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In this paper, we study the shape and dynamics of helical coherent structures found in the flow field of an annular swirling jet undergoing vortex breakdown. The flow field is studied by means of time-resolved tomographic particle image velocimetry measurements. The obtained flow fields are analysed using both classic and spectral proper orthogonal decomposition. Despite the simple geometrical set-up of the annular jet, the flow field is very complex. Two distinct large-scale helical flow structures are identified: a single and a double helix, both co-rotating with the swirl direction, and it is revealed that these structures are not higher harmonics of each other. The structures have a relatively low energy content which makes it hard to separate them from other dynamics of the flow field, notably turbulent motions. Because of this, classic proper orthogonal decomposition fails to identify both structures properly. Spectral proper orthogonal decomposition, on the other hand, allows them to be identified accurately when the filter size is set at around eight times the precession period. The precession frequencies of the single and double helices correspond to Strouhal numbers of 0.273 and$0.536\\pm 0.005$, respectively. A global stability analysis of the mean flow field shows that these structures correspond to two separate global modes. The precessing frequencies obtained by the stability analysis and the related spatial structures match very well with the experimental observations. The current work extends our knowledge on turbulent vortex breakdown and on mean field global stability theory in general. It leads to the following conclusions. Firstly, single- and double-helix vortex breakdown are both manifestations of global modes. Previous studies have shown that both$m=1$and$m=2$modes can coexist in swirling jets. However, the$m=2$mode has been identified as a second harmonic of the first mode, while this study identifies both as two independent global modes. Secondly, this work shows that the simultaneous occurrence of multiple helical global modes is possible within a turbulent flow and their shapes and frequencies are very well predicted by mean field stability analysis. The latter finding is of general interest as it applies to a wide class of fluid problems dominated by multiple oscillatory structures.

The low-frequency unsteady motions behind a backward-facing step (BFS) in a turbulent flow at $Ma=1.7$ and $Re_\\infty =1.3718\\times 10^7 \\ {\\rm m}^{-1}$ are investigated using a well-resolved large-eddy simulation. The instantaneous flow field illustrates the unsteady phenomena of the shock wave/boundary layer interaction (SWBLI) system, including vortex shedding in the shear layer, the flapping motions of the shock and breathing of the separation bubble, streamwise streaks near the wall and arc-shaped vortices in the turbulent boundary layer downstream of the separation bubble. A spectral analysis reveals that the low-frequency behaviour of the system is related to the interaction between shock wave and separated shear layer, while the medium-frequency motions are associated with the shedding of shear layer vortices. Using a three-dimensional dynamic mode decomposition (DMD), we analyse the individual contributions of selected modes to the unsteadiness of the shock and streamwise-elongated vortices around the reattachment region. Görtler-like vortices, which are induced by the centrifugal forces originating from the strong curvature of the streamlines in the reattachment region, are strongly correlated with the low-frequency unsteadiness in the current BFS case. Our DMD analysis and the comparison with an identical but laminar case provide evidence that these unsteady Görtler-like vortices are affected by fluctuations in the incoming boundary layer. Compared with SWBLI in flat plate and ramp configurations, we observe a slightly higher non-dimensional frequency (based on the separation length) of the low-frequency mode.

The flow over a forward-facing step (FFS) at $Ma_\\infty =1.7$ and $Re_{\\delta _0}=1.3718\\times 10^{4}$ is investigated by well-resolved large-eddy simulation. To investigate effects of upstream flow structures and turbulence on the low-frequency dynamics of the shock wave/boundary layer interaction (SWBLI), two cases are considered: one with a laminar inflow and one with a turbulent inflow. The laminar inflow case shows signs of a rapid transition to turbulence upstream of the step, as inferred from the streamwise variation of $\\langle C_f \\rangle$ and the evolution of the coherent vortical structures. Nevertheless, the separation length is more than twice as large for the laminar inflow case, and the coalescence of compression waves into a separation shock is observed only for the fully turbulent inflow case. The dynamics at low and medium frequencies is characterized by a spectral analysis, where the lower frequency range is related to the unsteady separation region, and the intermediate one is associated with the shedding of shear layer vortices. For the turbulent inflow case, we furthermore use a three-dimensional dynamic mode decomposition to analyse the individual contributions of selected modes to the unsteadiness of the SWBLI. The separation shock and Görtler-like vortices, which are induced by the centrifugal forces in the separation region, are strongly correlated with the low-frequency unsteadiness in the current FFS case. Similarly as observed previously for the backward-facing steps, we observe a slightly higher non-dimensional frequency (based on the separation length) of the low-frequency mode than for SWBLI in flat plate and ramp configurations.

