed a connection between the spiral point SP5 in Fig. 7 and a flow feature that is tentatively identified as a tornado-like vortex filament, Fig. 10. Numerical simulations confirm this feature. For example, Fig. 11 shows streamlines originating from SP5 at the same location as the experimental ‘‘tornado’’. It is worth noting that such small

Fig. 9. Five-pair vortex model of Li and Liu [25].

Fig. 7. Numerical visualization showing singularities around MVG trailing edge; AL, attachment line, SDP, saddle, SL, separation line, SP, spiral [43].

Fig. 10. Panoramic visualization showing vortex filaments [43].

Fig. 8. LES and experimental visualizations showing a pair of spiral points on the flat plate at the MVG trailing edge [43].

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Fig. 11. Streamlines emanating from SP5 [43].

tornado-like features have been seen in flows past the sides of three-dimensional protuberances and junctions [44]. Fig. 10 shows another possible vortex filament emanating from the top rear of the MVG. However, the flow feature seen at the top may be a combination of a secondary vortex shed from the top slant edge of the MVG plus the vortex filament.2 This feature is likely not just an expansion fan, which would be revealed in schlieren imaging but not always clearly seen in seeded flows, that also exists at the top of the MVG trailing edge. Based on these observations, Lu et al. [40] proposed a detailed flowfield topology, Fig. 12. Most of the previously reported topological features remain [14]. But, vortex filaments associated with surface spiral points are included to demonstrate the complex flow topology. Turning next to the near wake of the MVG, complex flow features are also evident in this region. Time-averaged data, either through RANS [18,16] or PIV/LDV [14,17,45] reveal a streamwise momentum deficit around the centerline of the wake and regions of higher momentum further outboard on either side of the MVG as well as nearest to the surface, beneath the low momentum region, Fig. 13. Interestingly, the laser lightsheet visualizations by Bur et al. [46] of counter-rotating micro-vane vortex generators (Fig. 1(b)) show two spots which they identify as trailing vortices, Fig. 14. Whether these are high momentum regions as in the above discussion is not known. It is suggested that this momentum redistribution is due to entrainment of high momentum fluid from the freestream into the boundary layer by the trailing primary vortices. This experimental observation was also confirmed by numerical simulations [16,18,25]. Li and Liu [25] showed heuristically through streamline tracking that the flow in the momentum deficit region originates from the top of the MVG. This observation can be further reinforced by noting that the flow over the MVG top has suffered momentum loss in passing over the leading edge shock; see also [16]. To further understand the MVG wake, Blinde et al. [15] interpreted their detailed stereo PIV maps, producing a conceptual sketch as shown in Fig. 16. The figure shows high-speed regions outboard of each MVG that serve to channel an array of hairpin vortices directly downstream of an MVG. It should be noted that the schematic shown in Fig. 16 is an instantaneous snapshot so that the flowfield is regarded as unsteady. Blinde et al. stated that no trailing vortices are apparent in instantaneous snapshots. Instead, large structures in the form of pairs of counter-rotating vortices are convected in the boundary layer. These authors further remarked that their observations are consistent with observations in the wake of protuberances at low speeds, experimentally and also computationally using DNS

2 Note that these vortex filaments were identified previously as secondary vortices although, strictly speaking, the former terminology is the correct one.

Fig. 12. Postulated mean flowfield topology past an MVG (dashed lines indicate surface flow) [40].

[47–49]. Note that while Blinde et al. identified outboard highspeed (or high momentum) regions, they suggested a different vortex structure for entraining freestream fluid. This sub-boundary-layer vortex shedding mechanism with its unsteadiness has also recently been studied in low-speed flows [32,50–52]. Specifically, Angele and Grewe [32] suggested that the unsteadiness contributes to maximum Reynolds stresses around the mean vortex centers which should not be the case if the vortices were steady. Li and Liu [21] noted that the mean velocity profile downstream of the MVG exhibits an ‘‘inflection surface’’ that is unstable, thereby causing a Kelvin–Helmholtz instability to occur [53]. There has been previous suggestions that such a mechanism is the cause of turbulent vortex rings [54]. A subsequent study where the MVG wake was reconstructed using tomographic PIV is shown in Fig. 17 [45]. These authors identify the presence of a pair of counter-rotating trailing vortices. Additionally, the isosurface of the magnitude of the crossqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi wise vorticity o2y þ o2z reveals the presence of hairpin or ‘‘arch’’ vortices wrapping over the trailing counter-rotating vortex pair. This is a more complicated structure than that depicted in Fig. 16. Regardless of the nomenclature, evidence of such ring vortices surrounding a trailing counter-rotating vortex pair is also provided by high-order LES [21]. Fig. 18 displays the isosurface of a small negative value of l2 , commonly used for numerical visualization of vortices [55]. These ring vortices can be related to the experimentally observed hairpin or arch vortices. There does not appear to be any difference between the ring and the hairpin vortices. Experimentally, the bottom region is not easily accessible to PIV instrumentation and thus is not properly observed, unlike high-order LES data. Moreover, the instantaneous numerical schlieren of Fig. 21 shows large, intermittent density structures. Time-averaging of these structures will give the impression of a thickened boundary layer. The numerical visualizations are supported by experiment [56]. Fig. 22(a) shows a global lightsheet visualization where the freestream flow is seeded with calcium carbonate particles with

