Turbulent Particle Transport Research Articles

Edge shear flows and particle transport near the density limit of the HL-2A tokamak

Edge shear flow and its effect on regulating turbulent transport have long been suspected to play an important role in plasmas operating near the Greenwald density limit nG. In this study, equilibrium profiles as well as the turbulent particle flux and Reynolds stress across the separatrix in the HL-2A tokamak are examined as is approached in ohmic L-mode discharges. As the normalized line-averaged density is raised, the shearing rate of the mean poloidal flow drops, and the turbulent drive for the low-frequency zonal flow (the Reynolds power ) collapses. Correspondingly, the turbulent particle transport increases drastically with increasing collision rates. The geodesic acoustic modes (GAMs) gain more energy from the ambient turbulence at higher densities, but have smaller shearing rate than low-frequency zonal flows. The increased density also introduces decreased adiabaticity which not only enhances the particle transport but is also related to reduction in the eddy-tilting and the Reynolds power. Both effects may lead to cooling of edge plasmas and therefore the onset of MHD instabilities that limit the plasma density.

Separation and energy efficiency of packed apparatuses for purifying gases from aerosols

A mathematical model of the turbulent transport of liquid aerosol particles has been considered using an approach in which the transport of a finely dispersed phase is conditionally described as a diffusion process with mass-transfer theory equations. The main parameter in this formulation is the coefficient of the velocity of particle transport (turbulent migration), which is an analogue of the mass transfer coefficient. The use of flow pattern models with a bulk source of the mass of sedimenting particles in a random packed bed and wire-mesh demisters is demonstrated. The equations for calculating the separation zone length and the process efficiency have been derived with allowance for the inlet section and the back mixing of the gas flow. Some calculation results are given for the aerosol separation efficiency and the energy coefficient compared with experimental data.

Impact of a hollow density profile on turbulent particle fluxes: Gyrokinetic and fluid simulations

Hollow density profiles may occur in connection with pellet fuelling and L to H transitions. A positive density gradient could potentially stabilize the turbulence or change the relation between convective and diffusive fluxes, thereby reducing the turbulent transport of particles towards the center, making the pellet fuelling scheme inefficient. In the present work, the particle transport driven by Ion Temperature Gradient/Trapped Electron (ITG/TE) mode turbulence in hollow density profiles is studied by fluid as well as gyrokinetic simulations. The fluid model used, an extended version of the Weiland transport model, Extended Drift Wave Model (EDWM), incorporates an arbitrary number of ion species in a multi-fluid description and an extended wavelength spectrum. The fluid model, which is fast and hence suitable for use in predictive simulations, is compared to gyrokinetic simulations using the code GENE. Typical tokamak parameters are used based on the Cyclone Base Case. Parameter scans in key plasma parameters like plasma β, R/LT, and magnetic shear are investigated. In addition, the effects of a fast species are studied and global ITG simulations in a simplified physics description are performed in order to investigate nonlocal effects. It is found that β in particular, has a stabilizing effect in the negative R/Ln region. Both nonlinear GENE and EDWM simulations show a decrease in inward flux for negative R/Ln and a change in the direction from inward to outward for positive R/Ln. Moreover, the addition of fast particles was shown to decrease the inward main ion particle flux in the positive gradient region further. This might have serious consequences for pellet fuelling of high β plasmas. Additionally, the heat flux in global ITG turbulence simulations indicates that nonlocal effects can play a different role from usual in connection with pellet fuelling.

Turbulent transport of alpha particles in tokamak plasmas

We investigate the diffusion of fusion born particles in tokamak plasmas. We determine the transport regimes for a realistic model that has the characteristics of the ion temperature gradient (ITG) or of the trapped electron mode (TEM) driven turbulence. It includes a spectrum of potential fluctuations that is modeled using the results of the numerical simulations, the drift of the potential with the effective diamagnetic velocity and the parallel motion. Our semi-analytical statistical approach is based on the decorrelation trajectory method (DTM), which is adapted to the gyrokinetic approximation. We obtain the transport coefficients as a function of the parameters of the turbulence and of the energy of the particles. According to our results, significant turbulent transport of the particles can appear only at energies of the order of 100 KeV. We determine the corresponding conditions.

