Turbulent Flow Of Liquid Sodium Research Articles

Numerical simulation of a low Prandtl number flow over a backward facing step with an anisotropic four-equation turbulence model

In recent years the use of liquid metals has become more and more popular for heat transfer applications in many fields ranging from IV generation fast nuclear reactors to solar power plants. Due to their low Prandtl number values, the similarity between dynamical and thermal fields cannot be assumed and sophisticated heat turbulence models are required to take into account the anisotropy of the turbulent heat transfer involving liquid metals. In the present work, we solve an anisotropic four-equation turbulence model coupled with the Reynolds Averaged Navier Stokes system of equations to simulate a turbulent flow of liquid sodium over a vertical backward-facing step. We implement an explicit algebraic model for Reynolds stress tensor and turbulent heat flux that takes into account flow anisotropic behavior. We study forced and mixed convection regimes when a uniform heat flux is applied on the wall behind the step. Linear isotropic approximations for eddy viscosity and eddy thermal diffusivity underestimate the turbulent heat flux components while this anisotropic model shows a better agreement with DNS results.

Numerical simulation of forced and mixed convection turbulent liquid sodium flow over a vertical backward facing step with a four parameter turbulence model

Liquid metals are promising fluids for engineering applications since they have interesting physical properties such as high thermal conductivity and low kinematic viscosity with respect to the values of common operating fluids, i.e. air and water. This implies low Prandtl number values and therefore the similarity assumption between velocity and temperature fields does not hold. In the present work we solve a four parameter turbulence model coupled with the Reynolds Averaged Navier Stokes system of equations to simulate a turbulent flow of liquid sodium over a vertical backward facing step. On the wall behind the step a uniform heat flux is applied in order to study both forced and mixed convection flow regimes. This model for turbulent heat transfer, taking into account different boundary conditions, is analyzed and compared with the Kays correlation and Direct Numerical Simulation data. Profiles of velocity, turbulent kinetic energy, turbulent heat flux, temperature and its squared fluctuations are provided for two simulated Richardson number values, namely 0 and 0.338. Obtained results show a reasonable agreement with reference Direct Numerical Simulation values.

Steady-state turbulent flow of liquid sodium in a channel

We investigate the operation of several MHD-devices in a liquid metallic sodium circuit. A common feature of these devises is the presence of a cylindrical channel, 68mm in diameter, and the interaction of the liquid sodium flow with the magnetic fields. The first device is the linear cylindrical MHD pump for pushing liquid sodium through the channel. The other device is the flow meter for measuring the flow rate of the liquid sodium. Particular attention is given to three methods of measuring the flow rate of liquid sodium - conductive and inductive methods and cross-correlation technique, which is based on the signals of low-inertia thermocouples. The paper presents the results of the experiments and numerical computation.

Instabilities on a turbulent background

We present a review of several experimental results that concern the problem of hydrodynamic instabilities occurring in turbulent flows. The first experiment is related to the generation of a magnetic field by a turbulent flow of liquid sodium, i.e. the dynamo effect. We show how the bifurcation to the dynamo regime is affected by turbulent fluctuations. Above the dynamo threshold, we study the reversal dynamics of the magnetic field and present a model showing the respective contributions of deterministic and stochastic aspects. The second experiment is a nearly two-dimensional turbulent flow forced in a confined domain. We study a sequence of bifurcations that involve a large scale flow that develops over a turbulent background and displays random reversals. We emphasize both the similarities and differences with the magnetic reversal problem.

Decay rates of magnetic modes below the threshold of a turbulent dynamo.

We measure the decay rates of magnetic field modes in a turbulent flow of liquid sodium below the dynamo threshold. We observe that turbulent fluctuations induce energy transfers between modes with different symmetries (dipolar and quadrupolar). Using symmetry properties, we show how to measure the decay rate of each mode without being restricted to the one with the smallest damping rate. We observe that the respective values of the decay rates of these modes depend on the shape of the propellers driving the flow. Dynamical regimes, including field reversals, are observed only when the modes are both nearly marginal. This is in line with a recently proposed model.

Direct Measurement of Effective Magnetic Diffusivity in Turbulent Flow of Liquid Sodium

The first direct measurements of effective magnetic diffusivity in turbulent flow of electroconductive fluids (the so-called β effect) under the magnetic Reynolds number Rm≫1 are reported. The measurements are performed in a nonstationary turbulent flow of liquid sodium, generated in a closed toroidal channel. The peak level of the Reynolds number reached Re≈3×10(6), which corresponds to the magnetic Reynolds number Rm≈30. The magnetic diffusivity of the liquid metal was determined by measuring the phase shift between the induced and the applied magnetic fields. The maximal deviation of magnetic diffusivity from its laminar value reaches about 50%.

Bistability between a stationary and an oscillatory dynamo in a turbulent flow of liquid sodium

We report the first experimental observation of a bistable dynamo regime. A turbulent flow of liquid sodium is generated between two disks in the von Kármán geometry (VKS experiment). When one disk is kept at rest, bistability is observed between a stationary and an oscillatory magnetic field. The stationary and oscillatory branches occur in the vicinity of a codimension-two bifurcation that results from the coupling between two modes of magnetic field. We present an experimental study of the two regimes and study in detail the region of bistability that we understand in terms of dynamical system theory. Despite the very turbulent nature of the flow, the bifurcations of the magnetic field are correctly described by a low-dimensional model. In addition, the different regimes are robust; i.e. turbulent fluctuations do not drive any transition between the oscillatory and stationary states in the region of bistability.