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Fig. 13. Streamwise momentum deficit and surplus in the wake of an MVG [14].

Fig. 14. Pairs of dark spots identified as counter-rotating vortex pairs from an array of micro-vane vortex generators [46]. Fig. 16. Postulated hairpin vortex train in the wake of an MVG [15].

Fig. 15. Tracing the momentum deficit in the MVG wake to flow over the top [25].

a median size of 0:7 mm. In this seeding technique, the MVG wake is devoid of scattering particles and thus appears dark. The ragged interface between the wake and the freestream appears similar to the numerical schlieren of Fig. 21. A local lightsheet technique with acetone fog injected from an upstream pressure tap shows large billowing structures, Fig. 22(b), complementing the global

lightsheet visualization. These structures are attributed to the MVG since they are not present in lightsheet visualization of the boundary-layer flow past the flat plate, Fig. 22(c). Panaras (private communication) [57] remarked that the downstream vortex impingement appears similar to that due to crossing shock/boundary-layer interactions, Fig. 19 [58,59]. In such an interaction, opposing vortices impinge to create a complicated interaction between themselves and the crossing shock system. An example is given in Fig. 20 which shows crosscuts of computed stream surfaces in different cross planes of a Mach 3.95 flow at a Reynolds number of 76 million/m past a pair of opposing fins, both with apex angles of 151. Figs. 20(a) and (b) show the approach of the vortices from the two swept SBLIs. In addition, the stream surfaces are seen to wrap around the vortices. The reattachment streamline is also clearly seen. At these stages, there is evidently common features with single swept shock interactions [60]. Fig. 20(c) shows that a dipole structure has formed and Fig. 20(d) shows the liftoff of the structure to take on a mushroom shape. Panaras suggests that the liftoff is to be expected due to the mutual interaction of the two opposite vortices. This is analogous to the uplift of the primary vortices in the MVG wake. The region occupied by the mushroom structure is also a region of reduced total pressure

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Fig. 17. Visualization from tomographic PIV of conditionally averaged vorticity distribution in the wake of a micro-ramp. Vorticity isosurfaces of streamwise component qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ox (green) and spanwise-wall normal component o2y þ o2z (light blue) [45]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 18. Vortex rings shown by l2 isosurface [21]. (a) Figure also shows vortex ring breakdown as the vortex train interacts with the leading shock. (b) Enlargement showing train of vortex rings downstream of MVG.

wake. The major feature is instead a pair of primary vortices that trails from the sides of the MVG with associated secondary vortices and vortex filaments. A momentum deficit region is observed behind the MVG that is circular in shape. A circular velocity inflection is observed which is thought to initiate a Kelvin–Helmholtz instability mechanism. This instability is likely aggravated by symmetry breaking as the two primary vortices impinge on one another. This unsteady, instability mechanism leads to the formation of a train of vortex rings which draw in energetic, freestream fluid and distribute it to the sides. These rings convect over a long distance downstream.

3. Effect of MVGs on SBLI Fig. 19. Crossing SBLI induced by a pair of sharp fins.

[59]. The total pressure deficit in the mushroom structure can be compared against the momentum deficit in the MVG wake as presented in Figs. 13 and 15. In summary, the flowfield around an MVG is extremely complex due to the three-dimensional nature. The horseshoe vortex that wraps around the MVG is not a major topological feature but is crucial in serving to channel the individual MVG

The interest in installing MVGs ahead of potential locations for SBLIs is to reduce the adverse effects of shock-induced, boundarylayer separation. Reducing the size of the separation zone may by itself be a sufficient performance metric but more specific metrics may include improving pressure recovery, reducing unsteadiness and reducing drag. (As a counterpoint, most studies show a gross distortion of the interaction zone, determined from the surface footprint, but without quantifying it. Thus, the size of the footprint remains an unknown performance metric.) At this stage,

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Fig. 20. Evolution of cross-plane streamlines of crossing SBLIs [57].

Fig. 21. Instantaneous numerical schlieren of centerplane showing large flow structures.

