arXiv subjects

Jörg Schumacher

Publications and source records attributed to Jörg Schumacher.

87 records · Page 5Linked to original sources

arXiv2017

Predicting transition ranges to turbulent viscous boundary layers in low Prandtl number convection flows

We discuss two aspects of turbulent Rayleigh-Bénard convection (RBC) on the basis of high-resolution direct numerical simulations in a unique setting; a closed cylindrical cell of aspect ratio of one. First, we present a comprehensive comparison of statistical quantities such as energy dissipation rates and boundary layer thickness scales. Data are used from three simulation run series at Prandtl numbers $Pr$ that cover two orders of magnitude. In contrast to most previous studies in RBC the focus of the present work is on convective turbulence at very low Prandtl numbers including $Pr=0.021$ for liquid mercury or gallium and $Pr=0.005$ for liquid sodium. In this parameter range of RBC, inertial effects cause a dominating turbulent momentum transport that is in line with highly intermittent fluid turbulence both in the bulk and in the boundary layers and thus should be able to trigger a transition to the fully turbulent boundary layers of the ultimate regime of convection for higher Rayleigh number. Secondly, we predict the ranges of Rayleigh numbers for which the viscous boundary layer will transition to turbulence and the flow as a whole will cross over into the ultimate regime. These transition ranges are obtained by extrapolation from our simulation data. The extrapolation methods are based on the large-scale properties of the velocity profile. Two of the three methods predict similar ranges for the transition to ultimate convection when their uncertainties are taken into account. All three extrapolation methods indicate that the range of critical Rayleigh numbers $Ra_c$ is shifted to smaller magnitudes as the Prandtl number becomes smaller.

physics.flu-dyn↗

arXiv2017

Local Lorentz force and ultrasound Doppler velocimetry in a vertical convection liquid metal flow

We report velocity measurements in a vertical turbulent convection flow cell that is filled with the eutectic liquid metal alloy gallium-indium-tin by the use of local Lorentz force velocimetry (LLFV) and ultrasound Doppler velocimetry (UDV). We demonstrate the applicability of LLFV for a thermal convection flow and reproduce a linear dependence of the measured force in the range of micronewtons on the local flow velocity magnitude. Furthermore, the presented experiment is used to explore scaling laws of the global turbulent transport of heat and momentum in this low-Prandtl-number convection flow. Our results are found to be consistent with theoretical predictions and recent direct numerical simulations.

physics.flu-dyn↗

arXiv2017

Thermal Rayleigh-Marangoni convection in a three-layer liquid-metal-battery model

The combined effects of buoyancy-driven Rayleigh-Bénard convection (RC) and surface tension-driven Marangoni convection (MC) are studied in a triple-layer configuration which serves as a simplified model for a liquid metal battery (LMB). The three-layer model consists of a liquid metal alloy cathode, a molten salt separation layer, and a liquid metal anode at the top. Convection is triggered by the temperature gradient between the hot electrolyte and the colder electrodes, which is a consequence of the release of resistive heat during operation. We present a linear stability analysis of the state of pure thermal conduction in combination with three-dimensional direct numerical simulations of the nonlinear turbulent evolution on the basis of a pseudospectral method. Five different modes of convection are identified in the configuration, which are partly coupled to each other: RC in the upper electrode, RC with internal heating in the molten salt layer, MC at both interfaces between molten salt and electrode as well as anti-convectionin the middle layer and lower electrode. The linear stability analysis confirms that the additional Marangoni effect in the present setup increases the growth rates of the linearly unstable modes, i.e. Marangoni and Rayleigh-Bénard instability act together in the molten salt layer. The critical Grashof and Marangoni numbers decrease with increasing middle layer thickness. The calculated thresholds for the onset of convection are found for realistic current densities of laboratory-sized LMBs. The global turbulent heat transfer follows scaling predictions for internally heated RC. The global turbulent momentum transfer is comparable with turbulent convection in the classical Rayleigh-Bénard case.

physics.flu-dyn↗

arXiv2017

GlnK facilitates the dynamic regulation of bacterial nitrogen assimilation

Ammonium assimilation in E. coli is regulated by two paralogous proteins (GlnB and GlnK), which orchestrate interactions with regulators of gene expression, transport proteins and metabolic pathways. Yet how they conjointly modulate the activity of glutamine synthetase (GS), the key enzyme for nitrogen assimilation, is poorly understood. We combine experiments and theory to study the dynamic roles of GlnB and GlnK during nitrogen starvation and upshift. We measure time-resolved in vivo concentrations of metabolites, total and post-translationally modified proteins, and develop a concise biochemical model of GlnB and GlnK that incorporates competition for active and allosteric sites, as well as functional sequestration of GlnK. The model predicts the responses of GS, GlnB and GlnK under time-varying external ammonium level in the wild type and two genetic knock-outs. Our results show that GlnK is tightly regulated under nitrogen-rich conditions, yet it is expressed during ammonium run-out and starvation. This suggests a role for GlnK as a buffer of nitrogen shock after starvation, and provides a further functional link between nitrogen and carbon metabolisms.

