9 research outputs found
Role of critical points of the skin friction field in formation of plumes in thermal convection
The dynamics in the thin boundary layers of temperature and velocity is the
key to a deeper understanding of turbulent transport of heat and momentum in
thermal convection. The velocity gradient at the hot and cold plates of a
Rayleigh-B\'{e}nard convection cell forms the two-dimensional skin friction
field and is related to the formation of thermal plumes in the respective
boundary layers. Our analysis is based on a direct numerical simulation of
Rayleigh-B\'{e}nard convection in a closed cylindrical cell of aspect ratio
and focused on the critical points of the skin friction field. We
identify triplets of critical points, which are composed of two unstable nodes
and a saddle between them, as the characteristic building block of the skin
friction field. Isolated triplets as well as networks of triplets are detected.
The majority of the ridges of line-like thermal plumes coincide with the
unstable manifolds of the saddles. From a dynamical Lagrangian perspective,
thermal plumes are formed together with an attractive hyperbolic Lagrangian
Coherent Structure of the skin friction field. We also discuss the differences
from the skin friction field in turbulent channel flows from the perspective of
the Poincar\'{e}-Hopf index theorem for two-dimensional vector fields
Magnetohydrodynamic duct and channel flows at finite magnetic Reynolds numbers
Magnetohydrodynamic duct flows have so far been studied only in the limit of negligible magnetic Reynolds numbers (). When is finite,
the secondary magnetic field becomes significant, leading to a fully coupled evolution of the magnetic field and the conducting flow. Characterization of
such flows is essential in understanding wall-bounded magnetohydrodynamic turbulence at finite as well as in industrial applications like the design of
electromagnetic pumps and measurement of transient flows using techniques such as Lorentz force velocimetry. This thesis presents the development of a numerical
framework for direct numerical simulations (DNS) of magnetohydrodynamic flows in straight rectagular ducts at finite , which is subsequently used to study three
specific problems.
The thesis opens with a brief overview of MHD and a review of the existing state of art in duct and channel MHD flows. This is followed by a description of the physical
model governing the problem of MHD duct flow with insulating walls and streamwise periodicity. In the main part of the thesis, a hybrid
finite difference-boundary element computational procedure is developed that is used to solve the magnetic induction equation with
boundary conditions that satisfy interior-exterior matching of the magnetic field at the domain wall boundaries. The numerical procedure is implemented into a code
and a detailed verification of the same is performed in the limit of low by comparing with the results obtained using a quasistatic approach that has no
coupling with the exterior.
Following this, the effect of on the transient response of Lorentz force is studied using the problem of a strongly accelerated solid conducting bar in the presence of
an imposed localized magnetic field. The response time of Lorentz force depends linearly on and shows a good agreement with the existing experiments.
For sufficiently large values of , the peak Lorentz force is found to show an dependence.
After this, the phenomenon of dynamic runaway due to magnetic flux expulsion in a two-dimensional channel flow is studied. Comparison with an existing
one-dimensional model shows a close agreement for the Hartmann regime and the bifurcation location but the model overpredicts the core velocities in the
Poisuelle regime significantly. Parametric studies indicate the importance of the streamwise wavenumber of the imposed magnetic field on the bifurcation point.
Finally, turbulent Hartmann duct flow is investigated at moderate vaues of . A higher is found to delay the onset of relaminarization
to a higher value of Hartmann number. Large scale turbulence is induced at moderate and the effect increases with . Between the core
and the Shercliff layers, Reynolds stresses decrease with increase in , leading to larger mean velocities in that region.Magnetohydrodynamische Kanalströmungen (MHD-KS) wurden bisher nur bei vernachlÀssigbar kleiner magnetischer
Reynoldszahl untersucht. Bei endlichem wird das sekundÀre Magnetfeld signifikant, was zu einer gekoppelten
Entwicklung von Magnetfeld und leitfĂ€higer Strömung fĂŒhrt. Die Charakterisierung solcher Strömungen
ist essentiell fĂŒr das VerstĂ€ndnis von wandbegrenzter MHD-Turbulenz und in Anwendungen wie z.B. elektromagnetischen
Pumpen und der induktiven Strömungsmessung. Die Dissertation stellt ein Verfahren fĂŒr die direkte numerische
Simulation (DNS) von MHD-KS bei endlichem vor, welches dann auf drei Probleme angewendet wird.
Am Anfang der Arbeit steht eine kurze Ăbersicht zur MHD und zum Stand des Wissens zu MHD-KS. Danach folgt eine
Beschreibung des physikalischen Modells fĂŒr die MHD-KS mit elektrisch isolierenden WĂ€nden. Im Hauptteil der
Arbeit wird ein hybrides Berechnungsverfahren entwickelt und implementiert, das auf finiten Differenzen sowie dem
Randintegralverfahren basiert. Es dient zur Lösung der Induktionsgleichung mit Randbedingungen, die fĂŒr einen
stetigen Anschluss des Magnetfelds auf den GebietsrĂ€ndern zwischen Innen- und AuĂenraum sorgen. Eine detaillierte
Verifikation des Codes wird durch Vergleich mit der quasistatischen NĂ€herung vorgenommen.
