Unstable Modes Research Articles

Can boundary slip destabilize rotating microchannel flows?

Deviation from the traditional no-slip boundary condition due to factors like surface roughness and wettability is of paramount importance in microfluidics and nanofluidics, as it is attributable to its significance in drag reduction, flow control and enhancement and improved mixing. Augmentation in mixing, in turn, is known to strongly correlate with potential instabilities in the flow structure. Reported research studies indicate that slip is an inherent flow stabilizer in microfluidics, to the extent that with sufficient slip, the flow becomes linearly stable against all wavelike disturbances for all wavelengths and Reynolds numbers [“The linear stability of slip channel flows,” Phys. Fluids 34,074103(2022)]. Contrary to such intuitive proposition, here we show that slip effects can destabilize microchannel flows under spanwise rotation, delving on the interplay of rotational forces and slippery hydrodynamics. Our results reveal that increasing the slip length decreases the critical rotation speed, indicating lower rotational effort required to destabilize the flow, whereas the critical Reynolds number for the flow remains effectively unaltered for different slip lengths in a spanwise rotating system. As the slip length increases progressively, the critical rotation number (dimensionless rotational speed) for the onset of instability decreases further, then remains constant up to a certain limit, and subsequently declines with additional enhancement in the slip length. This indicates the potential for deploying customized hydrophobic (slippery) substrates to facilitate transitions from stable to unstable modes by simple tuning of the rotational speed—a paradigm that offers great promise in various applications ranging from materials synthesis to biomedical technology.

Effects of combustor wall temperature on the outer recirculation zone combustion modes transition in lean premixed DME/air swirling flames

In this study, the effects of wall thermal boundary conditions on the outer recirculation zone (ORZ) combustion modes transition in the DME/air swirling flames were investigated using the Large Eddy Simulation (LES) and Flamelet Generated Manifold (FGM) method. The results show that the ORZ chemistry and temperature are highly sensitive to the wall thermal boundary condition. Based on the correlation between the temperature and species observed in the time-averaged numerical results, the relation between the combustion mode and temperature in the ORZ was discovered. Through temporal analysis of species and heat release rate in the ORZ, the stable Mode II and Mode IV as well as the unstable Mode III were identified. The chemical reaction pathway analysis for typical probe in the ORZ reveals that different combustion modes undergo distinct (low-temperature or high-temperature) chemical reaction pathways. Afterwards, the definition of ORZ combustion modes used in experiments was refined by utilizing the chemical reaction data from the simulations. And it was applied to identify the combustion mode across the entire computational domain. The results confirm the consistency between the combustion modes determined in experiments based on OH and CH2O and those determined in simulations using chemical reaction rates. Finally, this explains the mechanism of the flickering flame in Mode III is the competition between the low-temperature and high-temperature reaction in the ORZ. Whereas the unstable Mode III can be stabilized by changing the wall temperature to reach the stable Mode II or Mode IV.

The effect of hydrogen enrichment on the conical premixed methane–air flame response and thermoacoustic modes coupling

This paper investigates the thermoacoustic dynamic responses of hydrogen-enriched laminar premixed conical methane–air flames under dual-mode coupling. Utilizing the level set method and the G-equation model, one meticulously derives the flame describing function (FDF) in relation to variations in hydrogen enrichment levels (ηH). This precisely derived FDF is then integrated into the low-order network model of the Rijke tube to analyze the thermoacoustic unstable modes of the system. Finally, dual-frequencies incoming flow velocity perturbations are reintroduced as inputs to obtain the flame response under thermoacoustic modes coupling. Results show that while keeping the unstretched steady flame aspect ratio constant, an increase in ηH not only raises the FDF’s cut-off frequency but also enhances the FDF gain within the nonlinear frequency region, leading to more unstable modes, especially high frequency modes within the Rijke tube system. Furthermore, the flame response is further altered under the excitation of dual unstable modes. When both modes are within the linear frequency region of the FDF, the flame response is co-controlled by the two modes, predominantly by the mode with a larger velocity perturbation amplitude, with weaker modes coupling leading to the additional frequency perturbation having a suppressive effect on the flame response at the original frequency. Conversely, when one or two modes are within the nonlinear frequency region of the FDF, the flame response is dominated by the lower-frequency mode, with higher nonlinear modes coupling allowing the additional frequency perturbation to both promote and suppress the response at the original frequency and also couple to produce a significant difference frequency response. Novelty and significance The novelty of this paper lies in the determination of the flame describing function (FDF) with varying hydrogen enrichment levels and the stability of thermoacoustic systems, and more significantly, conducting an in-depth and comprehensive investigation into the nonlinear dynamic responses of hydrogen-enriched flames to different types of dual-mode coupling perturbations. The dual-mode perturbations result in either attenuation or amplification of the flame response, depending on whether the corresponding frequencies lie within the linear or nonlinear frequency regions of the FDF, which innovatively incorporates the influence of the FDF phase and examines the responses at the difference frequencies generated by the coupling. This lays a foundation for further exploration into the mechanisms of modes coupling in hydrogen-enriched and other thermoacoustic systems.

