Unsteady Dynamics Research Articles

Lift enhancement by a flapped trailing edge at low Reynolds number: A frequency response approach

The capability of an oscillating trailing edge flap to enhance the lift generated by a rigid NACA-0012 airfoil at 2.1×104 Reynolds number is investigated. Experiments are performed at two angles of attack, namely α0=0∘ that represents a fully attached flow and α0=10∘ that represents a near-stall flow condition. The presented data and analysis cover sinusoidal oscillations of the flap at five reduced frequencies between k=0.02 and 0.12, and three oscillating amplitudes δA=5∘, 8° and 10° relative to the airfoil’s angle of attack. Enhancement to the mean lift, lift-to-drag ratio, and unsteady lift dynamics are discussed. The validity of quasi-steady formulation of Leishman’s model in predicting the lift is quantitatively assessed in light of the measurements. The unsteady lift dynamics generated by flap oscillations are modeled by constructing frequency response functions with the quasi-steady lift as the input and unsteady lift as the output. The experimentally determined gain variations are compared with analytically-derived gain functions. The effects of rate and amplitude of flap oscillations on lift cycle variations are examined using aerodynamic hysteresis response.

Modeling and Simulation of Unsteady Flow in Multistage Compressors Using Interdomain Boundaries

In this paper, a model for simulating the intrinsic fast dynamics of flow in a multistage, axi-centrifugal compressor is presented. The model treats the flow through the stage elements, i.e., rotors and stators, as curved stream-tube elements along the mean line. The model captures unsteady flow dynamics in respective frames for stators and rotors of individual stages, alternating between stationary and rotating frames as needed. Accelerations associated with the rotating frames are represented as body forces. Unique characteristics-based compact interfaces that account for the transformations between the frames (and also serve as compact loss zones) are used. Simulation results for an industrial four-stage axial compressor are presented that illustrate the propagation of waves through the compressor segments as the throttle is moved. In particular, the dynamic processes that can lead a compressor to either of the opposite ends of its operation, i.e., loss of stability or choked flow, are investigated. Simulation results demonstrate that the model accounts for the acoustic impedance that is responsible for choked flow. In throttling toward stall, the simulation results show, as expected, that with large plenum the compressor loses stability when it is driven beyond the peak of its characteristics. Further, the capabilities of the developed model as a diagnostic tool are demonstrated by analyzing “pseudomeasured” pressure signals in two possible scenarios of stability loss.

Effect of unsteady flow dynamics on the impact of monodisperse and bidisperse granular flow

Effect of unsteady flow dynamics on the impact of monodisperse and bidisperse granular flow

Low Reynolds number stall flutter of a linear cascade with large amplitudes at low reduced frequencies: Unsteady loads and flow features

In this paper, we report on an experimental investigation of stall flutter of a linear cascade undergoing large amplitude heave oscillations (≈ 10% of chord) at low reduced frequencies (k<0.1) and at low Reynolds number (Re≈50,000). Three blade incidence cases are studied representing light, moderate, and deep stall conditions of the cascade. Simultaneous measurements of energy transfer to the blade using a load cell, and flow field measurements using Particle Image Velocimetry (PIV) are carried out while the blades in the cascade are allowed to perform large amplitude heaving oscillations at the prescribed reduced frequency (k) and Inter Blade Phase angle (σ). The resulting normalized energy transfer values (CE¯) indicate that the cascade becomes unstable at low k values for a range of σ values with the range of σ and k within the unstable region increasing as the cascade is pushed deeper into stall. The energy transfer variation with k and σ, for a given blade incidence, are observed to fit the empirical model CE¯=a(k)+b(k)sin(σ+c(k)) with the terms a and c corresponding to quadratic and linear functions of k for all the incidence cases. At very low k values (k∼0.03), the quadratic term is small, and the energy transfer curves are observed to be broadly consistent with the trends reported by Corral and Vega (2016a), with the terms a(k) and c(k) being linear and b(k) being a constant. As the cascade is pushed gradually deeper into stall, the term b(k), which represents the influence of adjacent blades, is observed to go from being nearly a constant value with k for light stall, to a quadratic function of k at deep stall. More importantly, the deviation of b from being a constant is observed to occur at lower k values as the cascade goes deeper into stall. These results indicate that the additional quadratic terms need to be considered in the classical flutter based linear models for the case with deep stall and large oscillation amplitudes. The flow field measurements using PIV indicate the presence of a completely separated shear layer that is alternating between a state of being attached and detached to the blade surface during the oscillation cycle. The results show the shear layer phase (ϕs) with respect to the blade displacement to be close to the phase of the unsteady force (ϕ), thus helping to link the flutter behavior with the unsteady shear layer dynamics for stall flutter of a cascade at low Re.

