Mode Instability Research Articles

Role of electrostatic perturbation on kinetic resistive wall mode with application to spherical tokamak

A more complete non-perturbative magnetohydrodynamic (MHD)-kinetic hybrid formulation is developed by including the perturbed electrostatic potential δφ in the particle Lagrangian. The fluid-like counter-parts of the hybrid equations, in the Chew-Goldberger-Low high-frequency limit, are also derived and utilized to test the new toroidal implementation in the MARS-K code. Application of the updated non-perturbative hybrid model for a high-β spherical tokamak plasma in MAST finds that the perturbed electrostatic potential generally plays a minor role in the n = 1 (n is the toroidal mode number) resistive wall mode instability. The effect of δφ is largely destabilizing, with the growth rate of the instability increased by several (up to 20) percent as compared to the case without including δφ. A similar relative change is also obtained for the kinetic-induced resonant field amplification effect at high-β in the MAST plasma considered. The updated capability of the MARS-K code allows quantitative exploration of drift kinetic effects on various MHD instabilities and the antenna-driven plasma response where the electrostatic perturbation, coupled to magnetic perturbations, may play important roles.

Концентрационная конвекция в замкнутой области пористой среды при заданном вертикальном перепаде концентрации и учете иммобилизации примеси

This work is devoted to the study of stability of horizontal filtration flow of a mixture through a closed porous domain taking into account impurity immobilization. The instability arises due to the vertical concentration difference of heavy impurities, which creates unstable density stratification. A general mathematical model describing the transport of an impurity through a porous medium is presented. The equations are simplified for the case of low impurity concentration. Simplification made it possible to analytically obtain the solution corresponding to homogeneous horizontal filtration and to study its stability. It is known that, in the narrow regions of porous medium and at weak intensities of the external flow, convection is excited in a monotonous manner. On the contrary, in the case of an infinite horizontal layer, oscillatory instability is observed. A study of the transition between the instability modes is presented. It is shown that the oscillatory regime is observed in long regions or at significant intensity of the external horizontal flow. At low flow intensities, convective cells do not move relative to the region and, hence, there is no reason for oscillations. It has been established that the range of flow intensity values, in which oscillations are observed, grows with increasing length of the domain. Impurity immobilization leads to the stabilization of horizontal filtration with respect to convective perturbations. Critical curves and stability maps are obtained in a wide range of problem parameters and then analyzed. For limiting cases, a comparison is made with the known results obtained for an infinite layer.

Large Eddy Simulation and Acoustic Analysis of Combustion Instability in an Annular Combustor with Low-Swirl Flames.

Self-excited combustion instability in an annular combustor with low-swirl flames is studied with a combination of large eddy simulation (LES) and acoustic solvers. Acoustic analysis with a Helmholtz solver provides an estimate of frequencies and modal structures in the annular combustor. LES gives detailed modal dynamics for specific instability modes. Combustion instabilities in the annular combustor including longitudinal, spinning, and standing modes are successfully captured in a single LES. Numerical results show that the instability modes are not constant; they switch among these modes randomly and rapidly. The flow oscillates back and forth in phase with the largest pressure amplitude located near the outlet of the injectors for the longitudinal mode. The azimuthal instability oscillates in the 1A2L mode of the annular system. In the spinning mode, the pressure antinodes move forward while the modal structure keeps constant. For the standing mode, the locations of pressure antinodes are fixed in the annular combustor and the fluctuations at the pressure antinodes keep out of phase. The near-zero value of the mean spin ratio indicates that the dominant azimuthal mode is the standing mode. The azimuthal modes captured by LES are in good agreement with that predicted by Helmholtz solver in terms of frequency and modal structure. The maximum deviation of the predicted frequency is less than 5%. This adds values before the low-swirl injector is placed into the actual annular combustor.

