Damping Region Research Articles

Stability and receptivity analyses of the heated flat-plate boundary layer with variable viscosity

This article presents the modal, non-modal, and resolvent analyses of the boundary layer developed over a heated flat-plate with temperature-dependent viscosity using linear stability theory. The governing equations are derived in the normal velocity–vorticity form by imposing small infinitesimal disturbances on the base flow with the Oberbeck-Boussinesq (OB) approximation. The spectral method is employed to discretize the governing stability equations in the wall-normal direction. The base flow comes from the similarity solution using R-K4th order method along with shooting techniques. The effects of viscosity stratification, inertia, shearing, and buoyancy on the stability of the boundary layer are investigated by varying the sensitivity parameter (ϵ), Reynolds (Re), Prandtl (Pr), and Richardson numbers (Ri). The modal analysis shows the time-asymptotic behavior of the disturbances and onset of instability is mainly caused by amplification of Tollmien–Schlichting (T-S) waves similar to as observe in the traditional Blasius case. The modal stability increases with increase in sensitivity parameter and stabilizing effects become more pronounced for liquid than gas. However, the thermal effects lead to destabilize the flow and strong destabilizing effects produced for higher Prandtl number. On the other hand, non-modal analysis displays an early transient growth of disturbances and an existence of these non-normality effects identified from the pseudospectra via. resolvent analysis. The non-modal growth increases with increase in ϵ even though T-S modes shift towards the damped region, which indicates the continuous modes in the eigenspectrum are more dominated than the discrete T-S modes due to the thermal effects. To clarify this qualitative change, a component-wise input–output analysis is performed to measure the receptivity to particular external disturbances. The results show the thermal energy of the disturbances is converted into kinetic energy due to thermal effects, resulting in strong receptivity amplification at the continuous mode due to the non-normality of the linear operator. Thus, the boundary layer under the influence of viscosity stratification, heating, and shearing effects is vulnerable to free-stream disturbances that could significantly affect bypass transition

A Joint Active Damping Strategy Based on LCL-Type Grid-Connected Inverters for Grid Current Feedback and PCC Voltage Unit Feedforward.

The negative high-pass filter feedback of the grid current (NFGCF) can offer active damping for the LCL-type grid-connected inverter. Due to the control delay in digital control systems, this damping can cause the system to exhibit non-minimum phase behavior within specific frequency ranges. This study proposes a joint active damping approach that combines grid current feedback and the point of common coupling (PCC) voltage unit feedforward. The proposed method introduces a dynamic damping region that varies with grid impedance. By developing suitable damping loop control parameters, this region can span the entire frequency range, even exceeding the Nyquist frequency fs/2. The research results demonstrate that the proposed approach enhances robustness against variations in grid impedance and eliminates non-minimum phase behavior. Simulation and experimental outcomes validate the effectiveness of this joint active damping method.

Improved scheme of grid-connected inverters based on virtual PCC and impedance remodeling with enhanced steady-state and dynamic performance

The issue of low-frequency oscillation (LFO) becomes more prominent when considering the phase-locked loop (PLL) impact of grid-connected inverter (GCI) under weak grid. Impedance analysis shows that the frequency interaction point outside the capacitive negative damping region can effectively avoid the oscillation. Therefore, a modified PLL scheme is designed to shape the characteristics of the GCI output impedances, which effectively tracks the grid phase through the virtual point of common coupling and adjusts the phase- frequency characteristic of the GCI equivalent output impedance towards an increasing phase angle. On this basis, the impedance remodeling strategy is used to improve the system, which further broadens the feasible range of stable operation and ensures the phase margin of the GCI. The comparison results indicate that proposed scheme demonstrates enhanced capability in suppressing LFO and exhibits a wider range of adaptability to grid impedance. Experimental validation has verified the accuracy of the theoretical analysis, leading to the conclusion that the GCI with proposed scheme possesses superior dynamic performance.