Fig. 22. Lightsheet visualizations. (a) Global lightsheet visualization with lightsheet aligned along MVG axis. (b) With MVG. (c) Flat plate, without MVG.

it appears that studies are still primarily unearthing the physics of the phenomena and any discussion of performance gains may be premature. These fundamental studies tend to use simple geometries for inducing the shock.

Two classes of interactions have been studied thus far. The first is of transonic interactions with a normal or near normal shock impinging the boundary layer. The second mostly concerns supersonic incident oblique shock interactions with a turbulent

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Fig. 23. Conceptual sketch of two-dimensional, separated SBLI modified by wake from MVG array [15].

boundary layer except for the numerical study by Li and Liu [21,25] which is of a ramp-induced shock interaction. While not critical in numerical studies, experimental studies of incident shocks have been found to suffer from serious, wind tunnel sidewall interference, even with large wind tunnels [61–64]. Sidewall interference takes at least two forms. First, the shock generator may produce what Skews [64] calls edge effects that propagate from the tip of the shock generator, thereby modifying the shape of the shock from the planar. Secondly, these shock generators produce a glancing SBLI with the wind tunnel’s sidewalls which is prone to open separation [60]. The interference between these sidewall interactions and the interaction of interest can be severe with the two-dimensional interaction being lost into an oval shape. Thus, extreme care must be exercised in evaluating the effect of MVGs in such distorted but nominally two-dimensional interactions. Another observation is that numerical studies are predominantly of interactions with a single MVG while experiments generally involve an array of them. As will be evident, the MVG array yields features that are not seen when only a single MVG is placed ahead of a separated SBLI. All the studies thus far involve configurations that theoretically produce two-dimensional SBLIs, despite well-known experimental difficulties such as the aforementioned sidewall interference. As to be expected, these studies also observed that the SBLIs take on a three-dimensional nature when MVGs are placed ahead of them, Fig. 23. However, many open questions remain unanswered as to how such three-dimensionality is introduced and how the adverse characteristics of separation are mitigated by the upstream MVG array. Many of these questions can be posed from fundamental fluid mechanics considerations:

 Are upwash and downwash from a Biot–Savart-like behavior 



of the counter-rotating vortices sufficient to account for the momentum redistribution? Are mean observations, such as obtained from surface flow visualizations or other time-averaged data, sufficient to describe the three-dimensionality or the unsteadiness or should more sophisticated statistical approaches be applied to elucidate the space–time behavior of such structures? How does baroclinic torque affect the incoming vorticity as it interacts with the separation shock and the separation bubble downstream?

Finally, a practical question is whether disrupting the interaction footprint, however it is defined, by itself is adequate since it is not merely reducing the upstream extent of the interaction but also how the flowfield evolves downstream that needs to be considered. If

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further disturbances are introduced into the flowfield that can create downstream instabilities to cause the possibility of unstart, for example, or cause an increase in flow oscillations downstream, then the local benefit may not be entirely worthwhile. There is general consensus that vortices are involved in disrupting the SBLI. Now, at low speeds, as reviewed by Lin [8], vortices introduce high-momentum freestream fluid into the separated zone downstream. While these vortices were initially thought to be streaming in the axial direction increasing evidence as reviewed above shows that the vortical structures to be complex. As is clearly evident at low speeds, the high-momentum fluid is able to reduce the separated zone, in some cases by a substantial amount. However, in separated SBLIs, these vortices encounter the leading shock of a lambda-foot shock structure, producing a shock/vortex interaction (SVI), a phenomenon that is impossible at low speeds. SVI introduces extra complications. Such interactions have been studied in many contexts and one possible outcome is ‘‘vortex bursting’’ regardless of whether the vortex is parallel or perpendicular to the shock. Vortex bursting is regarded as adverse in some circumstances, for example, when they occur over delta wings or are regarded as beneficial as in supersonic combustion [65–72]. In the following subsections, a number of studies in the transonic and supersonic regime are reviewed to draw some general conclusions regarding the physics of such flow interactions; see Table 1 for a listing. 3.1. Transonic Mach numbers (normal shock) Vane [12,46] and ramp [12,17] MVGs, and contoured bumps [74,75] were studied. The incoming flow for most of these studies was slightly supersonic, being in the range of Mach 1.3–1.5, that allowed a normal or nearly normal shock to stably impinge a turbulent boundary layer which serves as the transonic criterion. A subsonic diffuser follows downstream of the interaction, its location being varied per the different investigations. In this sense, these studies were primarily interested in examining ¨ transonic diffuser-type flows. The exception is the study by Konig et al. [75] where an incoming flow at a high subsonic Mach number of 0.79 passes over an airfoil to produce a local supersonic pocket. Note that the vane configuration of Ref. [12] is similar to the third figure in the right of Fig. 1(b), with the apex pointing downstream. In Ref. [46], the vanes have their apex pointed upstream. Except for the contoured bump, the MVGs were placed ahead of the shock impingement location. In the case of the contoured bump, the shock impinged on the bump. The presence of the MVG array appears to create a ‘‘global distortion’’ of the separated flowfield, as revealed by surface flow visualization [12,46]. Except for a region near the center of the interaction, the surface streamlines turn inward in the outboard regions. The distortions appear to be more serious in [46] perhaps because of its unusual MVG configuration. These global distortions are likely due to so-called corner effects as discussed above [61–64] and which has recently been revisited [76]. Unfortunately, these distortions complicate the understanding of how an MVG array affects transonic SBLI. Bur et al. [46] concluded that the spanwise spacing of MVGs and their distance ahead of the shock impingement location play important roles in affecting separated SBLI. A close spacing allows the vortices to merge to reduce separation while sufficient distance must be provided to allow entrainment of the highmomentum freestream fluid; see also [11] where optimal geometries were proposed. In terms of potential benefits, Holden and Babinsky [12] suggested that the vane-type MVG causes a lower wave drag rise while Bur et al. suggested that the MVG height should be less than the sonic line of the incoming boundary layer. Holden and Babinsky observed that vortices from vane-type

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F.K. Lu et al. / Progress in Aerospace Sciences 53 (2012) 30–45

Table 1 Selected MVG studies. Ref.

Transonic Bur et al. [46]

Test conditions M1

Re

1.45

14  106, 3500b

Diagnosticsa

Remarks

TF, channel, NS, counter- and co-rotating vane; large distortions to surface flow, unsteadiness observed TF, NS, counter-rotating vane and ramp, shock impinges MVG and downstream, separation eliminated at centerline; global distortion TF, NS, counter-rotating vane and ramp, MVG ahead of shock, separation reduced at centerline, separated tunnel sidewall interactions TF, NS, ramp, MVG improves boundary-layer health

do (mm)

c

5.3

HSS (4000 fps), LLS, SP Pit, S, SFV, SP

Titchener and Babinsky [73] 1.4

26 000c

5.3

Pit, S, SFV, SP

Herges et al. [17]

1.4

30.4  106

4.77

Ogawa et al. [74]

1.3

33 000

7.13

HSS (2000 fps), PIV, PSP, SFV, SP S, Pit, SP

1.3

33 000c

6.98

(RANS)

Konig et al. [75]

0.79 0.79

5  106d 5  106d

– –

PSP, wake survey (RANS)

Rybalko et al. [22]

1.4

26  106

5.3

Lee et al. [23]

1.3

4.55  105c 1600b

– –

HSS (2000 fps), SFV, SP (RANS) (ILES)

Supersonic Anderson et al. [11] Babinsky et al. [14]

2 2.5

– 40  106

– 6

(RANS) LDV, S, SFV, SP

Ghosh et al. [16]

2.5

40  106

6

(RANS)

Lee et al. [18]

3

4000c

6

S, Pit (MILES, RANS)

Blinde et al. [15] Li and Liu [21,43,53]

1.84 2.5

36.6  106 1440b

19 –

Stereo PIV (ILES)

Holden and Babinsky [12]

1.5

26 000

4

TF, diffuser, NS impinging on various single and tandem contoured bumps, unsteadiness observed Airfoil, similar trends as experiment, proposed performance metrics: total pressure recovery and b.l. growth Airfoil, spanwise array of‘‘shock control bumps’’, drag reduction Detailed design of control bumps, drag reduction identified cause of tunnel interference TF; diffuser; NS; ‘‘split-vane’’ and ‘‘ramped-vane’’; separation eliminated at centerline; large global distortion TF; diffuser; NS; ‘‘split-vane’’ and ‘‘ramped-vane’’ Separation eliminated at centerline; large global distortion Optimization of vane- and ramped-types TF; OS (71); detailed flow mapping; large distortions; smaller MVGs possibly more effective due to lower drag Array of three MVGs shedding vortical structures; attempt to simulate Babinsky et al.’s experiment [14] FP; OS (81); performance criteria using integrated, spanwise b.l. parameters; small MVGs closer to the separation zone are more effective than larger MVGs TF; OS (101); single and double array ramps OS (251 ramp); MVG with 45 and 701 trailing edges

Notes: FP: flat plate; TF: tunnel floor, HSS: high-speed schlieren; IRT: infra-red thermography; LDV: laser Doppler velocimetry; LLS: laser light-sheet visualization; Pit: pitot survey; PIV: particle image velocimetry; PSP: pressure sensitive paint; S: schlieren; SFV: surface flow visualization; SP: surface pressure, NS: normal shock; OS: oblique incident shock (shock generator angle indicated in parenthesis). a

Numerical studies indicated by parenthesis. Based on momentum thickness. c Based on displacement thickness. d Based on airfoil chord length. b

MVGs do not lift off as fast as ramp-type MVGs and are more effective in energizing the boundary layer. These investigators also observed that the MVGs successfully eliminated shockinduced separation. The study of Bur et al. elicits a further comment vis-a -vis Mehta’s [26] study with an axisymmetric transonic bump. The latter study utilizes a single, conventional vortex generator, as shown schematically in Fig. 25(a). Mehta’s surface flow visualization shows a spiral similar to the spiral array of Bur et al., Fig. 24(b). As was observed by Lin [8] in subsonic flows, qualitatively, the effect of microvortex generators on mitigating separation is the same as conventional ones, even in SBLIs. Holden and Babinsky [12] examined the effect of MVGs on a normal SBLI at Mach 1.5. While this study was at a Mach number higher than that of Bur et al., this interaction possesses characteristics of transonic flow with its mixed character. These authors suggested that MVGs placed ahead of a separated SBLI may cause an increase in wave drag although they appeared to eliminate separation, with an overall benefit. Titchener and Babinsky [73] extended the above study with particular attention paid on the effect of the tunnel span. Without MVGs, a separated interaction occurs when the shock impinged the boundary layer close to the diffuser. The separated interaction also gives rise to corner separations, namely, interactions with the

tunnel sidewall boundary layers. The MVGs reduce the extent of the separation from the centerline with a resulting increase in total pressure recovery. However, the MVGs tend to enlarge and elongate the corner separation structures, as was also observed by Bur et al. [46]. In certain situations, the presence of the MVG array creates an asymmetrical flow. Reasons for this are still unknown. Finally, the authors concluded that the benefits of MVGs may be lost due to an increase in the size and severity of corner separations. In view of this, one can conclude that further detailed understanding of corner effects is necessary for MVGs to be applied in transonic inlets. Herges et al. [17] deployed a comprehensive array of diagnostics and offered somewhat modest conclusions. They found that MVGs improve the health of the boundary and could help resist separation in SBLIs. They suggested that MVGs be used to augment or replace bleed for future supersonic inlets. Ogawa et al. [74] were interested in the effects of a contoured bump on the performance of an airfoil at Mach 1.3, pertaining to reducing drag and buffeting arising from SBLI. The contoured hump is different from the usual MVG element but its height is still less than the boundary-layer thickness and thus falls into the MVG category. The study placed the hump under the shock. By doing so, the intention is to reduce wave drag and not necessarily to exploit the vortices produced downstream to mitigate SBLI effects. These investigators examined six bump configurations.

F.K. Lu et al. / Progress in Aerospace Sciences 53 (2012) 30–45

41

Fig. 25. Mehta’s study of a single conventional vortex generator upstream of an axisymmetric transonic bump [26]. (a) Schematic of test configuration. (b) Surface flow visualization at M 1 ¼ 0:862.

Fig. 24. Surface flow visualization from Bur et al. (flow from right to left) [46]. (a) No vane showing a nominally two-dimensional separated SBLI. (b) With subboundary layer co-rotating vane array showing a highly distorted surface flow pattern.

Without the bumps, a near normal shock impinge the boundary layer. The bumps induce a lambda-foot shock configuration to produce a weaker SBLI. With the associated numerical simulations, a side-by-side pair of narrow rounded bumps was found to achieve the best performance by wave drag reduction through modifying the wave pattern with little viscous penalty. Another joint experimental–computational study on the possibility of sub-boundary-layer protuberances for mitigating the ¨ effects of SBLI over transonic airfoils was reported by Konig et al. [75]. With an incoming freestream Mach number of 0.79, a mixed flow regime occurs over the airfoil to produce a normal shock impinging the boundary layer. Great effort was placed in designing the control bumps distributed spanwise across the airfoil. Despite the use of fences and adaptive walls, some wall interference effects were noted. Through numerical simulations, the interference was found to arise from shock waves originating from the junction of the airfoil’s leading edge and the tunnel sidewalls. Detailed comparisons between experiment and computation suggest that there is a decrease in drag. However, the occurrence of drag reduction for the experiment starts at an angle

