Simulations Of Turbulent Transport Research Articles

Large eddy simulation of turbulent transport and thermal enhancement in a steam-cooled ribbed channel

Pulsating flow, as an active heat transfer enhancement technique, is expected to further improve thermal performance. To demonstrate the potential value of pulsating flow in blade cooling, a numerical investigation is conducted on the flow and heat transfer in a steam-cooled ribbed channel under steady and pulsating inflow at Re = 12000. LES, based on OpenFOAM-8, is employed and precursor simulation method is used to generate fully developed turbulent inflow. Three operating conditions, steady inflow (StF = 0), low frequency pulsation (StF = 0.02) and medium frequency pulsation (StF = 0.08), are studied. The features under steady inflow condition (StF = 0) are firstly discussed, indicating that, due to the entry effect, the ribbed channel can be divided into two regions with different vortex motion behaviors. The ejections induced by vortex evolution enhance turbulent and energy transport between the sidewall and mainstream. Two cases of pulsating inflow are then carried out, finding that stronger ejections appear and low heat transfer area is significantly improved. Corresponding to low frequency pulsation (StF = 0.02) and medium frequency pulsation (StF = 0.08), the Nusselt number has an increase of 3.511 % and 14.242 %, respectively, and friction factor has a rise of 3.934 % and 8.253 %, compared with steady inflow. The thermal performance factor is increased by 11.262 % at StF = 0.08, indicating better cooling performance than the rise of 2.188 % at StF = 0.02. It is suggested that pulsating flow with medium frequency pulsation has positive performance in a steam-cooled ribbed channel.

Spectral transition of multiscale turbulence in the tokamak pedestal

The transition in the turbulence spectrum from ion-scale dominated regimes to multiscale transport regimes that couple ion and electron scales is studied with gyrokinetic simulations of turbulent transport. The simulations are based on DIII-D high-confinement mode (H-mode) plasma parameters in the tokamak pedestal. The transition is initiated by varying the ion temperature gradient. To our knowledge, no full multiscale simulations of pedestal-like transport have been done previously. The experimental parameters lie in a bifurcation region between the two regimes. At long wavelengths, a complex, ion-direction hybrid mode is the dominant linearly unstable drift wave, while an electron temperature gradient-driven mode is unstable at short wavelengths. In the transition from the multiscale branch to the ion-scale branch, the magnitude of the ion-scale poloidal wavenumber spectrum of the nonlinear turbulent energy flux increases and the magnitude of the high-wavenumber spectrum decreases. The decrease in the electron-scale transport is due to nonlinear mixing with ion-scale fluctuations and the ion-scale-driven zonal flows. A shift in the total energy associated with the fluctuating electrostatic potential intensity from dominantly drift kinetic energy in the multiscale regime to dominantly potential intensity in the ion-scale regime is well-correlated with the trend in the total energy flux.

Simulation of equilibrium and transport in advanced FRCS

The advanced beam-driven FRC is a field reversed configuration (FRC) with the addition of neutral beam (NB) injection, electrode biasing, and magnetic expander divertors. The resulting configuration has novel features that make it necessary to revisit many key results in FRC theory. Three of these features include (i) a large energetic ion population, (ii) in-principle capability to adjust the electric field and rotation profiles, and (iii) a combination of magnetic and electrostatic confinement of electrons in the SOL. In some fueling scenarios the electron density profile may exhibit a significant peak outside of the separatrix. To explore these features a hybrid fluid/kinetic equilibrium model has been used to reconstruct typical experimental profiles of the C-2W experiment. Results indicate that the energetic ions provide at least 50% of the total plasma pressure. These equilibrium profiles have been used as initial conditions for global, cross-separatrix, turbulent transport simulations using the 3D electrostatic particle-in-cell code ANC. Electrostatic fluctuations were found to nonlinearly saturate at an amplitude which is an order magnitude lower than that observed previously. The tokamak turbulence code GTC code has also been extended to handle FRC physics in the new GTC-X version, which has been used to perform simulations of turbulent transport in the SOL relevant to electrode biasing. It is found that equilibrium E × B flow shear significantly decreases ion temperature gradient saturation amplitude and ion heat transport. Also in the SOL, a 1D2V continuum code has been developed and applied to parallel electron heat transport. Results show the formation of pre-sheath potential and reduction of parallel electron heat loss close to the ideal ambipolar limit, a result which has been validated by experimental diagnostics. These transport modifications caused by the three novel configuration features help to explain the remarkable plasma performance of the C-2W experiment.

Turbulent pinch in whole-plasma simulations of a dipole-confined plasma.

