A benchmark road vehicle geometry – the square-back Windsor body with wheels and at zero yaw angle – is simulated using high-fidelity wall-resolved large eddy simulation. Passive control for drag reduction, in the form of optimisation of its rear roof extension, is performed. The rear roof extension is parameterised by its taper penetration distance, angle of incidence and length. This optimisation process uses Gaussian process-based surrogate modelling combined with Bayesian optimisation (Kriging), guided by an expected improvement criterion. The optimisation converged in six iterations (60 simulations), achieving a $6.5\,\%$ drag reduction. Six distinct drag-reduction mechanisms were identified: diffuser-induced pressure recovery, base-size reduction, vertical wake balance modification, separation effects, recirculation region core relocation and spanwise re-symmetrisation. Rather than isolating individual mechanisms, the study reveals how they interact when multiple geometric parameters are varied concurrently, providing a system-level picture that yields practical design rules. The optimal configuration was found at a roof extension angle of incidence corresponding to the onset of separation, with taper penetration distance and extension length at their maximum values within the analysed domain. These findings establish a robust framework for aerodynamic optimisation and reinforce the effectiveness of Bayesian optimisation in Computational Fluid Dynamics-based design. In this way, the work bridges fundamental wake studies with applied design practice, showing how coupled wake–geometry interactions can be harnessed for improved aerodynamic performance.

We investigate the control effects of spanwise heterogeneous roughness on shock-wave/turbulent boundary-layer interactions (STBLIs) using wall-resolved large-eddy simulations. The roughness extends over the entire computational domain and consists of streamwise-aligned sinusoidal ridges alternating with flat valleys. The baseline case is a Mach 2.0 impinging STBLI flow with a 40$^\circ$ impinging-shock angle, for which we consider incoming turbulent boundary layers at two friction Reynolds numbers, $Re_\tau \approx$ 350 and 1200. Multiple roughness configurations are analysed, which maintain consistent geometric characteristics under either inner or outer scaling. The results show that the rough-wall configurations introduce a moderate increase in mean drag, while substantially modifying the dynamics of the interaction. The wall-pressure fluctuations near the separation-shock foot consist of two components: low-frequency fluctuations associated with large-scale shock excursions and high-frequency fluctuations linked to amplified turbulence. We find that both spectral components can be significantly attenuated by the investigated wall roughness. At low Reynolds number, the attenuation of low- and high-frequency components contributes comparably to the overall reduction. At high Reynolds number, an overall stronger reduction of the pressure fluctuation peak is observed and is mainly attributed to the effective suppression of the low-frequency component. Cross-correlation analyses support downstream mechanisms for the low-frequency dynamics in the current strong interaction regime, where large-scale shock excursions are mainly driven by the breathing of the reverse-flow bubble. Large-scale Görtler-like vortices are identified around the reattachment location in all cases. They appear largely unaffected by roughness geometry and contribute to the flow dynamics over a wide range of frequencies.

The present study experimentally investigates the onset of ventilation of surface-piercing hydrofoils. Under steady-state conditions, the depth-based Froude number $\textit{Fr}$ and the angle of attack $\alpha$ define regions in which distinct flow regimes are either locally or globally stable. To map the boundary between these stability regions, the parameter space $(\alpha , \textit{Fr})$ was systematically surveyed by increasing $\alpha$ until the onset of ventilation while maintaining a constant $\textit{Fr}$. Two simplified model hydrofoils were examined: a semi-ogive with a blunt trailing edge and a modified NACA 0010-34. Tests were conducted in a towing tank under quasi-steady-state conditions for aspect ratios of $1.0$ and $1.5$, and for $\textit{Fr}$ ranging from $0.5$ to $2.5$. Ventilation occurred spontaneously for all test conditions as $\alpha$ increased. Three distinct trigger mechanisms were identified: nose, tail and base ventilation. Nose ventilation is prevalent at $\textit{Fr} \lt 1.0$ and $\textit{Fr} \lt 1.25$ for aspect ratios of $1.0$ and $1.5$, respectively, and is associated with an increase in the inception angle of attack. Tail ventilation becomes prevalent at higher $\textit{Fr}$, and the inception angle of attack exhibits a negative trend. Base ventilation was only observed for the semi-ogive profile, but it did not lead to the development of a stable ventilated cavity. Notably, the measurements indicate that the boundary between bistable and globally stable regions is not uniform and extends to significantly higher $\alpha$ than previously estimated. A revised stability map is proposed to reconcile previously published and current data, demonstrating how two alternative paths to a steady-state condition can lead to different flow regimes.