Damp and droop coefficient stability region analysis for interlinking converters with virtual asynchronous machine controllers in virtual energy storage systems

Although virtual energy storage systems (VESSs) based on virtual asynchronous machine (VAM) control strategy have been widely applied to microgrids to achieve power balance between supply and demand sides, damp and droop coefficients are variable due to the system operation state. It is prone to causing wideband oscillation, such as low-frequency and sub/super-synchronous oscillation. Thus, this paper proposes one damp and droop coefficient stability region identification approach based on the Guardian map theory for the interlinking converter (IC) of VESSs. Firstly, the VAM control method of IC is derived through the traditional asynchronous machine, and its small-signal model is further built. The aforesaid process is the important modeling basic. Secondly, the concept of the practical small signal stability region (P-SSSR) is proposed to make up for the deficiency of the traditional small signal stability region (SSSR) that cannot ensure system robustness. Thirdly, the mapping method based on translation and rotation mapping is introduced to ensure that the identification of the P-SSSR problem is switched into the Hurwitz matrix identification problem. Furthermore, the high-dimensional parameter stability region can be obtained through the Guardian map theory. Finally, the performance of the proposed method can be verified through simulation and experiment results.

Excitation signatures of isochorically heated electrons in solids at finite wave number explored from first principles

Ultrafast heating of solids with modern x-ray free electron lasers (XFELs) leads to a unique set of conditions characterized by the simultaneous presence of heated electrons in a cold ionic lattice. In this work, we analyze the effect of electronic heating on the dynamic structure factor (DSF) in bulk aluminum (Al) with a face-centered cubic lattice and in silicon (Si) with a crystal diamond structure using first-principles linear-response time-dependent density functional theory simulations. We find a thermally induced red shift of the collective plasmon excitation in both materials. In addition, we show that the heating of the electrons in Al can lead to the formation of a double-plasmon peak due to the extension of the Landau damping region to smaller wave numbers. Finally, we demonstrate that thermal effects generate a measurable and distinct signature (peak-valley structure) in the DSF of Si at small frequencies. Our simulations indicate a variety of new features in the spectrum of x-ray-driven solids, specifically at finite momentum transfer, which can be probed in upcoming x-ray Thomson scattering experiments at various XFEL facilities. Published by the American Physical Society 2024

Output feedback pole-placement in damping region for discrete-time uncertain polytopic systems

ABSTRACT Pole placement with specified damping and decay rate is one of the primary criteria for ensuring good transient response. This control design problem has known solutions for continuous-time systems in terms of the linear matrix inequality (LMI) region. However, a systematic solution for a discrete-time system is an open problem due to the non-convexity of the constant damping locus. This paper addresses the problem of placing the closed-loop poles of linear discrete-time uncertain polytopic systems in a constant damping region. The non-convex damping region is approximated to an elliptical segment that represents an LMI region. Criteria for designing state and output feedback (static as well as dynamic) controllers are then derived. The effectiveness of the proposed approach is demonstrated with examples including a boost converter to improve its transient behaviour in the presence of input voltage and load variations.

An Active Damping Method With Improved Capacitor Current Feedback

Abstract Capacitor-Current Feedback Active Damping (CCFAD) is widely employed in LCL grid-tied inverters. However, the delay introduced by digital control can alter the traditional active damping characteristics, with the equivalent virtual resistance having a positive/negative crossover frequency of f s/6. The LCL filter’s resonant frequency may change due to the extensive variation in grid impedance under weak grid conditions. When the resonant frequency of the LCL filter exceeds f s/6, the stability of the system is severely compromised. A better approach is to add a lead compensation element to the current feedback branch of traditional CCFAD in response to these issues. This compensates for the phase lag caused by control delay, effectively extending the active damping region to (0, f R), f R ∈ (f s/3, f s/2), thereby enhancing system stability and robustness. The proposed method’s effectiveness has been confirmed by theoretical analysis and simulation on the MATLAB/Simulink platform, which utilizes a single-phase LCL grid-tied inverter model.

Hydrodynamic damping in laminar, transient and turbulent regimes: Analytical and computational study

A study of oscillating flow over a flat plate using RANS modeling was conducted to investigate hydrodynamic damping and its correlation with the unsteady and oscillating boundary layer. It is found that the predictions with the γ SST turbulence model was more consistent with the experimental results compared to the SST turbulence models. Two distinct damping behaviors were observed in the flow. For Reδ<400, the damping remained constant and matched the laminar solution of Stokes’ second problem. In this scenario, the flow regime was quasi-laminar, and an increase in free-stream velocity did not lead to a rise in the fluid damping coefficient. Conversely, for Reδ>400, the increase in Reδ induced turbulence during the deceleration phase, resulting in an amplification of the phase difference between displacement and wall shear stress, consequently increasing damping. This trend continued at higher values of Reδ and during the quasi-steady regime. The results indicated that the existence of different damping regions, as reported in previous studies, occurred within a range similar to that of Stokes’ second problem. A transition in the boundary layer regime at higher Reδ could be a contributing factor to the variations in damping behavior.