Chaotic Dynamos Generated by a Turbulent Flow of Liquid Sodium

We report the observation of several dynamical regimes of the magnetic field generated by a turbulent flow of liquid sodium (VKS experiment). Stationary dynamos, transitions to relaxation cycles or to intermittent bursts, and random field reversals occur in a fairly small range of parameters. Large scale dynamics of the magnetic field result from the interactions of a few modes. The low dimensional nature of these dynamics is not smeared out by the very strong turbulent fluctuations of the flow.

Turbulent Diamagnetism in Flowing Liquid Sodium

The nature of Ohm's law is examined in a turbulent flow of liquid sodium. A magnetic field is applied to the flowing sodium, and the resulting magnetic field is measured. The mean velocity field of the sodium is also measured in an identical-scale water model of the experiment. These two fields are used to determine the terms in Ohm's law, indicating the presence of currents driven by a turbulent electromotive force. These currents result in a diamagnetic effect, generating magnetic field in opposition to the dominant fields of the experiment. The magnitude of the fluctuation-driven magnetic field is comparable to that of the field induced by the sodium's mean flow.

Generation of a Magnetic Field by Dynamo Action in a Turbulent Flow of Liquid Sodium

We report the observation of dynamo action in the von Kármán sodium experiment, i.e., the generation of a magnetic field by a strongly turbulent swirling flow of liquid sodium. Both mean and fluctuating parts of the field are studied. The dynamo threshold corresponds to a magnetic Reynolds number R(m) approximately 30. A mean magnetic field of the order of 40 G is observed 30% above threshold at the flow lateral boundary. The rms fluctuations are larger than the corresponding mean value for two of the components. The scaling of the mean square magnetic field is compared to a prediction previously made for high Reynolds number flows.

Transport of Magnetic Field by a Turbulent Flow of Liquid Sodium

We study the effect of a turbulent flow of liquid sodium generated in the von Kármán geometry, on the localized field of a magnet placed close to the frontier of the flow. We observe that the field can be transported by the flow on distances larger than its integral length scale. In the most turbulent configurations, the mean value of the field advected at large distance vanishes. However, the rms value of the fluctuations increases linearly with the magnetic Reynolds number. The advected field is strongly intermittent.

Intermittent Magnetic Field Excitation by a Turbulent Flow of Liquid Sodium

The magnetic field measured in the Madison dynamo experiment shows intermittent periods of growth when an axial magnetic field is applied. The geometry of the intermittent field is consistent with the fastest-growing magnetic eigenmode predicted by kinematic dynamo theory using a laminar model of the mean flow. Though the eigenmodes of the mean flow are decaying, it is postulated that turbulent fluctuations of the velocity field change the flow geometry such that the eigenmode growth rate is temporarily positive. Therefore, it is expected that a characteristic of the onset of a turbulent dynamo is magnetic intermittency.

Measurements of the magnetic field induced by a turbulent flow of liquid metal

Initial results from the Madison Dynamo Experiment provide details of the inductive response of a turbulent flow of liquid sodium to an applied magnetic field. The magnetic field structure is reconstructed from both internal and external measurements. A mean toroidal magnetic field is induced by the flow when an axial field is applied, thereby demonstrating the omega effect. Poloidal magnetic flux is expelled from the fluid by the poloidal flow. Small-scale magnetic field structures are generated by turbulence in the flow. The resulting magnetic power spectrum exhibits a power-law scaling consistent with the equipartition of the magnetic field with a turbulent velocity field. The magnetic power spectrum has an apparent knee at the resistive dissipation scale. Large-scale eddies in the flow cause significant changes to the instantaneous flow profile resulting in intermittent bursts of nonaxisymmetric magnetic fields, demonstrating that the transition to a dynamo is not smooth for a turbulent flow.

Observation of a Turbulence-Induced Large Scale Magnetic Field

An axisymmetric magnetic field is applied to a spherical, turbulent flow of liquid sodium. An induced magnetic dipole moment is measured which cannot be generated by the interaction of the axisymmetric mean flow with the applied field, indicating the presence of a turbulent electromotive force. It is shown that the induced dipole moment should vanish for any axisymmetric laminar flow. Also observed is the production of toroidal magnetic field from applied poloidal magnetic field (the omega effect). Its potential role in the production of the induced dipole is discussed.

Lorentz force effects in magneto-turbulence

We experimentally characterize magnetic field fluctuations in a strongly turbulent flow of liquid sodium in the presence of a large externally applied field. We reach high interaction parameter (up to N=17) for moderate magnetic Reynolds number (up to Re m=18), a previously unexplored parameter range for liquid metal flows. As the interaction parameter (i.e. the ratio of Lorentz to inertial forces) is increased, the system passes through distinct regimes, which we classify. We find that for certain ranges of the applied magnetic field, particularly at high values, the induced magnetic field exhibits large, coherent oscillations. Spatial structure in these induced field oscillations suggests the formation of non-axisymmetric vortices that precess at a fraction of the impeller rotation rate. We also investigate the effect of rough versus smooth boundaries and relate these results to topographic core–mantle coupling in the Earth.

Toward a self-generating magnetic dynamo: the role of turbulence

Turbulent flow of liquid sodium is driven toward the transition to self-generating magnetic fields. The approach toward the transition is monitored with decay measurements of pulsed magnetic fields. These measurements show significant fluctuations due to the underlying turbulent fluid flow field. This paper presents experimental characterizations of the fluctuations in the decay rates and induced magnetic fields. These fluctuations imply that the transition to self-generation, which should occur at larger magnetic Reynolds number, will exhibit intermittent bursts of magnetic fields.