Control of flow distortion in offset diffusers using trapped vorticity

International Journal of Heat and Fluid Flow 75 (2019) 122–134

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International Journal of Heat and Fluid Flow journal homepage: www.elsevier.com/locate/ijhff

Control of flow distortion in offset diffusers using trapped vorticity a

a,⁎

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b

a

Travis J. Burrows , Bojan Vukasinovic , Matthew T. Lakebrink , Mortaza Mani , Ari Glezer a b

T

Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405, United States The Boeing Company, St. Louis, MO, 63042, United States

ABSTRACT

Controlled concentrations of trapped vorticity within an offset, subsonic (MAIP ≤ 0.7) diffuser are explored for active suppression of flow distortion in joint experimental and numerical investigations. The coupling between trapped vorticity, used to model boundary-layer separation, and secondary-flow vortices is manipulated using an array of fluidic oscillating jets, which are spanwise distributed just upstream of the trapped vortex. Actuation energizes the separated shear layer, reducing the size of separation and effecting an earlier reattachment of the boundary layer, which favorably effects the flow field downstream of reattachment. It is shown that optimal interactions between actuation and the trapped vortex fully suppress the central vortex pair, and redistributes the residual vorticity around the diffuser's circumference. This results in a 68% reduction in circumferential distortion at the Aerodynamic Interface Plane (AIP), using an actuation mass flow rate that is only 0.25% of the diffuser mass flow rate.

1. Introduction Future supersonic aircraft will use embedded engines to attain both aerodynamic efficiency and stealth with extremely compact, offset inlet systems to enable efficient inlet-airframe integration. These next-generation inlet systems pose significant flow-management challenges in both the supersonic-inlet aperture and the compact, offset diffuser. Performance of such diffusers is adversely impacted by the evolution of large-scale vortices generated by secondary flow, and boundary-layer separation which can be affected by and coupled to shock-induced fluctuations in the inlet aperture. These phenomena result in significant penalties to total-pressure recovery and distortion at the engine face, which could be mitigated by the development and implementation of active flow-control technologies. The primary focus of the present study is application of flow control within a highly offset diffuser to mitigate formation of secondary-flow vortices and boundary-layer separation, and thereby minimize total-pressure losses and distortion at the AIP. The flow control approach considered in the present work relies on the existence of trapped vorticity in a diffuser, which would occur naturally in an actual inlet system as a result of boundary-layer separation. Manipulation of trapped vorticity is not new in either external or internal aerodynamics. Many interesting concepts have been developed for external aerodynamics, predominantly motivated by the notion that airfoil circulation can be either enhanced or reduced when vorticity becomes bound to the surface (e.g., Saffman and Sheffield, 1977). Early work by Hurley (1959) considered improvements of low-speed characteristics of a nominally high-speed airfoil profile by introduction of a large forward flap that would trap a vortex

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over the leading suction side. In order to maintain ‘free-streamline’ attachment over the downstream flap surface (and full confinement of the vortex), Hurley utilized steady jets over the leading Coanda surface. Another concept, proposed by Kasper and published by Cox (1973), made use of upstream and downstream flaps without any active control. Rossow (1978) expanded on the application of trapped spanwise vorticity along the leading edge by utilization of end-plate suction for vortex stabilization, and claimed an increase in the resulting lift coefficient of up to 10. More relevant to the present study, several prior investigations considered utilization of trapped vorticity in diffusers, primarily motivated by reduction of total-pressure losses. Ringleb (1960) proposed the cusp diffuser, which is characterized by a vortex-shaped cusp on a portion of the diffuser meant to generate a stationary vortex rotating in the direction of the flow. In practice, it was found difficult to maintain a stable standing vortex, which was attributed to the skin friction within the cusps (Adkins, 1975; Lee and Price, 1986). In an attempt to improve upon the cusp diffuser, a trapped-vortex diffuser was developed by Heskestad (1966), and further by Adkins (1975). This design utilized an annular vortex chamber to trap low-momentum fluid which would otherwise lead to separation downstream in the diffuser. To maintain a vortex in the chamber, it was bled continuously such that flow from the diffuser constantly energized the vortex. Designed primarily for gas turbine combustors, it was surmissed that about 3% of the bleed air flow would be needed. Subsequently, Adkins et al. (1981) refined this design to create a ‘hybrid diffuser’ which provided the same benefits with a third of the bleed, and also can achieve a 25% increase in recovery, relative to a conventional divergent duct of the same length, with no bleed. More recently,

Corresponding author. E-mail address: [email protected] (B. Vukasinovic).

https://doi.org/10.1016/j.ijheatfluidflow.2018.11.003 Received 21 June 2018; Received in revised form 2 November 2018; Accepted 6 November 2018 0142-727X/ Published by Elsevier Inc.

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numerical investigations have been performed by Mariotti et al. (2014) on the effect of altering a two-dimensional diffuser surface to include contoured cavities. It was found that inclusion of one cavity increased total-pressure recovery by 6.9% and two cavities led to an increase of 9.6%. The physically robust, passive-flow-control techniques that have been applied to improve performance of inlet systems (Vakili et al., 1985; Reichert and Wendt 1996; Jirásek 2006; Owens et al., 2008) inherently lack real-time adjustability and also necessarily generate total-pressure losses. Alternatively, active-flow-control techniques such as jets can provide significant performance improvements, with flexibility for development of control schemes, and little or no drag penalty in the absence of actuation. Application of active flow control affords optimization and in-flight performance control both in the absence (Weigl et al., 1997; Scribben et al., 2006; Anderson et al. 2004a,b) and presence (Vaccaro et al., 2008; Rabe, 2003) of boundary-layer separation. Amitay et al., (2002) demonstrated active control of localized separation in a two-dimensional S-duct using synthetic jets. Anderson et al. (2004b) preformed a design-of-experiments (DOE) analysis to optimize the use of skewed jets with significant improvements in total-pressure recovery and distortion at the AIP. Scribben et al. (2006) used micro-jets in an offset diffuser and showed drastic improvements in distortion with small reductions in drag. In similar experiments, Owens et al. (2008) used arrays of jets in a boundary-layer-ingesting (BLI) S-duct diffuser at freestream Mach number of 0.85 to gain insight into optimal design. A hybrid control approach, which incorporates the advantages of both passive and active control, has been shown to be effective in the reduction of parasitic drag while maintaining fail-safe attributes and satisfying the need for adjustable flow control (Owens et al., 2008; Anderson et al., 2009). Owens et al. (2008) combined active and passive flow control using vanes and jets to improve performance of an offset diffuser over a range of flow rates, especially at low velocities for which the micro-vanes were not optimized. In an effort to reduce engine bleed, Anderson et al. (2009) combined the micro-ramps used in their earlier work (2006) with flow injection resulting in an almost tenfold reduction in required engine bleed. Vane vortex generators have been extensively studied as a means for controlling separation in adverse pressure gradients (Godard and Stanislas 2006), as well as for use in s-ducts (Anabtawi et al., 1999; Anderson et al. 2004a; Tournier and Paduano 2005) and as the passive component of hybrid-flow-control systems (Owens et al., 2008; Dagget et al., 2003). Delot et al. (2011) experimentally evaluated the effectiveness of passive vortex generators and continuous and pulsed micro-jets for reducing distortion in an offset diffuser, and reported a reduction of the circumferential distortion parameter DC60 by 50% at MAIP = 0.2 and up to 20% at MAIP = 0.4. Harrison et al. (2013) simulated and experimentally verified the effect of various blowing and suction schemes for a BLI serpentine diffuser using swirl and circumferential-flow-distortion analysis. They realized a 50% reduction in total-pressure

