Phase Velocity Of Fluctuations Research Articles

A Two-Fluid Model Simulation of Vertical Gas-Solid Flow With a Multiphase Turbulence Model

A modified form of the Two-Fluid Model (TFM) incorporating a multiphase turbulence model is implemented in an in-house code for a downward gas-solid channel flow (Kulick et al., 1994). The TFM works on the principle of dividing the particle phase velocity fluctuations into spatially correlated and uncorrelated forms. The results from the modified TFM are compared with the experimental data as well as the predictions of a conventional TFM formulation. The difference between the two approaches in terms of the kinetic energy couplings of the two model formulations is discussed. The modified TFM was able to predict an enhanced gradient in the particle phase mean velocity close to the wall for a downward flow. The uncorrelated particle fluctuations showed a peak close to the wall and decreased toward the center of the channel, compared to a more uniform prediction by the conventional TFM. The correlated fluctuations showed a minimum value at the wall and increased to the same level as the uncorrelated fluctuations in the center of the channel. The prediction of the modified TFM for the solids volume fraction profile was closer to the experimental profile than the conventional model. Both TFM formulations were unable to capture the anisotropy associated with the fluid phase velocity fluctuations and its possible effects on the particle phase close to the wall.

A dynamical–system description of precipitation over the tropics and the midlatitudes

A dynamical–system approach is proposed to describe the relationship between precipitation and a chosen predictor. This is done by constructing a two dimensional phase space spanned by predictor and predictant. This study uses two sounding data sets from the Tropical Western Pacific and Friuli Venezia Giulia (FVG) over North–East Italy as representatives of the tropics and midlatitudes, in addition to a basin–scale average over the winter–period North Atlantic from global re–analysis data. In contrast to conventional correlation-based approaches, the proposed approach depicts periodic cycles, as well as discharge–recharge cycles as its nonlinear extension. Discharge–recharge cycles for tropical convection are identified by using both the convective available potential energy (CAPE) and the column–integrated water vapor (CIW) as predictors, as well as the baroclinicity for the winter–period North–Atlantic rain. On the other hand, the midlatitude rain, as seen over FVG as well as the winter–period North Atlantic, does not constitute a well–defined periodic cycle either with CAPE or CIW as a predictor. The inferred phase–space trajectories are more deterministic at peripheries of dense data areas rather than at a middle in the phase space. Data–dense areas in phase space, where traditional approaches primarily focus, are associated with more prediction uncertainties in our analysis due to more phase-velocity fluctuations.

The influence of gas phase velocity fluctuations on primary atomization and droplet deformation

The effects of grid-generated velocity fluctuations on the primary atomization and subsequent droplet deformation of a range of laminar liquid jets are examined using microscopic high-speed backlit imaging of the break-up zone and laser Doppler anemometry of the gas phase separately. This is done for fixed gas mean flow conditions in a miniature wind tunnel experiment utilizing a selection of fuels, turbulence-generating grids and two syringe sizes. The constant mean flow allows for an isolated study of velocity fluctuation effects on primary atomization in a close approximation to homogeneous decaying turbulence. The qualitative morphology of the primary break-up region is examined over a range of turbulence intensities, and spectral analysis is performed in order to ascertain the break-up frequency which, for a case of no grid, compares well with the existing literature. The addition of velocity fluctuations tends to randomize the break-up process. Slightly downstream of the break-up region, image processing is conducted in order to extract a number of metrics, which do not depend on droplet sphericity, and these include droplet aspect ratio and orientation, the latter quantity being somewhat unconventional in spray characterization. A turbulent Weber number \(We^{\prime}\) which takes into account gas phase fluctuations is utilized to characterize the resulting droplet shapes, in addition to a mean Weber number . Above a \(We^{\prime}>0.05\) a clear positive relationship exists between the mean aspect ratio of droplets and the turbulent Weber number where \(We^{\prime}\) is varied by altering all relevant variables including the velocity root mean square, the initial droplet diameter, the surface tension and the density.

Reply to the Comment on: The quantum vacuum as the origin of the speed of light

We reply to the comment by Schiller on our paper “The quantum vacuum as the origin of the speed of light” [M. Urban et al., Eur. Phys. J. D 67, 58 (2013)]. We further detail our model and explain why the limits provided by ultra-stable optical cavities on the amplitude of fluctuations of the light speed do not apply to the predictions on group velocity that we gave in [M. Urban et al., Eur. Phys. J. D 67, 58 (2013)]. We then estimate the magnitude of phase velocity fluctuations expected in our model, showing that they are much smaller than those of the group velocity, and hence, well below the best present limits obtained either with ultra-stable resonators or large interferometers.

Direct Numerical Simulation of Particles-Bubbles Collisions Kernel in Homogeneous Isotropic Turbulence

Particles and bubbles suspended in homogeneous isotropic turbulence are tracked and their collisions frequency is determined as a function of particle Stokes number. The carrier phase velocity fluctuations are determined by Direct Numerical Simulations (DNS). The effects of the dispersed phases on the carrier phase are neglected. Particles and bubbles of sizes on the order of Kolmogorov length scale are treated as point masses. In addition to Stokes drag, the pressure gradient in the carrier phase and added-mass forces are also included. Equations of motion of dispersed phases are integrated simultaneously with the equations of the carrier phase using the same time stepping scheme. The collision model used here allows overlap of particles and bubbles. Simulations for three turbulence Reynolds numbers ReΛ = 57, 77, and 96 have been performed. Collisions kernel, radial relative velocity, and radial distribution function found by DNS are compared to theoretical models over a range of particle Stokes number. Comparisons are made with Zaichik et al. [22] model, which is applicable to heavy particles, and Zaichik et al. [23] model which is valid for an arbitrary Stokes number. Zaichik et al. [23] is essentially a model for the radial relative velocity, and for the purpose of computing the collision kernel, it assumes the radial distribution function to be one. In general, good agreement between DNS and Zaichik et al. models is obtained for radial relative velocity for both particle-particle and particle-bubble collisions. The DNS results show that around Stokes number of unity particles of the same group undergo expected preferential concentration while particles and bubbles are segregated. The segregation behavior of particles and bubbles leads to a radial distribution function that is less than one. Existing theoretical models do not account for effects of this segregation behavior of particles and bubbles on the radial distribution function.

Turbulent bubbly flow in pipe under gravity and microgravity conditions

AbstractExperiments on vertical turbulent flow with millimetric bubbles, under three gravity conditions, upward, downward and microgravity flows ($1g$, $\ensuremath{-} 1g$ and $0g$), have been performed to understand the influence of gravity upon the flow structure and the phase distribution. The mean and fluctuating phase velocities, shear stress, turbulence production, gas fraction and bubble size have been measured or determined. The results for $0g$ flow obtained during parabolic flights are taken as reference for buoyant $1g$ and $\ensuremath{-} 1g$ flows. Three buoyancy numbers are introduced to understand and quantify the effects of gravity with respect to friction. We show that the kinematic structure of the liquid is similar to single-phase flow for $0g$ flow whereas it deviates in $1g$ and $\ensuremath{-} 1g$ buoyant flows. The present results confirm the existence of a two-layer structure for buoyant flows with a nearly homogeneous core and a wall layer similar to the single-phase inertial layer whose thickness seems to result from a friction–gravity balance. The distributions of phase velocity, shear stress and turbulence are discussed in the light of various existing physical models. This leads to a dimensionless correlation that quantifies the wall shear stress increase due to buoyancy. The turbulent dispersion, the lift and the nonlinear effects of added mass are taken into account in a simplified model for the phase distribution. Its analytical solution gives a qualitative description of the gas fraction distribution in the wall layer.

Edge turbulence scaling in RFX-mod as measured using GPI diagnostic

The nature of plasma edge turbulence has been studied in the Reversed Field Pinch (RFP) RFX-mod, making use of a Gas Puffing Imaging (GPI) diagnostic, with high time (2 MHz) and space (5 mm) resolution. The edge turbulence has been characterized in terms of toroidal phase velocity of fluctuations, v ϕ , of the width of emission structures, 2 σ, and of their linear density in the toroidal direction. The packing fraction ƒ p of intermittent structures has been estimated as the fraction of occupied area in a plane perpendicular to the magnetic field. The behaviors of v ϕ , ƒ p, and 2 σ are reported as functions of the density normalized to its Greenwald value, n/n G . A comparison at different plasma regimes of an effective diffusion coefficient D p due to the plasma trapped in coherent structures has been discussed. A decreasing trend of D p with n/n G values has been guessed.