Accuracy of kinetic equilibrium reconstruction of NSTX and NSTX-U plasmas and its impact on the transport and stability analysis

Abstract An accurate magnetohydrodynamic (MHD) equilibrium reconstruction is an essential starting point for stability and transport plasma analysis. This work describes an approach for obtaining kinetic equilibrium reconstructions using the OMFIT framework, which has been applied for the first time to spherical tokamak data from NSTX and NSTX-U. The EFIT equilibrium solver is integrated with experimental data analysis procedures and subsequent TRANSP transport simulations to enhance the accuracy of the reconstruction, in particular at the edge region, by adding constraints on the total pressure and current density profiles, based on the transport code solution. The accuracy of the equilibrium depends on the uncertainty and number of constraints, as well as the choice of basis functions to represent the pressure and current density profiles. An improved fidelity of the equilibrium reconstruction is demonstrated by reducing the variability of the magnetic axis and boundary locations from several centimeters for reconstructions based on magnetic and experimental pressure constraints to only several millimeters for kinetic reconstructions based on transport code constraints, when different representations for basis functions were tested. Variability of the safety factor on-axis was reduced ten times in the same sensitivity study. The accuracy of the equilibrium reconstruction and subsequent mapping of experimental kinetic profile data have a significant impact on TGLF and linear CGYRO turbulence simulations, which predict different spectra of unstable modes and turbulent fluxes for cases with different numbers of constraints in the equilibrium reconstruction. Conversely, the stability analysis performed with the GATO code shows plasmas stable to n = 1 MHD modes in both equilibria using magnetic and experimental pressure constraints as well as the transport code constrained equilibrium. However, a scan of parameters away from these conditions shows considerable deviation in the threshold of unstable modes between these reconstructions. Therefore, for reliable plasma analysis and use in turbulence and stability calculations, a high fidelity equilibrium reconstruction with accurate kinetic constraints based on transport code solutions is necessary.

Vertical Shear Instability with Partially Reflecting Boundary Conditions

Abstract The vertical shear instability (VSI) is widely believed to be effective in driving turbulence in protoplanetary disks. Prior studies on VSI exclusively exploit the reflecting boundary conditions (BCs) at the disk surfaces. VSI depends critically on the boundary behaviors of waves at the disk surfaces. We extend earlier studies by performing a comprehensive numerical analysis of VSI with partially reflecting BCs for both the axisymmetric and non-axisymmetric unstable VSI modes. We find that the growth rates of the unstable modes diminish when the outgoing component of the flow is greater than the incoming one for high-order body modes. When the outgoing wave component dominates, the growth of VSI is notably suppressed. We find that the non-axisymmetric modes are unstable and they grow at a rate that decreases with the azimuthal wavenumber. The different BCs at the lower and upper disk surfaces naturally lead to non-symmetric modes relative to the disk midplane. The potential implications of our studies for further understanding planetary formation and evolution in protoplanetary disks (PPDs) are also briefly discussed.

A microscopic approach to crystallization: Challenging the classical/non-classical dichotomy.

