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Natural oscillations of sessile drops with a free or pinned contact line in different gravity environments are studied based on a linear inviscid irrotational theory. The inviscid Navier–Stokes equations and boundary conditions are reduced to a functional eigenvalue problem by the normal-mode decomposition. We develop a boundary element method model to numerically solve the eigenvalue problem for predicting the natural frequencies. Emphasis is placed on the frequency shifts of modes due to gravity for a wide range of contact angles $\alpha$ and Bond numbers $Bo$. Three types of $\alpha$–$Bo$ diagrams reflecting how gravity shifts the frequency are identified. Specifically, the frequency of zonal modes shifts downwards (upwards) when $\alpha$ is smaller (larger) than a critical value, while the frequencies of most sectoral modes are shifted downwards regardless of $\alpha$. As a result, gravity can transform the lowest mode from a zonal mode to a sectoral mode. The spectral degeneracy of hemispherical drops inherited from the Rayleigh–Lamb spectrum is also broken by gravity. However, we discover that gravity has no effect on the mode associated with the horizontal motion of the centre of mass, whose frequency is always zero regardless of $\alpha$ and $Bo$. This implies that the ‘walking’ drop instability reported in previous literature does not exist.
In this work, the linear responses of turbulent mean flow to both harmonic and stochastic forcing are investigated for supersonic channel flow. Well-established universal relations are utilized to obtain efficiently the mean profiles with a large parameter space, with the bulk Mach number up to 5 and the friction Reynolds number up to $10^4$, so a systematic parameter study is feasible. The most amplified structure takes the form of streamwise velocity and temperature streaks forced optimally by the streamwise vortices. The outer peak of the pre-multiplied energy amplification corresponds to the large-scale motion, whose spanwise wavelength ($\lambda _z^+$) is very insensitive to compressibility effects. In contrast, the classic inner peak representing small-scale near-wall motions disappears for the stochastic response with increasing Mach number. Meanwhile, the small-scale motions become much less coherent. A decomposition of the forcing identifies different effects of the incompressible counterpart and the thermodynamic components. Wall-cooling effects, arising with high Mach number, increase the spacing of the most amplified near-wall streaks; the spacing becomes nearly invariant with Mach number if expressed in semi-local units. Meanwhile, the coherence of stochastic response with $\lambda _z^+>90$ is enhanced, but on the other hand, with $\lambda _z^+<90$ it is decreased. The geometrical self-similarity of the response in the mid-$\lambda _z$ range is still roughly satisfied, insensitive to Mach number. Finally, theoretical analyses of the perturbation equations are presented to help with understanding the scaling of energy amplification.
The transport phenomena of dust particles have been widely observed in fusion plasmas. In this article, we report the observations of dust fragmentations in the Experimental Advanced Superconducting Tokamak (EAST). A dust particle splits into two daughter particles and their motions are recorded before and after the breakup with a fast video camera. The trajectories of the daughter particles in the experiment are consistent with equation-of-motion simulations. The stability of a rotating charged particle in the plasma is briefly discussed.
Natural ventilation can play an important role towards preventing the spread of airborne infections in indoor environments. However, quantifying natural ventilation flow rates is a challenging task due to significant variability in the boundary conditions that drive the flow. In the current study, we propose and validate an efficient strategy for using computational fluid dynamics to assess natural ventilation flow rates under variable conditions, considering the test case of a single-room home in a dense urban slum. The method characterizes the dimensionless ventilation rate as a function of the dimensionless ventilation Richardson number and the wind direction. First, the high-fidelity large-eddy simulation (LES) predictions are validated against full-scale ventilation rate measurements. Next, simulations with identical Richardson numbers, but varying dimensional wind speeds and temperatures, are compared to verify the proposed similarity relationship. Last, the functional form of the similarity relationship is determined based on 32 LES. Validation of the surrogate model against full-scale measurements demonstrates that the proposed strategy can efficiently inform accurate building-specific similarity relationships for natural ventilation flow rates in complex urban environments.