of attack of a  21 whereas the computations show a drag reduction at a lower value of a  1:31. New compound MVGs known as split-ramps and rampedvanes were studied experimentally by Rybalko et al. [22] and numerically by Lee et al. [23], with multiple and single protuberances respectively. Rybalko et al. observed that flow separation was eliminated in the vicinity of the center but increased sidewall interference was observed compared to the simple vane or ramp geometries. The sidewall interference was labeled as ‘‘corner vortices’’ although these may actually be open separation which features strong vortices [60]. These results are consistent with other transonic investigations [12,46,73] although such interference was not reported nor observed in [17]. Lee et al. found that a ‘‘ramped-vane’’ configuration produces the most effective flow entrainment far downstream, reducing the total separation area but with spanwise distortions. 3.2. Supersonic Mach numbers (oblique incident shock or rampinduced shock) The primary difference between the transonic studies discussed above and supersonic studies is that, for the latter, the Mach number of the incoming flow is sufficiently past unity and that the flow downstream of the incident shock remains supersonic. The recent studies were spurred by Anderson et al. [11] who provided guidelines on MVG geometries based on a large test matrix. It can be noted that other than this seminal study, there has not been further optimization studies. This cited study was concerned with a single MVG in a Mach 2 flow. The optimization metric is the ‘‘health’’ of the boundary layer as characterized by a transformed boundary-layer form factor. However, subsequent

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studies point to a complex interactive flowfield and different optima may have to be considered. For example, lowering flow distortion may be more important for internal flows than for external flows where, despite flow distortion, a more relevant performance metric may be drag reduction. As reviewed above, the wakes of individual elements of an MVG array appear to stream in isolation, as if contained by the horseshoe vortices until they impinge into the SBLI region. There is the possibility of a synergistic interference between these vortices. Finally, a preliminary study of Mach number effects was performed by Lee et al. [24]. Experimental studies thus far involve incident shocks [14,15] which are pertinent to internal flows. The surface flow visualizations of Babinsky et al. [14] show substantial disruptions to nominal two-dimensionality, as to be expected, similar to observations in the transonic regime. It is probably appropriate to conclude that there is a disruption instead of a reduction of separation since the latter claim requires further substantiation. These authors suggested that smaller MVGs may be better in having lower wave drag, a conclusion reached separately by Bur et al. [46]. Due to their small size, MVGs should be placed closer to the interaction region, a conclusion that was also made for low speeds [8]. Both of these conclusions were further confirmed by Lee et al. [18] who performed MILES of a Mach 3 configuration. Ghosh et al. [16] simulated Babinsky et al.’s [14] experiments. Unlike most numerical simulations, these authors were able to introduce three MVGs. They found vortical structures forming downstream of the MVGs. The numerical results suggested that the experimental data may be affected by tunnel wall interference, which may be interpreted to be a glancing shock/boundarylayer interaction [61–63]. Blinde et al.’s [15] study involved detailed stereo particle image velocimetry mapping. An important aspect of their study is determining the size of the reversed flow region, using this to indicate separation. They found that the MVGs affected the spanwise distribution of the reversed flow and caused it to be broken up into isolated clumps. Blinde et al. suggested that this is consistent with Babinsky et al.’s [14] findings as well as those of Bur et al. [46] reviewed earlier. Blinde et al. also distributed two spanwise rows of MVGs next to one another. They found that two rows are more effective in disrupting the shock-induced separation zone. Lee et al. [18] reported a joint experimental–computational study, with emphasis on computations. These authors considered the flow downstream of an isolated MVG interacting with an impinging shock in a Mach 3 flow. The impinging shock was generated by an 81 wedge which is sufficiently strong to cause the turbulent boundary layer to separate. These authors found that the counter-rotating, trailing vortices from the MVG dominated the streamwise vorticity in the vicinity of the shock interaction. They stated that the MVG improved the ‘‘overall recovery of the structures’’. These authors considered that a small MVG that does not protrude too deeply outside the boundary layer will be beneficial. The smaller streamwise vortices also will be able to stay closer to the wall. These authors further stated that small ramps close to the shock interaction reduced the displacement