We present a fundamental framework for the study of crystallization based on a combination of classical density functional theory and fluctuating hydrodynamics that is free of any assumptions regarding order parameters and that requires no input other than molecular interaction potentials. We use it to study the nucleation of both droplets and crystalline solids from a low-concentration solution of colloidal particles using two different interaction potentials. We find that the nucleation pathways of both droplets and crystals are remarkably similar at the early stages of nucleation until they diverge due to a rapid ordering along the solid pathways in line with the paradigm of "non-classical" crystallization. We compute the unstable modes at the critical clusters and find that despite the non-classical nature of solid nucleation, the size of the nucleating clusters remains the principle order parameter in all cases, supporting a "classical" description of the dynamics of crystallization. We show that nucleation rates can be extracted from our formalism in a systematic way. Our results suggest that in some cases, despite the non-classical nature of the nucleation pathways, classical nucleation theory can give reasonable results for solids but that there are circumstances where it may fail. This contributes a nuanced perspective to recent experimental and simulation work, suggesting that important aspects of crystal nucleation can be described within a classical framework.

Plasmon scattering at a junction in double-layer two-dimensional electron gas plasmonic waveguide

Abstract The scattering of plasmons at a junction within a double-layer two-dimensional electron gas plasmonic waveguide is studied via a full electromagnetic method. The dispersion relation is derived by utilizing the transfer matrix method and can be extended to the situation of an arbitrary number of layers. By numerically solving the dispersion equations, both the acoustic and optical plasmon modes are identified in this double layer system, and the unstable plasmon modes arising from plasmon coupling in different layers are discussed elaborately. Subsequently, the total fields are expanded with eigenmodes and matched at the interface to analyze the scattering characteristics at the junction. The results indicate that the total power of the plasmon mode is amplified when the electron fluid flows from a high concentration region to a low concentration region, and the amplification is more evident at a higher drift velocity. Additionally, we address the scattering of unstable plasmons caused by the two-stream instability and find that the transmitted plasmons are excited intensively at the incidence of the growing plasmon, leading to the plasmon amplification. The detailed examination of plasmon scattering at junction is the prerequisite for studying more complex structures of terahertz plasmonic devices and comprehending the corresponding amplification mechanism.

Nonlinear simulations of GAEs in NSTX-U

A set of nonlinear simulations has been performed in order to study the nonlinear evolution of unstable global Alfvén eigenmodes in the National Spherical Torus Experiment-Upgrade (NSTX-U). Results of the single toroidal mode number, n, simulations are compared with a full nonlinear simulation (all toroidal harmonics included). In single-n simulations, the conservation of two integrals of motion of a particle in a cyclotron resonance with a monochromatic wave is demonstrated, resulting in a one-dimensional evolution of the particle distribution in (E,μ,pϕ) phase-space. Nonlinear simulations (both single-n and full nonlinear) show a significant redistribution of the resonant fast ions, especially in the pitch parameter. Thus, the changes in the resonant particle's parallel and perpendicular energies can be several times larger than the total particle energy change, with only a small fraction transferring into the excitation of the mode itself. This implies that even a relatively small amplitude mode can significantly modify the beam distribution in the resonant region. For the NSTX-U case considered, the single-n simulation results are close to full nonlinear simulation only for the most unstable mode, in which case the saturation amplitudes and changes in the fast ion distribution are comparable. In contrast, peak amplitudes of subdominant modes in all-n simulations are smaller by a factor of 3–10 compared to single-n runs due to the flattening of the beam ion distribution by the fastest growing mode.

Mechanism of sinuous and varicose modes in electrokinetic instability.

The flow of miscible electrolyte streams with mismatched electrical conductivities in the presence of a parallel applied electric field is known to exhibit electrokinetic instability (EKI). This paper deals with EKI in a configuration where the base state is established by electro-osmotic flow (EOF) of three coflowing streams, with the center stream having different conductivity than the sheath streams. All reported experiments of this EKI have shown that the instability exhibits either sinuous or varicose modes depending upon whether the center stream has higher or lower conductivity than the sheath streams, respectively. In this paper we elucidate the physical mechanism underlying the selection of these unstable modes in EKI using linear stability analysis. The stability analysis shows that the EOF simply convects the unstable modes besides establishing the base state. The instability occurs due to stationary convection cells, in the reference frame moving with the EOF, resulting from the coupling of the applied electric field with free charge in the regions with conductivity gradients. Importantly, we show that the unstable and stable disturbances for the configuration with a higher conductivity center stream have opposite stability characteristics when the center stream has lower conductivity than the sheath streams. Our analysis correctly explains the numerous experimental observations showing the consistent appearance of sinuous modes for higher conductivity and varicose modes for lower conductivity center streams.