Fluid and gyrokinetic modelling of particle transport in plasmas with hollow density profiles

Hollow density profiles occur in connection with pellet fuelling and L to H transitions. A positive density gradient could potentially stabilize the turbulence or change the relation between convective and diffusive fluxes, thereby reducing the turbulent transport of particles towards the center, making the fuelling scheme inefficient. In the present work, the particle transport driven by ITG/TE mode turbulence in regions of hollow density profiles is studied by fluid as well as gyrokinetic simulations. The fluid model used, an extended version of the Weiland transport model, Extended Drift Wave Model (EDWM), incorporates an arbitrary number of ion species in a multi-fluid description, and an extended wavelength spectrum. The fluid model, which is fast and hence suitable for use in predictive simulations, is compared to gyrokinetic simulations using the code GENE. Typical tokamak parameters are used based on the Cyclone Base Case. Parameter scans in key plasma parameters like plasma β, R/LT, and magnetic shear are investigated. It is found that β in particular has a stabilizing effect in the negative R/Ln region, both nonlinear GENE and EDWM show a decrease in inward flux for negative R/Ln and a change of direction from inward to outward for positive R/Ln. This might have serious consequences for pellet fuelling of high β plasmas.

Lattice Boltzmann method and RANS approach for simulation of turbulent flows and particle transport and deposition

Using the lattice-Boltzmann computational approach in conjunction with the Reynolds averaged Navier–Stokes (RANS) model, several turbulent flows and the transport and deposition of particles in different passages were studied. The new lattice Boltzmann method (LBM) solved the RANS equations coupled with the standard and renormalization group k−ɛ turbulence models. In particular, the LBM formulation was augmented by the addition of two transport equations for the probability distribution function of populations of k and ɛ. The discrete random walk model was used to generate the instantaneous turbulence fluctuations. For turbulent channel flows, the analytical fits to the root mean-square velocity fluctuations obtained by the direct numerical simulation of the turbulent flow were used in the analysis. Attention was given to the proper evaluation of the wall normal turbulent velocity fluctuations particularly near the wall. The simulation results were compared with the available numerical simulation and experimental data. The new LBM–RANS model is shown to provide a reasonably accurate description of turbulent flows and particle transport and deposition at modest computational cost.

Turbulence induced radial transport of toroidal momentum in boundary plasma of EAST tokamak

Turbulence induced toroidal momentum transport in boundary plasma is investigated in H-mode discharge using Langmuir-Mach probes on EAST. The Reynolds stress is found to drive an inward toroidal momentum transport, while the outflow of particles convects the toroidal momentum outwards in the edge plasma. The Reynolds stress driven momentum transport dominates over the passive momentum transport carried by particle flux, which potentially provides a momentum source for the edge plasma. The outflow of particles delivers a momentum flux into the scrape-off layer (SOL) region, contributing as a momentum source for the SOL flows. At the L-H transitions, the outward momentum transport suddenly decreases due to the suppression of edge turbulence and associated particle transport. The SOL flows start to decelerate as plasma entering into H-mode. The contributions from turbulent Reynolds stress and particle transport for the toroidal momentum transport are identified. These results shed lights on the understanding of edge plasma accelerating at L-H transitions.

Spontaneous profile self-organization in a simple realization of drift-wave turbulence

We report the observation of a transport bifurcation that occurs by spontaneous self-organization of a drift-wave and shear flow system in a linear plasma device. As we increase the magnetic field above a threshold (BCr = 1200 G), a global transition occurs, with steepening of mean density and ion pressure profiles, onset of strong E×B shearing, a reduction of turbulence, and improved turbulent radial particle transport. An abrupt transition appears in the graph of turbulent particle flux versus density gradient. Hysteresis in the density gradient further confirms this transport bifurcation. The total Reynolds work on the flow sharply increases above threshold. This correlates with the increase of density steepness, which suggests the Reynolds stress-driven flow that plays an essential role in density steepening and transport bifurcation. A change in turbulence feature from drift waves (DWs) to a mix of DWs and ion temperature gradients also coincides with the transport bifurcation. Interesting phenomena related to the transport bifurcation are also reported; a local inward particle flux, the co-existence of ion and electron features, and a self-sustained axial flow absent momentum input.