In many electrochemical systems, variations in fluid density due to salinity gradients are unavoidable, leading to solutally driven Rayleigh–Bénard convection (RBC). In this study, we perform direct numerical simulations and theoretical analyses of two-dimensional solutal convection near perfectly cation-selective membranes by incorporating buoyancy and electrostatic forces into the Navier–Stokes and Poisson–Nernst–Planck equations. When electroconvection (EC) is negligible, we observe a flow reversal of large-scale circulation (LSC) in salt-driven RBC within a square-cavity electrochemical system, triggered by the periodic reconfiguration of corner vortices. Furthermore, we found that the competition between RBC and EC determines the dominant flow pattern. The buoyancy-driven convection and the LSC are suppressed at sufficiently strong EC flow, leading to a transition from buoyancy-driven flow to electrically driven flow. Consequently, the flow structures into a pair of EC vortices, driven by strong electric field forces within the extended space charge layer. Using Grossmann–Lohse theory, we derive a critical scaling law that describes the flow pattern selection, governed by the combined effects of the Rayleigh number, voltage difference and hydrodynamic coupling coefficient. Our work presents a novel approach to controlling flow patterns, distinct from existing strategies in thermally driven RBC.

We integrate a discrete vortex method (DVM) with complex network analysis to strategise dynamic stall mitigation over aerofoils with active flow control. The objective is to inform the actuator placement and the timing to introduce control inputs during the highly transient process of dynamic stall. To this end, we treat a massively separated flow as a network of discrete vortical elements and quantify the interactions among the vortical nodes by tracking the spread of displacement perturbations between each pair of vortical elements using a DVM. This allows us to perform network broadcast mode analysis to identify an optimal set of discrete vortices, the critical timing and the direction to seed perturbations as control inputs. Motivated by the objective of dynamic stall mitigation, the optimality is defined as maximising the reduction of total circulation of the free vortices generated from the leading edge over a prescribed time horizon. We demonstrate the use of the analysis on a two-dimensional flow over a flat plate aerofoil and a three-dimensional turbulent flow over an SD$7003$ aerofoil. The results from the network analysis reveal that the optimal timing for introducing disturbances occurs slightly after the onset of flow separation, before the shear layer rolls up and forms the core of the dynamic stall vortex. The broadcast modes also show that the vortical nodes along the shear layer are optimal for introducing disturbances, hence providing guidance to actuator placement. Leveraging these insights, we perform nonlinear simulations of controlled flows by introducing flow actuation that targets the shear layer slightly after the separation onset. We observe that the network-guided control results in a $21 \,\%$ and $14\,\%$ reduction in peak lift for flows over the flat plate and SD$7003$ aerofoil, respectively. A corresponding decrease in vorticity injection from the aerofoil surface under the influence of control is observed from simulations, which aligns with the objective of the network broadcast analysis. The study highlights the potential of integrating the DVMs with the network analysis to design an effective active flow control strategy for unsteady aerodynamics.