Electrothermal filamentation of igniting plasmas.

Dense, hot plasmas are susceptible to the electrothermal instability: a collisional process which permits temperature perturbations in electron currents to grow. It is shown here that linearizing a system comprised of two opposing currents and a mobile ion background as three distinct fluids yields unstable modes with rapid growth rates (∼10^{13}s^{-1}) for wavenumbers below a threshold k_{th}. An analytical threshold condition is derived, this being surpassed for typical hot-spot and shell parameters. Particle-in-cell simulations successfully benchmark the predicted growth rates and threshold behavior. Electrothermal filamentation within the shell will impact the burn wave propagation into the cold fuel and resulting burn dynamics.

Modelling and analysis of two-dimensional static and dynamic aeroelasticity of Fish Bone Active Camber morphing aerofoils

As a continuous and smooth morphing concept for aerofoils, the Fish Bone Active Camber (FishBAC) concept has demonstrated significant aerodynamic efficiency improvements over traditional hinged flaps. In this paper, to investigate the static and dynamic aeroelasticity of FishBAC aerofoils, an unsteady two dimensional coupled fluid-structure interaction model is developed, which includes the structural response of the FishBAC spine, skin, stringers, tendons and actuator, coupled to an unsteady aerodynamics model. The structural dynamic model is Timoshenko beam-theory-based, while the aerodynamic model is based on Peters’ unsteady model. The static and dynamic aeroelasticity is studied after the model is validated. Results show that the increase in pulley rotational angle reduces the zero-lift angle of attack, while keeping the slope between the lift coefficient and angle of attack the same. A shorter morphing region closer to the trailing edge is beneficial for generating larger lift coefficient with the same tendon moment and angle of attack. Flutter occurs with the increase of the air speed. When the morphing end position is fixed at 0.9 chord, increasing the morphing length reduces the critical flutter speed significantly, with the second bending mode tending to drive instability. With the same morphing length, moving the morphing region closer to the leading edge increases the critical flutter speed, and the unstable mode changes from the second mode into the first mode.

Linear stability analysis of a combustor model with a delayed feedback tube

We conducted a linear stability analysis of a laboratory-scale combustor to develop a delayed feedback method for mitigating combustion oscillations. We employed linearized hydrodynamic equations and a flame transfer function in the frequency domain to assess the stability under various feedback tube configurations, including changes in the length, radius, and connection position. The results of the stability analysis demonstrated a significant improvement in stability when the length of the feedback tube was 0.56 times the wavelength of the unstable mode. Furthermore, the tube radius had an optimal value for stabilizing the system. The connection position also played a crucial role in stability. The effective feedback tube conditions determined in the analysis were applied to a real combustor to demonstrate the successful suppression of oscillations experimentally. The suppression mechanism is discussed using the acoustic power based on the calculation results. The acoustic power profile of the system revealed that the oscillation suppression was not simply an addition of acoustic dissipation, but importantly, a reduction in acoustic power generation at the flame.