Anschliessend wird das Zeitverhalten der Lorentzkraft bei beschleunigter Bewegung einer leitfÀhigen rechteckigen
Stange in einem lokalisierten Magnetfeld untersucht. Die Zeitantwort der Lorentzkraft hÀngt linear von ab
und stimmt gut mit Experimenten ĂŒberein. FĂŒr groĂe sind die Maximalwerte der Lorentzkraft umgekehrt
proportional zu .
Im weiteren wird das dynamische ``Weglaufen'' der Geschwindigkeit infolge von magnetischer FlussverdrÀngung in einer
zweidimensionalen MHD-KS untersucht. Der Vergleich mit einem eindimensionalen
Modell zeigt eine gute Ăbereinstimmung fĂŒr das sogenannte Hartmann-Regime und den Bifurkationspunkt zum sogenannten
Poiseuille-Regime, bei dem allerdings die Geschwindigkeit vom Modell ĂŒberschĂ€tzt wird. Die WellenlĂ€nge des Magnetfelds
ist fĂŒr den Bifurkationspunkt entscheidend.
Abschliessend wird die turbulente Hartmannströmung untersucht. Bei endlichem verschiebt sich die Relaminarisierung
zu gröĂeren Hartmannzahlen und es wird groĂsk-alige Turbulenz angeregt. Zwischen den Shercliff-Schichten und dem
Strömungskern verringern sich die Reynoldsspannungen mit steigendem , was zu höherer mittlerer Geschwindigkeit
und flacheren Geschwindigkeitsprofilen fĂŒhrt
The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas
JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied.Peer ReviewedPostprint (published version
Turbulent magnetohydrodynamic flow in a square duct: Comparison of zero and finite magnetic Reynolds number cases
Three-dimensional turbulent magnetohydrodynamic flow in a duct with a square cross section and insulating walls is investigated by direct numerical simulations. The flow evolves in the presence of a uniform vertical magnetic field and is driven by an applied mean pressure gradient. A boundary element technique is applied to treat the magnetic field boundary conditions at the walls consistently. Our primary focus is on the large- and small-scale characteristics of turbulence in the regime of moderate magnetic Reynolds numbers up to Rm and a comparison of the simulations with the quasistatic limit at Rm=0. The present simulations demonstrate that differences to the quasistatic case arise for the accessible magnetic Prandtl number Pm and different Hartmann numbers up to Ha=43.5. Hartmann and Shercliff layers at the duct walls are affected differently when a dynamical coupling to secondary magnetic fields is present. This becomes manifest by the comparison of the mean streamwise velocity profiles as well as the skin friction coefficients. While large-scale properties change only moderately, the impact on small-scale statistics is much stronger as quantified by an analysis of local anisotropy based on velocity derivatives. The small-scale anisotropy is found to increase at moderate Rm. These differences can be attributed to the additional physical phenomena which are present when secondary magnetic fields evolve, such as the expulsion of magnetic flux in the bulk of the duct or the presence of turbulent electromotive forces
A hybrid finite differenceâboundary element procedure for the simulation of turbulent MHD duct flow at finite magnetic Reynolds number
A conservative coupled finite difference-boundary element computational
procedure for the simulation of turbulent magnetohydrodynamic flow in a
straight rectangular duct at finite magnetic Reynolds number is presented. The
flow is assumed to be periodic in the streamwise direction and is driven by a
mean pressure gradient. The duct walls are considered to be electrically
insulating. The co-evolution of the velocity and magnetic fields as described
respectively by the Navier-Stokes and the magnetic induction equations,
together with the coupling of the magnetic field between the conducting domain
and the non-conducting exterior is solved using the magnetic field formulation.
The aim is to simulate localized magnetic fields interacting with turbulent
duct flow. Detailed verification of the implementation of the numerical scheme
is conducted in the limiting case of low magnetic Reynolds number by comparing
with the results obtained using a quasistatic approach that has no coupling
with the exterior. The rigorous procedure with non-local magnetic boundary
conditions is compared versus simplified pseudo-vacuum boundary conditions and
the differences are quantified. Our first direct numerical simulations of
turbulent Hartmann duct flow at moderate magnetic Reynolds numbers and a low
flow Reynolds number show significant differences in the duct flow turbulence,
even at low interaction level between the flow and magnetic fiel
The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas
International audienceJOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic(MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybridkinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied