Turbulence Suppression Research Articles

Limitations of the clump-correlation theories of shear-induced turbulence suppression

The clump theory, primarily constructed by Dupree [Phys. Fluids 15, 334 (1972)] based on the moment approach and then generalized to the correlation theory [Y. Z. Zhang and S. M. Mahajan, Phys. Fluids B 5, 2000 (1993)], has long served as a basis for constructing theories of turbulence suppression by shear flow. In order to reveal the “intrinsic approximation” invoked in the clump-correlation theory, we examine a model based on two dimensional magnetized drift waves. After a rigorous derivation of the exact response function—a key to average the Green function of the system—we show that the Dupree, Zhang-Mahajan approach is recovered as the lowest order approximation in a small dimensionless parameter ϒ which is a triple product of the correlation time, wave number, and fluctuating drift velocity. The clump-correlation theory, thus, constitutes the Gaussian and lowest order non-Markovian process for a homogeneous stationary turbulence. We also provide, especially for the tokamak community, a readily usable formula to evaluate the effectiveness of shear-flow suppression; this formula pertains regardless of the specific model of correlation time.

EDGE2D-EIRENE modelling of near SOL Er: possible impact on the H-mode power threshold

Recent EDGE2D-EIRENE simulations of JET plasmas showed a significant difference between radial electric field (Er) profiles across the separatrix in two divertor configurations, with the outer strike point on the horizontal target (HT) and vertical target (VT) (Chankin et al 2016 Nucl. Mater. Energy, doi: 10.1016/j.nme.2016.10.004). Under conditions (input power, plasma density) where the HT plasma went into the H-mode, a large positive Er spike in the near scrape-off layer (SOL) was seen in the code output, leading to a very large E × B shear across the separatrix over a narrow region of a fraction of a cm width. No such Er feature was obtained in the code solution for the VT configuration, where the H-mode power threshold was found to be twice as high as in the HT configuration. It was hypothesised that the large E × B shear across the separatrix in the HT configuration could be responsible for the turbulence suppression leading to an earlier (at lower input power) L–H transition compared to the VT configuration. In the present work these ideas are extended to cover some other experimental observations on the H-mode power threshold variation with parameters which typically are not included in the multi-machine H-mode power threshold scalings, namely: ion mass dependence (isotope H–D–T exchange), dependence on the ion ∇B drift direction, and dependence on the wall material composition (ITER-like wall versus carbon wall in JET). In all these cases EDGE2D-EIRENE modelling shows larger positive Er spikes in the near SOL under conditions where the H-mode power threshold is lower, at least in the HT configuration.

Zonal flow energy ratio evolution during L-H and H-L transitions in EAST plasmas

The essential role of zonal flow in the L-H transition and the suppression of turbulence have been studied with a long range correlation technique using Langmuir probe arrays in EAST tokamak. Two toroidally localized probe arrays are used to measure the zonal flow during L-H transition and H-L back transition. The energy ratio of the low frequency zonal flow to the total drift wave turbulence is calculated. During ELM-free H mode, the energy ratio is higher than that in L mode, which reveals the important role of zonal flows in regulating turbulence amplitude in L-H transition.

Implementation of Neoclassical Effects in Momentum Transport Analysis at LHD

Plasma rotation plays an important role in the suppression of turbulence, leading to an increase in energy and particle confinement. Significant rotation also leads to a stabilisation of the resistive wall mode. The external momentum input from Neutral Beam Injection (NBI) in current generation fusion plasmas may not be available for future self-heated fusion reactors. Therefore it is important to analyse the phenomenon of spontaneous rotation. At NIFS plasma rotation and momentum transport of the Large Helical Device (LHD) plasma is analysed using a code suite called TASK3D-a. In this work neoclassical effects, which can be especially significant in non-axisymmetric plasmas, were implemented in TASK3D-a. Initial analysis of neoclassical radial momentum flux profiles shows that in NBI-driven momentum input neoclassical effects, especially neoclassical damping, become dominant in the non-center plasma region. It was also found that during and after pellet-injection the neoclassical damping force becomes strong. With the implementation of neoclassical effects new features can be examined in the momentum flux-gradient relations; in the damping-dominated situation following pellet injection a large excursion in momentum flux is found. This work can aid in the search for neoclassical transport-optimised configurations for enhanced (spontaneous) plasma rotation.