Nonlinear modulation of dispersive fast magnetosonic waves in an inhomogeneous rotating solar low-β magnetoplasma

Abstract We study the modulation of fast magnetosonic waves (MSWs) in rotating inhomogeneous low-β magnetoplasmas with the effects of gravitation and the Coriolis force. By employing the standard multiple-scale reductive perturbation technique (RPT), we derive a nonlinear Schrödinger (NLS) equation that governs the evolution of slowly varying MSW envelopes. The fast MSW becomes dispersive by the effects of the Coriolis force in the fluid motion, and the magnetic field and density inhomogeneity effects favor the Jeans instability in self-gravitating plasmas in a larger domain of the wave number (k, below the Jeans critical wave number, kJ) than homogeneous plasmas. The relative influence of the Jeans frequency (ωJ, associated with the gravitational force) and the angular frequency (Ω0, relating to the Coriolis force) on the Jeans carrier MSW mode and the modulational instability (MI) of the MSW envelope is studied. We show that the MSW envelope (corresponding to the unstable carrier Jeans mode with ωJ > 2Ω0 and k < kJ) is always unstable against the plane wave perturbation with no cut-offs for growth rates. In contrast, the stable Jeans mode with ωJ > 2Ω0 but k > kJ manifests either modulational stability or MI having a finite growth rate before being cut off. We find an enhancement of the MI growth rate by the influence of magnetic field or density inhomogeneity. The case with constant gravity force (other than the self-gravity) perpendicular to the magnetic field is also briefly discussed to show that the fast magnetosonic carrier mode is always unstable, giving MI of slowly varying envelopes with no cut-offs for the growth rates. Possible applications of MI in solar plasmas, such as those in the X-ray corona, are also briefly discussed.

Uncertainty quantification of structural blade parameters for the aeroelastic damping of wind turbines: a code-to-code comparison

Abstract. Uncertainty quantification (UQ) is a well-established category of methods to estimate the effect of parameter variations on a quantity of interest based on a solid mathematical foundation. In the wind energy field most UQ studies focus on the sensitivity of turbine loads. This article presents a framework, wrapped around a modern Python UQ library, to analyze the impact of uncertain turbine properties on aeroelastic stability. The UQ methodology applies a polynomial chaos expansion surrogate model. A comparison is made between different wind turbine simulation tools on the engineering model level (alaska/Wind, Bladed, HAWC2/HAWCStab2, and Simpack). Two case studies are used to demonstrate the effectiveness of the method to analyze the sensitivity of the aeroelastic damping of an unstable turbine mode to variations of structural blade cross-section parameters. The code-to-code comparison shows good agreement between the simulation tools for the reference model, but also significant differences in the sensitivities.

A Comparative Evaluation of Conveyor Belt Disc Brakes and Drum Brakes: Integrating Structural Topology Optimization and Weight Reduction

Topology optimization is a well known and sophisticated method for designing structures. Through a finite element analysis, this method optimizes the design and material distribution to obtain an ideal strength-to-weight ratio and improved strain-to-weight ratio. This study involves the development of a comprehensive model for a brake using the ANSYS Parametric Design Language. The purpose of the model is to accurately characterize the geometry of the disc or drum. The technique of a complex eigenvalue analysis is used to identify the presence of unstable modes occurring at distinct frequencies, indicating instability. A braking force of 17,492 kN was exerted at a rotational velocity of 55 rad/s for 10 s. The optimization process resulted in significant mass reduction while maintaining structural integrity. In the drum brake, the mass was reduced from 114.01 kg to 104.07 kg, while the disc brake’s mass decreased from 68.81 kg to 56.68 kg.

Asynchronous control of continuous‐time switched systems with all unstable modes under DoS attacks

Asynchronous control of continuous‐time switched systems with all unstable modes under DoS attacks

Instability and Mesoscale Eddy Fluxes in an Idealized 3‐Layer Beaufort Gyre

AbstractWe study the impacts of a continental slope on instability and mesoscale eddy fluxes in idealized 3‐layer numerical model simulations. The simulations are inspired by and mimic the situation in the Arctic Ocean's Beaufort Gyre, where anti‐cyclonic winds drive anti‐cyclonic currents that are guided by the continental slope. The forcing and currents are retrograde with respect to topographic Rossby waves. The focus of the analysis is on eddy potential vorticity (PV) fluxes and eddy‐mean flow interactions under the Transformed Eulerian Mean framework. Eddy lateral vorticity fluxes dominate over the continental slope where eddy form stress, that is, vertical momentum flux, is suppressed due to the topographic PV gradient. The diagnosis also shows that while eddy momentum fluxes are up‐gradient over parts of the slope, the total quasi‐geostrophic PV flux is down‐gradient everywhere. We then calculate the linearly unstable modes of the time‐mean state and find that the most unstable mode contains several key features of the observed finite‐amplitude fluxes over the slope, including down‐gradient PV fluxes. When accounting for additional unstable modes, more qualitative features of the observed eddy fluxes in the numerical model are reproduced.