Flow visualisations are essential to better understand the unsteady aerodynamics of flapping wing flight. The issues inherent to animal experiments, such as poor controllability and unnatural flapping when tethered, can be avoided by using robotic flyers that promise for a more systematic and repeatable methodology. Here, we present a new flapping-wing micro air vehicle (FWMAV)-specific control approach that, by employing an external motion tracking system, achieved autonomous wind tunnel flight with a maximum root-mean-square position error of 28 mm at low speeds (0.8–1.2 m/s) and 75 mm at high speeds (2–2.4 m/s). This allowed the first free-flight flow visualisation experiments to be conducted with an FWMAV. Time-resolved stereoscopic particle image velocimetry was used to reconstruct the three-dimensional flow patterns of the FWMAV wake. A good qualitative match was found in comparison to a tethered configuration at similar conditions, suggesting that the obtained free-flight measurements are reliable and meaningful.

In this paper the configurations of shock wave–boundary layer interactions (SWBLI) are studied theoretically and experimentally in Mach number 2 and 2.5 flows on test models with various wedge angles ranging from $9^\\circ$ to $21^\\circ$. The proposed theoretical method couples the free interaction theory (FIT) with the minimum entropy production (MEP) principle to predict the appearance of separation shock, resulting in convex, straight and concave separation shock waves according to different solution combinations, which agree well with current experiments. Additionally, several influences on SWBLI are studied experimentally, in which the parameters related to theoretical solutions are found mostly determining the flow configuration, and SWBLI is much more sensitive to incident shock strength than incoming flow properties. Separation could be suppressed by incident shock when the MEP solution is smaller than the FIT, while it could be intensified when the MEP solution is larger than FIT; by contrast, the effects of separation position and model mounting height could be very weak.

To generate aerodynamic forces required for flight, two-winged insects (Diptera) move their wings back and forth at high wing-beat frequencies. This results in exceptionally high wing-stroke accelerations, and consequently relatively high acceleration-dependent fluid forces. Quasi-steady fluid force models have reasonable success in relating the generated aerodynamic forces to the instantaneous wing motion kinematics. However, existing approaches model the stroke-rate and stroke-acceleration effects independently from each other, which might be too simplified for capturing the complex unsteady aerodynamics of accelerating wings. Here, we use computational-fluid-dynamics simulations to systematically explore how aerodynamic forces and flow dynamics depend on wing-stroke rate, wing-stroke acceleration and wing-planform geometry. Based on this, we developed and calibrated a novel unsteady aerodynamic force model for insect wings with stroke accelerations. This includes improved versions of the translational-force model and the added-mass force model, and we identify a third novel component generated by the interaction of the two. This term reflects the delay in bound-circulation build-up as the wing accelerates. The physical interpretation of this effect is analogous to the Wagner effect experienced by a wing starting from rest. Here, we show that this effect can be modelled in the context of flapping wings as a stroke-acceleration-dependent correction on the translational-force model. Our revised added-mass model includes a viscous force component, which is relatively small but not negligible. We subsequently applied our new model to realistic wing-beat kinematics of hovering Dipteran insects, in a quasi-steady approach. This revealed that stroke-acceleration-related aerodynamic forces contribute substantially to lift and drag production, particularly for high-frequency flapping mosquito wings.