The CFD modeling of two-dimensional turbulent MHD channel flow

In this paper, influence of magnetic field on turbulence characteristics of twodimensional flow is investigated. The present study has been undertaken to understand the effects of a magnetic field on mean velocities and turbulence parameters in turbulent 2-D channel flow. Several cases are considered. First laminar flow in a channel and MHD laminar channel flow are analyzed in order to validate model of magnetic field influence on electrically conducting fluid flow. Main part of the paper is focused on MHD turbulence suppression for 2-D turbulent flow in a channel and around the flat plate. The simulations are performed using ANSYS CFX software. Simulations results are obtained with BSL Reynolds stress model for turbulent and MHD turbulent flow around flat plate. The nature of the flow has been examined through distribution of mean velocities, turbulent fluctuations, vorticity, Reynolds stresses and turbulent kinetic energy.

ANOMALOUS COOLING OF CORONAL LOOPS WITH TURBULENT SUPPRESSION OF THERMAL CONDUCTION

ABSTRACT We investigate the impact of turbulent suppression of parallel heat conduction on the cooling of post-flare coronal loops. Depending on the value of the mean free path associated with the turbulent scattering process, we identify four main cooling scenarios. The overall temperature evolution, from an initial temperature in excess of 107 K, is modeled in each case, highlighting the evolution of the dominant cooling mechanism throughout the cooling process. Comparison with observed cooling times allows the value of to be constrained, and interestingly this range corresponds to situations where collision-dominated conduction plays a very limited role, or even no role at all, in the cooling of post-flare coronal loops.

Proper orthogonal decomposition analysis for two-oscillating grid turbulence with viscoelastic fluids

In this article, the experiments of two-oscillating grid turbulence with viscoelastic fluids were carried out using particle image velocimetry. Two classical drag-reducing additives with viscoelastic characteristics were chosen: polymer (polyacrylamide) and cationic surfactant (cetyltrimethyl ammonium chloride). In order to investigate the viscoelastic effect on coherent structures, proper orthogonal decomposition was performed to identify coherent structures based on particle image velocimetry data. The results show that the minimum number for eigenmodes required for capturing coherent structures, which contains 90% of total turbulent kinetic energy, is 127, 19, and 117 for the Newtonian fluid case, 25 ppm polyacrylamide solution case, and 25 ppm cetyltrimethyl ammonium chloride solution case at grid oscillating frequency f = 7.5 Hz, respectively. It means that coherent structures can be inhibited due to the addition of polyacrylamide additives but not remarkable in 25 ppm cetyltrimethyl ammonium chloride solution case, in other words, the decrease in flow complexity in 25 ppm polyacrylamide solution case. This phenomenon also appears at grid oscillating frequency f = 5 Hz. However, as cetyltrimethyl ammonium chloride solution concentration increases up to 50 ppm, the cetyltrimethyl ammonium chloride solution case shows similar trends as those in 50 ppm polyacrylamide solution case (the number for eigenmodes required for capturing coherent structures is approximate). Therefore, compared with a channel flow with cetyltrimethyl ammonium chloride solution, there exists the larger critical concentration in two-oscillating grid turbulence to show turbulence suppression effect.

Possible influence of near SOL plasma on the H-mode power threshold

A strong effect of divertor configuration on the threshold power for the L-H transition (PLH) was observed in recent JET experiments in the new ITER-like Wall (ILW) [1–3]. Following a series of EDGE2D-EIRENE code simulations with Be impurity and drifts a possible mechanism for the PLH variation with the divertor geometry is proposed. Both experiment and code simulations show that in the configuration with lower neutral recycling near the outer strike point (OSP), electron temperature (Te) peaks near the OSP prior to the L-H transition, while in the configuration with higher OSP recycling Te peaks further out in the scrape-off layer (SOL) and the plasma stays in the L-mode at the same input power. Code results show large positive radial electric field (Er) in the near SOL under lower recycling conditions leading to a large E×B shear across the separatrix which may trigger earlier (at lower input power) edge turbulence suppression and lower PLH. Suppressed Te‘s at OSP in configurations with strike points on vertical targets (VT) were observed earlier and explained by a geometrical effect of neutral recycling near this particular position, whereas in configurations with strike points on horizontal targets (HT) the OSP appears to be more open for neutrals (see e.g. review paper [4]).

A numerical study of diffusive effects in turbulent lean premixed hydrogen flames

Three-dimensional direct numerical simulation of lean premixed hydrogen flames is used to explore the influence of species and thermal diffusion and viscosity on the flame structure and turbulent flame response. The leading-order flame response is shown to be due to the global Lewis number with little influence from the other species. The previously-reported observation of decorrelation of fuel consumption and heat release at high Karlovitz numbers is shown to be solely due to atomic hydrogen diffusion. Finally, it is shown that the suppression of turbulence through the flame cannot be attributed to an increase in viscosity due to the increase in temperature, but that the effect is not negligible. It is further argued that turbulence–flame interactions are better described considering Kolmogorov’s second similarity hypothesis (rather than the first); specifically, by a Karlovitz number that is defined based on the inertial subrange (i.e. the energy dissipation rate) rather than the dissipation subrange (i.e. viscosity or equivalently Kolmogorov scale quantities).

Scenario development for high βp low torque plasma with qmin above 2 and large-radius internal transport barrier in DIII-D

A recent experiment on DIII-D, which was conducted by the joint research team from DIII-D and EAST, has extended the previous high , high qmin regime, which has been tested in the 2013 DIII-D/EAST joint experiment, to inductive operation at higher plasma current ( MA) and significantly higher normalized fusion performance (). The experiment aims at exploring high performance scenario with and reduced torque for long pulse operation, which can be potentially extrapolated to EAST. The effort was largely motivated by the interest in developing a feasible scenario for long-pulse high performance operation with low torque on EAST. Very high confinement, H89 = 3.5 or with , has been achieved transiently in this experiment together with and reduced NBI torque ( N m). The excellent confinement is associated with the spontaneous formation of an internal transport barrier (ITB) in plasmas with MA at large minor radius (normalized ) in all channels (ne, Te, Ti, , especially strong in the Te channel). Fluctuation measurements show a significant reduction in the fluctuation levels, including AE modes and broadband turbulence, at the location where an ITB forms. Linear gyrokinetic simulations also support the decrease of the growth rate of the most unstable mode during strong ITB formation. The simulation implies that strong suppression of turbulence and a positive feedback loop may be active in this process and is responsible for the spontaneous formation of large-radius ITB. In an unstable ITB phase, an ELM crash is observed to have a positive effect on transient formation of large-radius ITB. The formation of this kind of ITB is found to have a shielding (protecting) effect on the core plasma while isolating the perturbation due to ELM crash.

Gyrokinetic study of turbulence suppression in a JET-ILW power scan

For exploring tokamak operation regimes that deliver both high β and good energy confinement, power scans at JET with ITER-like wall have been performed. Relatively weak degradation of the confinement time coincides with increased core temperature of the ions at high power. The changes in core turbulence characteristics during a power scan with an optimized (broad) q profile are analyzed by means of nonlinear gyrokinetic simulations. The increase in β is crucial for stabilizing ion temperature gradient driven turbulence, accompanied by increased ion to electron temperature ratio, the presence of a dynamic fast ion species, as well as the geometric stabilization by increased thermal and suprathermal pressure. A sensitivity study with respect to the q profile reveals that electromagnetic effects are more pronounced at larger values of q. Further, it is confirmed that turbulence suppression due to rotation becomes less effective in such strongly electromagnetic systems. Electrostatic simplified models may thus perform well in present-day devices, in which high β is often correlated with high rotation, but provide poor extrapolation towards low rotation devices. Implications for ITER and reactor plasmas are discussed.