circumferential distortion parameter DC60 by using a circumferential blowing scheme. In addition, they noted that blowing and suction could be strategically combined to produce reductions in distortion of up to 75%. Gissen et al. (2014a,b) used both active and hybrid flow control in an offset diffuser and showed reductions in distortion at the AIP. They also indicated that the governing control mechanism in the diffuser was related to the dynamics of a large-scale counter-rotating vortex pair formed from coalescence of the array of small-scale vortices imposed by the flow control. Gartner and Amitay (2014) studied the effect of introducing a honeycomb mesh upstream of an offset rectangular duct, and showed improvements in the symmetry of the pressure distribution while minimally decreasing total-pressure recovery. The mesh accomplished this by pushing the saddle-saddle point, responsible for the onset of an instability leading to asymmetry, farther downstream. Gartner and Amitay (2015) experimentally tested the effect of sweeping, pulsed, and two-dimensional jet actuators on the total-pressure recovery of a rectangular diffuser under transonic-flow conditions, and showed that sweeping jets produced the greater recovery at comparable mass-flow rates. In the present study, which is a collaboration between experimental and computational techniques at Georgia Tech and the Boeing Company, application of novel flow-control technologies to a highly offset diffuser is investigated. The losses and distortion inherent in the baseline flow are mitigated by suppressing boundary-layer separation and secondary-flow vortices using fluidic oscillators. Prior findings of Burrows et al. (2016) demonstrate feasibility of fluidic oscillators for such control, and the present study further matures the capability. This is accomplished after developing a solid understanding of the physical details governing the baseline and actuated flows. 2. Experimental and computational tools The experimental investigations were performed in an open-return, pull-down, high-speed subsonic wind tunnel that is driven by a 150 hp blower, and the temperature of the return air is controlled using a chiller, coupled with an ultra-low pressure drop heat exchanger. The offset diffuser (Fig. 1) is installed in place of the test section such that it couples upstream to the tunnel contraction, which can deliver throat Mach numbers up to 0.75. It has a D-shaped throat of H = 0.7⋅D in height, and a round, aerodynamic interface plane (AIP, interface between a diffuser and engine) with a diameter, D = DAIP = 12.7 cm. The centroid-to-centroid offset between the throat and AIP is DAIP. The computational domain used for CFD analysis (Fig. 2) incorporates key components of the wind tunnel at Georgia Tech, including the contraction, flow-control elements, and AIP-instrumentation housing. An unstructured surface grid consisting of triangular elements is created using the Modular Aerodynamic Design Computational Analysis Process (MADCAP). A volumetric grid comprising prisms, pyramids, and tetrahedra is then constructed using the Advancing Front Local Reconnection (AFLR) software. A grid-resolution

Fig. 1. Subsonic-inlet offset diffuser model's side (a) and downstream (b) views, with illustration of the flow over the trapped vortex. 123

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Fig. 2. Layout of the computational domain (a) with the symmetry boundary omitted for clarity and an upstream view of the flow control module (b) with an integrated array of fluidic oscillating jets.

study was performed to minimize numerical error, and the resulting element sizes are discussed below. Anisotropic triangular prisms were used to resolve the boundary layer. An initial normal spacing of 2.5 μm was held constant for three layers away from the boundary. The growth rate for the normal spacing grew from 1.05 at layer four, to a maximum value of 1.10. Element sizes were kept small near the flow-control orifice (38 μm) and in their vicinity around the flow-control module (0.25 mm). Element sizes along the lower and upper surfaces of the diffuser were not allowed to exceed 1 and 2.5 mm, respectively. Background Cartesian grids were used to enforce the size of tetrahedral elements outside of the prism layer, and the final mesh consisted of about 180-million elements. Second-order-accurate solutions to the compressible Navier–Stokes equations were obtained using the Boeing Computational Fluid Dynamic (BCFD) finite-volume flow solver (Mani et al., 2004). BCFD supports continuum-gas simulations of general-geometry structured and unstructured grids, for flows ranging from low subsonic to hypersonic. An extensive array of boundary conditions, numerical schemes, turbulence models, and gas models are available within BCFD for both steady-state and time-accurate simulations. In steady-state simulations, first-order implicit time integration is performed, and local eigenvalues are used to obtain a spatially varying time-step and accelerate convergence. For time-accurate simulations, a dual-time approach is used to obtain second-order temporal accuracy. The simulations conducted for the present study assumed calorically perfect air with constant laminar and turbulent Prandtl numbers of 0.72 and 0.90, respectively. Viscosity was computed using Sutherland's law. Solid boundaries were modeled as no-slip adiabatic walls, total pressure and total temperature were prescribed on the inflow boundary, and a uniform pressure was prescribed on the outflow boundary to achieve the desired flow rate. Delayed Detached Eddy Simulations (DDES) were conducted using Spalart–Allmaras with rotation correction and the quadratic constitutive relation (SA-RC-QCR) (Mani et al., 2013). Bounded central differencing was employed to reduce numerical dissipation and improve resolution of turbulent eddies. The simulated flow conditions are defined by the inflow total pressure and temperature (po = 98.5 kPa and To = 19 °C), and static pressure at the outflow boundary (pDS = 80.6 kPa, Fig. 2a), which induced a mass-flow rate of 2.45 kg/s. The upstream portion of the diffuser's lower surface incorporates a large, removable flow control insert, spanning 0.1 < x/D < 1 that is designed to accept a variety of flow-control devices. In order to cause boundary-layer separation, a recessed surface, which smoothly mates with both the upstream (x/D = 0.1) and downstream (x/D = 0.9) diffuser surfaces, is introduced on the lower surface (Fig. 1a). This modification is made within the same removable flow control module, and can be considered a passive-flow-control component relative to the unaltered offset diffuser. This particular geometry was utilized to assess