An Improved Active Damping Method for Enhancing Robustness of LCL-Type, Grid-Tied Inverters under Weak Grid Conditions.

The conventional proportional-gain-feedback link can only obtain the smallest effective damping region (EDR) due to the control delay among all the active damping methods regarding the capacitor current feedback. The digitally controlled system tends to be unstable when the system resonant frequency reaches the critical frequency caused by the grid impedance variation. To weaken the adverse effect on the system caused by the control delay, phase-lead feedback links are applied along the feedback path to provide phase compensation. By taking the simplicity and reliability of the feedback links into account, this paper proposes an alternative to an ideal differentiator, which consists of the Tustin discrete form of 's' and a digital low-pass filter. This proposed method has an identical phase frequency characteristic as an ideal differentiator but a better magnitude frequency characteristic, and its EDR can reach [0, fs/3]. The system stability analysis is conducted under different resonant frequencies, and under the condition of a weak grid, the co-design approach of the active damper and digital controller is presented. Finally, the experimental results are shown to verify the proposed method.

Synthetic route to low damping in ferromagnetic thin-films

Previous theory indicated that the individual monolayers within transition metal ferromagnet thin-films contribute different magnitudes to the total ferromagnetic damping. Here, the aim was to investigate if the thin-film damping could be reduced by electronic engineering of the higher damping regions via localized doping. We present new theoretical analysis and experimental results for sputtered Co thin-films in which the upper and lower surface regions were locally doped with Cr. Theory indicates that local doping does reduce the damping and the experiments show a comparable reduction of the damping with increasing local doping up to 30% Cr, while the measured damping falls further with higher local doping, which may be attributed to changes in the film structure. This work opens a route to create low-damping magnetic thin-films.

Identification of drought-responsive phenolic compounds and their biosynthetic regulation under drought stress in Ligularia fischeri.

Ligularia fischeri, a leafy edible plant found in damp shady regions, has been used as an herbal medicine and is also consumed as a horticultural crop. In this study, we investigated the physiological and transcriptomic changes, especially those involved in phenylpropanoid biosynthesis, induced by severe drought stress in L. fischeri plants. A distinguishing characteristic of L. fischeri is a color change from green to purple due to anthocyanin biosynthesis. We chromatographically isolated and identified two anthocyanins and two flavones upregulated by drought stress using liquid chromatography-mass spectrometry and nuclear magnetic resonance analyses in this plant for the first time. In contrast, all types of caffeoylquinic acids (CQAs) and flavonol contents were decreased under drought stress. Further, we performed RNA sequencing to examine the molecular changes in these phenolic compounds at the transcriptome level. In an overview of drought-inducible responses, we identified 2,105 hits for 516 distinct transcripts as drought-responsive genes. Moreover, differentially expressed genes (DEGs) associated with phenylpropanoid biosynthesis accounted for the greatest number of both up- and downregulated DEGs by Kyoto Encyclopedia of Genes and Genomes enrichment analysis. We identified 24 meaningful DEGs based on the regulation of phenylpropanoid biosynthetic genes. Potential drought-responsive genes included upregulated flavone synthase (LfFNS, TRINITY DN31661 c0 g1 i1) and anthocyanin 5-O-glucosyltransferase (LfA5GT1, TRINITY DN782 c0 g1 i1), which could contribute to the high levels of flavones and anthocyanins under drought stress in L. fischeri. In addition, the downregulated shikimate O-hydroxycinnamolytransferase (LfHCT, TRINITY DN31661 c0 g1 i1) and hydroxycinnamoyl-CoA quinate/shikimate transferase (LfHQT4, TRINITY DN15180 c0 g1 i1) genes led to a reduction in CQAs. Only one or two BLASTP hits for LfHCT were obtained for six different Asteraceae species. It is possible that the HCT gene plays a crucial role in CQAs biosynthesis in these species. These findings expand our knowledge of the response mechanisms to drought stress, particularly regarding the regulation of key phenylpropanoid biosynthetic genes in L. fischeri.

Stability analysis of a Timoshenko beam with local degenerate viscoelastic damping

We consider the Timoshenko beam with localized viscoelastic damping of Kelvin-Voigt type. The constitutive law has singularity at the interface of the damped and undamped region. More precisely, the damping coefficients are continuous, but their derivatives have singularities at the interface. We show that the system satisfies a sharper polynomial decay rate, which is consistent with the polynomial decay rate when the constitutive law is discontinuous and exponential stability when the law is of C1-type. This is a big step toward the goal of obtaining eventually the optimal decay rate.