Turbulent particle transport as a function of toroidal rotation in DIII-D H-mode plasmas

In this paper we show how changes in toroidal rotation, by controlling the injected torque, affect particle transport and confinement. The toroidal rotation is altered using the co- and counter neutral beam injection (NBI) in low collisionality H-mode plasmas on DIII-D (Luxon 2002 Nucl. Fusion 42 614) with dominant electron cyclotron heating (ECH). We find that there is no correlation between the toroidal rotation shear and the inverse density gradient, which is observed on AUG when is varied using ECH (Angioni et al 2011 Phys. Rev. Lett. 107 215003). In DIII-D, we find that in a discharge with balanced torque injection, the shear is smaller than the linear gyrokinetic growth rate for small for –0.85. This results in lower particle confinement. In the co- and counter- injected discharges the shear is larger or close to the linear growth rate at the plasma edge and both configurations have higher particle confinement. In order to measure particle transport, we use a small periodic perturbative gas puff. This gas puff perturbs the density profiles and allows us to extract the perturbed diffusion and inward pinch coefficients. We observe a strong increase in the inward particle pinch in the counter-torque injected plasma. Finally, the calculated quasi-linear particle flux, nor the linear growth rates using TGLF (Staebler et al 2005 Phys. Plasmas 12 102508) agree with experimental observations.

Transport matrix for particles and momentum in collisional drift waves turbulence in linear plasma devices

The relationship between the physics of turbulent transport of particles and azimuthal momentum in a linear plasma device is investigated using a simple model with a background density gradient and zonal flows driven by turbulent stresses. Pure shear flow driven Kelvin-Helmholtz instabilities (k∥=0) relax the flow and drive an outward (down gradient) flux of particles. However, instabilities at finite k∥ with flow enhanced pumping can locally drive an inward particle pinch. The turbulent vorticity flux consists of a turbulent viscosity term, which acts to reduce the global vorticity gradient and the residual vorticity flux term, accelerating the zonal flows from rest. Moreover, we use the positivity of the production of fluctuation potential enstrophy to obtain a constraint relation, which tightly links the vorticity transport to the particle transport. This relation can be useful in explaining the experimentally observed correlation between the presence of E×B flow shear and the measured inward particle flux in various magnetically confined plasma devices.

Simulation and validation of two-phase turbulent flow and particle transport in continuous casting of steel slabs

In continuous steel casting, argon gas is usually injected at the slide gate or stopper rod to prevent clogging, but entrapped bubbles may cause defects in the final product. To better understand this, the flow of molten steel and the transport and capture of argon gas bubbles have been simulated and compared with plant measurements. First, the flow field was solved with an Eulerian k-s model of the steel, which was two-way coupled with a Lagrangian model of the large bubbles using a Discrete Random Walk method to include dispersion of bubbles due to turbulence. The asymmetrical flow pattern predicted on the top surface agreed well with nailboard measurements. Then, the motion and capture of over two million bubbles were simulated using two different capture criteria. Results with the advanced capture criterion agreed well with measurements of the number, locations, and sizes of captured bubbles, especially for larger bubbles. The relative capture fraction of 0.3% was close to the measured 0.2% for 1mm bubbles, and occurred very near the top surface. The model presented here is an efficient tool to study the capture of bubbles and inclusion particles in solidification processes.

Multi-scale self-organisation of edge plasma turbulent transport in 3D global simulations

The 3D global edge turbulence code TOKAM3X is used to study the properties of edge particle turbulent transport in circular limited plasmas, including both closed and open flux surfaces. Turbulence is driven by an incoming particle flux from the core plasma and no scale separation between the equilibrium and the fluctuations is assumed. Simulations show the existence of a complex self-organization of turbulence transport coupling scales ranging from a few Larmor radii up to the machine scale. Particle transport is largely dominated by small scale turbulence with fluctuations forming quasi field-aligned filaments. Radial particle transport is intermittent and associated with the propagation of coherent structures on long distances via avalanches. Long range correlations are also found in the poloidal and toroidal direction. The statistical properties of fluctuations vary with the radial and poloidal directions, with larger fluctuation levels and intermittency found in the outboard scrape-off layer (SOL). Radial turbulent transport is strongly ballooned, with 90% of the flux at the separatrix flowing through the low-field side. One of the main consequences is the existence of quasi-sonic asymmetric parallel flows driving a net rotation of the plasma. Simulations also show the spontaneous onset of an intermittent E × B rotation characterized by a larger shear at the separatrix. Strong correlation is found between the turbulent particle flux and the E × B flow shear in a phenomenology reminiscent of H-mode physics. The poloidal position of the limiter is a key player in the observed dynamics.