To explore the effect of yield stress on the secondary breakup of gel drops, experimental and theoretical investigations are carried out by employing a high-speed camera. A unique hemline-type breakup, as a modified behaviour of sheet-thinning breakup, occurs when the air velocity increases to a high region. The edges of the drops constantly deform into thin membranes when the high-velocity air skims over the gel drops. These membranes vibrate vertically, and breaking points occur at high amplitudes, causing the formation of reticular fragments. The results of linear stability analysis indicated that the yield stress of the gel drops has an influence on the formation and breakup of the gel membranes. The breakup regime map and breakup times are also studied.
In this paper, the reflection of curved shock waves over a symmetry plane in planar supersonic flow is studied. This includes stable Mach reflection (MR) and the regular reflection (RR) to MR transition process. Curved shock theory (CST) is applied to derive the high-order parameters in front of and behind the shock wave. The method of curved shock characteristics is used to establish an analytical model to predict the wave configurations. The shock structures provided by the proposed model agree well with the numerical results. Flow structures, such as the height of the Mach stem and the shape of the shock wave and slip line, are studied by applying the analytical model. Isentropic waves generated from a curved wall are found to significantly influence the flow patterns. It appears that the compression waves obstruct the formation of the sonic throat and increase the Mach-stem height. The expansion waves have the opposite effect. The evolution mechanism of the Mach stem is found in conjunction with the RR-to-MR transition process. The CST is extended to a moving frame and used to model the transition. The time history of the moving triple point illustrates the effects of the incident shock angle and isentropic waves on the transition process.
A novel curved surface nanowire target is proposed to improve the cutoff energy of accelerated protons via target normal sheath acceleration. The interaction of a laser of intensity $1.37\times 10^{20}\ {\rm W}\ {\rm cm}^{-2}$ with a curved surface nanowire target is studied by two-dimensional particle-in-cell simulations. The numerical results indicate that the sheath electric field at the target rear side is significantly enhanced by this simple target design, compared with using the planar nanowire target. The transverse motion of hot electrons is effectively confined and the energy density of electrons is naturally increased. A series of simulations with various target parameters is carried out to investigate the performance of this novel target. This tailored target may provide implications for generating high-quality proton beams in experiments.
The physics and mechanism of sheet/cloud cavitation in a convergent–divergent channel are investigated using synchronized dynamic surface pressure measurement and high-speed imaging in a water tunnel to probe the cavity shedding mechanism. Experiments are conducted at a fixed Reynolds number of Re = 7.8 × 105 for different values of the cavitation number σ between 1.20 and 0.65, ranging from intermittent inception cavitation, sheet cavitation to quasi-periodic cloud cavitation. Two distinct cloud cavitation regimes, i.e. the re-entrant jet and shockwave shedding mechanism, are observed, accompanied by complex flow phenomenon and dynamics, and are examined in detail. An increase in pressure fluctuation intensity at the numbers 3 and 4 transducer locations are captured during the transition from re-entrant jet to shockwave shedding mechanism. The spectral content analysis shows that, in cloud cavitation, several frequency peaks are identified with the dominant frequency caused by the large-scale cavity shedding process and the secondary frequency related to re-entrant jet/shockwave dynamics. Statistical analysis based on defined grey level profiles reveals that, in cloud cavitation, the double-peak behaviours of the probability density functions with negative skewness values are found to be owing to the interactions of the re-entrant jet/shockwave with cavities in the region of 0.25 ~ 0.65 mean cavity length (Lc). In addition, multi-scale proper orthogonal decomposition analysis with an emphasis on the flow structures in the region of 0.25 ~ 0.65 Lc reveals that, under the shockwave shedding mechanism, both the re-entrant jet and shockwave are captured and their interactions are responsible for the dynamics and statistics of cloud shedding process.