Whole-plasma simulations of turbulent transport and upgradient plasma pinch are presented in a dipole magnetic geometry relevant to the Levitated Dipole Experiment (LDX). The self-consistent evolution of an inward particle pinch and the establishment of centrally peaked plasma profiles in a dipole field are explored from whole-plasma simulations using a flux-tube averaged fluid model. The nonlinear evolution of global drift-interchange modes leads to the development of large-scale turbulent convection. Global convective cells are shown to play an important role in radial turbulent transport that causes centrally peaked profiles in a dipole magnetic field. The simulations show that the system self-consistently evolves towards a nonlinear saturated state in which the plasma pressure and density profiles are marginally stable to both drift-interchange and entropy modes.

Improved linearized model collision operator for the highly collisional regime

The linearized model collision operator for multiple species plasmas given by Sugama et al. [Phys. Plasmas 16, 112503 (2009)] is improved to be properly applicable up to the highly collisional regime. The improved linearized model operator retains the conservation laws of particles, momentum, and energy, and it reproduces the same friction-flow relations as derived by the linearized Landau operator so that this model can be used to correctly evaluate neoclassical transport fluxes in all collisionality regimes. The adjointness relations and Boltzmann's H-theorem are exactly satisfied by the improved operator except in the case of collisions between unlike particle species with unequal temperatures where these relations and H-theorem still hold approximately because there is a large difference between the masses of the two species with significantly different temperatures. Even in the unequal-temperature case, the improved operator can also be modified so as to exactly satisfy the adjointness relations, while it causes the values of the friction coefficients to deviate from those given by the Landau operator. In addition, for application to gyrokinetic simulations of turbulent transport, the improved operator is transformed into the gyrophase-averaged form by keeping the finite gyroradius effect.

Overview of new MAST physics in anticipation of first results from MAST Upgrade

The mega amp spherical tokamak (MAST) was a low aspect ratio device (R/a = 0.85/0.65 ~ 1.3) with similar poloidal cross-section to other medium-size tokamaks. The physics programme concentrates on addressing key physics issues for the operation of ITER, design of DEMO and future spherical tokamaks by utilising high resolution diagnostic measurements closely coupled with theory and modelling to significantly advance our understanding. An empirical scaling of the energy confinement time that favours higher power, lower collisionality devices is consistent with gyrokinetic modelling of electron scale turbulence. Measurements of ion scale turbulence with beam emission spectroscopy and gyrokinetic modelling in up-down symmetric plasmas find that the symmetry of the turbulence is broken by flow shear. Near the non-linear stability threshold, flow shear tilts the density fluctuation correlation function and skews the fluctuation amplitude distribution. Results from fast particle physics studies include the observation that sawteeth are found to redistribute passing and trapped fast particles injected from neutral beam injectors in equal measure, suggesting that resonances between the m = 1 perturbation and the fast ion orbits may be playing a dominant role in the fast ion transport. Measured D–D fusion products from a neutron camera and a charged fusion product detector are 40% lower than predictions from TRANSP/NUBEAM, highlighting possible deficiencies in the guiding centre approximation. Modelling of fast ion losses in the presence of resonant magnetic perturbations (RMPs) can reproduce trends observed in experiments when the plasma response and charge-exchange losses are accounted for. Measurements with a neutral particle analyser during merging-compression start-up indicate the acceleration of ions and electrons. Transport at the plasma edge has been improved through reciprocating probe measurements that have characterised a geodesic acoustic mode at the edge of an ohmic L-mode plasma and particle-in-cell modelling has improved the interpretation of plasma potential estimates from ball-pen probes. The application of RMPs leads to a reduction in particle confinement in L-mode and H-mode and an increase in the core ionization source. The ejection of secondary filaments following type-I ELMs correlates with interactions with surfaces near the X-point. Simulations of the interaction between pairs of filaments in the scrape-off layer suggest this results in modest changes to their velocity, and in most cases can be treated as moving independently. A stochastic model of scrape-off layer profile formation based on the superposition of non-interacting filaments is in good agreement with measured time-average profiles. Transport in the divertor has been improved through fast camera imaging, indicating the presence of a quiescent region devoid of filament near the X-point, extending from the separatrix to ψn ~ 1.02. Simulations of turbulent transport in the divertor show that the angle between the divertor leg on the curvature vector strongly influences transport into the private flux region via the interchange mechanism. Coherence imaging measurements show counter-streaming flows of impurities due to gas puffing increasing the pressure on field lines where the gas is ionised. MAST Upgrade is based on the original MAST device, with substantially improved capabilities to operate with a Super-X divertor to test extended divertor leg concepts. SOLPS-ITER modelling predicts the detachment threshold will be reduced by more than a factor of 2, in terms of upstream density, in the Super-X compared with a conventional configuration and that the radiation front movement is passively stabilised before it reaches the X-point. 1D fluid modelling reveals the key role of momentum and power loss mechanisms in governing detachment onset and evolution. Analytic modelling indicates that long legs placed at large major radius, or equivalently low at the target compared with the X-point are more amenable to external control. With MAST Upgrade experiments expected in 2019, a thorough characterisation of the sources of the intrinsic error field has been carried out and a mitigation strategy developed.