the proposed flow-control approach, particularly applied to recirculating separated flow and secondary flow. Furthermore, the application of active flow control in this diffuser is a proof of concept intended to demonstrate its ability to locally affect separation and subsequently impact key figures of merit at the Aerodynamic Interface Plane (AIP), such as total-pressure recovery and distortion. The active component of the hybrid-flow-control approach is an array of fluidic oscillating jets distributed spanwise across the module. The fluidic oscillating jets are positioned immediately upstream of the separation line (x/D = 0.3) which was determined by surface oil-flow visualization over the modified geometry. Fig. 2b illustrates the flow-control array, which consists of twenty-one jets that are spaced equally at 7 mm, with each orifice measuring 1.5 × 2 mm. Due to inherent instabilities related to the two supply streams colliding inside the device, the jet oscillates at frequencies between 7 and 9 kHz depending on the supply pressure. More details about fluidic oscillating jet operation can be found in the work by Gregory et al. (2007) and Raghu (2013). The jets are used to control the strength and structure of the trapped vortex, and thereby affect flow throughout the diffuser. The actuators are integrated such that their orifices issue jets which are close to tangential to the local surface. The main flow-control parameter, Cq, is the ratio between the jet and diffuser mass-flow rates, and in the present investigations it is less than 0.7% in all cases. A bench test of a single fluidic oscillator was performed with the jet issuing into quiescent air. Experimental measurements were made with a single-wire hot-wire anemometer (HWA), and compared against DDES, wherein the oscillator geometry was modeled as part of the grid, and uniform total pressure and temperature were prescribed at the inflow boundary (Lakebrink et al., 2017). The oscillator is constructed with two inlets which encourage the generation of a flow instability upstream of the throat, causing the jets to oscillate, or ‘sweep’ back and forth. This oscillation enhances mixing with the surrounding air and rapidly expands the region affected by the jet. To measure the jet velocity, the bench-tested module was held stationary, while the hot-wire probe was traversed by a computer-controlled stepper motor. Profiles of mean in-plane velocities and their RMS fluctuations were measured at seven downstream locations from x/w = 5–20, where w is the orifice width and x is the distance from the orifice. Families of the velocity profiles for a given flow rate through the actuator are shown in Fig. 3. The dimensional profiles (Figs. 3a and b) indicate that all profiles, except those nearest the orifice, exhibit a saddle velocity profile, where the peak locations indicate predominant jet directions in the limit states of oscillation. Both the nearest RMS and velocity profiles (x/w = 5) indicate a possible transitional region prior to full jet oscillation, showing the bell-shaped jet profile and the peak RMS fluctuations about each side shear layer. Self-similarity of both the RMS and velocity profiles is shown in Fig. 3c and d. There is no dominant length scale in the free-evolving jet, so it is to be expected that its evolution depends 124

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Fig. 3. Time-averaged velocity magnitude q (a, c) and its standard deviation (b, d) profiles for an isolated fluidic-oscillating jet issuing into quiescent air at downstream positions x/w = 5 (♦), 7.5 (■), 10 (▲), 12.5 (×), 15 (*), 17.5 (●), and 20 (+); Q = 25 l/min.

only on local velocity and length scales. Hence, when the distances are scaled by the local half-width of the velocity peak zm and velocities by the local velocity peak qm, all but the nearest ‘transitional’ profiles collapse (Fig. 3c and d). The main flow-diagnostic equipment integrated into the diffuser was a total-pressure rake used to measure the flow at the AIP. The rake was constructed according to the industry standard ARP1420b (SAE, 2002), with 40 probes in eight equally spaced legs around the circumference of the AIP. The AIP total-pressure rake is supplemented with a matching ring of eight static-pressure ports along the diffuser wall, aligned with the tip of each rake leg. Additionally, twelve and five static-pressure ports were distributed along the bottom and top centerlines of the diffuser, respectively. Static and total pressures were measured using a dedicated PSI Netscanner system. Each mean static and total-pressure measurement was based on 6400 independent samples. Consequently, uncertainty in the mean pressures was estimated to be less than 1%. Among a suite of the circumferential and radial distortion parameters, the AIP face-averaged circumferential-distortion descriptor (DPCPavg) is used as the primary indicator of total-pressure distortion in this study. The experimental uncertainty in DPCPavg, was estimated to be less than 2%. Additionally, the time averaged circumferential tip (DPCPt) and hub (DPCPh) descriptors were computed, which are based, respectively, on the two outermost (rings 4 and 5) and innermost (rings 1 and 2) of the five total-pressure-probe rings at the AIP. Calibration of the offset-duct facility was performed relative to the reference static-pressure port upstream from the duct inlet, and the corresponding AIP Mach number was based on the mean rake total pressure and the mean wall static pressure. Surface oil-flow visualization and localized visualization of the ‘near field’ across the control surface were also performed and utilized to elucidate the near-wall flow topology.

Fig. 4. Mach (a) and the Mach RMS (b) profiles of the diffuser oncoming boundary layer (MAIP = 0.55) at three spanwise locations (see inset), and the contour plot of the corresponding total pressure (c) measured by the 40-probe AIP rake.

plane (z/H = 0) indicates a rather uniform approach boundary layer away from the corners. In the absence of the backward-step recess, the thin incoming vorticity layer interacts weakly with secondary flow along the diffuser's path, resulting in nearly negligible total-pressure distortion at the AIP. This is shown by the total-pressure contours in Fig. 5a, where the average distortion parameter DPCPavg is about 0.008. The AIP pattern for the recessed diffuser surface is shown in Fig. 5b, where the total-pressure contours indicate significant losses focused predominantly about the lower centerline. It should be noted that the total-pressure deficit measured for the recessed diffuser resembles that of a BLI diffuser in the absence of flow separation, which is known to be

3. Base flow characterization The boundary layer at an axial station of x/H = −1, where x = 0 is the throat, is illustrated in Fig. 4 for MAIP = 0.55. Measurements were taken at three spanwise locations corresponding to z/H = −0.5, 0, and 0.5. The resulting profiles of the mean and RMS velocity are shown in Fig. 4a and b, respectively, which indicate that the high-shear region associated with the boundary layer is confined to within about 2 mm of the surface. Furthermore, symmetry of the profiles about the central