Large scale unsteadiness during self-pulsation regime in a swirl coaxial injector and its influence on the downstream spray statistics

The focus of the present paper is to understand the large scale unsteadiness in the atomization of swirl coaxial jets and correlate it with the downstream spray statistics. A gas-centered swirl coaxial atomizer, in which a gaseous jet fragments an annular swirling liquid sheet, displays pulsating flow at certain momentum flux ratios (MFRs). These conditions were chosen to study the unsteady dynamics in the spray formation. Various zones of the spray such as near orifice region, primary atomization zone and far field spray were diagnosed using high-speed shadowgraphy technique. Proper orthogonal decomposition was employed on the time-resolved spray images to understand various unsteady modes. Three modes observed prominently were identified as large scale unsteady structures viz. axisymmetric pulsating mode, explosive mode and swirling mode. The pulsating mode was found to be more dominant in the pulsation regime, whereas the other modes gained significance at higher MFRs when the pulsation regime ceases to exist. Fourier analysis of temporal coefficients pertaining to pulsating mode showed a definitive frequency. The analysis of liquid shedding rate was found to be in synchronization with the pulsating mode which shows the upstream influence on periodic atomization. Spatio-temporal measurements of droplet sizes were carried out far from the atomizer. The temporal variation in the droplet number density and Sauter Mean Diameter depicted unsteady behavior; however, there is no preferred frequency in the power spectrum. This clearly indicates that the far field spray loses its memory of upstream periodic atomization in the pulsation regime of swirl coaxial atomizer.

Dual-FPGA-PIV measurements of unsteady flow dynamics resonated via the duct acoustic mode with half-wavelength arranged side-branches

Dual-FPGA-PIV measurements of unsteady flow dynamics resonated via the duct acoustic mode with half-wavelength arranged side-branches

Prescribed Thermal Activity in the Radiative Bidirectional Flow of Magnetized Hybrid Nanofluid: Keller‐Box Approach

In this exploration, we decided to investigate the significance of prescribed thermal conditions on unsteady 3D dynamics of water‐based radiative hybrid nanofluid with the impact of cylindrical‐shaped nanosized particles (alumina (Al2O3) and titania (TiO2)). For physical relevancy, the impact of the Lorentz force is also included. The combination of suitable variables has been used to transform the transport equations into the system of ordinary differential equations and then numerically solved via the Keller‐Box approach. Graphical illustrations have been used to predict the impact of the involved parameters on the thermal setup. Convergence analysis is presented via the grid independence approach. Skin frictions and local Nusselt numbers against various choices of involved parameters are plotted and arranged in tabular forms. It is observed through the present investigation that temperature distribution is increased with the higher choices of radiation parameter 0.0 ≤ Rd ≤ 2.0 and decreased with the improvement in the choices of temperature maintaining indices (i.e., −2.0 ≤ r, s ≤ 2.0). Moreover, the thermophysical properties except specific heat for hybrid nanofluid are improved with the involvement of cylindrical‐shaped nanoparticles. The temperature of the hybrid nanofluid is observed to be higher for variable thermal conditions as compared to uniform thermal conditions. Outfalls for a limited version of the report have been compared with a previous published paper.