Impact of convection and resistivity on angular momentum transport in dwarf novae

The eruptive cycles of dwarf novae are thought to be due to a thermal-viscous instability in the accretion disk surrounding the white dwarf. This model has long been known to imply enhanced angular momentum transport in the accretion disk during outburst. This is measured by the stress to pressure ratio α, with α ≈ 0.1 required in outburst compared to α ≈ 0.01 in quiescence. Such an enhancement in α has recently been observed in simulations of turbulent transport driven by the magneto-rotational instability (MRI) when convection is present, without requiring a net magnetic flux. We independently recover this result by carrying out PLUTO magnetohydrodynamic (MHD) simulations of vertically stratified, radiative, shearing boxes with the thermodynamics and opacities appropriate to dwarf novae. The results are robust against the choice of vertical boundary conditions. The thermal equilibrium solutions found by the simulations trace the well-known S-curve in the density-temperature plane that constitutes the core of the disk thermal-viscous instability model. We confirm that the high values of α ≈ 0.1 occur near the tip of the hot branch of the S-curve, where convection is active. However, we also present thermally stable simulations at lower temperatures that have standard values of α ≈ 0.03 despite the presence of vigorous convection. We find no simple relationship between α and the strength of the convection, as measured by the ratio of convective to radiative flux. The cold branch is only very weakly ionized so, in the second part of this work, we studied the impact of non-ideal MHD effects on transport. Ohmic dissipation is the dominant effect in the conditions of quiescent dwarf novae. We include resistivity in the simulations and find that the MRI-driven transport is quenched (α ≈ 0) below the critical density at which the magnetic Reynolds number Rm ≤ 104. This is problematic because the X-ray emission observed in quiescent systems requires ongoing accretion onto the white dwarf. We verify that these X-rays cannot self-sustain MRI-driven turbulence by photo-ionizing the disk and discuss possible solutions to the issue of accretion in quiescence.

Towards the optimization of a gyrokinetic Particle-In-Cell (PIC) code on large-scale hybrid architectures

With the aim of enabling state-of-the-art gyrokinetic PIC codes to benefit from the performance of recent multithreaded devices, we developed an application from a platform called the “PIC-engine” [1, 2, 3] embedding simplified basic features of the PIC method. The application solves the gyrokinetic equations in a sheared plasma slab using B-spline finite elements up to fourth order to represent the self-consistent electrostatic field. Preliminary studies of the so-called Particle-In-Fourier (PIF) approach, which uses Fourier modes as basis functions in the periodic dimensions of the system instead of the real-space grid, show that this method can be faster than PIC for simulations with a small number of Fourier modes. Similarly to the PIC-engine, multiple levels of parallelism have been implemented using MPI+OpenMP [2] and MPI+OpenACC [1], the latter exploiting the computational power of GPUs without requiring complete code rewriting. It is shown that sorting particles [3] can lead to performance improvement by increasing data locality and vectorizing grid memory access. Weak scalability tests have been successfully run on the GPU-equipped Cray XC30 Piz Daint (at CSCS) up to 4,096 nodes. The reduced time-to-solution will enable more realistic and thus more computationally intensive simulations of turbulent transport in magnetic fusion devices.

NERSC's Impact on Advances of Global Gyrokinetic PIC Codes for Fusion Energy Research

The National Energy Research Scientific Computing Center (NERSC) was originally launched as a computing center for the exclusive support of magnetic confinement fusion research in the US. There is, thus, a long history of computational advances and successes that ties fusion scientists with NERSC and its staff. One example of the numerous computational achievements enabled by NERSC in this field is the development of the global gyrokinetic particle-in-cell approach for the simulation of turbulent transport in tokamak fusion devices. This article describes the historical evolution of this method and the codes implementing it, and the impact that NERSC had in their development and the scientific discoveries that they allow.

