This paper provides a comprehensive explanation for the lift force acting on a freely deformable bubble rising in a linear shear flow and examines how the lift force scales with the undisturbed shear rate in cases governed by different lift force mechanisms. Four distinct flow mechanisms are identified from previous studies, and the associated bubble-induced vorticity dynamics are outlined. We provide a theoretical framework to qualitatively explain the lift force acting on a bubble in terms of moments of the bubble-induced vorticity. We support our theoretical framework with three-dimensional multiphase direct numerical simulations to illustrate how the vorticity dynamics associated with the four mechanisms generate the lift force. These findings provide a comprehensive explanation for the behaviour of the lift force in a wide range of relevant governing parameters. Additionally, our simulation results show how differently the lift force scales with the shear rate, depending on the dominating lift force mechanism. These results indicate that the shear rate should, in general, be accounted for in highly viscous flows (low Galilei numbers) or at significant bubble deformations (moderate-to-high Eötvös numbers) when modelling the lift force coefficient.

We present a numerical analysis of the lateral movement and equilibrium radial positions of red blood cells (RBCs) with major diameter 8 $\mathrm {\mu }$m under a Newtonian fluid in a circular channel with 50 $\mathrm {\mu }$m diameter. Each RBC, modelled as a biconcave capsule whose membrane satisfies strain-hardening characteristics, is simulated for different Reynolds numbers $Re$ and capillary numbers $Ca$, the latter of which indicates the ratio of the fluid viscous force to the membrane elastic force. The effects of initial orientation angles and positions on the equilibrium radial position of an RBC centroid are also investigated. The numerical results show that depending on their initial orientations, RBCs have bistable flow modes, so-called rolling and tumbling motions. Most RBCs have a rolling motion. These stable modes are accompanied by different equilibrium radial positions, where tumbling RBCs are further away from the channel axis than rolling ones. The inertial migration of RBCs is achieved by alternating orientation angles, which are affected primarily by the initial orientation angles. Then the RBCs assume the aforementioned bistable modes during the migration, followed by further migration to the equilibrium radial position at much longer time periods. The power (or energy dissipation) associated with membrane deformations is introduced to quantify the state of membrane loads. The energy expenditures rely on stable flow modes, the equilibrium radial positions of RBC centroids, and the viscosity ratio between the internal and external fluids.

We propose the first machine-learned control-oriented flow estimation for multiple-input, multiple-output plants. The starting point is constant actuation with open-loop actuation commands leading to a database with simultaneously recorded actuation commands, sensor signals and flow fields. A key enabler is an estimator input vector comprising sensor signals and actuation commands. The mapping from the sensor signals and actuation commands to the flow fields is realized in an analytically simple, data-centric and general nonlinear approach. The analytically simple estimator generalizes linear stochastic estimation for actuation commands. The data-centric approach yields flow fields from estimator inputs by interpolating from the database – similar to Loiseau, Noack & Brunton (J. Fluid Mech., vol. 844, 2018, pp. 459–490) for unforced flow. The interpolation is performed with $k$ nearest neighbours ($k$NN). The general global nonlinear mapping from inputs to flow fields is obtained from a deep neural network (DNN) via an iterative training approach. The estimator comparison is performed for the fluidic pinball plant, which is a multiple-input, multiple-output wake control benchmark (Deng et al., J. Fluid Mech., vol. 884, 2020, A37) featuring rich dynamics under steady controls. We conclude that the machine learning methods clearly outperform the linear model. The performance of $k$NN and DNN estimators are comparable for periodic dynamics. Yet the DNN performs consistently better when the flow is chaotic. Moreover, a thorough comparison regarding the complexity, computational cost and prediction accuracy is presented to demonstrate the relative merits of each estimator. The proposed method can be generalized for closed-loop flow control plants.

Direct numerical simulations of high-pressure binary-species temporal boundary layers are performed to investigate the flow physics for three situations: (1) uniform and equal composition, (2) uniform but unequal compositions and (3) non-uniform composition. Both colder- and hotter-wall situations compared with the free stream are simulated. The working fluid is a nitrogen/methane mixture. The analysis is performed at a case-specific self-similar state. Even when the initial composition is uniform, the methane mean mass fraction decreases near the colder wall, whereas it increases near the hotter wall and the mass fraction fluctuates in the entire boundary layer. Analysis of the species-mass diffusion balance and flow structures reveal that both mass-fraction variation and fluctuations are induced by the Soret effect. When the initial composition is non-uniform and the wall is colder, the methane mean mass fraction monotonically increases from the wall akin to its initial profile. However, when the wall is hotter the mean mass fraction decreases near the wall in contrast to its initial profile, a fact traced through the species-mass diffusion balance to the Soret effect being large and enriching methane near the wall. In contrast, the direction of the Soret flux is opposite for the colder wall, thus keeping the methane concentration small. Although the initial magnitude of the difference between the wall and free-stream temperature is the same in all cases, the situation is not symmetric between colder- and hotter-wall cases; the flow structure exhibits much smaller scales when the wall is hotter than when the wall is colder.