q-bio.SC↗

arXiv2016

Transitional boundary layers in low-Prandtl-number convection

The boundary layer structure of the velocity and temperature fields in turbulent Rayleigh-Benard flows in closed cylindrical cells of unit aspect ratio is revisited from a transitional and turbulent viscous boundary layer perspective. When the Rayleigh number is large enough, the dynamics at the bottom and top plates can be separated into an impact region of downwelling plumes, an ejection region of upwelling plumes and an interior region away from the side walls. The latter is dominated by the shear of the large-scale circulation (LSC) roll which fills the whole cell and continuously varies its orientation. The working fluid is liquid mercury or gallium at a Prandtl number Pr=0.021 for Rayleigh numbers between Ra=3e+5 and 4e+8. The generated turbulent momentum transfer corresponds to macroscopic flow Reynolds numbers with values between 1800 and 46000. It is shown that the viscous boundary layers for the largest Rayleigh numbers are highly transitional and obey properties that are directly comparable to transitional channel flows at friction Reynolds numbers Re_tau slightly below 100. The transitional character of the viscous boundary layer is also underlined by the strong enhancement of the fluctuations of the wall stress components with increasing Rayleigh number. An extrapolation of our analysis data suggests that the friction Reynolds number Re_tau in the velocity boundary layer can reach values of 200 for Ra beyond 1e+11. Thus the viscous boundary layer in a liquid metal flow would become turbulent at a much lower Rayleigh number than for turbulent convection in gases and gas mixtures.

physics.flu-dyn↗

arXiv2016

Heat and momentum transfer for magnetoconvection in a vertical external magnetic field

The scaling theory of Grossmann and Lohse (J. Fluid Mech. 407, 27 (2000)) for the turbulent heat and momentum transfer is extended to the magnetoconvection case in the presence of a (strong) vertical magnetic field. The comparison with existing laboratory experiments and direct numerical simulations in the quasistatic limit allows to restrict the parameter space to very low Prandtl and magnetic Prandtl numbers and thus to reduce the number of unknown parameters in the model. Also included is the Chandrasekhar limit for which the outer magnetic induction field B is large enough such that convective motion is suppressed and heat is transported by diffusion. Our theory identifies four distinct regimes of magnetoconvection which are distinguished by the strength of the outer magnetic field and the level of turbulence in the flow, respectively.

physics.flu-dyn↗

arXiv2015

A hybrid finite-difference/boundary element procedure for the simulation of turbulent MHD duct flow at finite magnetic Reynolds numbers

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 field

physics.flu-dyn↗

arXiv2015

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-Bénard 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-Bénard convection in a closed cylindrical cell of aspect ratio $Γ=1$ 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 Poincaré-Hopf index theorem for two-dimensional vector fields.

physics.flu-dyn↗

arXiv2015

Large-scale mean patterns in turbulent convection

Large-scale patterns, which are well-known from the spiral defect chaos regime of thermal convection at Rayleigh numbers $Ra < 10^4$, continue to exist in three-dimensional numerical simulations of turbulent Rayleigh-Bénard convection in extended cylindrical cells with an aspect ratio $Γ=50$ and $Ra>10^5$. They are uncovered when the turbulent fields are averaged in time and turbulent fluctuations are thus removed. We apply the Boussinesq closure to estimate turbulent viscosities and diffusivities, respectively. The resulting turbulent Rayleigh number $Ra_{\ast}$, that describes the convection of the mean patterns, is indeed in the spiral defect chaos range. The turbulent Prandtl numbers are smaller than one with $0.2\le Pr_{\ast}\le 0.4$ for Prandtl numbers $0.7 \le Pr\le 10$. Finally, we demonstrate that these mean flow patterns are robust to an additional finite-amplitude side wall-forcing when the level of turbulent fluctuations in the flow is sufficiently high.

physics.flu-dyn↗

arXiv2015

Simulation of flux expulsion and associated dynamics in a two-dimensional magnetohydrodynamic channel flow

We consider a plane channel flow of an electrically conducting fluid which is driven by a mean pressure gradient in the presence of an applied magnetic field that is streamwise periodic with zero mean. Magnetic flux expulsion and the associated bifurcation in such a configuration is explored using direct numerical simulations (DNS). The structure of the flow and magnetic fields in the Hartmann regime (where the dominant balance is through Lorentz forces) and the Poiseuille regime (where viscous effects play a significant role) are studied and detailed comparisons to the existing one-dimensional model of Kamkar and Moffatt (J. Fluid. Mech., Vol.90, pp 107-122, 1982) are drawn to evaluate the validity of the model. Comparisons show good agreement of the model with DNS in the Hartmann regime, but significant diferences arising in the Poiseuille regime when non-linear effects become important. The effects of various parameters like the magnetic Reynolds number, imposed field wavenumber etc. on the bifurcation of the flow are studied. Magnetic field line reconnections occuring during the dynamic runaway reveal a specific two-step pattern that leads to the gradual expulsion of flux in the core region.

