Alternating ‘flip’ solutions in ferrofluidic Taylor-Couette flow

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Precomputing Memory Locations for Parametric Allocations

Current worst-case execution time (WCET) analyses do not support programs using dynamic memory allocation. This is mainly due to the unpredictability of cache performance introduced by standard memory allocators. To overcome this problem, algorithms have been proposed that precompute static allocations for dynamically allocating programs with known numeric bounds on the number and sizes of allocated memory blocks. In this paper, we present a novel algorithm for computing such static allocations that can cope with parametric bounds on the number and sizes of allocated blocks. To demonstrate the usefulness of our approach, we precompute static allocations or a set of existing real-time applications and academic examples

Non-linear dynamics and alternating ‘flip’ solutions in ferrofluidic Taylor-Couette flow

This study treats with the influence of a symmetry-breaking transversal magnetic field on the nonlinear dynamics of ferrofluidic Taylor-Couette flow – flow confined between two concentric independently rotating cylinders. We detected alternating ‘flip’ solutions which are flow states featuring typical characteristics of slow-fast-dynamics in dynamical systems. The flip corresponds to a temporal change in the axial wavenumber and we find them to appear either as pure 2-fold axisymmetric (due to the symmetry-breaking nature of the applied transversal magnetic field) or involving non-axisymmetric, helical modes in its interim solution. The latter ones show features of typical ribbon solutions. In any case the flip solutions have a preferential first axial wavenumber which corresponds to the more stable state (slow dynamics) and second axial wavenumber, corresponding to the short appearing more unstable state (fast dynamics). However, in both cases the flip time grows exponential with increasing the magnetic field strength before the flip solutions, living on 2-tori invariant manifolds, cease to exist, with lifetime going to infinity. Further we show that ferrofluidic flow turbulence differ from the classical, ordinary (usually at high Reynolds number) turbulence. The applied magnetic field hinders the free motion of ferrofluid partials and therefore smoothen typical turbulent quantities and features so that speaking of mildly chaotic dynamics seems to be a more appropriate expression for the observed motion

Interaction of Magnetic Fields on Ferrofluidic Taylor-Couette Flow

When studying ferrofluidic flows, as one example of magnetic flow dynamics, in terms of instability, bifurcation, and properties, one quickly finds out the additional challenges magnetic fluids introduce compared to the investigation of “classical”, “ordinary” shear flows without any kind of particles. Approximation of ferrofluids as fluids including point-size particles or, more realistic fine size particles, the relaxation times of the magnetic particle, their interaction between each other, i.e., the agglomeration and chain forming effects, and the interaction/response between any external applied field and the internal magnetization are just few examples of challenges to overcome. Further dependence on the considered model system, the direction of the external applied magnetic field (homogeneous or inhomogeneous) is crucial, as it can break the system symmetry and thus generate new solutions. As a result, the classical Navier–Stokes equations become modified to the more complex ferrohydrodynamical equation of motion, incorporating magnetic field and magnetization of the fluid itself, which typically makes numerical simulations expensive and challenging. This chapter provides an overview of the tasks/difficulties from describing and simulating magnetic particles, their interaction, and thus finally resulting modification in rotating flow structures and in particular instabilities and bifurcation behavior

Transient behavior between multi-cell flow states in ferrofluidic Taylor-Couette flow

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Flow dynamics between two concentric counter-rotating porous cylinders with radial through-flow