Evidence of Kelvin-Helmholtz and tearing mode instabilities at the magnetopause during space weather events

Introduction: Kelvin-Helmholtz (KH) and tearing mode (TM) instabilities are one of the most important mechanisms of solar wind energy, momentum and plasma transport within the magnetosphere.Methods: To investigate the conditions under which KHTM instabilities occur in the Earth environment it is fundamental to combine simultaneous multipoint in situ measurements and MHD simulations. We analyzed data from the THEMIS and Cluster spacecraft considering two Space Weather (SWE) events starting with an M2.0 flare event (hereafter Case-1) that occurred on 21 June 2015 and the most-intensive flare (X9.3) of solar cycle 24 that occurred on 6 September 2017 (hereafter Case-2).Results: Our analysis utilized a 2D MHD model for incompressible and viscous flow. The results from Case-1 indicate the presence of KH and TM instabilities, suggesting existence of observed low-amplitude oscillations at the nose of the magnetopause. However, the MHD simulations for Case-2 did not show any evidence of KH vortices, but did reveal the presence of “magnetic island” structures during a low-shear condition. The reconnection rate derived from the observations is compared with the computed one in the presence of developed instabilities inside the Earth’s magnetopause.

Stability of convective rolls in a horizontal layer rotating about an inclined axis

We present three results on stability of rolls in Boussinesq convection in a plane horizontal layer with rigid boundaries that is rotating about an inclined axis with the angular velocity Ω = ( Ω 1 , Ω 2 , Ω 3 ) . (i) We call the full problem the set of equations governing the temporal behaviour of the flow and temperature for an arbitrary Ω , and by the reduced problem the set of equations for the angular velocity ( Ω 1 , 0 , Ω 3 ) . Here x,y are horizontal Cartesian coordinates in the layer and z is the vertical one. We prove that a y-independent solution to one of the two problems is also a solution to the second one. (ii) We calculate the critical Rayleigh number for the monotonic onset of convection. The instability mode in the form of rolls (a flow independent of a horizontal direction) is assumed. Let β be the angle between the horizontal projection of Ω and the rolls axes. We show that β = 0 for the least stable mode. When the axis of rotation is horizontal, this is proven analytically, and for Ω 3 ≠ 0 , the result is obtained numerically. Taking i into account, we conclude that the critical Rayleigh number for the onset of convection is independent of Ω 1 and Ω 2 and the emerging flow are rolls with axis aligned with the horizontal component of the rotation vector. (iii) We study the behaviour of convective flows by integrating numerically the three-dimensional equations of convection for Ω = ( 0 , Ω 2 , Ω 3 ) and a range of the Rayleigh numbers, other parameters of the problem being fixed. We assume square horizontal periodicity cells, whose sides are equal to the period of the most unstable mode. The computations indicate that, in general, in the nonlinear regime convective rolls become more stable as Ω 2 increases. Namely, on increasing Ω 2 , the interval of the Rayleigh numbers for which convective rolls are stable increases.

Impact of supra-thermal particles on plasma performance at ASDEX Upgrade with GENE-Tango simulations

This paper presents global gyrokinetic simulations on the transport time scale of an ASDEX Upgrade H-mode discharge showing a pronounced peaking of the on-axis ion temperature profiles. Leveraging the newly developed GENE-Tango tool, which combines the global gyrokinetic code GENE with the transport solver Tango, we investigate the impact of energetic particles and electromagnetic effects on the improved plasma performance observed in the experimental discharge. Our results reveal that a striking agreement between the GENE-Tango simulations and the experimental measurements can be achieved only when energetic particles and electromagnetic effects are simultaneously retained in the modeling. In contrast, when these are neglected we observed a significant underestimation of the on-axis ion temperature, aligning with profiles computed using TGLF-ASTRA. The peaking in the ion temperature profile observed in the simulations can be attributed to the effective suppression of turbulence by high-frequency electromagnetic modes, likely Kinetic Ballooning Modes/Alfvén eigenmodes. These modes play a critical role in enhancing zonal flow activity and shearing rate levels which thus lead to a localized increase in the temperature gradient. However, it is crucial to maintain these modes at a state of marginal stability or weak instability to prevent energetic particle turbulence destabilization. Otherwise, the result would be a flattening of all the thermal profiles. Interestingly, we found that global GENE-Tango simulations are required to model correctly the linear dynamics of these high-frequency modes. Additionally, global simulations demonstrate greater tolerance than flux-tube simulations for marginal instability of these high frequency modes while maintaining power balance agreement.