Jet vortex generators (JVGs) are a promising technique for controlling laminar separation in low-Reynolds-number aerofoils, such as those used in micro air vehicles (MAVs). While previous studies have demonstrated their aerodynamic benefits, the three-dimensional structure of the vortices they generate and their interaction with the boundary layer remain poorly characterised experimentally. In this study, volumetric velocity measurements are performed using the double-pulse Shake-the-Box (STB) technique on an SD7003 aerofoil equipped with skewed and pitched JVGs. Experiments are conducted at Reynolds numbers of 30 000 and 80 000, for angles of attack of 8$^{\circ}$, 10$^{\circ}$ and 14$^{\circ}$. The results provide the first experimental visualisation of the full three-dimensional vortex topology induced by JVGs, revealing asymmetric streamwise vortices that penetrate the separated shear layer and re-energise the near-wall region. In pre-stall conditions, the JVGs reshape the laminar separation bubble into a thinner and more stable structure, reducing its sensitivity to angle of attack. In stall conditions, they induce partial or full flow reattachment, delaying large-scale separation. The evolution of characteristic bubble parameters and the chordwise distribution of the shape factor $H = \delta ^{\ast }/\theta$, where $\delta ^{\ast }$ is the displacement thickness and $\theta$ is the momentum thickness, show a consistent trend of enhanced boundary-layer recovery. These findings offer new insight into the physical mechanisms underlying active separation control at low Reynolds numbers and establish a framework for evaluating vortex-based control strategies using volumetric diagnostics.

One-degree-of-freedom flow-induced vibration (FIV) and energy harvesting through FIV of an elastically mounted circular cylinder with mechanically coupled rotation were investigated numerically for low Reynolds number 100, mass ratio 8 and a wide range of reduced velocities. The aims of this study are to investigate the effect of the flow direction angle $\beta$ on the vibration and energy harvesting through FIV. Two types of lock-in are found: vortex-induced vibration (VIV) and galloping. The response amplitude increases with the increase of $\beta$ in both regimes. Both VIV response and galloping regimes are found for $\beta$ = 45° to $\beta$ = 90°. For $\beta$ = −90° to $\beta$ = 0°, only VIV response regimes are found. The fluid force and fluid torque play different roles in exciting/damping the vibration. In the high-amplitude gallop regime, the fluid force excites the vibration, and the torque damps the vibration. Energy harvesting at flow direction angle 90° is investigated as this flow direction has the maximum galloping amplitude. The energy harvesting is achieved by a linear electric damping coefficient in the numerical model. The maximum harvestable power in the galloping regime is significantly greater than that in the VIV regime, and it increases with the increase of the reduced velocity. When the reduced velocity is 20, the harvested power is over 20 times that in the VIV regime, and can further increase if reduced velocity further increases. The maximum efficiency over all simulated parameters is 0.424, occurring when the reduced velocity is 20, and electric damping factor is 0.04.

We address the Reynolds number dependence of the turbulent skin-friction drag reduction induced by streamwise-travelling waves of spanwise wall oscillations. The study relies on direct numerical simulations of drag-reduced flows in a plane open channel at friction Reynolds numbers in the range $1000 \leqslant Re_\tau \leqslant 6000$, which is the widest range considered so far in simulations with spanwise forcing. Our results corroborate the validity of the predictive model proposed by Gatti & Quadrio (J. Fluid Mech. vol. 802, 2016, pp. 553–558): regardless of the control parameters, the drag reduction decreases monotonically with $Re$ at a rate that depends on the drag reduction itself and on the skin-friction of the uncontrolled flow. We do not find evidence in support of the results of Marusic et al. (Nat. Commun. vol. 12, no. 1, 2021, pp. 5805), which instead report by experiments an increase of the drag reduction with $Re$ in turbulent boundary layers, for control parameters that target low-frequency, outer-scaled motions. Possible explanations for this discrepancy are provided, including obvious differences between open channel flows and boundary layers, and possible limitations of laboratory experiments.

We develop an optimal resolvent-based estimator and controller to predict and attenuate unsteady vortex-shedding fluctuations in the laminar wake of a NACA 0012 airfoil at an angle of attack of 6.5°, chord-based Reynolds number of 5000 and Mach number of 0.3. The resolvent-based estimation and control framework offers several advantages over standard methods. Under equivalent assumptions, the resolvent-based estimator and controller reproduce the Kalman filter and LQG controller, respectively, but at substantially lower computational cost using either an operator-based or data-driven implementation. Unlike these methods, the resolvent-based approach can naturally accommodate forcing terms (nonlinear terms from Navier–Stokes) with coloured-in-time statistics, significantly improving estimation accuracy and control efficacy. Causality is optimally enforced using a Wiener–Hopf formalism. We integrate these tools into a high-performance-computing-ready compressible flow solver and demonstrate their effectiveness for estimating and controlling velocity fluctuations in the wake of the airfoil immersed in clean and noisy free streams, the latter of which prevents the flow from falling into a periodic limit cycle. Using four shear–stress sensors on the surface of the airfoil, the resolvent-based estimator predicts a series of downstream targets with approximately $3\,\%$ and $30\,\%$ error for the clean and noisy free stream conditions, respectively. For the latter case, using four actuators on the airfoil surface, the resolvent-based controller reduces the turbulent kinetic energy in the wake by $98\,\%$.