We investigate the impact of radial mass flux on Taylor-Couette flow in counter-rotating configuration, in which a Hopf bifurcation gives rise to branches of nontrivial solutions. Using direct numerical simulation we elucidate structures, dynamics, stability, and bifurcation behavior in qualitative and quantitative detail as a function of inner Reynolds numbers (Rei) and radial mass flux (a) spanning a parameter space with a rich variety of solutions. Both radial inflow and strong radial outflow stabilize the system, whereas weak radial outflow has a strong destabilizing effect. We detected the existence of stable ribbons and mixed ribbons with low azimuthal wave number without symmetry restriction. In addition, ribbon solutions and mixed-ribbon solutions can be stable or unstable saddles. Furthermore, in the case of unstable saddles alternations between two different symmetrically related saddles generate different heteroclinic cycles. For alternating stationary (in co-moving frame) ribbons the persistence time in one saddle decreases with distance from the onset. The persistence time for the heteroclinic cycle of alternating mixed ribbons shows a more complicated dependence with variation in control parameters and seems to follow an intermittency scenario of type III. Depending on whether the symmetrically related solutions are stationary or time-dependent, the heteroclinic connection can be either of oscillatory or nonoscillatory type.Peer ReviewedPostprint (published version

Ferrofluidic wavy Taylor vortices under alternating magnetic field

Many natural and industrial flows are subject to time-dependent boundary conditions and temporal modulations (e.g. driving frequency), which significantly modify the dynamics compared with their static ounterparts. The present problem addresses ferrofluidic [1] wavy vortex flow in Taylor-Couette geometry [2], with the outer cylinder at rest in a spatially homogeneous magnetic field subject to an alternating modulation. Using a modified Niklas approximation, the effect of frequency modulation on non-linear flow dynamics and appearing resonance phenomena are investigated in the context of either period doubling or inverse period doubling. Flow structures of particular interest in the present work are wavy Taylor vortex flows (wTVFs) [3] (which already have a natural frequency) with main focus on resonance phenomena when the modulation frequency reaches multiples or ratios of the natural, that is characteristic, frequency of the studied flow states.Peer ReviewedPostprint (author's final draft

Forced vortex merging and splitting events in ferrofluidic Couette flow

Time-dependent boundary conditions being an ubiquitous observation in numerous natural and industrial flows. However, to date the influence of such temporal modulations has been given minor attention. The present problem addresses ferrofluidic Couette flow in between co-rotating cylinders in a spatially homogeneous magnetic field subject to time-periodic modulation. Using a modified Niklas approximation, we study the effect of amplitude and frequency modulation onto the the transition scenarios between different toroidal flow structures, nV states, via vortex merging and splitting. Thereby the system response appears to be quite sensitive/dependent on the driving frequency OH , which can cause a notable “delay” in the system response. Aside, as a result of the inertia of the ferrofluid, resisting the fast-changing accelerating Kelvin force, new, temporal nV states appear within an alternating field. These states are unstable under static fields. Finally we show that within the same nV state, while keeping similar flow dynamics, large discrepancies in angular momentum and torque can be observed.This work has been supported by the Spanish Ministerio de Ciencia e Innovación grant PID2019-105162RB-I00.Peer ReviewedPostprint (published version

Effect of axial and radial flow on the hydrodynamics in a Taylor reactor

This paper investigates the impact of combined axial through flow and radial mass flux on Taylor–Couette flow in a counter-rotating configuration, in which different branches of nontrivial solutions appear via Hopf bifurcations. Using direct numerical simulation, we elucidate flow structures, dynamics, and bifurcation behavior in qualitative and quantitative detail as a function of axial Reynolds numbers (Re) and radial mass flux (a) spanning a parameter space with a very rich variety of solutions. We have determined nonlinear properties such as anharmonicity, asymmetry, flow rates (axial and radial) and torque for toroidally closed Taylor vortices and helical spiral vortices. Small to moderate radial flow a initially decreases the symmetry of the different flows, before for larger values, a, the symmetry eventually increases, which appears to be congruent with the degree of anharmonicity. Enhancement in the total torque with a are elucidated whereby the strength varies for different flow structures, which allows for potential better selection and control. Further, depending on control parameters, heteroclinic connections (and cycles) of oscillatory type in between unstable and topological different flow structures are detected. The research results provide a theoretical basis for simple modification the conventional Taylor flow reactor with a combination of additional mass flux to enhance the mass transfer mechanism.This work has been financed by the Spanish Governments under grant PID2019-105162RB-I00.Peer ReviewedPostprint (published version