An alternative control synthesis for stability enhancement of digital-controlled LCL-filtered grid-connected inverter

• A control synthesis is proposed to damp capacitor current resonance for LCL-filtered GCI. • The stability and performance characteristics are analyzed and compared with methods from the literature. • Intuitive design, wider stable damping region, better dynamic performance, and higher parametric robustness are the potential benefits of the proposed control synthesis. In distributed power generation systems, the inherent resonance phenomena of LCL -filtered grid-connected inverter is one of the major challenges faced by the integration of renewable energy resources with the electric power grid. In this context, the capacitor current based multi-loop active damping method is employed due to lossless resonance damping and flexible control design. However, the damping loop with the feedback compensation design suffers from relatively higher parameters sensitivity unless employed with the reduced digital delays. The filter parameters fluctuation causes a shift in resonance frequency, which leads to ineffective damping at the critical resonance frequency and may risk the control loop stability. Therefore, an alternative linear control synthesis is proposed to design the capacitor current damping loop in order to reduce the filter parameters sensitivity. The proposed design realizes the equivalent virtual impedance in an alternative manner to suppress the resonance peak and enhanced the stability characteristics of the grid-connected inverter. A detailed stability and performance analysis have been done to show the widened stable damping region and high parametric robustness of the suggested design as compared to the literature method. Simulations and experimental results are presented to confirm the theoretical findings.

The memory effects in the Langevin description of nuclear fission

We have calculated the fission width Γf within a one-dimensional Langevin approach with the potential energy given by simple two-parabolic (Kramers) potential and found out that for excitation energies slightly above the fission barrier the Γf(E) calculated in constant energy regime is substantially smaller than Γf(T) calculated in constant temperature regime and popular Bohr-Wheeler or Kramers approximations. At small excitations Γf(E) is by one order of magnitude smaller than Γf(T).In order to clarify the role of memory effects we have carried out the calculations of fission width within the Markovian and non-Markovian Langevin approaches. It is shown that the magnitude of memory effects depends very much on the value of the damping of collective motion parameter η. In the low damping region, the fission width Γfgrows as a function of η and decreases as a function of the relaxation time τ. In the high damping region, the tendency is opposite. The fission width Γfdecreases as a function of η and increases as a function of τ. Such dependence is common both for small and large excitations. For the excitation energies above 10 MeV the memory effects are negligibly small and the Markovian limit is quite accurate.

LCL‐filter resonance suppression in grid‐connected inverter based on strictly real positive plant strategy

AbstractResonance is one of the most significant challenges in a voltage source inverter interfaced with the grid through an LCL filter. The capacitor current (CC) damping control methodology is considered due to its high‐quality of grid injected current feature. It is widely accepted that the proportional CC feedback compensation damping method becomes ineffective at critical resonance frequency due to control loop delays and may result in an unstable system under grid impedance or filter parameters variations. A suitable differential compensator placed in the CC feedback path can address this issue with a trade‐off between robustness and noise rejection capability. This paper offers a different design method called parallel feedforward compensation (PFC) method, which builds an almost strictly real positive (ASRP) plant and realized damping with enhanced stability features. In the proposed alternative, a compensator consisting of a damping gain and a sampled delay is placed across the filter plant and filter CC feedback loop and the joint output of this augmented plant is then transmitted back at the reference point on the input side of the inverter to attenuate the undesirable resonance peak. The control response and stability performance analysis show that the suggested methodology offers a wide damping region, high robustness, and improved control performance. Simulation and experimental results are presented to confirm the theoretical findings.

Dust charge fluctuation and ion acoustic wave propagation in dusty plasma with q-nonextensive hot and Maxwellian cold electrons

We have employed the self-consistent kinetic theory to study the linear dispersion relation of ion acoustic waves in a four-component plasma consisting of nonextensive hot electrons, Maxwellian cold electrons, positive ions, and dust particles. The dust charging process with the modified ion acoustic wave damping, as well as its unstable mode, has been graphically illustrated. It is found that the dust charging mechanism depends on the density of hot electrons, the degree of nonextensive electron distribution, and the temperature ratio of hot to cold electrons. It is shown that the damping and instability rates of ion acoustic waves due to dust charge fluctuations explicitly depend on the choice of electron distribution and the magnitude of dusty plasma parameters. In addition, we have studied the ion acoustic Landau damping in the absence of dust particles. It is found that the weak damping region broadens, while the strong damping region shrinks and is shifted toward the short wavelength region for the increase in the temperature ratio of hot to cold electrons.