thickness in the interaction and reduced the extent of the separated zone. These consequences can be attributed to a decrease in wave drag and the close proximity of the counterrotating vortex pair to the surface. Finally, Li and Liu [21,43,53] reported a high-order LES simulation that showed a train of vortex rings shed from an MVG. The MVG wake that consists of vortex rings ‘‘piggyback’’ on the counter-rotating, trailing vortex pair has been discussed at length previously. The MVG of these authors has a trailing edge inclined at either 451 or 701 from the flat plate. The smaller inclination allows the vortex train to be closer to the wall which is thought to be favorable for flow control; otherwise, the flow features around and downstream are not expected to be different from the usual trailing edge inclined perpendicularly to the test surface. Li and Liu found that the vortex rings interacted with the leading shock to cause serious distortion of the separation bubble. This is probably the first study to indicate that shock/vortex interaction is the crucial phenomenon for breaking up the separation bubble. For example, the instantaneous numerical schlieren visualizations of the ramp-induced SBLI in Fig. 26 show that the leading shock has disappeared and large structures billow further outward. Li and Liu also found a reduction of the extent of the separation zone which may be related to the disappearance of the leading (or separation) shock of the lambda-foot structure. This visualization is significant since the classical understanding of shock-induced boundary-layer separation requires the presence of a system of compression waves that generally coalesces into a leading shock [36], regardless of whether the boundary layer is laminar or turbulent or whether the interaction is two- or threedimensional, at least in the mean [77]. The absence of the leading shock does not necessarily imply that there is no separation since the numerical visualization is an instantaneous one. However, the phenomenon may suggest a highly unsteady interaction triggered by large, unsteady events. The authors above stated that distortions of the leading shock can occur from either axial, counter-rotating trailing vortices or from vortex rings. Here, it is further specified that it is the interaction of vortex rings that causes the massive disruption of separated SBLI. A set of visualizations showing the passage of a vortex ring through the leading and rear legs of a lambda-foot shock structure is given in Fig. 27. Fig. 27(a) shows the lambda-foot structure associated with SBLI. The visualization includes part of a large vortical structure impinging the leading shock. Fig. 27(b) shows the disruption of the leading shock as also revealed in Fig. 26(b) above. One can interpret these two visualizations to indicate that the leading shock is seriously disrupted. The subsequent disruption of the separation (or rear) shock is seen in Fig. 27(c). Finally, Fig. 27(d) shows the collapse of the separation bubble. Similar results have been seen in visualizations of shock/ turbulence interaction where holes appear to be punched into the shock [78] and in the interaction between a shock and a vortex ring [79,72]. Pirozzoli [72] particularly showed that the main immediate consequence of a shock/vortex ring interaction is distortion of the shock and of the vortex ring. Pirozzoli also found that, despite losing kinetic energy, the vortex ring is persistent and is not broken up by the shock.

Fig. 26. Instantaneous numerical schlieren [21]. (a) No MVG. (b) MVG upstream.

F.K. Lu et al. / Progress in Aerospace Sciences 53 (2012) 30–45

43

Fig. 27. Sequence of frames showing vortex ring interaction with the leading and rear legs of the lambda-foot shock in the context of SBLI separation control [25]. (a) Lambda-foot shock structure. (b) Vortex ring disruption of the separation shock. (c) Vortex ring penetrating the separation bubble and disrupting the reflection shock. (d) Disruption of the separation.

Returning to the topic under consideration, a more complex scenario exists in the MVG wake consisting at least of vortex rings superimposed on the counter-rotating vortex pair [15,25,45]. The vortex ring interaction with the shock described above is superposed upon an interaction between the axial, counter-rotating vortex pair and the same shock system. While the latter interaction has not been discussed further in this review, it is well described in the literature [69]. A point regarding this latter interaction, unlike the former, is that the literature describes vortex breakdown. In particular, a vortex with a wake-like velocity profile, as in MVG-generated vortices, is prone to breakdown. To summarize, the latest evidence suggests an extremely complex interaction between different types of vortices as these encounter the shock system of a separated SBLI. The complex interaction indicates a disruption of the shock system and the trailing vortices but allows the vortex rings to propagate through fairly intact. The interaction is highly unsteady due to the passage of a train of vortex rings.

4. Some related concepts Other than MVGs, there has been recent interest in a number of related passive and active concepts for high-speed boundarylayer control, some with potential for alleviating shock-induced separation. A simple extension is a hybrid concept that incorporates a high-pressure micro-jet with jet pressure ratios of 1–3 and mass flow ratios of 0.1–0.3% of the inlet flow, inclined to the surface a small distance ahead of a micro-vane or a micro-ramp [80]. The jet is placed so as to energize the vortex system created by the MVG. Note that such a system produces a ‘‘jet-like vortex’’

which has a different breakdown behavior from the ‘‘wake-like vortex’’ discussed above [69]. Anderson et al. [80] suggested that such a system can be used to simultaneously manage the boundary layer on a vehicle forebody and to control the flow in a serpentine or S-duct transonic inlet. The micro-jet flow requirements represent a 10-fold decrease from that of conventional bleed requirements. Souverein and Debie ve [81] described the effect of air jet vortex generators (AJVGs) for alleviating separation due to SBLI. The AJVG orifices with diameters less than 10% of the boundarylayer thickness are choked and inclined at 451 to the freestream. Separation is induced by an incident shock generated by a 9.51 sharp wedge in a Mach 2.3 flow. The mass flux of the AJVGs is 3% of the boundary layer mass flux deficit and the orifices are choked. The air jet in crossflow produces a pair of persistent, counter-rotating vortices in high-speed flow [82]. Souverein and Debie ve found that the separation bubble length and height are reduced by the jets. These authors also found that the energetic bandwidth of the shock oscillations increases by approximately 50%, which is consistent with the reduction in separation bubble size. It can be noted that active schemes such as AJVGs can be modulated to tailor to specific control needs as conditions change. These approaches should be evaluated against conventional active control approaches to determine their performance potential in applications.