Fig. 5. Contour plot of the measured total pressure pt/pto for the smooth diffuser (a), and with the trapped vortex (b). 125

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Fig. 6. Simulation of the baseline flow evolution in the SD-1 diffuser (a) and the simulated (b) total-pressure contours at the AIP. Total pressure recovery is 0.966.

effected by a pair of counter-rotating vortices (Gissen et al., 2014a,b). Therefore, it is to be expected that the similar underlying flow pattern is responsible for the deficit seen in Fig. 5b. This is verified by time-accurate simulations of the recessed diffuser. The simulation of the baseline diffuser flow is shown in Fig. 6a using Mach-number contours at eight equally-spaced cross sections. The recessed surface traps vorticity as flow over the recess separates and reattaches within the domain 0.81 < s/DAIP < 1.45 (s is measured along the lower surface starting at the throat). These data show evolution of the low-speed domain between the counter-rotating secondary vortices that form along opposite sides of the duct. These vortices manifest as flow distortion at the AIP as indicated by contours of the total pressure (MAIP = 0.63) in Fig. 6b. The total-pressure data shows that CFD slightly over-predicts both recovery and circumferential distortion, but both quantities are in very good agreement with the experiments (cf., Fig. 5b). Indeed, the time-resolved simulation clearly predicts a pair of streamwise vortices as the underlying cause of distortion at the AIP. Helicity iso-surfaces are used to elucidate the vortices in Fig. 7, which are clearly visible along the lower-surface centerline. The sense of rotation of these two vortices is such that they move the low-momentum wall flow towards the lower-surface central plane and then upward, away from the wall. These motions are directly responsible for the totalpressure deficit illustrated in Fig. 5b. In addition to the centerline vortices, Fig. 7 also highlights corner vortices along both outboard sides of the diffuser, which are shed from the edges of the recessed-cavity insert. Lastly, it should be pointed out that the streamwise switch in helicity sign is associated with flow reattachment, which marks a change in the sign of streamwise velocity. The similarity of this baseline AIP pattern to that of the BLI-diffuser flow highlights the dominant role of secondary flow. It can be argued that the local separation bubble provides losses and flow instabilities which are analogous to a thick incoming boundary layer. In either case, two large counter-rotating streamwise vortices are triggered on either side of the duct, across the vertical plane of symmetry. Their sense of rotation is such that they lift low momentum flow off the lower surface towards the AIP center. The qualitative similarities of these two flows also suggests that both flows should be receptive to similar flow-control

approaches. Therefore, design and implementation of the flow-control tools draws from prior studies of BLI diffusers (e.g., Gissen at al., 2014a,b). 4. Flow control effects The effectiveness of hybrid-flow control was first demonstrated for AIP Mach numbers ranging from 0.36 to 0.7. For each of the base flows, DPCPavg is based on the 40-probe rake measurements at the AIP. Baseline total-pressure contours at the AIP are shown in Figs. 8a–e for increasing diffuser flow rate. As flow rate increases, the intensity of the loss along the lower centerline also increases. A sharp-cusped pressure deficit develops about the bottom-wall plane of symmetry, spreading over a thin wall layer in the outward direction. As stated in Section 3, such a total-pressure deficit is qualitatively similar to that of a BLI offset diffuser without internal flow separation. In the BLI offset diffuser, the total-pressure pattern at the AIP is formed by a pair of large-scale secondary-flow vortices that act to redistribute the incoming momentum deficit from the boundary layer to the bottom central zone of the AIP. In the present experiments, there is no large momentum deficit carried into the diffuser, but rather it is generated over and downstream of the separation bubble. This similarly results in two large-scale counter-rotating vortical structures having a sense of vorticity such that they bring high-momentum fluid from the upper sidewalls and push the low momentum fluid towards the center of the duct (cf., Fig. 7). Controlled total-pressure contours at the AIP are shown in Figs. 8f–j. These patterns demonstrate that the jets effect a redistribution of low-momentum fluid from the central loss down and outward along the wall, thus forming a thin layer of low-momentum fluid along the wall, which spans about three quarters of the AIP circumference. This qualitative change indicates reduced distortion because the concentrated totalpressure deficit is nearly eliminated. Such a redistribution of the totalpressure deficit is also consistent with the dynamics of the two largescale vortices that are mirrored across the diffuser plane of symmetry, having a sense of rotation that carries the low-momentum fluid out of the central bottom wall, and along the wall upward. It is interesting to note that this total-pressure redistribution is analogous to the effect of active flow control in a BLI offset diffuser (Gissen et al., 2014a,b). A summary of how flow control effects total-pressure distortion, expressed by DPCPavg, is shown in Fig. 9a for each flow condition depicted in Fig. 8 over a range of Cq. At the two lowest AIP Mach numbers distortion is already low in the baseline flow (Cq = 0), and there is virtually no change at the lowest values of Cq. For Cq > 0.6% a sudden small drop is observed, followed by a plateau with increasing Cq. DPCPavg increases monotonically with Mach number, and for MAIP > 0.45 low levels of Cq induce a moderate decrease in DPCPavg. For 0.5% < Cq < 0.7%, sharp reductions in DPCPavg are observed at all Mach numbers, the magnitude of which is commensurate with the distortion level in the baseline flow. Increasing Cq beyond 0.7% does

Fig. 7. Top view of helicity iso-surfaces along the lower surface in the base flow. Inactive flow control jets are marked by gray arrows. 126

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Fig. 8. Total pressure contour plots at the AIP for the baseline (a–e) and controlled flows by Cq = 0.01 (f), 0.009 (g), 0.0075 (h), 0.007 (i), and 0.0068 (j) at MAIP = 0.36 (a,f), 0.45 (b,g), 0.58 (c,h), 0.64 (d,i), and 0.7 (e,j).

not afford any significant benefit. Summarizing, the flow-control effectiveness can be divided into three categories: (i) moderate reduction of DPCPavg for Cq = 0–0.5%, (ii) sharp reduction in DPCPavg for Cq = 0.5–0.7% and (iii) saturation of flow-control effectiveness for Cq > 0.7%. Another interesting insight can be gained by considering the reduction in total-pressure distortion for the controlled flow relative to baseline plotted in Fig. 9b. In addition to the aforementioned threezone trend, Fig. 9b indicates that flow-control effectiveness increases with M. Although this finding may appear counterintuitive, it can be argued that the base flows at lower Mach numbers have inherent lower levels of distortion, which makes them less susceptible to flow control. Fig. 10 further illustrates the relationship between the AIP patterns and DPCPavg for MAIP = 0.7. As Cq increases from zero (baseline), DPCPavg and the pattern change only slightly. As Cq increases further, the peak total-pressure deficit that was protruding up towards the duct axis begins to retreat toward the wall and spread outward at Cq = 0.3%. This reduction in intensity provides nearly 20% reduction in DPCPavg. DPCPavg continues to decrease with increasing Cq, and a notable redistribution of the low momentum fluid up the diffuser wall is observed in the AIP patterns near Cq = 0.5%. As already stated in discussion of Fig. 9, the greatest response to the flow control is achieved for 0.5% < Cq < 0.7%. In comparing the baseline pattern to that at Cq = 0.7%, one observes that the focused zone of low total pressure is completely swept away and up the diffuser wall.