The aeroacoustic characteristics of flying vehicles with pitch-fixed rotors differ from traditional helicopters with pitch-controlled rotor blades. Accurate predictions of rotor noise are still challenging because many uncertainty factors and unsteadinesses exist. This work investigates the aeroacoustic effects of rotational speed deviation, rotation speed fluctuation, blade vibration and blade geometric asymmetry. The analysis is based on the efficient computation of rotor noise under different working conditions. The mean aerodynamic variables are computed using the blade element moment theory, while small-amplitude fluctuations are introduced to account for the unsteadiness and uncertainty factors. It is shown that periodic rotation speed fluctuations and blade vibrations can produce significant extra tones. By contrast, if the fluctuations and vibrations are random, the noise level in a wide frequency range is increased. The intriguing result reminds us of the need to revisit the rotor broadband noise sources commonly attributed to turbulent flows. The influences are observer angle dependent, and the extra noise production is more significant in the upstream and downstream directions. The asymmetric blade geometry can cause extra tonal noise at the harmonics of the blade shaft frequency. The noise features of dual rotors are also investigated. Usually, the noise is sensitive to the initial phase difference and rotation directions due to the interference effect. However, the noise features are vastly altered if there are slight differences in the rotation speeds. Although the influences of some factors on rotor noise were already known, the present study provides a more comprehensive analysis of the problem. The results also highlight the need to consider these practical factors for accurate noise prediction of multi-rotor flying vehicles.
‘Freeze-out’ of amplitude growth, i.e. the amplitude growth stagnation of a shocked helium–air interface, is realized through a reflected shock, which produces baroclinic vorticity of the opposite sign to that deposited by the first shock. Theoretically, a model is constructed to calculate the relations among the initial parameters for achieving freeze-out. In particular, if the amplitude growth is within the linear regime at the arrival of the reflected shock, the time interval between the impacts of two shock waves is linearly related to the initial perturbation wavelength, and is independent of the initial perturbation amplitude. Experimentally, an air–SF$_6$ (or air–argon) plane interface is adopted to produce a weak reflected shock. Seven experimental runs with specific initial conditions are examined. For all cases, freeze-out is achieved after the reflected shock impact under the designed conditions.
A systematic simulation study of the $n/m=1/1$ instability driven by energetic counter-passing particles in tokamak plasmas has been carried out using the kinetic-MHD (Magnetohydrodynamics) hybrid code M3D-K. The safety factor's radial profile is monotonically increasing with central value $q_0$ less than unity. The linear simulation results show that the instability is either a $m/n=1/1$ energetic particle mode or a $m/n=1/1$ global Alfvén eigenmode depending on the value of the central safety factor. The mode frequencies are close to the tip of Alfvén continuum spectrum at the magnetic axis. The excited modes are radially localized near the magnetic axis well within the safety factor $q=1$ surface. The main wave particle resonance is found to be $\omega _\phi +2\omega _\theta =\omega$, where ω is the mode frequency. The nonlinear simulation results show that there is a long period of quasi-steady-state saturation phase with frequency chirping up after initial saturation. Correspondingly, the energetic particle distribution with low energies is flattened in the core of the plasma. After this quasi-steady phase, the mode amplitude grows again and frequency jumps down to a low value corresponding to a new mode similar to the energetic co-passing particle-driven low-frequency fishbone while the energetic particle distribution is flattened for higher energies in the core of plasma.
Plasma vertical displacement control is essential for the stable operation of tokamak devices. The traditional plasma vertical displacement calculation method is not suitable for balancing speed and accuracy simultaneously, which is necessary for real-time feedback control. In this study, neural networks are used to rapidly detect vertical displacement recognition. Based on a fully connected neural network, the vertical displacement calculation model is trained and tested using magnetic data of approximately 2000 shots. To compare the effects of different inputs on vertical displacement calculation, different magnetic measurement diagnostic signals are used to train and test the model. Compared with a full magnetic measurement dataset, 39 magnetic measurement signals (38 magnetic probes and plasma current) show better accuracy with mean square error <0.0005. The model is tested using historical experimental data, and it demonstrates accurate vertical displacement calculation even in the case of a vertical displacement event. In general, neural network algorithm has great application potential in vertical displacement calculation.