The effect of lateral thrust on the progressive slope failure under excavation and rainfall conditions

Large landslides can involve the multiple failures of regional slopes. To understand the effect of lateral thrust caused by the failure of one slope on its surroundings, the failures of two adjacent highway slopes in Guangdong Province, China, were investigated in detail. The interactive failure processes and landslide morphological characteristics of the two slopes were first analyzed based on the on-site investigation. Then, a plane mechanical model of a large-scale slope was established to evaluate the significant influence of the lateral thrust generated by the west slope acting on the east excavated slope. Furthermore, the extrusion effect of the west slope was modelled under the alternate excavation disturbance and rainfall by transferring the thrust forces onto the interface elements, and the induced failure mechanism and instability mode of the east slope under lateral thrust were reproduced numerically. The results show that the compression-shear failure occurred at the middle and rear slope bodies because of the lateral thrust, which led to the formation of a thrust landslide and the final instability of the east slope.

Controlling lasing around exceptional points in coupled nanolasers

Coupled nanolasers are of growing interest for on-chip optical computation and data transmission, which requires an understanding of how lasers interact to form complex systems. The non-Hermitian interaction between two coupled resonators, when excited selectively, can lead to parity-time symmetry, the formation of exceptional points, and subsequently spectral control and increased sensitivity. These investigations have been limited to pump energies close to the lasing threshold, and large or narrow-line lasers. Here, by programmable optical excitation we study two coupled nanolasers significantly above threshold, where mode instability plays an important role. We map the mode evolution around two exceptional points, and observe lasing gaps due to reversed pump dependence which compare well with non-linear theory. Finally, the coupling can be exploited to control the lasing threshold and wavelength, and for frequency switching around the lasing gap. Controlled and integrated nanolasers constitutes a promising platform for future highly sensitive and programmable on-chip laser sources.

Effects of streamwise-elongated and spanwise-periodic surface roughness arrays on supersonic boundary-layer instability

We investigate the influence of streamwise-elongated and spanwise-periodic roughness arrays on the supersonic boundary-layer instability under the assumption of a high Reynolds number. The main focus is on the lower-branch viscous instability modes, and the spanwise spacing of the roughness arrays is taken to be comparable to the characteristic wavelength of the modes (which is on the triple-deck scale), so that most significant effects can be generated. The streamwise length scale of the elements is much greater than the spanwise length scale. The roughness height is determined by requiring the change of the wall shear to be O(1). The equations governing the nonlinear roughness-induced streaky flow are deduced from the standard triple-deck theory. These equations are parabolic in the streamwise direction and are solved using a streamwise marching method to characterize the evolution of streaky structures. The linear stability of the streaky flow is analyzed. By exploiting the asymptotic structure, the bi-global eigenvalue problem is reduced to a one-dimensional one, where the stability is found to be controlled by the spanwise-dependent wall shear. The reduced eigenvalue problem is solved numerically. The results show that roughness arrays inhibit instability modes with moderate frequencies but promote high-frequency modes. Roughness elements of greater height have stronger effects on the linear stability. The shape of roughness elements plays an important role. A significant feature, different from the subsonic case, is that fundamental and superharmonic resonance modes radiate sound waves spontaneously into the far field.

High power cladding-pumped low quantum defect Raman fiber amplifier

Heat generated by the quantum defect (QD) in optically pumped lasers can result in detrimental effects such as mode instability, frequency noise, and even catastrophic damage. Previously, we demonstrated that boson-peak-based Raman fiber lasers have great potential in low QD laser generation. But their power scalability and heat load characteristics have yet to be investigated. Here, we demonstrate a boson-peak-based Raman fiber amplifier (RFA) with 815 W output power and a QD of 1.3%. The low heat generation characteristics of this low QD RFA are demonstrated. Both experimental and simulation results show that at this power level, the heat load of the low QD RFA is significantly lower than that of the conventional RFA with a QD of 4.8%. Thanks to its low heat generation characteristics, the proposed phosphosilicate-fiber-based low QD RFA provides an effective solution for the intractable thermal issue in optically pumped lasers, which is of significance in reducing the laser’s noise, improving the laser’s stability and safety, and solving the challenge of heat removing.

Linear stability analysis of the electrostatic drift wave in the electron thermal internal transport barrier in EAST

An alternative local electrostatic gyrokinetic eigenvalue code is developed for the ion-temperature-gradient-driven mode, the trapped-electron mode (TEM), and the electron-temperature-gradient (ETG)-driven mode. It numerically solves the linear eigenvalue problem for the electrostatic drift waves in the Fourier transformed space and benchmarks well with the HD-7 code and FULL code. The linear ETG and TEM instabilities in the electron thermal internal transport barrier (eITB) with dominant electron heating in experimental advanced superconducting tokamak are analyzed by using this code. The linear analysis results are consistent with that from the critical electron-temperature-gradient threshold analysis. Moreover, the sensitivity of ETG and TEM instabilities to parameters during the eITB formation has been investigated. For the typical eITB discharge, it is found that the instability of ETG mode is more sensitive to the stabilizing effect of the electron–ion temperature ratio (τe), while the instability of TEM is more sensitive to the destabilizing effect of ηe. In addition, mixing length estimation of the turbulent transport in the eITB is also discussed, which suggests that the TEM may be saturated by other nonlinear effects than the resonance broadening.

An image-based spatiotemporal approach for detecting coherence resonance in annular model gas-turbine combustor

When exposed to an intermediate level of noise, dynamical systems near a Hopf bifurcation can reveal deterministic information about the impending oscillatory mode. Known as the coherence resonance, this phenomenon can be used as a precursor to thermoacoustic instability, which is detrimental to practical combustors. In this study, we apply a spatiotemporal dimensionality reduction method, namely the sparsity-promoting dynamic mode decomposition, to detect coherence resonance in a combustor that exhibits a transition toward thermoacoustic instability. We stochastically excite the annular model gas-turbine combustor and acquire its high-speed image for spatiotemporal analysis. As a result, we find that the impending mode of instability is best identified with a maximum clustering level at the intermediate noise amplitude, implying the existence of coherence resonance. To the best of our knowledge, this is the first time that an image-based method has been used for the detection of coherence resonance, opening new possibilities for the prediction of combustion instability without requiring embedded sensors.

The onset of instability and bifurcations in the transitional wake of two tandem square cylinders

Unsteady three-dimensional simulations are performed to elucidate the hidden transitional flow dynamics and Hopf bifurcations along the topological corelines of the created von Kármán streets behind a pair of square cylinders positioned in tandem. Our simulations provide significant new insight into the three-dimensional wake evolution and governing flow physics. We explain how pressure, velocity, and vorticity fluctuation along the Kármán vortex corelines in the increasingly unstable wake amplify, facilitating the growth of various modal instability patterns. The existing knowledge of wake transition through the intertwining of modes A, B, and C instabilities and associated linear stability analysis helped to gain some insight into the overall wake feature. The current study explains how exactly the transitional disturbances physically spread behind a pair of inline and tandem cylinders through the self-excited spanwise-periodic oscillation of the wake and created a sequence of variable length scaled Hopf bifurcations and their swapping for varied gaps between the cylinders and Reynolds number. The growth of a slow mode of the spectral frequency at the bifurcation points seemed crucial in initiating the near-transitional flow irregularity.