Fig. 10. AIP total pressure distortion parameter DPCPavg with the flow control mass flow rate coefficient Cq at MAIP = 0.7, with characteristic contour plots of the AIP total pressure.

for a given configuration, motivated by a desire to more precisely effect the centerline vortices. Two cases were considered by reducing the number of active jets from n = 21 in the full array, to 13 and 7 in the reduced arrays. General trends in flow-control effectiveness with increasing Cq are depicted by total-pressure patterns at the AIP (Fig. 11) for n = 21 (Figs. 11a–d), 13 (Figs. 11e–h), and 7 (Figs. 11i–l). The qualitative trends with increasing Cq are largely independent of n. However, there are some important differences in these three cases. For instance, redistribution of the deficit from the lower central zone to the upper wall appears rather gradual for the full jet configuration

5. Flow control optimization Following the initial flow-control assessment, further improvements were sought by reducing the number of active jets across the span. This was done such that only central subsets of the full array were utilized

Fig. 9. Absolute (a) and relative (b) AIP total pressure distortion DPCPavg with the flow control mass flow rate coefficient Cq, at five diffuser Mach numbers MAIP = 0.36–0.7. 127

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Fig. 11. Contour plot of the total pressure pt/pto for the flow controlled by n = 21 (a–d), 13 (e–k), and 7 (i–l) central jets at MAIP = 0.7 by Cq = 0 (e,i), 0.008 (a,j), 0.0015 (k), 0.0023 (f), 0.03 (b,g), 0.038 (c,l), 0.063 (h), and 0.07 (d). Contour levels are the same as in Fig. 8.

(n = 21), while the lower number of jets (n = 13) more significantly impacts the deficit zone at lower Cq (Fig. 11f), which is followed by greater recovery at the central zone, but also greater losses along the upper wall with further increase in Cq (Fig. 11h). It appears that the smallest array (n = 7) does not as effectively suppress distortion at low Cq, while at the highest, it induces further enhancement of both positive and negative effects in the central zone and sidewalls, respectively (Fig. 11l). The three configurations discussed in Fig. 11 are further characterized by evolution of DPCPavg, with Cq, as well as their effect on the AIP Mach number of the diffuser flow. These results are shown in Fig. 12a for n = 21, 13, and 7. Changes in AIP Mach number are used for assessing the effect of flow-control on overall losses, because a decrease in AIP Mach number indicates increased losses. Data in Fig. 12a show that the array with fewest jets begins to introduce losses at the lowest Cq, while the AIP Mach number of other two doesn't decrease until a slightly higher Cq. Furthermore, there is a clear trend that the rate of a decrease of MAIP with Cq increases with a decrease in n. These drop-off levels of Cq at which MAIP begins to decrease represent an upper bound for a subset of the flow control rates that could be considered optimal. As for the decrease in DPCPavg with Cq, another clear trend is shown: the rate of DPCPavg decrease is inversely proportional to

the number of control jets. In each of the three cases a minimum DPCPavg of 0.01 is achieved. Although consideration of just distortion would indicate n = 7 is optimal, consideration of the changes in MAIP points to n = 13 as the best performing array, as it results in a reduction of DPCPavg to 0.015 while MAIP remains constant, at Cq = 0.25%. Since n is different for each of the tested cases, Fig. 12b examines both DPCPavg and MAIP dependence on Cq per active jet, rather than total Cq. Clearly, a unified dependence of DPCPavg is obtained relative to Cq/jet, which indicates that it is possible to reduce the total Cq while maintaining the same distortion reduction. Again, although this part of the analysis would point to n = 7 as the best configuration, analysis of its corresponding MAIP on Cq/jet shows MAIP -invariance for the highest Cq for n = 13, again indicating this case as the most effective one from the standpoint of both recovery and distortion. Lastly, three contour plots of AIP total pressure are plotted in Figs. 12c–e for the cases when Cq/jet is approximately the same for n = 7, 13, and 21, and as it can be expected, all of these arrays effect about the same distortion reduction in the diffuser flow. Given the analysis based on changes in DPCPavg and MAIP with flowcontrol actuation for the three pre-selected cases, a summary of flowcontrol effectiveness is shown in Fig. 13 for all eight jet configurations at MAIP = 0.7. As the number of jets and Cq are varied, the set Mach

Fig. 12. Average circumferential distortion DPCPavg (solid) and AIP Mach number (dashed) with Cq (a) and Cq/jet (b) for n = 21 (yellow), 13 (green), and 7 (black), and the three contour plots of total pressure pt/pt,o for Cq/jet ≈ 0.0003 and n = 21 (c), 13 (d), and 7 (e). Contour levels are the same as in Fig. 8. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 128

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Fig. 13. Total pressure distortion parameter DPCPavg with Mach number for the controlled flow at MAIP = 0.7, by n = 21 (●), 19 (▲), 17 (■), 15 (+), 13 (×), 11 (▾), 9 (♦), and 7 (−) active jets.