This paper presents an experimental and analytical investigation into the use of trailing edge slits for the reduction of aerofoil trailing edge noise. The noise reduction mechanism is shown to be fundamentally different from conventional trailing edge serrations, relying on destructive interference from highly compact and coherent sources generated at either ends of the slit. This novel approach is the first to exploit the coherence intrinsic to the boundary layer turbulence. Furthermore, the study demonstrates that trailing edge slits not only achieve superior noise reductions compared with sawtooth serrations of the same amplitude at certain conditions, but also offer frequency-tuning capability for noise reduction. Noise reduction is driven by the destructive interference between acoustic sources at the root and tip of the slit, which radiate with a phase difference determined by the difference in times taken for the boundary layer flow to convect between the root and tip. Maximum noise reductions occur at frequencies where the phase difference between these sources is $180^\circ$. The paper also presents a detailed parametric study into the variation in noise reductions due to the slit length, slit wavelength and slit root width. Additionally, a simple two-source analytic model is proposed to explain the observed results. Wind tunnel measurements of the unsteady flow field around the trailing edge slits are also presented, providing insights into the underlying flow physics.

Contactless manipulation of small objects is essential for biomedical and chemical applications, such as cell analysis, assisted fertilisation and precision chemistry. Established methods, including optical, acoustic and magnetic tweezers, are now complemented by flow control techniques that use flow-induced motion to enable precise and versatile manipulation. However, trapping multiple particles in fluid remains a challenge. This study introduces a novel control algorithm capable of steering multiple particles in flow. The system uses rotating disks to generate flow fields that transport particles to precise locations. Disk rotations are governed by a feedback control policy based on the optimising a discrete loss framework, which combines fluid dynamics equations with path objectives into a single loss function. Our experiments, conducted in both simulations and with the physical device, demonstrate the capability of the approach to transport two beads simultaneously to predefined locations, advancing robust contactless particle manipulation for biomedical applications.

Embedding the intrinsic symmetry of a flow system in training its machine learning algorithms has become a significant trend in the recent surge of their application in fluid mechanics. This paper leverages the geometric symmetry of a four-roll mill (FRM) to enhance its training efficiency. Stabilising and precisely controlling droplet trajectories in an FRM is challenging due to the unstable nature of the extensional flow with a saddle point. Extending the work of Vona & Lauga (Phys. Rev. E, vol. 104(5), 2021, p. 055108), this study applies deep reinforcement learning (DRL) to effectively guide a displaced droplet to the centre of the FRM. Through direct numerical simulations, we explore the applicability of DRL in controlling FRM flow with moderate inertial effects, i.e. Reynolds number $\sim \mathcal{O}(1)$, a nonlinear regime previously unexplored. The FRM’s geometric symmetry allows control policies trained in one of the eight sub-quadrants to be extended to the entire domain, reducing training costs. Our results indicate that the DRL-based control method can successfully guide a displaced droplet to the target centre with robust performance across various starting positions, even from substantially far distances. The work also highlights potential directions for future research, particularly focusing on efficiently addressing the delay effects in flow response caused by inertia. This study presents new advances in controlling droplet trajectories in more nonlinear and complex situations, with potential applications to other nonlinear flows. The geometric symmetry used in this cutting-edge reinforcement learning approach can also be applied to other control methods.