Flame height of turbulent fire whirls: A model study by concept of turbulence suppression

This paper presents a new semi-physical analysis for the flame height of turbulent fire whirls based on the concept of turbulence suppression. Turbulent fire whirl experiments were performed by a square channel model facility, using propane (30cm in burner diameter, 25–300kW in heat release rate) and heptane (15–50cm in pool size) as representative of gas and liquid fuels, respectively. The Richardson number (Ri), defined by the mean quantities of flow, is used to characterize the turbulence suppression in turbulent fire whirls by the mixing length being represented as a decreasing linear function of Ri. By using the radially-integrated mixture fraction equation and an equation for the radius of fire whirl plume, a flame height correlation is derived which couples the heat release rate, the Richardson number and the axial velocity parameters. The experimental data of propane and heptane fire whirls fit well with the new correlation, which indicates that the correlation can be used to determine the flame heights of fire whirls for different types of fuels. It is demonstrated that the turbulence suppression is the dominant mechanism which controls the flame elongation in turbulent fire whirls compared to free turbulent pool fires of equal fire size.

Regeneration of turbulent fluctuations in low-Froude-number flow over a sphere at a Reynolds number of 3700

Direct numerical simulations (DNS) are performed to study the behaviour of flow past a sphere in the regime of high stratification (low Froude number $Fr$). In contrast to previous results at lower Reynolds numbers, which suggest monotone suppression of turbulence with increasing stratification in flow past a sphere, it is found that, below a critical $Fr$, increasing the stratification induces unsteady vortical motion and turbulent fluctuations in the near wake. The near wake is quantified by computing the energy spectra, the turbulence energy equation, the partition of energy into horizontal and vertical components, and the buoyancy Reynolds number. These diagnostics show that the stabilizing effect of buoyancy changes flow over the sphere to flow around the sphere. This qualitative change in the flow leads to a new regime of unsteady vortex shedding in the horizontal planes and intensified horizontal shear which result in turbulence regeneration.

ExB shear and precession shear induced turbulence suppression and its influence on electron thermal internal transport barrier formation

E × B shear and trapped electron precession shear induced suppression of micro-turbulence is studied in general tokamak geometry. A systematic derivation of a two-point equation for trapped electron related turbulence based on modern bounce kinetic formalism is performed. A two-point nonlinear analysis yields the new criterion for the turbulence suppression |ωE×B+ωPS|>ΔωT, where ΔωT is decorrelation rate of the ambient turbulence, ωE×B is E×B shearing rate in general tokamak geometry [Hahm and Burrell, Phys. Plasmas 2, 1648 (1995)], and ωPS is precession shearing rate. Therefore, both E×B shear and trapped electron precession shear can contribute to suppression of turbulence, and these effects can either add up or subtract depending on their relative sign. This result provides a better understanding of electron thermal internal transport barrier formation under various conditions.

On the Origin of Steep and Localized Radial Electric Field in the Transport Barrier at Plasma Edge

AbstractTheories to understand the steep and localized radial electric field in the edge of toroidal plasma, which appears in conjunction with H‐mode, is revisited based on the electric field bifurcation model. Key elements in the models of the L‐H transition (including the toroidal effects on the dielectric constant and the effects of the curvature of radial electric field on turbulence suppression) are assessed. Results are applied to tokamak and helical plasmas, for which data with high‐resolution have been obtained recently. The status of quantitative tests on various mechanisms through comparison with experimental observations is also addressed. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Axisymmetric electrostatic magnetohydrodynamic oscillations in tokamaks with general cross-sections and toroidal flow