The flow past a cylinder in proximity to a plane wall is investigated numerically for small gap ratios. Three vortex dynamic processes associated with different hairpin vortex generation mechanisms are identified for the first time, and the wake-induced turbulent transition is analysed. The vortex shedding is suppressed at $G/D = 0.1$, while the spanwise vortex is generated via a Kelvin–Helmholtz instability and evolves into hairpin vortices. For $G/D= 0.3$, the upper and lower rollers alternatively shedding from the cylinder, interact with the secondary vortex. The split secondary vortex merges with the upper roller and results in a new vortex downstream, which develops into hairpin vortices. When $G/D = 0.9$, the secondary vortex interacts with the lower roller and then evolves into hairpin vortices. A tertiary vortex induced by the secondary vortex is observed, rotating in the opposite direction to the secondary vortex the wake-induced transitions share the same route. The velocity fluctuations deviate from the optimal growth theory in the pre-transitional region. In the transitional region low-frequency disturbances penetrate the sheltering edge to generate streaks where the disturbance energy declines. In the turbulent region the logarithmic layer is formed, indicating that the turbulent equilibrium is established.
The kinetic–magnetohydrodynamic (MHD) hybrid simulation approach for macroscopic instabilities in plasmas can be extended to include the kinetic effects of both thermal ions and energetic ions. The new coupling scheme includes synchronization of the density and parallel velocity between thermal ions and MHD, in addition to pressure coupling, to ensure the quasineutrality condition and avoid numerical errors. The new approach has been implemented in the kinetic-MHD code M3D-C1-K, and was used to study the thermal ion kinetic effects and Landau damping in fishbone modes in both DIII-D and NSTX. It is found that the thermal ion kinetic effects can cause an increase of the frequencies of the non-resonant $n=1$ fishbone modes driven by energetic particles for $q_\mathrm {min}>1$, and Landau damping can provide additional stabilization effects. A nonlinear simulation for $n=1$ fishbone mode in NSTX is also performed, and the perturbation on magnetic flux surfaces and the transport of energetic particles are calculated.
One novel trend in reducing aero-engine noise is to utilize the silent flight mechanism of owls by applying perforations on fan stator vanes. Consequently, the establishment of relevant theoretical models is of particular interest. The current efforts made in this regard are just targeting the features based on two-dimensional models without including the three-dimensionality. In this paper, we present a three-dimensional solution for acoustic scattering by annular perforated cascades, and the dipole source corresponding to the unsteady pressure loading on the vanes is identified as the dominant sound source. By the singularity method, the acoustic response is obtained with the soft boundary condition applied on the vane surfaces. It is found that considerable noise reduction can be achieved for rotor–stator interaction with a modest uniform porosity, and accordingly two mechanisms are proposed to understand the effect of porosity on propagating sound. The first is that the perforations allowing a normal velocity across the vane reduce the unsteady loading induced by the incident disturbances. The second is that the three-dimensional interactions among the dipole sources at different positions are also dampened by the soft boundaries, thus the distribution of the unsteady pressure loading on the vanes will also change significantly compared to hard-vane cases. Non-uniform distributions of porosity are investigated further, indicating that perforations in the vane upstream area are more effective in reducing propagating noise. Our method is fully three-dimensional and capable of investigating non-uniform porosity, and thus is able to provide useful guidance for future soft vane designs.
Effects of plasma non-uniformities and kinetic dispersiveness on the spontaneous excitation of geodesic acoustic mode (GAM) by reversed shear Alfvén eigenmode (RSAE) are investigated numerically. It is found that, due to the turning points induced by the shear Alfvén continuum structure, the nonlinear excitation of GAM is a quasiexponentially growing absolute instability. As the radial dependence of GAM frequency and pump RSAE mode structure are accounted for, the radially inward propagating GAM is preferentially excited, leading to core localized thermal plasma heating by GAM collisionless damping. Our work, thus, suggests that GAM excitation plays a crucial role in not only RSAE nonlinear saturation, but also anomalous fuel ion heating in future reactors.