Failure probability analysis of high fill levee considering multiple uncertainties and correlated failure modes

Such complex causative factors in current failure probability models are represented by simply random uncertainty and completely independent or correlation of failure modes, which can often limit the model utility. In this study, we developed a methodology to construct failure probability models for high fill levees, incorporating the identification of uncertainties and an analysis of failure modes. Based on quantification of stochastic-grey-fuzzy uncertainties, probability analysis involved with overtopping, instability and seepage failure modes was implemented combined with probability and non-probability methods. Given that the interaction among failure modes typically exhibits nonlinear behavior, rather than linear correlation or complete independence, a simple methodology for the binary Copula function was established and implemented in MATLAB. This methodology was applied to the high fill segments of a long-distance water transfer project characterized by high population density. It shows that the failure probability of a single failure mode is overestimated when uncertainties are not considered, because of the randomness and fuzziness of some parameters and the greyness of information. Meanwhile, it is found that the magnitude of failure probability related to levee breach is overestimated without respect to failure modes correlation, especially when the probabilities of seepage and instability are both significant and closely aligned.

Full-scale experimental investigation into stability of segment-SCC-steel tube lining under external pressure

To investigate the mechanical deformation characteristics of the ‘Segment-SCC-Steel Tube’ combined bearing lining structure under internal and external pressure, the loading device and monitoring system for the stability analysis of the full-scale lining were proposed. The effect of cracked encased concrete and local external pressure on the instability mode of thin-walled steel pipes was explored by full-scale model experiment and three-dimensional FEM numerical simulation. The influence of SCC (Self-Compacting Concrete) and stiffening rings on the stability of steel pipes subjected to external pressure was discussed. The results show that SCC cracks occur and intensify with increasing internal pressure. The external water acts directly on the steel tube through cracking, resulting in wavy deformation, and the gap between the SCC and steel tube further increases. When calculating the critical external pressure for the steel pipe, the constraint of encased concrete can be ignored, and only the constraint effect of the stiffening ring can be considered. Therefore, the Von Mises formula was used to predict the critical external pressure between the stiffening rings with high accuracy. In addition, the stiffening ring can mitigate the crack propagation of nearby SCC. The steel tube remained in the elastic stage under internal pressure. In the full-scale experiment, the external pressure could not continue to rise after reaching 0.65 MPa. Nevertheless, the amplitude of the buckling wave continued to increase. It is considered that the steel pipe is in an unstable state, and the failure mode is dominated by single-lobe buckling.

Complex Deposit Slope Excavation Deformation Mechanism and Seismic Reinforcement Effect Evaluation

Background To further investigate the excavation deformation mechanism and remedial strategies for slope reinforcement in the southwest mountain area, the Baihetan-Jiangsu (Zhejiang) UHV transmission project deposit slope deformation reinforcement was used as a case study. Methods Deep displacement monitoring, on-site testing, and FLAC3D numerical simulation techniques were employed. The assessment of the deposit slope excavation deformation mechanism and the effectiveness of seismic reinforcement for different design options and pile parameters are conducted while analyzing the seismic reinforcement mechanism. Results and Discussions The results showed that (1) The deposit slope composed of “multi-genetic type soil” in the converter station is prone to deformation, where the dominant instability mode is “traction creep and tension failure mode.” (2) Both circular and rectangular anti-slide piles significantly reduce the amount of slope body deformation; employing circular anti-slide piles for addressing this type of deposit slope provides enhanced anti-slide retention and economic benefits. (3) Under the influence of an earthquake, the shear force and bending moment of the anti-slide pile first increase and then decrease with the increase of seismic intensity. Conclusion The distribution law of shear force and bending moment in a pile should be considered comprehensively in slope support design.

Impact of thermal lensing on the TMI threshold powers in rod-type Yb-doped fiber amplifiers

The impact of thermal lensing (TL) on the transverse mode instability (TMI) threshold power in rod-type fiber amplifiers is investigated. Simulations are conducted with a 3D coupled mode analysis on a set of five scaled large pitch fiber (LPF) amplifiers. The LPF fibers are represented by surrogate step-index fibers (SIFs) with scaled cladding diameters, core diameters, and numerical apertures for a fixed normalized frequency V equal to 3.0 and scaled modal field overlap integrals with the core and cladding. It is found that thermal lensing decreases the TMI threshold powers due to increases in the TMI nonlinear gain. This gain increase is attributed to an increase in the nonlinear gain overlap integrals that occurs with the reduction in the fundamental mode effective area. Estimates for the TMI threshold power are in good agreement with measurements; however, the simulations overestimate the mode shrinkage factor. This discrepancy is tentatively attributed to the representation of the LPF by an effective SIF. These results may offer opportunities for fiber designs that increase the TMI threshold powers.