The frequency spectrum and mode structure of axisymmetric electrostatic oscillations [the zonal flow (ZF), sound waves (SW), geodesic acoustic modes (GAM), and electrostatic mean flows (EMF)] in tokamaks with general cross-sections and toroidal flows are studied analytically using the electrostatic approximation for magnetohydrodynamic modes. These modes constitute the “electrostatic continua.” Starting from the energy principle for a tokamak plasma with toroidal rotation, we showed that these modes are completely stable. The ZF, the SW, and the EMF could all be viewed as special cases of the general GAM. The Euler equations for the general GAM are obtained and are solved analytically for both the low and high range of Mach numbers. The solution consists of the usual countable infinite set of eigen-modes with discrete eigen-frequencies, and two modes with lower frequencies. The countable infinite set is identified with the regular GAM. The lower frequency mode, which is also divergence free as the plasma rotation tends to zero, is identified as the ZF. The other lower (zero) frequency mode is a pure geodesic E×B flow and not divergence free is identified as the EMF. The frequency of the EMF is shown to be exactly 0 independent of plasma cross-section or its flow Mach number. We also show that in general, sound waves with no geodesic components are (almost) completely lost in tokamaks with a general cross-sectional shape. The exception is the special case of strict up-down symmetry. In this case, half of the GAMs would have no geodesic displacements. They are identified as the SW. Present day tokamaks, although not strictly up-down symmetric, usually are only slightly up-down asymmetric. They are expected to share the property with the up-down symmetric tokamak in that half of the GAMs would be more sound wave-like, i.e., have much weaker coupling to the geodesic components than the other half of non-sound-wave-like modes with stronger coupling to the geodesic displacements. Based on the general notion that the geodesic component of the GAM is more effective in tearing up the eddies in the electrostatic turbulence, it is important to preferentially excite the GAMs that are non-sound-wave like to maximize the efficiency on turbulence suppression through external means. Finally, approximate formulae for the frequencies of the EMF, ZF, SW, and the GAM for a large aspect ratio circular tokamak rotating at low Mach numbers are also provided.

The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence

The 2D spectrum of the saturated electric potential from gyrokinetic turbulence simulations that include both ion and electron scales (multi-scale) in axisymmetric tokamak geometry is analyzed. The paradigm that the turbulence is saturated when the zonal (axisymmetic) ExB flow shearing rate competes with linear growth is shown to not apply to the electron scale turbulence. Instead, it is the mixing rate by the zonal ExB velocity spectrum with the turbulent distribution function that competes with linear growth. A model of this mechanism is shown to be able to capture the suppression of electron-scale turbulence by ion-scale turbulence and the threshold for the increase in electron scale turbulence when the ion-scale turbulence is reduced. The model computes the strength of the zonal flow velocity and the saturated potential spectrum from the linear growth rate spectrum. The model for the saturated electric potential spectrum is applied to a quasilinear transport model and shown to accurately reproduce the electron and ion energy fluxes of the non-linear gyrokinetic multi-scale simulations. The zonal flow mixing saturation model is also shown to reproduce the non-linear upshift in the critical temperature gradient caused by zonal flows in ion-scale gyrokinetic simulations.

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.

The effect of drop evaporation on gas turbulence and heat transfer for two-phase flow behind sudden pipe expansion

The effect of drop evaporation on turbulence and heat transfer in a two-phase separated axisymmetric flow was studied numerically. The comparison between the calculation data for evaporating and nonevaporating particles under otherwise identical conditions is given. In the zone adjacent to the wall, drop evaporation was shown to proceed most intensively and almost no suppression of turbulence was observed in this case. The turbulence level is close to that in a single-phase flow regime. In the flow core where virtually no evaporation occurs, there was a decrease in the gas turbulence level (down to 15% compared to singlephase flow).

E × B flow velocity deduced from the poloidal motion of fluctuation patterns in neutral beam injected L-mode plasmas on KSTAR

A method for direct assessment of the equilibrium E × B flow velocity (E×B flow shear is responsible for the turbulence suppression and transport reduction in tokamak plasmas) is investigated based on two facts. The first one is that the apparent poloidal rotation speed of density fluctuation patterns is close to the turbulence rotation speed in the direction perpendicular to the local magnetic field line within the flux surface. And the second “well-known” fact is that the turbulence rotation velocity consists of the equilibrium E × B flow velocity and intrinsic phase velocity of turbulence in the E × B flow frame. In the core region of the low confinement (L-mode) discharges where a strong toroidal rotation is induced by neutral beam injection, the apparent poloidal velocities (and turbulence rotation velocities) are good approximations of the E×B flow velocities since linear gyrokinetic simulations suggest that the intrinsic phase velocity of the dominant turbulence is significantly lower than the apparent poloidal velocity. In the neutral beam injected L-mode plasmas, temporal and spatial scales of the measured turbulence are studied by comparing with the local equilibrium parameters relevant to the ion-scale turbulence.