physics.flu-dyn↗

arXiv2013

Laminar and transitional liquid metal duct flow near a magnetic point dipole

The flow transformation and the generation of vortex structures by a strong magnetic dipole field in a liquid metal duct flow is studied by means of three-dimensional direct numerical simulations. The dipole is considered as the paradigm for a magnetic obstacle which will deviate the streamlines due to Lorentz forces acting on the fluid elements. The duct is of square cross-section. The dipole is located above the top wall and is centered in spanwise direction. Our model uses the quasi-static approximation which is applicable in the limit of small magnetic Reynolds numbers. The analysis covers the stationary flow regime at small hydrodynamic Reynolds numbers Re as well as the transitional time-dependent regime at higher values which may generate a turbulent flow in the wake of the magnetic obstacle. We present a systematic study of these two basic flow regimes and their dependence on Re and on the Hartmann number Ha, a measure of the strength of the magnetic dipole field. Furthermore, three orientations of the dipole are compared: streamwise, spanwise and wall-normal oriented dipole axes. The most efficient generation of turbulence at a fixed distance above the duct follows for the spanwise orientation, which is caused by a certain configuration of Hartmann layers and reversed flow at the top plate. The enstrophy in the turbulent wake grows linearly with Ha which is connected with a dominance of the wall-normal z-derivative of the streamwise velocity.

physics.flu-dyn↗

arXiv2011

Statistics of the Energy Dissipation Rate and Local Enstrophy in Turbulent Channel Flow

Using high-resolution direct numerical simulations, the height and Reynolds number dependence of higher-order statistics of the energy dissipation rate and local enstrophy are examined in incompressible, fully-developed turbulent channel flow. The statistics are studied over a range of wall distances, spanning the viscous sublayer to the channel flow centerline, for friction Reynolds numbers $Re_τ= 180$ and $Re_τ= 381$. The high resolution of the simulations allows dissipation and enstrophy moments up to fourth order to be calculated. These moments show a dependence on wall distance, and Reynolds number effects are observed at the edge of the logarithmic layer. Conditional analyses based on locations of intense rotation are also carried out in order to determine the contribution of vortical structures to the dissipation and enstrophy moments. Our analysis shows that, for the simulation at the larger Reynolds number, small-scale fluctuations of both dissipation and enstrophy become relatively constant for $z^+ \gtrsim 100$.

physics.flu-dyn↗

arXiv2008

Direct Assessment of Vorticity Alignment with Local and Nonlocal Strain Rates in Turbulent Flows

A direct Biot-Savart integration is used to decompose the strain rate into its local and nonlocal constituents, allowing the vorticity alignment with the local and nonlocal strain rate eigenvectors to be investigated. These strain rate tensor constituents are evaluated in a turbulent flow using data from highly-resolved direct numerical simulations. While the vorticity aligns preferentially with the intermediate eigenvector of the \textit{combined} strain rate, as has been observed previously, the present results for the first time clearly show that the vorticity aligns with the most extensional eigenvector of the \textit{nonlocal} strain rate. This in turn reveals a significant linear contribution to the vortex stretching dynamics in turbulent flows.

physics.flu-dyn↗

arXiv2008

Local and Nonlocal Strain Rate Fields and Vorticity Alignment in Turbulent Flows

Local and nonlocal contributions to the total strain rate tensor at any point in a flow are formulated from an expansion of the vorticity field in a local spherical neighborhood of radius R centered on x. The resulting exact expression allows the nonlocal (background) strain rate tensor to be obtained from the total strain rate tensor. In turbulent flows, where the vorticity naturally concentrates into relatively compact structures, this allows the local alignment of vorticity with the most extensional principal axis of the background strain rate tensor to be evaluated. In the vicinity of any vortical structure, the required radius R and corresponding order n to which the expansion must be carried are determined by the viscous lengthscale. We demonstrate the convergence to the background strain rate field with increasing R and n for an equilibrium Burgers vortex, and show that this resolves the anomalous alignment of vorticity with the intermediate eigenvector of the total strain rate tensor. We then evaluate the background strain field in DNS of homogeneous isotropic turbulence where, even for the limited R and n corresponding to the truncated series expansion, the results show an increase in the expected equilibrium alignment of vorticity with the most extensional principal axis of the background strain rate tensor.

physics.flu-dyn↗

arXiv2003

Asymmetric time correlations in turbulent shear flows

Cross correlations between normal and downstream velocity fluctuations in a turbulent shear flow are shown to carry information about the non-normal amplification process. The creation of spanwise modulated streaks by downstream vortices implies an asymmetry in temporal correlation functions. We verify this in numerical simulations in shear flows with $Re_λ\approx 100$.

nlin.CD↗