Particle image velocimetry measurements and simultaneous force measurements have been performed on the DelFly II flapping-wing MAV, to investigate the flow-field behavior and the aerodynamic forces generated. For flapping wing motion it is expected that both the clap and peel mechanism and the occurrence of a leading edge vortex during the translational phase play an important role in unsteady lift generation. Furthermore, the flexibility of the wing foil is also considered of primary relevance. The PIV analysis shows a strong influx between the wings during the peel but no downward expelling jet during the clap. The force measurements reveal that the peel, oppositely to the clap, contributes significantly to the lift. The PIV visualization suggests the occurrence of a leading edge vortex during the first half of the in- and outstroke, which is supported by a simultaneous augmentation in lift. The early generation of a leading edge vortex during the flex cannot be assessed from the PIV images due to optical obstruction, but is likely to appear since the wing flexing is accompanied with a large increase in lift.

The low-frequency unsteady motions behind a backward-facing step (BFS) in a turbulent flow at \\(Ma=1.7\\) and \\(Re_\\infty=1.3718\\times 10^5\\) is investigated using a well-resolved large-eddy simulation (LES). The instantaneous flow field illustrates the unsteady phenomena of the shock wave/boundary layer interaction (SWBLI) system, including vortex shedding in the shear layer, the flapping motions of the shock and breathing of the separation bubble, streamwise streaks near the wall and arc-shaped vortices in the turbulent boundary layer downstream of the separation bubble. A spectral analysis reveals that the low-frequency behaviour of the system is related to the interaction between shock wave and separated shear layer, while the medium-frequency motions are associated with the shedding of shear layer vortices. Using a three-dimensional dynamic mode decomposition (DMD), we analyse the individual contributions of selected modes to the unsteadiness of the shock and streamwise-elongated vortices around the reattachment region. G\"ortler-like vortices, which are induced by the centrifugal forces originating from the strong curvature of the streamlines in the reattachment region, are strongly correlated with the low-frequency unsteadiness in the current BFS case. Our DMD analysis and the comparison with an identical but laminar case provide evidence that these unsteady G\"ortler-like vortices are affected by fluctuations in the incoming boundary layer. Compared to SWBLI in flat plate and ramp configurations, we observe a slightly higher non-dimensional frequency (based on the separation length) of the low-frequency mode.

We present an experimental realisation of spatial spanwise forcing in a turbulent boundary layer flow, aimed at reducing the frictional drag. The forcing is achieved by a series of spanwise running belts, running in alternating spanwise direction, thereby generating a steady spatial square-wave forcing. SPIV in the streamwise-wall-normal plane is used to investigate the impact of actuation on the flow in terms of turbulence statistics, drag performance characteristics, and spanwise velocity profiles, for a non-dimensional wavelength of \\(\\lambda_x^+ = 397\\). We confirm that a significant flow control effect can be realised with this type of forcing. The scalar fields of the higher-order turbulence statistics show a strong attenuation of stresses and production of turbulence kinetic energy over the first belt already, followed by a more gradual decrease to a steady-state energy response over the second belt. The streamwise velocity in the near-wall region is reduced, indicative of a drag-reduced flow state. The profiles of the higher-order turbulence statistics are attenuated up to a wall-normal height of \\(y^+ \\approx 100\\), with a maximum streamwise stress reduction of 45% and a reduction of integral turbulence kinetic energy production of 39%, for a non-dimensional actuation amplitude of \\(A^+ = 12.7\\). An extension of the classical laminar Stokes layer theory is introduced, to describe the non-sinusoidal boundary condition that corresponds to the current case. The spanwise velocity profiles show good agreement with this extended theoretical model. The drag reduction was estimated from a linear fit in the viscous sublayer in the range \\(2 \\leq y^+\\leq 5\\). The results are found to be in good qualitative agreement with the numerical implementations of Viotti et al. (2009), matching the drag reduction trend with \\(A^+\\), and reaching a maximum of 20%.