МЕТОД РАСЧЕТА ВЗАИМОДЕЙСТВИЯ МОСТОВОГО ПЕРЕХОДА И СКОРОСТНОГО ЖЕЛЕЗНОДОРОЖНОГО СОСТАВА ПРИ ПЕРЕМЕННОЙ СКОРОСТИ ДВИЖЕНИЯ (к формированию норм для ВСМ)

Boundary elements for rods on an elastic base are proposed for the calculation of bridges on the HSR when moving at a variable speed of an inertial load (railway train). A set of linear and trigonometric functions is used to approximate the displacements at the construction of boundary elements. These elements are used to calculate the vibrations of the rail track outside the bridge and the track on the bridge, together with double-track girder superstructures connected through the interlayers at high-speed movement of arbitrary power and inertial loads. To construct the methodology, the step method proposed earlier by the author of the article for solving problems of unsteady dynamics of structures and the method of calculating structures for the action of mobile force and inertial loads (the method of nodal accelerations) are used.

A reduced-order model for the near wake dynamics of a wind turbine: Model development and uncertainty quantification

Wind turbine power production and its variability are affected by unsteady, turbulent structures that are induced in the wake and emerge over a range of disparate length scales. However, the inclusion of the unsteady dynamics in wake models remains difficult in kinematic modeling where steady-state conditions are assumed. We develop and quantify the uncertainty of an unsteady wake model by leveraging model-order reduction. The wake is modeled as a dynamical system based on dynamic mode decomposition and compressive sensing, where the system is reduced by designating an objective function to select energetic turbulent structures represented by dynamic modes. A series of large-eddy simulations are undertaken using the actuator line model and the actuator surface with nacelle model for training and testing data. Differences in the turbine parameterizations of near wake simulations are used to identify how modes are related to turbulent structures and are selected through compressive sensing. The results showed that the flow field can be constructed with few modes. The modes are the most energetic and have frequencies related to pertinent features such as tip and hub vortices. While the error in the training phase is dependent on the number of modes, the relative error remains less than 6% and is largely independent of the number of modes during the prediction phase if certain modes are retained. The error accumulates over time near the turbine blades. However, error accumulation does not have a significant impact on the prediction of instantaneous velocity in the wake further downwind.

Modal Analysis of Cylinder-Induced Transitional Shock-Wave/Boundary-Layer Interaction Unsteadiness

Shock-wave/boundary-layer interactions (SWBLIs) are critical phenomena in the design of high-speed vehicles as they exhibit inherent unsteadiness that can damage airframes and lead to engine unstart. This paper presents a novel characterization of the unsteady dynamics of cylinder-induced SWBLIs at Reynolds numbers of and using proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). Data sets analyzed in this paper were obtained from experiments conducted in the NASA Langley Research Center’s 20-Inch Mach 6 blowdown wind tunnel. The experiments used a cylinder protuberance model mounted on a 10° half-angle wedge to create the interaction. The lower-Reynolds-number case was observed to have a transitional incoming boundary layer, whereas a swept ramp array trip was used in the higher-Reynolds-number case to generate a turbulent incoming boundary layer. The POD analysis from both cases helped isolate spatial regions in the separation bubble that contained the highest percentage of energy for each case, which correlate to the dominant structures in the flow. A power spectral density analysis on the POD temporal components of the highest-energy POD mode (mode 1) revealed a frequency spectrum with a distinct peak at in the lower-Reynolds-number case and a band of high-energy peaks in the range of 0.05–0.2 for the tripped SWBLI case. Through the DMD analysis, an unsteadiness mode was isolated at and an asymmetric motion of the forward lambda shock was identified in the lower-Reynolds-number case. This dynamic asymmetry was not detected in the higher-Reynolds-number case, suggesting that the asymmetric effect may be unique to interactions in transitional incoming boundary layers. Additional spectral-kernel-based POD analysis identified primary unsteadiness frequencies that were in agreement with the DMD findings. A low-frequency mode at , exhibiting relatively high energy, was obtained for the lower-Reynolds-number (transitional) case, whereas a broadband “bump” with increased energy over a frequency range of was observed for the higher-Reynolds-number (tripped) case. Through these analysis techniques, a mode, likely connected to a shock-breathing mechanism, was identified at . In the assessment of the structural motion occurring in the shock-breathing mode, the phenomenon in the lower-Reynolds-number case was found to traverse a longer upstream distance and compress to a larger degree when compared with the breathing behavior in the higher-Reynolds-number case.