5. Conclusions and outlook A review is presented of the flowfield around an MVG immersed in a supersonic boundary layer and the subsequent

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interaction downstream with shock-separated flow. The flowfield around an MVG is dominated by a pair of primary vortices that trail from the MVG sides. A complex topology is revealed that includes two pairs of secondary vortices. Two pairs of vortex filaments emanating from the rear of the MVG were also identified and there is the possibility of more of such filaments. There are at least two schools of thought regarding the wake of the MVG. First, the MVG wake is thought to be a pair of counterrotating trailing vortices that entrain high momentum, freestream fluid. A nonuniform spanwise region is formed where low momentum fluid exists around the centerline and higher momentum fluid exists further outboard. An analogy is drawn between this particular confluence of counter-rotating trailing vortices and that arising from cross-shock/boundary-layer interactions with an upwelling of the boundary layer variously described as a mushroom or a hairpin. It is thought that the higher momentum energizes the boundary layer to reduce the subsequent separation. Secondly, an instability mechanism is thought to produce a train of vortex rings superimposed on the counter-rotating, trailing vortex pair. The vortex train draws in high momentum, freestream fluid, as in the first model. However, the vortex train interacts differently with the downstream shock in an SBLI. The vortex rings are sufficiently robust to penetrate through the separation bubble, leading to substantial distortions of the lambda-foot shock structure. In particular, the weak leading shock may become further weakened. It appears that the interaction creates substantial unsteadiness in the upstream region of the separation zone arising from the vortex ring interaction. This unsteadiness may produce the impression of a reduced separation zone. Detailed study of the leading edge of the separation zone in these circumstances is needed. In many of the experimental studies, tunnel sidewall interference may make it difficult to properly interpret the results. Thus, it is recommended that attempts be made to avoid such interference. Axisymmetric configurations may be suitable for this purpose. Otherwise, the possibility of using fences to isolate a two-dimensional interaction should be considered. Computationally, it appears that high-order schemes are needed to capture the fine scales present in the flowfield. In addition, a proper identification of the vortical structures and how they interact with the shock-induced separation may be best handled by numerical simulations integrated with experiment. While the theme of this review has been that there is still much to be understood in high-speed MVGs, a different vein on optimizing MVG configurations is indicated for applications. In this respect, performance metrics from an applications standpoint need to be developed to substantiate the effectiveness of MVGs. For example, the reduction of the separation zone, say, based on surface flow visualization may be quantified by defining an average separation line after the introduction of an MVG array. The metrics need to quantify the performance penalty of MVGs relative to the performance gains.

Acknowledgments The authors gratefully acknowledge funding for this work via AFOSR Grant No. FA9550-08-1-0201 monitored by Dr. John Schmisseur. The authors also thank their students, especially Adam J. Pierce and Yusi Shih, who performed some of the studies that were incorporated as part of this review. The authors thank Yusi Shih and Zhengzhong Sun for Figs. 1 and 17 respectively. The first author would like to thank Professors Fulvio Scarano and Jagadeesh Gopalan, and Mr. Zhengzhong Sun for reading an earlier draft of the paper, including Professor Scarano’s suggestion of Ref. [44]. He also would like to thank Dr. Len Squire, and

Professors Holger Babinsky and Argyris Panaras for enlightening discussions. The comments and suggestions have strengthened the manuscript. In particular, Professor Panaras pointed to the analogy between the vortex shed from an MVG and the counterrotating vortex pair in a cross-shock boundary-layer interaction. References [1] Delery JM. Shock wave/turbulent boundary layer interaction and its control. Progress in Aerospace Sciences 1985;22(4):209–80. http://dx.doi.org/10.1016/ 0376-0421(85)90001-6. [2] Raghunathan S. Passive control of shock–boundary layer interaction. Progress in Aerospace Sciences 1988;25(3):271–96. http://dx.doi.org/10.1016/03760421(88)90002-4. [3] Collis SS, Joslin RD, Seifert A, Theofilis V. Issues in active flow control: theory, control, simulation, and experiment. Progress in Aerospace Sciences 2004;40(4–5):237–89. http://dx.doi.org/10.1016/j.paerosci.2004.06.001. [4] Seifert A, Greenblatt D, Wygnanski IJ. 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