With the severity and frequency of significant weather events increasing, methods for alleviating unsteady wind loading for high-rise buildings are gaining interest. This study numerically investigates the three-dimensional flow structures around a canonical high-rise building immersed in an atmospheric boundary layer at different oncoming wind angles, using wall-resolved large eddy simulations. A synthetic jet located on the top surface is used as open-loop active actuation with the aim of suppressing the building's side-force fluctuations when exposed to oncoming wind variations. Three different frequencies of jet forcing are considered, all half an order of magnitude larger than the vortex shedding frequency. The behaviour of the synthetic jet and its effect on the building's unsteady side force, time-averaged flow fields and unsteady flow structures are investigated numerically. The synthetic jet actuation is found to reduce the side-force fluctuation of the building, enhance the downwash flow and successfully attenuate the antisymmetric vortex shedding. This was achieved to different extents across the range of oncoming wind angles considered and may motivate future attempts to explore experimental active control strategies for attenuation of unsteady wind loading.

We design an open-loop active flow control for separated flows around a plunging circular cylinder based on resolvent analysis. The cylinder is plunging at a Strouhal number of 0.36 and a Reynolds number of 500. A linear time-periodic system for control is obtained by linearizing the non-inertial incompressible vorticity equation in the cylinder-fixed frame about a time-averaged base flow. Using the Lyapunouv–Floquet transformation, the linear time-periodic system is transformed into a similar linear time-invariant system, whose resolvent is analysed to obtain an optimal actuating Strouhal number of 0.1464 for the transformed linear system. Simulations show that the active control with tangential actuations is capable of reducing the lift fluctuation by up to 25.7 % when the flow is actuated near the predicted harmonic and subharmonic frequencies.

This work proposes a machine-learning or artificial intelligence (AI) control of a low-drag Ahmed body with a rear slant angle φ = 35° with a view to finding strategies for efficient drag reduction (DR). The Reynolds number Re investigated is 1.7 × 105 based on the square root of the body cross-sectional area. The control system comprises of five independently operated arrays of steady microjets blowing along the edges of the rear window and vertical base, twenty-six pressure taps on the rear end of the body and a controller based on an ant colony algorithm for unsupervised learning of a near-optimal control law. The cost function is designed such that both DR and control power input are considered. The learning process of the AI control discovers forcing that produces a DR up to 18 %, corresponding to a drag coefficient reduction of 0.06, greatly exceeding any previously reported DR for this body. Furthermore, the discovered forcings may provide alternative solutions, i.e. a tremendously increased control efficiency given a small sacrifice in DR. Extensive flow measurements performed with and without control indicate significant alterations in the flow structure around the body, such as flow separation over the rear window, recirculation bubbles and C-pillar vortices, which are linked to the pressure rise on the window and base. The physical mechanism for DR is unveiled, along with a conceptual model for the altered flow structure under the optimum control or biggest DR. This mechanism is further compared with that under the highest control efficiency.

Machine learning frameworks such as genetic programming and reinforcement learning (RL) are gaining popularity in flow control. This work presents a comparative analysis of the two, benchmarking some of their most representative algorithms against global optimization techniques such as Bayesian optimization and Lipschitz global optimization. First, we review the general framework of the model-free control problem, bringing together all methods as black-box optimization problems. Then, we test the control algorithms on three test cases. These are (1) the stabilization of a nonlinear dynamical system featuring frequency cross-talk, (2) the wave cancellation from a Burgers’ flow and (3) the drag reduction in a cylinder wake flow. We present a comprehensive comparison to illustrate their differences in exploration versus exploitation and their balance between ‘model capacity’ in the control law definition versus ‘required complexity’. Indeed, we discovered that previous RL control attempts of controlling the cylinder wake were performing linear control and that the wide observation space was limiting their performances. We believe that such a comparison paves the way towards the hybridization of the various methods, and we offer some perspective on their future development in the literature of flow control problems.