Identification of droplet burning modes in lean, partially prevaporized swirl-stabilized spray flames

Experimental and numerical investigations of single droplet burning modes in a lean, partially prevaporized swirl-stabilized spray flame are reported. In the experiment single droplet flames have been visualized by CH-PLIF and simultaneous recording of the Mie signal. Two single droplet burning modes were identified: the envelope flame is a spherical diffusion flame burning at near-stoichiometric conditions. The wake flame is a potentially lean, partially premixed flame located downstream of the droplet. The droplet burning mode is of practical relevance, since it has significant impact on NO formation due to incomplete prevaporization. The droplet burning mode is determined by the ratio of chemical and convective time scales. The convective time scale is related to the droplet slip velocity. The impact of turbulent gas phase velocity fluctuations on droplet mechanics and droplet burning is discussed, based on a previous numerical investigation. In the present study the droplet slip velocity was measured with the 3D Phase Doppler (3D-PD) technique. For the measured slip velocities and ambient conditions in the hot gas region of the spray flame, simulations of single droplet burning were performed utilizing detailed models for chemical reaction, diffusive transport and vaporization. An agreement between the droplet burning modes predicted by the simulation and the droplet burning modes observed in the experiments was found.

Numerical Investigation of the Time Scales of Single Droplet Burning

The effect of gas phase velocity fluctuations on single droplet burning is investigated numerically. The main objective of this study is to understand the effect of gas phase turbulence on nitric oxide formation in single droplet flames. Since the interaction of gas phase velocity fluctuations with droplet burning is of sequential character, a separate investigation of droplet momentum coupling and droplet burning is performed. Momentum coupling controls droplet relaxation against changes of the gas phase velocity along the droplet trajectory and, thereby, determines to what extend gas phase velocity fluctuations translate into droplet slip velocity fluctuations. This coupling effect acts as a high pass filter with a cutoff frequency determined by the droplet Reynolds number and diameter. In the simulation of single droplet burning detailed models for chemical reaction, diffusive species transport and evaporation are used. A significant effect of slip velocity fluctuations on the mean values of NO formation rate is observed. The effect of slip velocity fluctuations on the mean NO formation rate is frequency dependent. The frequency response of the droplet flame is similar to that of a low pass filter. The droplet flame time scale characterizing the response to slip velocity fluctuations is found to correlate with chemical time scales. This time scale is not affected by droplet diameter.

Phase velocity fluctuations and gain in Cherenkov free-electron lasers

We report on the influence that waveguide-induced fluctuations in the phase velocity of the radiation wave have on the gain of Cherenkov-type free-electron lasers. We theoretically analyze low-gain Cherenkov free-electron lasers with a compact design that require resonator feedback for operation. We find that even small spatial variations of the waveguide parameters along the propagation direction can lead to significant degradation of the gain, and we present typical values for the required degree in waveguide precision that would eliminate such effects.

Experimental study of particle transport and density fluctuations in LHD

A variety of electron density (ne) profiles have been observed in the Large Helical Device (LHD). The density profiles change dramatically with heating power and toroidal magnetic field (Bt). The particle transport coefficients, i.e. diffusion coefficient (D) and convection velocity (V) are experimentally obtained in the standard configuration from density modulation experiments. The values of D and V are estimated separately in the core and edge. The diffusion coefficients are found to be a function of electron temperature (Te), and vary with Bt. Edge diffusion coefficients are proportional to . Non-zero V is observed, and it is found that the electron temperature gradient can drive particle convection, particularly in the core region. The convection velocity both in the core and edge reverses direction from inward to outward as the Te gradient increases. However, the toroidal magnetic field also significantly affects the value and direction of V. The density fluctuation profiles are measured by a two-dimensional phase contrast interferometer. It was found that fluctuations which are localized in the edge propagate towards the ion diamagnetic direction in the laboratory frame, while the phase velocity of fluctuations around mid-radius is close to the plasma poloidal Er × Bt rotation velocity. The fluctuation level becomes larger as particle flux becomes larger in the edge region.