Radiation pressure-driven Rayleigh–Taylor instability in compressible strongly magnetized ultra-relativistic degenerate plasmas

The radiation pressure and strong magnetic fields are prominent in the structures of Rayleigh–Taylor (R–T) instability in the interior of white dwarfs. This paper investigates the radiation pressure-driven R–T instability in a compressible and magnetized ultra-relativistic degenerate strongly coupled plasma. The equation of state has been derived for such systems incorporating ultra-relativistic degenerate electrons with their radiation pressure and ion gas compressibility. The dispersion relation of the density gradients driven R–T instability is analyzed using the generalized hydrodynamic fluid model in the strongly coupled and weakly coupled limits. It is observed that the R–T instability criterion has been modified significantly due to radiation pressure, ion gas compressibility and degeneracy parameters. In the kinetic limit, the instability region is shorter than the hydrodynamic limit due to the dominance of plasma frequency over the viscoelastic relaxation frequency. The outcomes are explored in analyzing the development of R–T instability in the strongly magnetized carbon–oxygen white dwarfs. The radiation pressure, electron temperature and ion density strongly suppress the growth rate of the R–T instability in the interior of white dwarfs. The strong magnetic fields introduce asymmetry to the system by destabilizing the R–T unstable modes. The present results are also useful for understanding the R–T instability in the star formation and dense plasmas in inertial confinement fusion in some limiting cases.

Modal and non-modal stability for Hagen–Poiseuille flow with non-ideal fluid

Modal and non-modal stability analyses are applied to Hagen–Poiseuille flow with a non-ideal fluid. The non-ideal fluid is defined as a fluid close to its vapor–liquid critical point. In this region, properties of the fluid deviate significantly from the assumptions of the ideal gas model. In this paper, the specific example of CO2 near the critical point is taken as a non-ideal fluid. We studied fluids at supercritical pressure and different wall temperatures so that the centerline temperatures can be lower, equal, and higher than the pseudo-critical temperature. Flow instability is characterized by the Reynolds number, and the product of the Prandtl and Eckert numbers. In modal stability analysis, we observe that there is no unstable mode in Hagen–Poiseuille flow with a non-ideal fluid. Regarding the growth rate, as the axial wavenumber increases, another mode becomes the least stable. The non-modal theory is employed to investigate the optimal response to harmonic external force and transient energy growth. The influence of axial and azimuthal wave numbers, Prandtl and Eckert numbers, and thermodynamic states are also taken into account. In this study, we identify an generalized inflection point in the transcritical base profile, causing the transcritical state to be the most unstable. In non-modal instability, we observe that the optimal response mainly occurs at time invariant axisymmetric disturbance. This suggests that the axisymmetric disturbance could potentially initiate the transition to turbulence.

Nonmodal linear stability analysis of hypersonic flow over an inclined cone

Nonmodal linear stability analysis results are presented for hypersonic flow over a cone at 6° angle of attack complementing earlier modal stability analysis. Based on the parallel flow assumption, singular value decomposition is applied to obtain the optimal linear combination of global crossflow modes. The optimal disturbance exhibits significant transient growth in the initial short distance and progressively follows the path of the most unstable mode downstream. The largest transient energy gain is observed for disturbances at around 40 kHz close to the most amplified modal frequency and tends to increase with the Reynolds number. The optimal disturbance initially exhibits two amplitude peaks in the azimuthal direction, one lying in the leeward region where the unstable crossflow modes reside and the other in the windward region where the adjoint modes exist. As the optimal disturbance travels downstream, the second amplitude peak rapidly shifts toward the leeward side and reaches the optimal energy gain when it eventually merges with the first amplitude peak. The evolution process of the optimal disturbance indicates that the optimal disturbance might have exploited the locally crossflow instability through traveling from the windward side to the leeward side.