Freestream turbulence effects on low Reynolds number NACA 0012 airfoil laminar separation bubble and lift generation

Laminar separation bubbles (LSB's) over the suction surface of a wing at low Reynolds number (O(104)−O(106) based on the airfoil chord length) can significantly affect the aerodynamic performance of the wing, and pose a unique challenge for the predictive capabilities of simulation tools due to their high sensitivity to flow environments and wing surface conditions. In this work a series of two-dimensional (2D) and three-dimensional (3D) low-order, and high-order accurate unstructured-grid-based numerical methods with varying model fidelity levels were used to study LSB physics over a NACA 0012 airfoil both in a clean freestream and in a turbulent freestream at a chord-based Reynolds number of 12,000. Lift production and time-averaged flow fields were compared with available experimental results. A major discovery is that in clean freestream flow a 3D high-order numerical scheme is necessary to capture LSB physics. This is due to the sensitivity of LSB-induced laminar-turbulent transition to flow conditions and boundary geometry at low Reynolds number. In freestream flows with moderate background turbulence (∼5%), 2D simulations failed to capture subtle 3D flow physics due to their intrinsic limitation, but can reasonably predict time-averaged airfoil performance. Similarity and distinction between freestream vortex-LSB interaction in 2D and eddy-LSB interaction in 3D were explained. The role of the Kelvin-Helmholtz instability and Klebanoff modes in the transition of 3D airfoils were shown to be critical for understanding laminar-turbulent transition and LSB formation on airfoils in clean and turbulent freestreams.

Novel Combustion Instability Diagnosis Method With Upstream Pulsation of Repetitive Laser-Induced Plasmas

Abstract In this experimental study, we are presenting the ability of laser-induced plasmas with successive pulsation to identify combustion instabilities (CI) of a premixed lab-scale combustor. An acoustic disturbance equivalent to a shockwave perturbation is generated in the main air supply line of a swirled injector prior to the fuel addition by focusing nanosecond laser pulses of 1.6 W average power at 10 Hz. The shockwaves are attenuated to be strong pressure waves when reaching the combustor and impact the pressure field for short periods. After plasma breakdowns, the system returns back to its original state after 4 ms once the added acoustic energy has been fully dissipated. Given a set geometry, it is observed that the laser-induced breakdown amplifies the characteristic frequency peaks of the combustor system when actuated in cold flow. Furthermore, when applied to reacting flows, the pulsating acoustic perturbations impact the pressure fluctuation in the combustor, e.g., reducing the amplitude of the primary characteristic frequency peak at certain conditions. The identification of the main instability modes thanks to the plasma shockwave provides proof of the potential use of this novel diagnosis strategy in various and complex combustion systems.

Roughness-Induced Transition in Supersonic Boundary Layers with Wall Heating and Cooling Effects

The laminar–turbulent transition of a supersonic boundary layer induced by an isolated roughness element is investigated using direct numerical simulation, BiGlobal linear stability theory, and the three-dimensional parabolized stability equation. Cylindrical and diamond-shaped roughness elements are investigated in combination with different wall temperatures. Direct numerical simulations show that the cylinder configuration induces an earlier transition than the diamond configuration, with the interaction between the separated shear layer and the counter-rotating vortices causing the transition. BiGlobal analysis and the parabolized stability equation confirm the existence of two unstable instability modes in the wake region, namely, a symmetric mode and an antisymmetric mode, with the former being strongly dominant. The wall cooling and heating effects are studied by changing the wall temperature. Wall heating lifts the inlet boundary layer and weakens the separated shear layer. This, in turn, weakens the wake instability and delays the transition. The antisymmetric model disappears as the wall heating increases. Wall cooling accelerates the transition by enhancing the distortion of the roughness wake, resulting in stronger instabilities. Finally, the Reynolds number based on the momentum defect is used to define the transition criterion, and this is found to be in good agreement with the present simulation results.