Investigating profile stiffness and critical gradients in shaped TCV discharges using local gyrokinetic simulations of turbulent transport

The experimental observation made on the TCV tokamak of a significant confinement improvement in plasmas with negative triangularity (δ < 0) compared to those with standard positive triangularity has been interpreted in terms of different degrees of profile stiffness (Sauter et al 2014 Phys. Plasmas 21 055906) and/or different critical gradients. Employing the Eulerian gyrokinetic code GENE (Jenko et al 2000 Phys. Plasmas 7 1904), profile stiffness and critical gradients are studied under TCV relevant conditions. For the considered experimental discharges, trapped electron modes (TEMs) and electron temperature gradient (ETG) modes are the dominant microinstabilities, with the latter providing a significant contribution to the non-linear electron heat fluxes near the plasma edge. Two series of simulations with different levels of realism are performed, addressing the question of profile stiffness at various radial locations. Retaining finite collisionality, impurities and electromagnetic effects, as well as the physical electron-to-ion mass ratio are all necessary in order to approach the experimental flux measurements. However, flux-tube simulations are unable to fully reproduce the TCV results, pointing towards the need to carry out radially nonlocal (global) simulations, i.e. retaining finite machine size effects, in a future study. Some conclusions about the effect of triangularity can nevertheless be drawn based on the flux-tube results. In particular, the importance of considering the sensitivity to both temperature and density gradient is shown. The flux tube results show an increase of the critical gradients towards the edge, further enhanced when δ < 0, and they also appear to indicate a reduction of profile stiffness towards plasma edge.

New prescriptions of turbulent transport from local numerical simulations

AbstractMassive stars often experience fast rotation, which is known to induce turbulent mixing with a strong impact on the evolution of these stars. Local direct numerical simulations of turbulent transport in stellar radiative zones are a promising way to constrain phenomenological transport models currently used in many stellar evolution codes. We present here the results of such simulations of stably-stratified sheared turbulence taking notably into account the effects of thermal diffusion and chemical stratification. We also discuss the impact of theses results on stellar evolution theory.

Exploring phase space turbulence in magnetic fusion plasmas

Plasma turbulence accompanied with fluctuations of the distribution function and the electromagnetic fields develops on the phase space composed of the configuration space and the velocity space. Detailed structures of the distribution function in magnetic fusion plasmas are investigated by means of gyrokinetic simulations performed on massively parallel supercomputers. The gyrokinetic simulations of drift wave turbulence have demonstrated entropy transfer in the phase space, zonal flow enhancement by helical fields and the resultant transport reduction. The state-of-the-art high performance computing is utilized for a multi-scale turbulence simulation covering ion- and electron-scales and for a global-scale simulation of turbulent transport in a sub-ITER sized plasma.

Numerical Simulation of Turbulent Transport and Structures in Temporally Developing Plane Mixing Layers

The investigation on the sensitivity of the flows to the initial conditions was carried with varying grid resolutions, turbulence models and perturbations. The Direct Numerical Simulation study of Pantano and Sarkar [1] was taken as the reference study and the computational model used in this study was built with a similar configuration of theirs except for the perturbations used. Important results were arrived pertaining to the effect of initial conditions on the turbulent properties and the turbulent structures of the flow.

Non-local approach to kinetic effects on parallel transport in fluid models of the scrape-off layer

Using a non-local model, fluid simulations can capture kinetic effects in the parallel electron heat-flux better than is possible using flux limiters in the usual diffusive models. Non-local and diffusive models are compared using a test case representative of an edge-localized mode crash in the JET scrape-off layer (SOL), simulated in one dimension. The non-local model shows substantially enhanced electron temperature gradients, which cannot be achieved using a flux limiter. The performance of the implementation, in the BOUT++ framework, is also analysed to demonstrate its suitability for application in three-dimensional simulations of turbulent transport in the SOL.

Guiding-center simulations on curvilinear meshes

The purpose of this work is to design simulation tools for magnetised plasmas in the ITER project framework. The specific issue we consider is the simulation of turbulent transport in the core of a Tokamak plasma, for which a 5D gyrokinetic model is generally used, where the fast gyromotion of the particles in the strong magnetic field is averaged in order to remove the associated fast time-scale and to reduce the dimension of 6D phase space involved in the full Vlasov model. Very accurate schemes and efficient parallel algorithms are required to cope with these still very costly simulations. The presence of a strong magnetic field constrains the time scales of the particle motion along and accross the magnetic field line, the latter being at least an order of magnitude slower. This also has an impact on the spatial variations of the observables. Therefore, the efficiency of the algorithm can be improved considerably by aligning the mesh with the magnetic field lines. For this reason, we study the behavior of semi-Lagrangian solvers in curvilinear coordinates. Before tackling the full gyrokinetic model in a future work, we consider here the reduced 2D Guiding-Center model. We introduce our numerical algorithm and provide some numerical results showing its good properties.