Turbulent transport of heat and particles in a high ion temperature discharge of the Large Helical Device

Turbulent transport in a high ion temperature discharge of the Large Helical Device (LHD) is investigated by means of electromagnetic gyrokinetic simulations, which include kinetic electrons, magnetic perturbations, and full geometrical effects. Including kinetic electrons enables us to firstly evaluate the particle and the electron heat fluxes caused by turbulence in LHD plasmas. It is found that the electron energy transport reproduces the experimental result, and that the particle flux is negative. The contribution of magnetic perturbation to the transport is small because of very low beta. The turbulence is driven by the ion temperature gradient instability, and the effect of kinetic electrons enhances the growth rate larger than that from the adiabatic electron calculation. The ion energy flux is larger than that observed in the experiment, while the flux is close to the experimental observation when the temperature gradient is reduced 20% in the simulation. This significant sensitivity of the energy flux implies that the profile in the experiment is close to the critical temperature gradient. The critical gradient for turbulent energy flux is similar to that for the linear instability, i.e., the Dimits shift is small. This is because the zonal flow in the LHD is weaker than that in tokamaks.

PITCH-ANGLE SCATTERING OF ENERGETIC PARTICLES WITH ADIABATIC FOCUSING

Understanding turbulent transport of charged particles in magnetized plasmas often requires a model for the description of random variations in the particle's pitch angle. The Fokker-Planck coefficient of pitch-angle scattering, which is used to describe scattering parallel to the mean magnetic field, is therefore of central importance. Whereas quasi-linear theory assumes a homogeneous mean magnetic field, such a condition is often not fulfilled, especially for high-energy particles. Here, a new derivation of the quasi-linear approach is given that is based on the unperturbed orbit found for an adiabatically focused mean magnetic field. The results show that, depending on the ratio of the focusing length and the particle's Larmor radius, the Fokker-Planck coefficient is significantly modified but agrees with the classical expression in the limit of a homogeneous mean magnetic field.

Scientific Discovery in Fusion Plasma Turbulence Simulations at Extreme Scale

The primary goal of the extreme-scale plasma turbulence studies described in this article is to gain new insights on confinement scaling in magnetic fusion systems by using powerful, world-class supercomputers to carry out simulations with unprecedented resolution and temporal duration. New insights have been gained on the key question of how the turbulent transport of thermal energy and particles in the plasma and the associated confinement scale from present-generation devices to much larger ITER-size plasmas. In particular, new results from large-scale simulation studies have demonstrated that improvement in confinement as devices grow larger is far more gradual, with significantly lower loss rates than less-powerful computer simulations have indicated in research carried out over the past decade.

Core intrinsic rotation behaviour in ASDEX Upgrade ohmic L-mode plasmas

The ASDEX Upgrade intrinsic rotation database has been expanded to include a large number of measurements from ohmic L-mode discharges covering a wide range of plasma densities, currents and magnetic fields. This database was then used to study the rotation behaviour across the transition from linear to saturated ohmic confinement (LOC/SOC). At low collisionality the plasma is in the LOC regime and the toroidal rotation profile is in the co-current direction. As the collisionality is increased and the plasma transitions from LOC to SOC, the core rotation decreases resulting in a hollow, counter-current profile. Even deeper in the SOC regime, however, a second reversal back towards the co-current direction occurs. Linear gyrokinetic calculations indicate that these reversals cannot be explained by a transition from a trapped electron mode (TEM) to an ion temperature gradient (ITG) dominated regime. Rather, the analysis indicates that the intrinsic normalized rotation gradient, u′, depends strongly on local plasma parameters, in particular on . Taken together with turbulent particle transport theory, these results suggest that the co- to counter-current directed rotation reversal occurs in the TEM regime due to profile changes and not due to transition from TEM to ITG. The second reversal back to the co-current direction is explained by the reduction of observed in ITG dominated plasmas. Lastly, a simple linear model for the residual stress assuming a fixed poloidal tilt angle of the turbulent eddies was applied to the database. This model is able to capture the main parameter dependencies observed in the data and demonstrates that at least two processes contributing to the poloidal tilt of the turbulent eddies are needed to reproduce the experimentally observed u′ values: one proportional to the sign of the turbulence propagation and the second independent of ωr.