Numerical study on the effects of modulated ventilation on unsteady cavity dynamics and noise patterns

Supercavitating flow is accompanied by significant unsteady characteristics, and it is therefore very important to find methods to control this multiphase flow phenomenon. Ventilation is an important method for creating supercavitation and it affects the evolution, load, and noise characteristics. In this paper, cavity flows with and without modulated ventilation (i.e., the imposition of a sinusoidal component on the ventilation rate) are investigated using computational fluid dynamics techniques incorporating large eddy simulation, coupled with the Ffowcs Williams–Hawkings (FW–H) method. The effects of modulated ventilation on cavity shedding, vortex structure, and the noise characteristics of the cavity are compared and analyzed. The results show that modulated ventilation can change the shedding period of the ventilated cavity and can slightly improve its lift and drag performance. It can also promote the formation and growth of hairpin vortices and impose a periodicity on the evolution of the vortex structure. Furthermore, although modulated ventilation cavitation enhances pressure fluctuations near the vent and increases the self-noise of ventilation, it has little impact on far-field noise while reducing the turbulence of the far field, which decreases the total sound pressure level in the wake of the cavitator.

Impact of Hydrogen Addition on the Thermoacoustic Instability and Precessing Vortex Core Dynamics in a CH4/H2/Air Technically Premixed Combustor

Abstract We study the impact of H2 enrichment on the unsteady flow dynamics and thermoacoustic instability in the prediction and control of instabilities in industrial turbines (PRECCINSTA) swirl combustor. The experiments were performed at atmospheric conditions with H2/CH4 fuel mixtures at a global equivalence ratio of 0.65 and a constant thermal power of 20 kW. We analyze data with three fuel compositions: 0%, 20%, and 50% H2 in two operating modes, premixed (PM) and technically premixed (TPM). A new multiresolution modal decomposition method, using a combination of wavelet transforms and proper orthogonal decomposition (WPOD) is performed on time resolved flow velocity and OH planar laser induced fluorescence (OH planar laser induced fluorescence (OH-PLIF)) measurements. Thermoacoustic oscillations are observed in the TPM operating mode alone, indicating that the primary heat release driving mechanism is due to fuel-air ratio oscillations. WPOD results for the 0% H2 TPM case reveal intermittent helical precessing vortex core (PVC) oscillations along with axisymmetric hydrodynamic flow oscillations due to the thermoacoustic oscillations. These oscillations cause local flame extinction near the nozzle centerbody resulting in liftoff. A PVC then develops in the flow and enables intermittent flame reattachment. In the 0% H2 premixed case, the flame remains lifted off the centerbody despite the presence of PVC oscillations. H2 enrichment results in the suppression of flame liftoff and the PVC in both operating modes. We show from flow strain rate statistics and extinction strain rate calculations that the increase of the latter with H2 addition, allows the flame to stabilize in the region near the centerbody where the pure CH4 cases show lift off.

Numerical Investigation of Unsteady Flow Dynamics in a Packed Bed

Numerical simulation of unsteady flow of a compressible fluid in a fixed bed filled with porous elements has been performed. The research was carried out via ANSYS Fluent software. The scientific substantiation and verification of the physical and mathematical approaches incorporated in ANSYS Fluent for the problem of unsteady flow in a fixed bed has been carried out. For the computational domain, the interfaces of the flow area and the surface of porous particles are coupled by combining the contacts into a component part. The numerical results were verified using experimental data. The study was carried out in the range of velocity from 0.25 to 3.25 m/s. An expression is proposed for determining the pressure drop in a fixed bed, in which the pressure drop depends on the velocity, flow properties and the linear coefficient of local resistance. The values of the linear coefficient of local resistance are determined for the most common nozzle shapes in the industry: cylinder, Raschig ring, convex cylinder with 7 holes, sphere with 7 holes. It was found that with an increase in velocity, the value of the linear coefficient of local resistance decreases.