Experimental evidence of coupling between sheared-flow development and an increase in the level of turbulence in theTJ−IIstellarator

The link between the development of sheared flows and the structure of turbulence has been investigated in the plasma boundary region of the TJ-II stellarator. The development of the naturally occurring velocity shear layer requires a minimum plasma density. Near this critical density, the level of edge turbulent transport and the turbulent kinetic energy significantly increases in the plasma edge. The resulting shearing rate in the phase velocity of fluctuations is comparable to the one required to trigger a transition to improved confinement regimes with reduction of edge turbulence, suggesting that spontaneous sheared flows and fluctuations keep themselves near marginal stability. These findings provide the experimental evidence of coupling between sheared flows development and increasing in the level of edge turbulence. The experimental results are consistent with the expectations of second-order transition models of turbulence-driven sheared flows.

Modification of Boundary Parameters and Fluctuations by IBW and LHCD in the HT-7 Tokamak

Measurements of boundary parameters and their fluctuations have been performed in ohmic (OH) plasma and Ion Bernstein Wave (IBW) and Lower Hybrid Current Drive (LHCD) enhanced confinement plasma using a pneumatically driven Langmuir probe array on HT-7 tokamak. In the enhanced confinement plasma, the gradients of electron density and temperature become higher and a transport barrier comes into being in the vicinity of the limiter. The boundary potential shows a clear modification in the same region. The fluctuation levels are significantly depressed and the coherences between fluctuations are reduced evidently in the enhanced plasma. Meanwhile, we obtained the spectral features and the poloidal phase velocity of fluctuations using a two-point correlation technique and found obvious modifications of the turbulence and the poloidal flow. The results suggest that the improved confinement in the IBW and LHCD enhanced plasma is at least partially due to the modification of the boundary parameters and the suppression of the boundary fluctuations and fluctuation induced fluxes.

Velocity fluctuations and time dependent E×B flows in the JET boundary region

Fluctuations in the phase velocity of fluctuations have been computed from floating potential fluctuations in the JET plasma boundary region. Experimental results reinforce the idea that, in some conditions, fluctuations in the phase velocity are linked with fluctuations in radial–poloidal electric fields opening the possibility to investigate turbulent transport in the plasma core region from measurements of density fluctuations. These results indicate that time dependent radial electric fields and E×B shearing rates might be computed in the plasma core from measurement of density fluctuations.

Experimental evidence of fluctuations and flows near marginal stability and dynamical interplay between gradients and transport in the JET plasma boundary region

The structure of the naturally occurring velocity shear layer and the dynamical coupling between gradients and transport have been investigated in the JET plasma boundary region. The velocity shear layer appears to organize itself to reach a condition in which the radial gradient in the poloidal phase velocity of fluctuations is comparable to the inverse of the correlation time of fluctuations (1/ τ). This result suggests that E× B sheared flows organized themselves to be close to marginal stability (i.e. ω E× B ≈1/ τ). The size of turbulent events increases when the plasma deviates from the average gradient. The resulting radial velocity of fluctuations is of the order of 20 m/s for transport events implying a small deviation from the most probable gradient. This value is consistent with a diffusive modeling with B2-Eirene. The radial velocity increases up to 500 m/s for large transport events.

Reynolds Stress and Sheared Poloidal Flow in the Edge PlasmaRegion of the HT-6M Tokamak

High spatial resolution measurements of the electrostatic Reynolds stress,radial electric field and poloidal phase velocity of fluctuations in theedge region of the HT-6M tokamak are carried out. The Reynolds stressshows a radial gradient in proximity to the poloidal velocity shear. Acomparison of the profiles between the Reynolds stress gradient and thepoloidal velocity damping reveals some similarity in their magnitude andradial structure. These facts suggest that the turbulence-induced Reynoldsstress may play a significant role in generating the poloidal flow in theplasma edge region.

Velocity Fluctuations and Transport in the JET Boundary Region

A new approach for turbulent fluxes and ωE×B measurements in the bulk plasma is proposed. It is based in the measurement of fluctuations in the phase velocity of fluctuations. The structure of turbulence has been investigated in the JET plasma boundary region with a fast reciprocating Langmuir probe system. Fluctuations in the radial and poloidal phase velocity have been computed from floating potential and ion saturation current measurements. The correlation between density fluctuations and fluctuations in the radial velocity of fluctuations signals show a good agreement with the turbulent transport computed from the correlation between density and poloidal electric field fluctuations. These results suggest that turbulent transport might be computed in the plasma core from measurement of density fluctuations. E×B sheared flows, both constant and varying in time, are close to the critical value to trigger the transition to improve confinement regimes below the power threshold to trigger the formation of transport barriers.