Analysis of Transient Transport and Entrapment of Particle in Continuous Casting Mold

A mathematical model has been developed to simulate the transient turbulent flow, solidification, transport and entrapment of particles in a continuous casting mold. The turbulence of molten steel inside the liquid pool is calculated using the large eddy simulation (LES). The enthalpy-porosity approach is used to simulate the solidification of steel. A Laplacian equation is used to approximate the pull velocity in the solid region. The transport of particle (bubble and non-metallic inclusion) inside the liquid pool is considered according to the Lagrangian approach. A criterion for particle entrapment in the solidified front is developed using the user-defined functions (UDF) of FLUENT software, considering force balance involving eight different forces acting on a particle at the mushy-zone. The predicted asymmetrical flow pattern is compared with the water model experiment results. The entrapped positions of particles in the solidified shell are predicted and compared with the ultrasonic flaw results of rolled steel plates and the previous study of inclusions distribution in slabs. The model has successfully reproduced many known phenomena and other new predictions, including the transient asymmetrical flow pattern, transient asymmetrical distribution of particles inside the liquid pool, transient entrapment ratios and asymmetrical positions of different particles in the solidified shell.

The influence of electrode biasing on plasma confinement in the J-TEXT tokamak

The influence of both positive and negative bias on global and plasma-edge parameters has been comparatively studied with a newly designed electrode biasing system in the J-TEXT tokamak. Compared to the 0 V bias case, the global particle confinement of plasma is enhanced under bias with both polarities, with the increments of the central line-averaged density and the soft x-ray emission, as well as the reduction of the edge Hα radiation level. The suppression of plasma-edge fluctuations and turbulent particle transport are obviously observed under bias, in different degrees with different polarities. The potential fluctuation amplitude is observed to be increased at the vicinity of the limiter under positive bias, with the existence of a peaked low-frequency mode characterized as high coherence and near-zero cross-phase poloidally in the edge region, which is not found in the negative bias case. The poloidal correlation length of turbulence is greatly enhanced under bias with both polarities; it shows a positive correlation with the amplitude of the poloidal phase velocity, which is mainly driven by the local Jr × B torque at the plasma edge under bias. The characteristic parameters of intermittent events (i.e. blobs), including amplitude, radial velocity, related particle flux and radial size, decreased dramatically under bias in the edge region.

Modeling study of soot formation and oxidation in DI diesel engine using an improved soot model

Particulate emission is one of the most deleterious pollutants generated by Diesel fuel combustion. The ability to predict soot formation is one of the key elements needed to optimize the engine performance and minimize soot emissions. This paper reports work on developing, a phenomenological soot model to better model the physical and chemical processes of soot formation in Diesel fuel combustion. This hybrid model features that the effect of turbulence on the chemical reaction rate was considered in soot oxidation. Soot formation and oxidation processes were modeled with the application of a hybrid method involving particle turbulent transport controlled rate and soot oxidation rate. Compared with the original soot model, the in-cylinder pressures, heat release rate and soot emissions predicted by this hybrid model agreed better with the experimental results. The verified hybrid model was used to investigate the effect of injection timing on engine performance. The results show that the new soot model predicted reasonable soot spatial profiles within the combustion chamber. The high temperature gas zone in cylinder for hybrid model case is distributed broadly soot and NOx emission dependence on the start-of-injection (SOI) timing. Retarded SOI timing increased the portion of diffusion combustion and the soot concentration increased significantly with retarding of the fuel injection timing. The predicted distributions of soot concentration and particle mass provide some new insights on the soot formation and oxidation processes in direct injection (DI) engines. The hybrid phenomenological soot model shows greater potential for enhancing understanding of combustion and soot formation processes in DI diesel engines.

Transport and Entrapment of Particles in Steel Continuous Casting

A particle-capture model based on local force balances has been developed, implemented into computational models of turbulent fluid flow and particle transport, and applied to simulate the entrapment of slag inclusions and bubbles during the continuous casting of steel slabs. Turbulent flow of molten steel is computed in the nozzle and mold using transient computational fluid flow models, both with and without the effects of argon gas injection. Next, the transport and capture of many particles are simulated using a Lagrangian approach. Particles touching the dendritic interface may be pushed away, dragged away by the transverse flow, or captured into the solidifying shell according to the results of a local balance of ten different forces. This criterion was validated by reproducing experimental results in two different systems. The implications of this criterion are discussed quantitatively. Finally, the fluid flow/particle transport model results and capture criterion are applied together to predict the entrapment distributions of different sized particles in a typical slab caster. More large particles are safely removed than small ones, but the entrapment rate into the solidifying shell as defects is still very high.