number in the facility Mo can vary due to the interactions of the jet array with the cross flow. Fig. 13 therefore shows the variation of DPCPavg in the presence of actuation with the normalized deviation from the base flow Mach number ΔMAIP /Mo (Mo = 0.7) for different jet subsets. Again, there is a clear unified trend for all the data and varying n. Initially, there is a sharp decrease in distortion (top right), associated with weakly positive or neutral effect on MAIP, as the total Cq begins to increase from zero. As saturation is reached (middle right), the jets also reach maximum effectiveness, and further increases in Cq result in increased losses, manifested as a decrease in MAIP. These compound data further show that a reduction of about two-thirds in the distortion of the base flow (DPCPavg,o) can be attained with about half the number of active jets of the full array, at just a third of the actuation flow rate (compared to the full array control) and negligible change in Mach number ΔMAIP/Mo = −0.2%. Based on the aforementioned criteria, the two most effective arrays are determined to be n = 11 and 13. Further insight into the effectiveness of n = 11 and 13 configurations is gained by examination of a broader range of the distortion

parameters and recovery of the diffuser flow. A subset of this comparison is shown in Fig. 14, where evolutions of the three distortion parameters (DPCPavg, DPCPh and DPCPt) and recovery with Cq are shown for the two best cases (n = 11 and 13), and the full array for reference. These data show that the actuation significantly reduces all the three circumferential distortion measures. Perhaps the most striking feature of the effect of reducing the number of jets in the array is that it significantly enhances the receptivity of the base flow to the actuation. Actuation with the reduced number of jets leads to a sharp suppression in all distortion parameters, even at the lowest levels of Cq compared to the full actuation array. More importantly, however, is the demonstration that the most effective flow control configuration (n = 13) that yields a reduction in DPCPavg of about 68%, utilizes nearly half the number of active jets and almost a third of the actuation flow rate (Cq down from about 0.7% for the full array to about 0.25% for n = 13). This study clearly indicates that there is no sharp cutoff in the optimal performance of the flow control sub-arrays, while still pointing out that among the tested cases, n = 13 can be selected as the best candidate for Fig. 14. Total pressure distortion parameter DPCPavg (a), DPCPt (b), DPCPh (d) and recovery (c) at MAIP = 0.7 with the control parameter Cq for the flow control configurations with n = 21 (yellow), 13 (green), and 11 (blue) active jets. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 16. Circumferential distortion for each of the AIP rake rings for the measured (solid) and CFD (dashed) baseline (●) and controlled (■) flows (M = 0.63, Cq = 0.75%).

Fig. 15. Average circumferential distortion DPCPavg and the corresponding contour plots of the total pressure with Cq for the optimal n = 13 jets configuration.

CFD simulations of the baseline flow and optimally controlled (n = 13, Cq = 0.25%) flow are utilized to understand the underlying changes in flow dynamics that result in reduced distortion. First, Fig. 17 examines instantaneous flow structures about and immediately downstream of the flow control source, located just upstream of the surface depression, without (Figs. 17a and b) and with (Figs. 17c and d) flow control. Flow separation over the depressed surface, from the centerline to the sidewall, is depicted in Fig. 17 using an iso-surface of q-criteria colored by Mach number. In all the plots, only one half of the flow field is shown to illustrate the wall-normal variations in turbulent eddies. Figs. 17a and c are shown in isometric views, oriented from the centerline to the sidewall, with flow from upper left to lower right, while Figs. 17b and d are top-down views with flow from left to right. Flowcontrol orifices are visible in the upstream row, particularly in the top views. Note that all twenty-one actuators are embedded in the surface, but only the central thirteen of them are active during the flow-control activation. For the base flow (Figs. 17a and b), as the main flow separates off the leading edge of the depression, the resulting shear layer evolves into pockets of identifiable large-scale turbulent eddies, which appear fairly uniformly distributed across the diffuser span. Underneath the shear layer, separated flow forms a slowly-recirculating bubble (in the mean sense), which is somewhat featureless in the instantaneous view. There are several important features of the instantaneous controlled flow, as depicted in Figs. 17c and d. First, as the flow control is activated through the central jets, all active jet orifices indicate intense small-scale vortical motions being issued into the bulk flow. As a result, lower left side of the flow in Fig. 17c and bottom portion of the flow in Fig. 17d exhibit trains of small-scale eddies that appear to quickly interact and presumably disrupt large-scale eddy formation and dynamics through enhanced mixing, production and dissipation of turbulent kinetic energy (Vukasinovic et al., 2010). This region of the flow immediately downstream from the jets appears to be divided into two regions: a central region that is affected by the flow control actuation, and a side region that initially begins to evolve in a similar fashion as in the base flow, exhibiting similar flow structure of the evolving shear layer. The second important feature of the controlled flow is seen when comparing the recirculating zones in Figs. 17a (base) and c (controlled). Although there is apparently some effect on the earlier flow reattachment on the downstream side of the bubble in the controlled flow, the initial increased mixing in the controlled shear layer spreads it immediately downward towards the lower surface, and the whole subsequent shear layer appears to be better ‘aligned’ with the bulk downward flow in the diffuser. Consequently, the recirculating bubble does not only become shortened due to the earlier reattachment, but also compressed towards the wall, which allows for more streamlined flow

optimized effectiveness. Furthermore, the present study indicates that more effective actuation configurations can be sought and optimized in both n and Cq, as a balance between n and Cq is shown to be the most critical for optimized performance. It is believed that the present findings also have broader implications on optimization of flow control effectiveness, in particular for internal flows, where both total-pressure distortion and recovery need to be considered simultaneously. A more detailed look at AIP total-pressure distortion for the selected flow-control configuration, n = 13, is shown in Fig. 15. Although it is expected that all controlled cases would result in total-pressure contours symmetric about the vertical plane of symmetry, some asymmetries are observed, which are attributed to the geometrical imperfections in the actuators’ manufactured geometry. Nevertheless, the results clearly indicate that DPCPavg decreases with Cq as the lower-centerline losses are pushed towards the wall and up, in a thin near-wall layer. This trend breaks down when the lower-centerline losses are completely spread around the AIP Cq = 0.25%. Beyond this, further increases in Cq continue to increase total pressure about the central zone, also pushing the two halves of low-momentum fluid farther outward near the wall. These two effects oppose each other, resulting in a negligible reduction in distortion. This is a reason that the optimum Cq for this flow configuration is attained near Cq = 0.25%. It is possible that greater flowcontrol effectiveness could be realized through further optimization efforts, involving considerations such as jet placement along the sidewall surface. Besides examining integral measures that quantify area-averaged distortion at the AIP, such as circumferential (DPCP) and radial (DPRP) descriptors, it is illustrative to assess circumferential distortion for each of the five rings on the AIP rake(DPCPRi), as shown in Fig. 16, where rings #1 and #5 are the innermost (hub) and outermost (tip) circumferential arrays of probes. These data show that experiment and CFD are in reasonable agreement, and that actuation reduces distortion by factors of 2–3 over the entire AIP. It is noted that for the base flow, the simulations over-predict the measured DPCPRi over rings #2 and #3 and slightly under-predict the measured DPCPRi for rings #1 and #5. In the presence of AFC, agreement between the simulations and the measurements appears to improve with slight under- and over-predictions of the measured data for rings #2 and #4, respectively. Other integral distortion measures include, for example, hub and tip distortions (the averages of rings #1 and 2, and of rings #4 and 5), and equivalent measures can be computed for the radial distortion. The present simulations and measurements of total-pressure distributions over the AIP corroborate the favorable effects of applying flow control. 130