Large eddy simulation and finite-volume conditional moment closure modelling of a turbulent lifted H2/N2 flame

Large eddy simulations with three-dimensional finite-volume Conditional Moment Closure (CMC) model are performed for a hydrogen/nitrogen lifted flame with detailed chemical mechanism. The emphasis is laid on the influences of mesh resolution and convection scheme of finite-volume CMC equations on predictions of reactive scalars and unsteady flame dynamics. The results show that the lift-off height is underestimated and the reactive scalars are over-predicted with coarser CMC mesh. It is also found that further refinement of the CMC mesh would not considerably improve the results. The time sequences of the most reactive and stoichiometric hydroxyl radical mass fractions indicate that finer CMC mesh can capture more unsteady details than the coarser CMC mesh. Moreover, the coarse CMC mesh has lower conditional scalar dissipation rate, which would promote the earlier auto-ignition of the flame base. Besides, the effects of the convection scheme for the CMC equations (i.e., upwind, central differencing and their blends) on the lifted flame characteristics are also investigated. It is shown that different convection schemes lead to limited differences on the time-averaged temperature, mixture fraction and species mass fractions. Moreover, the root-mean square values of hydrogen and hydroxyl mass fractions show larger deviation from the measurements with hybrid upwind and central differencing scheme, especially around the flame base. Furthermore, the distributions of the numerical fluxes on the CMC faces also show obvious distinctions between the upwind and blending schemes. The budget analysis of the individual CMC terms shows that a sequence of CMC faces has comparable contributions with upwind scheme. However, with the hybrid schemes, the instantaneous flux is dominantly from limited CMC faces. The reactivity of a CMC cell is more easily to be affected by its neighbors when the upwind scheme is used.

Comparative study between turbulence models in unsteady cavitating flow with special emphasis on shock wave propagation

The generation and propagation of shock waves are important sources of cavitation instability and material damage. This paper describes an evaluation of the predictive ability of different turbulence models in a compressible cavitation flow for shock wave propagation. The Schnerr–Sauer cavitation model is used to model cavitation and the volume of fluid method is used to capture the water/vapor interface. The pressure pulsations and cavity evolution given by numerical simulations and experimental results are compared to evaluate the correctness of the numerical method and the prediction accuracy of different turbulence models. The propagation mechanism of the shock wave, the evolution of vortex structures, and the temporal and spatial distribution characteristics of the cavitating flow are analyzed. The results show that the results predicted by the large-eddy simulation (LES) model are in good agreement with the experimental results. The shock wave is caused by a pressure wave that is generated by the collapse of the previously detached cloud cavity. This pressure wave hits the trailing edge of the cavity, thus inhibiting the development of the cavity and delaying the period of the cavity. In the process of shock wave propagation, the peak pressure and the peak lift (drag) coefficient appear at the same time. The propagation of the shock wave strongly disturbs the motion of the vortices, causing the large-scale vortex structure on the trailing edge of the hydrofoil to be depressed and the stable vortex on the hydrofoil to lift. The vortex stretching term and vortex dilatation term dominate the transmission process of the eddy current, and the vortex dilatation term is the most important in the process of shock wave propagation. The pressure fluctuations in the evolution of the cavity lead to changes in the statistical structure of the velocity field. Moreover, the anisotropy of velocity fluctuations in the cloud-cavity region is higher than that in the region of the sheet cavity. The Reynolds-averaged Navier–Stokes (RANS) model underestimates the cavity volume and the pulsation characteristics of the flow field, and cannot capture the negative X-direction velocity and vortex structure changes in the shock wave propagation process. Moreover, the RANS model and detached-eddy simulation (DES) model cannot accurately predict the characteristics of the flow field near the wall, and overestimate the dominant frequency of the cavity oscillations. The LES model is better at capturing the flow field characteristics in unsteady dynamics, and reproduces the shock wave propagation process well.