Conservative mixing, competitive mixing and their applications

In many of the models applied to simulations of turbulent transport and turbulent combustion, the mixing between particles is used to reflect the influence of the continuous diffusion terms in the transport equations. Stochastic particles with properties and mixing can be used not only for simulating turbulent combustion, but also for modeling a large spectrum of physical phenomena. Traditional mixing, which is commonly used in the modeling of turbulent reacting flows, is conservative: the total amount of scalar is (or should be) preserved during a mixing event. It is worthwhile, however, to consider a more general mixing that does not possess these conservative properties; hence, our consideration lies beyond traditional mixing. In non-conservative mixing, the particle post-mixing average becomes biased towards one of the particles participating in mixing. The extreme form of non-conservative mixing can be called competitive mixing or competition: after a mixing event, the loser particle simply receives the properties of the winner particle. Particles with non-conservative mixing can be used to emulate various phenomena involving competition. In particular, we investigate cyclic behavior that can be attributed to complex competing systems. We show that the localness and intransitivity of competitive mixing are linked to the cyclic behavior.

Gyrokinetic Simulations of Turbulent Transport in a Ring Dipole Plasma

Gyrokinetic flux-tube simulations of turbulent transport due to small-scale entropy modes are presented in a ring-dipole magnetic geometry relevant to the Columbia-MIT levitated dipole experiment (LDX) [J. Kesner, Plasma Phys. J. 23, 742 (1997)]. Far from the current ring, the dipolar magnetic field leads to strong parallel variations, while close to the ring the system becomes nearly uniform along circular magnetic field lines. The transport in these two limits are found to be quantitatively similar given an appropriate normalization based on the local out-board parameters. The transport increases strongly with the density gradient, and for small eta=L(n)/L(T)<<1, T(i) approximately T(e), and typical LDX parameters, can reach large levels. Consistent with linear theory, temperature gradients are stabilizing, and for T(i) approximately T(e) can completely cut off the transport when eta greater or similar to 0.6.

Particle-in-cell simulation with Vlasov ions and drift kinetic electrons

There are certain limitations in using gyrokinetic ions for simulations of turbulent transport in tokamak plasmas. Applications where Vlasov ions might be more appropriate include the electron temperature gradient driven turbulence, edge turbulence with steep density gradient, and magnetic reconnection in a weak guide field. In such cases the ion gyrokinetic model presently used in simulations needs to be extended, but a satisfactory extension valid for fully electromagnetic turbulence is not presently available. Even if an accurate model is found, its numerical implementation could be very challenging. We propose a kinetic model that combines Vlasov ions with gyrokinetic electrons to avoid the difficulties with gyrokinetic ions. The field equations of this model are the Faraday’s equation and the Ampere’s equation without the displacement current. The perturbed fields B1 and E1 rather than the scalar and vector potentials are used to formulate the field equations. We have devised an implicit scheme for this model, demonstrated in three-dimensional slab for the Alfvén waves, the drift Alfvén instability and the ion acoustic waves.

Random walk, diffusion and mixing in simulations of scalar transport in fluid flows

Physical similarity and mathematical equivalence of continuous diffusion and particle random walk form one of the cornerstones of modern physics and the theory of stochastic processes. In many applied models used in simulation of turbulent transport and turbulent combustion, mixing between particles is used to reflect the influence of the continuous diffusion terms in the transport equations. We show that the continuous scalar transport and diffusion can be accurately specified by means of mixing between randomly walking Lagrangian particles with scalar properties and assess errors associated with this scheme. This gives an alternative formulation for the stochastic process which is selected to represent the continuous diffusion. This paper focuses on statistical errors and deals with relatively simple cases, where one-particle distributions are sufficient for a complete description of the problem.

Large eddy simulation in pebble bed gas cooled core reactors

A high temperature gas-cooled reactor (HTGR) is one of the renewed reactor designs to play a role in nuclear power generation. This reactor design concept is currently under consideration and development worldwide. The combination of coated particle fuel, inert helium gas as coolant and graphite moderated reactor makes possible to operate at high temperature yielding a high efficiency. In this study the simulation of turbulent transport for the gas through the gaps of the spherical fuel elements (fuel pebbles) was performed using the large eddy simulation. This would help in understanding the highly three-dimensional, complex flow phenomena caused by flow curvature in the pebble bed. Resolving all the scales of a turbulent flow is too costly, while employing highly empirical turbulence models to complex problems could give inaccurate simulation results. The large eddy simulation (LES) method would overcome these shortcomings. An attempt to obtain experimental velocity flow patterns using particle image velocimetry technique combined with matched refractive index liquid was pursued.