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Fig. 17. Simulated baseline (a,b) and controlled (d,e) flow isosurfaces of Q-criterion colored by Mach number for MAIP = 0.7 and Cq = 0.25%. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 18. Experimental (a,c) and numerical (b,d) surface-oil-flow visualization over the flow control insert for the MAIP = 0.7 baseline (a,b) and the flow controlled by the central n = 13 jets at Cq = 0.25%.

reattachment. Assessment of the flow control effect over the surface depression is further assisted by experimental surface oil-flow visualization for elucidation of local and global flow topology within the diffuser and, in particular, downstream from the flow control jets. Oil for visualization is made out of a mixture of linseed oil and titanium-dioxide paint, where a balance between the two was determined iteratively, yielding a viscosity that matches the Mach number range and responds to the shear at the diffuser operating condition. Insight into the base and controlled flow topologies is gained by utilizing surface oil-flow

visualization over the flow control insert, where the oil is applied from just downstream from the jets array to the downstream end of the flow control insert. As an illustration of the flow-control effect, two traces are shown in Fig. 18 for MAIP = 0.7, where the flow direction is from bottom to top. Fig. 18a indicates the base flow topology, which is dominated by two reattachment domains separated by a central saddle point, each having a node close to the sidewall, as marked on the image. It is argued that corner/end effects of the D-shaped diffuser inlet geometry induce local corner-flow reattachment at the nodes, which in turn forces flow symmetry about the central plane through the saddle 131

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point. This reattachment dynamic also indicates highly three-dimensional flow in the separation bubble, and points to the near-wall flow directionality towards the central plane. The CFD counterpart of the base-flow oil visualization is also shown in Fig. 18b and exhibits some subtle differences in the exact nodal positions, but good overall agreement with the wind-tunnel data. The experimental and numerical flow topologies for the controlled (n = 13, Cq = 0.25%) flow are shown in Figs. 18c and d, respectively. As it can be expected from analysis of Fig. 17, the jets’ effect is reflected in the reduction of the reattachment length of the separated flow. More importantly, the reattaching flow topology becomes completely altered from the base flow. In addition to the corner reattachment nodes, a central node forms due to the jetforced flow attachment. Furthermore, having the two nodal streams colliding on each half of the flow creates the two saddle points that bound a large central region of the reattaching flow, occupying about 2/3 of the span. Just as the colliding streams about the central saddle point in the base flow (Fig. 18a) induce a pair of streamwise vortices (cf. Fig. 7) that are responsible for the large central zone of the flow distortion (cf., Fig. 5b), the altered flow topology in Fig. 18b suggests that such a central source of distortion would be suppressed under the flow control imposed by the central active jets. After assessing the ‘local’ flow control effect immediately downstream from the flow control source, a broader look at its global effects is sought through examination of the full simulated diffuser flow fields, with and without the optimal flow control. Instantaneous and timeaveraged contours of the predicted streamwise velocity on the center plane between the throat and AIP are shown in Figs. 19a and c, and Figs. 19b and d, respectively. Base flow is shown in Figs. 19a and b, while Figs. 19c and d depict the controlled flow. Following separation, a thick region of momentum deficit is formed along the bottom wall in the base flow, and it persists downstream all the way to the AIP. Even as the flow reattaches past the surface depression, the velocity deficit is created and no recovery in the base flow is facilitated prior to the AIP. The base flow (Fig. 19b) reaches the AIP with a considerable velocity deficit that extends off the wall to nearly the core of the duct. As already seen in the near field of Fig. 17, earlier reattachment of the separated flow is also associated with increased vectoring of the shear layer and its ‘alignment’ with the diffuser wall, which leads to significant suppression of the velocity deficit in the mean sense, as seen in Fig. 19d. In

an instantaneous sense, even with the flow control active, there are unsteady pockets of lower momentum fluid that continue to convect along the lower diffuser wall, as can be seen in a snapshot in Fig. 19c. The flow fields in Figs. 19c and d suggest that the separated flow becomes fully attached at the downstream end of the flow control insert when the diffuser flow is controlled, and a very small residual momentum deficit convects to the AIP. This earlier shear-layer reattachment also results in the observed near-wall flow acceleration at the end of the recessed surface (Fig. 19d). In addition, there is global increase in the velocity magnitude across the whole flow field in the controlled flow relative to the baseline. Vorticity fields corresponding to the flow fields shown in Fig. 19 are presented in Fig. 20 in terms of instantaneous q-criterion iso-surfaces. The q-criterion for the base flow (Fig. 20a) shows strong vorticity formation across the full span, once the flow separates over the surface depression, which is associated with the resulting shear layer. However, once the flow reattaches, the turbulent eddies remain dense about the centerline of the diffuser, which is attributed to the formation of the pair of counter-rotating streamwise vortices, and along the corners, due to the roll-up of the corner vortices. There is a clear separation between the two clusters of vorticity, with the central one being dominant. Although the jets serve as vorticity sources themselves, their small-scale mixing and dissipative action on the base large-scale vortical structures act to greatly reduce the presence of turbulent eddies in the controlled flow, along the central path (Fig. 20b). As already discussed in conjunction with Fig. 17, there is a distinct interaction region between the jets and the shear layer immediately downstream from the jet orifices. Moreover, once the flow reattaches, the central region of the diffuser becomes nearly void of turbulent eddies that were dominant in the base flow. In addition to suppression of turbulent eddies in the central zone, flow control appears to induce a greater number of eddies on the sidewalls (Fig. 20b), which presumably originates from the two saddle points created upon the controlled-flow reattachment (cf., Fig. 18). Hence, the flow control effect on the vorticity field can be seen in diminishing the large-scale vortices along the centerline of the base flow, while introducing a distribution of smaller vortices at outboard locations, which eventually mix with the corner vortices and presumably dissipate their coherence.

Fig. 19. Central-plane contours of the simulated baseline (a,b) at MAIP = 0.7 and the flow controlled by the central n = 13 jets at Cq = 0.25% (c,d): instantaneous (a,c) and time-averaged (b,d) contour plots of the streamwise velocity component U.