The spatio-temporal pattern of release signals and tree growth in Fagus-Abies-Picea old-growth forests reveals unsteady gap-phase dynamics

Disturbances have been recognized as a key factor shaping the species composition, structure and dynamics of natural forest ecosystems. In Europe, where forests driven by spontaneous processes have survived in relic form, knowledge about natural disturbance regimes is still fragmentary. To expand this knowledge, we reconstructed stand-level growth and analyzed the spatio-temporal pattern of release signals in the increment chronologies of individual trees as indicators of disturbance events in the Western Carpathians (Central Europe). The study was carried out in five old-growth forests formed by Fagus sylvatica L., Abies alba Mill. and Picea abies (L.) H. Karst. Depending on the stand, the analyses included tree-ring series of 84–193 trees sampled over areas of 5.9–13.6 ha and aimed at determining (1) the spatio-temporal pattern of disturbance severity over the last two centuries, (2) whether disturbances have been synchronized in time across the study sites and (3) whether disturbances have induced pulsed dynamics of stand development manifested as fluctuations in radial tree increment at the level of entire stands. In the period 1850–2010, the percentage of decades with the proportion of released trees < 10, 10–20, 20–30 or more than 30% was 38, 41, 14 and 7%, respectively, and no instances of severe disturbances simultaneously impacting an extensive area and releasing the vast majority of trees were found. The release events were only weakly synchronized at the between-stand level. The spatial distribution of released trees varied over the decades, with a shift toward spatial independence for the most severe disturbances. At the stand level, the interchanging periods of increasing/decreasing tree growth lasted between 24 and 36 years, with the exception of one stand in which this period lasted 54 years. The revealed fluctuations in tree growth attributable to changes in stand density were relatively small and accounted on average for 7% of the total variation in annual tree increments. This suggests that local level disturbances introduce structural heterogeneity and strongly modify tree growth, but at the stand level, their effect is dispersed and causes only minor fluctuations. An over-dispersion of decadal release frequencies compared to the random model and spatial correlation of disturbing events on the one hand, and the lack of extensive disturbances, frequent occurrence of multiple releases in tree life histories, and small fluctuations in the reconstructed growth at the stand level on the other hand, suggest a disturbance regime which goes beyond random processes in a strict sense and is thus not entirely compatible with the classical model of gap-phase stand dynamics.

On the unsteady dynamics of partially shrouded compressible jets

We experimentally investigate a partially shrouded sonic jet (a sonic free-jet shielded by a solid wall-extension on one side) exiting from a planar nozzle at two different nozzle pressure ratio ($\zeta=4$ and $5$). We experimentally show that the inherent jet unsteadiness from the shock-induced flow separation on the wall and the emitted noise in the far-field is strongly coupled through a series of experiments like high-speed schlieren, wall-static pressure, unsteady pressure spectra, and microphone measurements. The partially shrouded jet's lateral free expansion is also identified to be complicated, three-dimensional, and the produced noise is directional. The emitted acoustic pulses from the flapping-jet, the radiated noise from the shock-induced separation on the wall, and the shock-shear layer interaction on the other side of the wall are responsible for the generated acoustic disturbances. The non-uniform aeroacoustic forcing on the top and bottom portion of the partially wall-bounded jet shear layer leads to a self-sustained jet oscillation and a discrete sound emission. The vital features are identified through the proper orthogonal decomposition of high-speed schlieren images and supplemented by other measurements.