Toroidal drops, embedded in viscous flow, have a large range of stationary shapes that are challenging to compute numerically due to their inherent instability. When both the drop and the outer fluid are Newtonian liquids, the only reported cases of such stable configurations are of highly expanded drops rotating in an axisymmetrical extensional flow. In this study, we propose a method for stabilizing the stationary shapes of inherently unstable rotating toroidal drops, embedded in extensional or biextensional flow, by subjecting the system to feedback control stabilization. The proposed controller is designed using a two-state dynamic model of the system and is tested on a high-order nonlinear dynamic model of the drop deformation. It is demonstrated that, through this simplified feedback-control-centred approach, an extended collection of stabilized stationary solutions is generated, which spans the range from highly expanded drops to almost collapsed ones. In the latter region, that was never obtained in previous studies, multiplicity of solutions is identified. Furthermore, our method is more accurate and more efficient compared with the previously used ones.

The dispersed phase in turbulence can vary from almost inviscid fluid to highly viscous fluid. By changing the viscosity of the dispersed droplet phase, we experimentally investigate how the deformability of dispersed droplets affects the global transport quantity of the turbulent emulsion. Different kinds of silicone oil are employed to result in the viscosity ratio, $\zeta$, ranging from $0.53$ to $8.02$. The droplet volume fraction, $\phi$, is varied from 0 % to 10 % with a spacing of 2 %. The global transport quantity, quantified by the normalized friction coefficient $c_{f,\phi }/c_{f,\phi =0}$, shows a weak dependence on the turbulent intensity due to the vanishing finite-size effect of the droplets. The interesting fact is that, with increasing $\zeta$, $c_{f,\phi }/c_{f,\phi =0}$ first increases and then saturates to a plateau value which is similar to that of the rigid particle suspension. By performing image analysis, this drag modification is interpreted from the point of view of droplet deformability, which is responsible for the breakup and coalescence effect of the droplets. The statistics of the droplet size distribution show that, with increasing $\zeta$, the stabilizing effect induced by interfacial tension becomes substantial and the pure inertial breakup process becomes dominant. The measurement of the droplet distribution along the radial direction of the system shows a bulk-clustering effect, which can be attributed to the non-negligible coalescence effect of the droplet. It is found that the droplet coalescence effect could be suppressed as $\zeta$ increases, thereby affecting the contribution of interfacial tension to the total stress, and accounting for the observed emulsion rheology.

This study demonstrates an experimental platform for active jet noise reduction comprising of an automated system that performs a search for the optimal actuator locations and parameters, powered by a genetic algorithm (GA). Sideline noise reduction levels of 7.3 dB were achieved for a cold overexpanded (nozzle pressure ratio, $NPR=2.8$) jet, beyond the state-of-the-art for jet noise reduction with air injection. The reduction in noise was achieved at a mass flow rate of 1.4 % of the main jet, requiring no prior knowledge of the flow physics to inform the placement of the actuators. The same actuator pattern was tested in hot conditions (nozzle temperature ratio, $NTR=1.88$), achieving 4.7 dB sideline noise reduction. Detailed examination of the solutions obtained unveils some of the mechanisms leveraged by the GA to accomplish these high levels of noise reduction through microphone measurements and schlieren flow visualization. The GA found that actuating at the diverging wall of the convergent–divergent nozzle, where flow is supersonic, is very effective when combined with air injection near the nozzle lip, outside of the nozzle. Although the external actuation is effective at eliminating the screech tone, it is by actuating inside the nozzle at the diverging wall that sufficient disruption of the shock cell train can be achieved in order to reduce the broadband shock-associated noise.

A strongly nonlinear long-wave approximation is adopted to obtain a high-order model for large-amplitude long internal waves in a two-layer system by assuming the water depth is much smaller than the typical wavelength. When truncated at the first order, the model can be reduced to the regularized strongly nonlinear model of Choi et al. (J. Fluid Mech., vol. 629, 2009, pp. 73–85), which lessens the Kelvin–Helmholtz instability excited by the tangential velocity jump across the interface in the inviscid Miyata–Choi–Camassa (MCC) equations. Using the second-order model, the next-order correction to the internal solitary wave solution of the MCC equations is found and its validity is examined with the Euler solution in terms of the wave profile, the effective wavelength and the velocity profile. It is shown that the correction greatly improves the comparison with the Euler solution for the whole range of wave amplitudes and no further correction is necessary for practical applications. Based on a local stability analysis, the region of stability for the second-order long-wave model is identified in the physical parameter space so that the efficient numerical scheme developed for the first-order model can be used for the second-order model.