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Fig. 20. Simulated baseline (a) and controlled (b) flow iso-surfaces of Q-criterion for MAIP = 0.7 and Cq = 0.25%, colored by Mach number. Active jets are marked by red arrows. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 21. Simulated baseline (a,b) and controlled (d,e) flow helicity and AIP total-pressure contours, respectively, and the experimental baseline (c) and controlled (f) AIP total-pressure contours for MAIP = 0.7, and n = 13 and Cq = 0.25%.

6. Topology of streamwise vorticity concentrations

each corner (CCW on the left and CW on the right) intensifies somewhat. The result at the AIP is that the distortion caused by upwelling at the center subsides and there is a small increase in pressure deficit caused by upwelling of low-momentum fluid from each corner of the diffuser (Figs. 21e and f, note that the deficit is a bit stronger in the simulations). It is noted that this control can be further optimized to diminish this effect as well. These flow structures can be connected to the topology at the local reattachment in the presence of fluidic actuation. As the two colliding saddle points are formed closer to the sidewalls in the presence of actuation (Figs. 21c and d), two strong sources of vorticity originate along these two sides in Fig. 21d. Furthermore, ‘smooth’ flow reattachment over the center of the diffuser prevents formation of the central pair of counter-rotating streamwise vortices leading to nearly complete suppression of helicity about the centerplane. It is noted that the AIP simulations and measurements are in good agreement and the respective recovery and DPCPavg in the presence of actuation are 0.971 and 0.015 (measurements) and 0.970 and 0.014 (simulations). Although no time-resolved measurements are conducted in the present investigation, some insight into the base and controlled-flow unsteadiness is gained by the RMS of simulated totalpressure fluctuations. From these time-accurate simulations it is observed that the dominant flow unsteadiness of the base flow about the central-vortex pair is suppressed by flow control, but flow unsteadiness along the walls is amplified. As an overall measure, the spatial peak of the RMS total-pressure fluctuation decreases by about 10%, while the spatial-averaged RMS total-pressure fluctuation increases by about 15%, predominantly focused along the lower surface, in accord with the vortex signatures seen in Figs. 21d and e.

The underlying flow dynamics that give rise to flow distortion within the diffuser are illustrated in Fig. 21 for the base and controlled (Cq = 0.25%) flows using 3-D concentrations of the streamwise vorticity. Helicity surfaces that are extracted from the CFD simulations are shown in an isometric view, extending from the onset of the separation domain downstream to the AIP (represented by an oval) in both the base and controlled flows (Figs. 21a and b, respectively). The corresponding simulated and measured total-pressure distributions are shown in Figs. 21b and e, and Figs. 21c and f, respectively. The helicity surfaces in the base flow (Fig. 21a) show the formation of two streamwise vorticity concentrations symmetrically about each side of the centerplane of the diffuser. These vortices originate from the separated-flow domain at the turn of the diffuser. On each side of the centerplane there is a weak counter-rotating vortex pair that forms near the corner of the diffuser. It is noteworthy that on each side, one of the counter-rotating concentrations is more pronounced (CW on the left and CCW on the right). More importantly, a strong central counterrotating vortex pair that originates from the separation domain gives rise to upwelling of low momentum fluid at the center of the AIP (Figs. 21b and c). It appears that the stronger, single sense vortex at each corner is affected by the neighboring central vortex. It is argued that these streamwise vortices originate at the point where the two streams collide about the saddle reattachment (Figs. 18a and b). In the presence of actuation, the central vortices are greatly weakened and effectively disappear at the center of flow at the AIP. Simultaneously, the stronger of the two counter-rotating vortices in 133

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7. Conclusions

References

The performance of aggressive diffusers designed for use in advanced supersonic propulsion systems is hampered by internal-flow separation coupled with secondary-flow vortices which give rise to severe flow distortion at the AIP. Vorticity concentrations trapped within confined separated flow domains are susceptible to flow actuation, which provides a mechanism by which to apply flow control and improve diffuser performance. The present investigation focused on developing novel flow-control techniques for minimizing flow losses, distortion, and angularity in a diffuser with fundamental physics elements relevant to aircraft diffusers. Although primarily conducted as a proof of concept study, the demonstrated advances may be viable for improving engine operability, cruise efficiency, and maneuverability of next-generation aircraft. The present work showed that hybrid flow control, which targets the coupling between boundary-layer separation and secondary-flow vortices, can significantly diminish the inherent flow distortion and losses. Control of streamwise vortices is achieved by suppressing boundary-layer separation using surface-integrated fluidic actuation to manipulate concentrations of trapped vorticity within the separation. Trapped vorticity was engendered by a recess in the diffuser surface and was controlled using a spanwise array of surface-integrated fluidic-oscillating jets. The local and global characteristics of the diffuser flow in the absence and presence of the actuation were investigated up to MAIP = 0.7, using experimental diagnostics (a forty-probe AIP total pressure rake, surface oil-flow visualization, hot-wire anemometry), and numerical prediction tools. The measurements coupled with CFD simulations demonstrated that actuation controls the strength, scale, and structural topology of trapped vorticity within the surface recess, and consequently its interactions with the cross flow. These interactions were leveraged to control separation and weaken secondary flow within the diffuser, which led to reduced upwash of the low-momentum fluid and total-pressure distortion at the AIP. It was shown that the effectiveness of fluidic actuation increases with AIP Mach number, reaching about 80% reduction in distortion at MAIP = 0.7 at jet mass flow rate ratio Cq of less than 0.7%. Another important finding of the present investigations is that conformation of the jet array to the base flow structure significantly enhances the receptivity of the base flow to actuation. Thus, further improvement of the flow control application was sought by tuning the interaction between the jet array and the trapped vorticity with targeted jet placement. It was shown that a reduction of about 67% in the distortion of the base flow (DPCPavg,o) can be attained with half the number of active jets at almost a third of the actuation flow rate (equivalent to Cq reduction to about 0.25% from 0.7%). This study clearly indicates that more effective actuation configurations can be sought and optimized, and it is anticipated that CFD will play a crucial role in such optimizations. CFD results were validated by adequately predicting the face-averaged total-pressure recovery and steady-state distortion measured in experiments. These simulations resolve the flow field of the fluidic oscillators and their interaction with the trapped vortex and the separated shear layer and shed light on the physical mechanisms of these interactions and their coupling to the global flow and the effects at the AIP. The combined numerical experimental investigations also demonstrated the utility of a simplified fluidic oscillator model (without internal feedback loops) that mimics the effects of the physical actuator under high-pressure operation.

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Acknowledgment This work has been supported by ONR (Grant number: N00014-141-00142017), monitored by Dr. Knox Millsaps.

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