Computational investigation of oxy-combustion of pulverized coal and biomass in a swirl burner

Swirling pulverized coal and biomass flames are computationally investigated for oxy-combustion. The two-phase flow is described by a Eulerian-Eulerian approach. For radiation, the absorption coefficient is approximated by superposing particle and gas contributions, considering oxy-combustion conditions for the latter. Turbulence is modelled within a URANS framework, using the standard k-ε model and Reynolds Stress Model (RSM). It is observed that RSM captures the unsteady dynamics of the coherent structures, whereas they are not captured by k-ε model. Predicted velocities are compared with measurements. It is observed that the RSM predictions are in a better agreement with the measurements compared to the k-ε model. The discrepancy between the predictions and measurements can most clearly be quantified in terms of the peak values of the axial velocity in the forward flow region enveloping the inner recirculation zone. The calculations constantly underpredict the measurements. On the average, this is about 32% for the RSM and 52% for the k-ε model, for both flames. The biomass flame is predicted nearly twice as long compared to the coal flame. As means of verification, the coal flame is additionally calculated using a classical Eulerian-Lagrangian two-phase formulation, leading to quite similar results to the Eulerian-Eulerian formulation.

Interplay of Active Stress and Driven Flow in Self-Assembled, Tumbling Active Nematics

Lyotropic chromonic liquid crystals (LCLCs) are a special type of hierarchical material in which self-assembled molecular aggregates are responsible for the formation of liquid crystal phases. Thanks to its unusual material properties and bio compatibility, it has found wide applications including the formation of active nematic liquid crystals. Recent experiments have uncovered tumbling character of certain LCLCs. However, how tumbling behavior modifies structure and flow in driven and active nematics is poorly understood. Here, we rely on continuum simulation to study the interplay of extensile active stress and externally driven flow in a flow-tumbling nematic with a low twist modulus to mimic nematic LCLCs. We find that a spontaneous transverse flow can be developed in a flow-tumbling active nematic confined to a hybrid alignment cell when it is in log-rolling mode at sufficiently high activities. The orientation of the total spontaneous flow is tunable by tuning the active stress. We further show that activity can suppress pressure-driven flow of a flow-tumbling nematic in a planar-anchoring cell but can also promote a transition of the director field under a pressure gradient in a homeotropic-anchoring cell. Remarkably, we demonstrate that the frequency of unsteady director dynamics in a tumbling nematic under Couette flow is invariant against active stress when below a threshold activity but exhibits a discontinuous increase when above the threshold at which a complex, periodic spatiotemporal director pattern emerges. Taken together, our simulations reveal qualitative differences between flow-tumbling and flow-aligning active nematics and suggest potential applications of tumbling nematics in microfluidics.

Modal decomposition analysis of unsteady viscous liquid sheet flows

The unsteady dynamics of a gravitational liquid sheet, driven by a continuous harmonic perturbation in the lateral velocity component applied at the inlet section, is analyzed. The topology and the dynamics of the relevant flow structures are characterized by applying POD (Proper Orthogonal Decomposition) and spectral POD (SPOD) modal decompositions on two-dimensional two-phase numerical simulation data obtained with the volume-of-fluid approach. The investigation is carried out by varying the Weber number, the forcing frequency (Strouhal number), and the Reynolds number. The supercritical regime (We &amp;gt; 1) features a traveling perturbation, exhibiting a spatial structure with leading sinuous modes. SPOD spectra confirm the occurrence of a discontinuity in frequency response between the supercritical and subcritical regimes. In the subcritical regime (We &amp;lt; 1), the investigation highlights the excitation of a combined sinuous–varicose motion when the system is driven at resonance frequency for a relatively high Reynolds number (approaching the inviscid limit). The emergence of varicose modes is favored by low Weber numbers. The excitation of these modes occurs when the Weber number is decreased from We = 0.90 down to 0.75, with a progressive shift of the varicose mode from higher harmonics toward the main frequency; it can be considered as a possible mechanism of breakup observed in experiments when the inlet flow rate is progressively reduced. The flow reconstruction based on both POD and SPOD confirms the good capability of SPOD modes to capture dynamically relevant features of the fluid motion in subcritical conditions.