The effect of sheared E × B flow on the blob dynamics in the scrape-off layer (SOL) of HL-2A tokamak has been studied during the plasma current ramp-up in ohmically heated deuterium plasmas by the combination of poloidal and radial Langmuir probe arrays. The experimental results indicate that the SOL sheared E × B flow is substantially enhanced as the plasma current exceeds a certain value and the strong sheared E × B flow has the ability to slow the blob radial motion via stretching its poloidal correlation length. The locally accumulated blobs are suggested to be responsible for the increase of plasma density just outside the Last Closed Flux Surface (LCFS) observed in this experiment. The results presented here reveal the significant role played by the strong sheared E × B flow on the blob dynamics, which provides a potential method to control the SOL width by modifying the sheared E × B flow in future tokamak plasmas.
We report a systematic experimental study of the mean temperature profile $\theta (\delta z)$ and temperature variance profile $\eta (\delta z)$ across a stable and immiscible liquid–liquid (water–FC770) interface formed in two-layer turbulent Rayleigh–Bénard convection. The measured $\theta (\delta z)$ and $\eta (\delta z)$ as a function of distance $\delta z$ away from the interface for different Rayleigh numbers are found to have the scaling forms $\theta (\delta z/\lambda )$ and $\eta (\delta z/\lambda )$, respectively, with varying thermal boundary layer (BL) thickness $\lambda$. By a careful comparison with the simultaneously measured BL profiles near a solid conducting surface, we find that the measured $\theta (\delta z)$ and $\eta (\delta z)$ near the liquid interface can be well described by the BL equations for a solid wall, so long as a thermal slip length $\ell _T$ is introduced to account for the convective heat flux passing through the liquid interface. Direct numerical simulation results further confirm that the turbulent thermal diffusivity $\kappa _t$ near a stable liquid interface has a complete cubic form, $\kappa _t(\xi )/\kappa \sim (\xi +\xi _0)^3$, where $\kappa$ is the molecular thermal diffusivity of the convecting fluid, $\xi =\delta z/\lambda$ is the normalized distance away from the liquid interface and $\xi _0$ is the normalized slip length associated with $\ell _T$.
An experimental investigation of the stereocamera's systematic error is carried out to optimize three-dimensional (3-D) dust observation on the HL-2A tokamak. It is found that a larger 3-D region occupied by all calibration points is able to reduce the 3-D reconstruction systematic error of the stereocamera. In addition, the 3-D reconstruction is the most accurate around the region where the calibration points are located. Based on these experimental results, the design of the stereocamera on the HL-2A tokamak is presented, and a set of practical procedures to optimize the 3-D reconstruction accuracy of the stereocamera are proposed.
We present an experimental study of Rayleigh–Bénard convection using liquid metal alloy gallium-indium-tin as the working fluid with a Prandtl number of $Pr=0.029$. The flow state and the heat transport were measured in a Rayleigh number range of $1.2\times 10^{4} \le Ra \le 1.3\times 10^{7}$. The temperature fluctuation at the cell centre is used as a proxy for the flow state. It is found that, as $Ra$ increases from the lower end of the parameter range, the flow evolves from a convection state to an oscillation state, a chaotic state and finally a turbulent state for $Ra>10^5$. The study suggests that the large-scale circulation in the turbulent state is a residual of the cell structure near the onset of convection, which is in contrast with the case of $Pr\sim 1$, where the cell structure is transiently replaced by high order flow modes before the emergence of the large-scale circulation in the turbulent state. The evolution of the flow state is also reflected by the heat transport characterised by the Nusselt number $Nu$ and the probability density function (p.d.f.) of the temperature fluctuation at the cell centre. It is found that the effective local heat transport scaling exponent $\gamma$, i.e. $Nu\sim Ra^{\gamma }$, changes continuously from $\gamma =0.49$ at $Ra\sim 10^4$ to $\gamma =0.25$ for $Ra>10^6$. Meanwhile, the p.d.f. at the cell centre gradually evolves from a Gaussian-like shape before the transition to turbulence to an exponential-like shape in the turbulent state. For $Ra>10^6$, the flow shows self-similar behaviour, which is revealed by the universal shape of the p.d.f. of the temperature fluctuation at the cell centre and a $Nu=0.19Ra^{0.25}$ scaling for the heat transport.