Direct Measurements of E × B Flow and Its Impact on Edge Turbulence in the CASTOR Tokamak Using an Optimized Gundestrup Probe

New experimental evidence of the correlation between edge sheared E×B flow and reduction of turbulence has been measured in the CASTOR tokamak (R = 0.4 m, a = 0.085 m, B T = 1 T). A biasing electrode is placed at the separatrix in a configuration which has demonstrated strongly sheared electric fields and consequent improvement of the global particle confinement. A set of movable electrostatic probes (rake, Langmuir, Gundestrup, and rotating Mach) provide redundant, simultaneous measurements of poloidal flow, toroidal flow, electron temperature, density, and radial electric field with high temporal resolution and at the same poloidal location. Particular effort has been made in the optimization of the Gundestrup probe collector geometry in order to reduce the relative uncertainty of Mach number measurements in plasmas with weak flow (M ∥, M ⊥ < 0.1). The measurements from the rake, Gundestrup, and rotating Mach probes give three independent radial profiles of E×B shear in ohmic and biased modes. Good agreement is obtained both for the profile shape and its absolute magnitude. The plasma flows, especially the poloidal E×B drift velocity, are strongly modified in the sheared region, reaching Mach numbers as high as half the sound speed. The corresponding shear rates (≈5×106 s-1) derived from both the flow and electric field profiles are in excellent agreement and are at least an order of magnitude higher than the growth rate of unstable turbulent modes as estimated from fluctuation measurements. In addition, we compare the measured E×B ion mass flow with the phase velocity of fluctuations moving poloidally across the Gundestrup collectors. Given the poloidal separation of the collecting plates and the sampling frequency (5 MHz), the maximum detectable phase velocity turns out to be rather modest compared to the measured bulk poloidal flow speed. Therefore the two quantities are only compared when the poloidal speed is low; in that case, they show similar behaviour in response to the applied bias.

Numerical and Experimental Performance Evaluation of the 3-Stage FROSTY Supercooled Cloud Collector

An evaluation of the collection characteristics of a new multistage cascade inertial impactor designed for size-resolved cloud drop collection has been performed. The FROSTY supercooled cloud collector is intended for the collection of supercooled cloud drops in a winter environment in three independent size fractions with stage 50% cut diameters of 15 μm, 10 μm, and 4 μm. Two approaches were selected for the evaluation of the collector. Numerical simulations provided a visualization of the airflow patterns and drop trajectories through the collector while experimental laboratory calibration provided a quantitative analysis of true collection performance. For each of these methods, 50% cut diameters, efficiency curves, and wall losses for each stage of the collector were determined. Collection characteristics were determined experimentally by introducing fluorescein-tagged monodisperse drops into the collector and analyzing collection patterns by fluorescence. The experimental measurements at laboratory conditions indicated 50% cut diameters of 19.0, 11.5, and 5.0 μm for the three stages. Adjusted for operation at collector design conditions, the 50% cut diameters were 17.0, 10.5, and 4.5 μm. Numerical modeling of the airflow patterns and drop trajectories through the collector was performed with the commercially available Computational Fluid Dynamics (CFD) software package FLUENT. Trajectory simulations based on the average continuous phase (air) velocity field as well as trajectory simulations which included the effects of statistically derived turbulent velocity fluctuations on drop motion were performed. Comparisons between the numerical and experimental work indicated that the inclusion of turbulent fluctuation effects on drop motion provided much better agreement with experimental observations than trajectories based solely on average flow field velocities. However, the use of continuous phase velocity fluctuations also produced unrealistic losses to wall surfaces for small drop sizes. Despite this shortcoming, numerically derived 50% cut diameters and overall collection efficiency curve shapes for drop trajectories including turbulent velocity fluctuations agreed reasonably well with experimental observations.

Direct numerical simulation of particle-turbulence interaction

This paper presents the results of a numerical simulation of the interaction between solid particles and near-wall turbulence. The fluid flow in a horizontal channel is solved using direct numerical simulation. For the particle motion, a Lagrangian approach is used. The particles are relatively large, and cover several collocation points in the fluid. Two-way coupling is used to account for the effect of the particles on the structure of the near-wall turbulence, and on the main stream. It is shown that the presence of large particles in the near-wall region enhances the intensity of the carrier phase velocity fluctuations. Based on the computational data, it was established that the particles with large relaxation time move in a random way and do not accumulate along the low velocity streaks, as smaller particles do.