Acoustic Feedback and Its Impact on Fan Flutter in Short Aeroengine Intakes

The authors have investigated pressure waves being emitted by the structural motion of a rotor blade and their impact on fan flutter sensitivity. This impact results from an acoustic feedback loop caused by reflection phenomena at the intake lip and may lead to a specific form of aeroelastic instability. Harmonic balance simulations of the fan/intake system over a wide operating range and blade eigenfrequencies were carried out. A significant impact on the rotor aerodynamic damping was observed as compared with the isolated rotor analysis due to the presence of the intake. This influence was either stabilizing or destabilizing, depending mainly on the phase relation between the emitted and reflected unsteady pressure fields. Computational fluid dynamics (CFD) data were analyzed accordingly, taking advantage of two-dimensional wave split as well as three-dimensional in-duct modal decomposition techniques. By deriving a simple analytical model based on eigenvalue analysis, a landscape showing regions of aerodynamic damping and excitation could be drawn over the investigated frequency–mass flow range. This analytical model and its verification with CFD data can help in identifying destabilizing areas at an early design stage, and hence support design decisions regarding flutter stability or give indications where analysis with higher fidelity is required.

Sharp Decay Rate for the Damped Wave Equation With Convex-Shaped Damping

Abstract We revisit the damped wave equation on two-dimensional torus where the damped region does not satisfy the geometric control condition. It was shown in [1] that, for sufficiently regular damping, the damped wave equation is stale at a rate sufficiently close to $t^{-1}$. We show that if the damping vanishes like a Hölder function $|x|^{\beta }$, and in addition, the boundary of the damped region is locally strictly convex with positive curvature, the wave is stable at rate $t^{-1+\frac {2}{2\beta +7}}$, which is better than the known optimal decay rate $t^{-1+\frac {1}{\beta +3}}$ for strip-shaped dampings of the same Hölder regularity. Moreover, we show by example that the decay rate is optimal. This illustrates the fact that the sharp energy decay rate depends not only on the order of vanishing of the damping but also on the shape of the damped region. The main ingredient of the proof is the averaging method (normal form reduction) developed by Hitrik and Sjöstrand ([20], [35]).

Eventual differentiability of coupled wave equations with local Kelvin-Voigt damping

&lt;p style='text-indent:20px;'&gt;In this work, we consider a coupled wave equations with partially and locally distributed Kelvin-Voigt damping, where only one equation is dissipative.&lt;/p&gt;&lt;p style='text-indent:20px;'&gt;Under the assumption that the damping coefficient changes smoothly near the interface of the damped and undamped regions, we investigate the effectiveness of the indirect control, and we prove that the associated semigroup is eventually differential.&lt;/p&gt;

Superlattice on the surface of a nanotube

The results of theoretical studies of the thermodynamic, kinetic, and high-frequency properties of the electron gas on the surface of a nanotube in a magnetic field in the presence of a longitudinal superlattice are presented. Nano-dimensions of the motion area lead to energy quantization. Its multiply connected structure in the presence of a magnetic field leads to effects that are derived from the Aharonov–Bohm effect. It is shown that the curvature of a nanotube, even in the absence of a magnetic field, causes new macroscopic oscillation effects such as de Haas–van Alphen oscillations, which are associated with the quantization of the transverse electron motion energy and with the root peculiarities of the density of electron states on the nanotube surface. Thermodynamic potentials and heat capacity of the electron gas on the tube are calculated in the gas approximation. The Kubo formula for the conductivity tensor of the electron gas on the nanotube surface is obtained. The Landau damping regions of electromagnetic waves on a tube are determined and the beats are theoretically predicted on the graph of the dependence of conductivity on tube parameters. In the hydrodynamic approximation, the plasma waves on the surface of a semiconductor nanotube with a superlattice are considered. It is shown that optical and acoustic plasmons can propagate along a tube with one kind of carrier. Electron spin waves on the surface of a semiconductor nanotube with a superlattice in a magnetic field are studied. The spectra and areas of collisionless damping of these waves are found. We have shown that the spin wave damping is absent in these areas if the tubes with a degenerate electron gas have small radius.