We stabilize an open cavity flow experiment to 1 % of its original fluctuation level. For the first time, a multi-modal feedback control is automatically learned for this configuration. The key enabler is automatic in situ optimization of control laws with machine learning augmented by a gradient descent algorithm, named gradient-enriched machine learning control (Cornejo Maceda et al., J. Fluid Mech., vol. 917, 2021, A42, gMLC). The physical interpretation of the feedback mechanism is assisted by a novel cluster-based control law visualization for the flow dynamics and corresponding actuation commands. Starting points of the control experiment are two unforced open cavity benchmark configurations: a narrow-bandwidth regime with a single dominant frequency and a mode-switching regime where two frequencies compete. The flow is forced by a dielectric barrier discharge actuator located at the leading edge and is monitored by a downstream hot-wire sensor over the trailing edge. The feedback law is optimized with respect to the monitored fluctuation level. As reference, the self-oscillations of the mixing layer are mitigated with steady actuation. Then, a feedback controller is optimized with gMLC. As expected, feedback control outperforms steady actuation by achieving a better amplitude reduction with approximately 1 % of the actuation energy required for similarly effective steady forcing. Intriguingly, optimized laws learned for one regime perform well for the other untested regime as well. The proposed control strategy can be expected to be applicable for many other shear flow experiments.

The role played by patterned heating in reducing pressure losses within vertical conduits is investigated. The heating generates flow separation structures which reduce the direct contact between the stream and the sidewalls, thereby limiting the frictional resistance. This also modifies the temperature field thereby inducing a net buoyancy force which may either assist or oppose the pressure gradient required to maintain a fixed flow rate. If the flow Reynolds number is increased sufficiently, the separation structures may be washed away, which means that the pressure-gradient-reducing mechanism is eliminated. The details of the system response are a function of the form of spatial heating distribution, its intensity, the flow Reynolds number and the fluid Prandtl number. Carefully chosen heating of the two walls can induce a pattern interaction effect and a judicious choice of the two patterns can have as much as an order of magnitude effect on the system response.

This experimental study investigated the control induced by a spanwise surface wire on a rigid circular cylinder undergoing vortex-induced vibration (VIV) under the conditions of low mass damping in the lower synchronization branch. Being motivated by the idea of VIV-based energy harvesting from ocean and river flows, this elastically mounted cylinder was immersed in a water channel, leaving a free end at its bottom spanwise end, while the free water surface bounded its top. The cylinder was constrained to vibrate in the cross-stream direction. The wire diameter was 6.25 % of the cylinder diameter. Experimental research was conducted by attaching this large-scale wire along the span of the cylinder at various angular positions ranging from 0° to 180° (with respect to the most upstream point of the cylinder) at a fixed Reynolds number of 104 (based on the cylinder diameter). Simultaneous to measuring the trajectory of the cylinder motion via a laser distance sensor, the instantaneous velocity field in the near wake of the cylinder was obtained using particle image velocimetry. Several VIV response categories were identified depending on the angular position of the wire, which led to the classification of distinct angular ranges for the wire application. Associated with the structural vibrations in these categories, different vortex-formation modes induced by the wire were revealed. For specific wire positions, decreases of up to 98 % and increases of up to 102 % were identified in the oscillation amplitude of the cylinder compared with the amplitude of the clean cylinder under similar conditions.

A set of several exact coherent states in plane Couette flow is computed under spanwise wall oscillation control, with a range of wall oscillation amplitudes and periods $({A_w}, T)$. It is found that the wall oscillation generally stabilises the upper branch of the equilibrium solutions and achieves the corresponding drag reduction, while it influences modestly the lower branch. The stabilisation effect is found to increase with the oscillation amplitude with an optimal time period around ${T^{+}} \approx 100$. The exact coherent states reproduce some key dynamical behaviours of streaks observed in previous studies, while exhibiting the rich coherent structure dynamics that cannot be extracted from a phase average of turbulent states. Visualisation of state portraits shows that the size of the state space supporting turbulent solution is reduced by the spanwise wall oscillation, and the upper-branch equilibrium solutions become less repelling, with many of their unstable manifolds being stabilised. This change of the state space dynamics leads to a significant reduction in lifetime of turbulence. Finally, the main stabilisation mechanism of the exact coherent states is found to be the suppression of the lift-up effect of streaks, explaining why previous linear analyses have been so successful for turbulence stabilisation modelling and the resulting drag reduction.