Janis Priede

Three-dimensional linear stability analysis of the flow in a liquid spherical droplet driven by an alternating magnetic field

The paper presents a numerical stability analysis of the flow driven by an alternating (ac) magnetic field in an electromagnetically levitated liquid metal droplet. The basic axisymmetric flow is found to become unstable at Reynolds numbers in the order of 100. The critical Reynolds number Rec and the corresponding most unstable azimuthal wave number m are found for several configurations of the magnetic field depending on the skin-depth δ. For a uniform external ac magnetic field the azimuthal wave number of the most unstable mode is m=3. An additional steady (dc) magnetic field imposed along the axis of symmetry increases the stability of the flow.

Experimental and numerical study of anomalous thermocapillary convection in liquid gallium

Thermocapillary Marangoni convection of liquid gallium was studied experimentally and numerically. A specially designed experimental setup ensured an oxide-free surface of the liquid gallium for a very long time. The convective flow at the free surface was found to be directed opposite to both buoyancy-driven and ordinary thermocapillary convection. The anomalous direction of the thermocapillary flow was explained by the presence of a small amount of a surface-active contaminant—lead adsorbed at the free surface. Two different approaches were used to describe the observed phenomenon. First, the flow was treated as a pure thermocapillary convection with a modified dependence of the surface tension on temperature so that to reproduce the measured velocity distribution. Second, a novel physical model was devised for the flow driven by the gradient of the surface tension induced by the temperature dependence of the concentration of the adsorbed layer of contaminant. In contrast to the ordinary thermocapillary...

Hydrothermal wave instability of thermocapillary-driven convection in a coplanar magnetic field

We study the linear stability of surface-tension-driven unidirectional shear flow in an unbounded electrically conducting liquid layer heated from the side and subjected to a uniform magnetic eld in the plane of the layer. The threshold of convective instability with respect to oblique travelling waves is calculated depending on the strength and orientation of the magnetic eld. For longitudinal waves the critical Marangoni number and the corresponding wavelength are found to increase directly with the induction of a suciently strong magnetic eld. In general, a coplanar magnetic eld causes stabilization of all disturbances except those aligned with the eld, which are not influenced at all. With increase of the magnetic eld this eect results in the alignment of the most unstable disturbance along the magnetic flux lines. The maximal stabilization is ensured by the magnetic eld being imposed spanwise to the basic flow. The corresponding critical Marangoni number is found to be almost insensitive to the thermal properties of the bottom. The strength of the magnetic eld necessary to attain the maximal stabilization for a thermally well-conducting bottom is considerably lower than that for an insulating bottom. The basic return flow is found to be linearly stable with respect to purely hydrodynamic disturbances. This eect determines the stability of the basic state with respect to transverse hydrothermal waves at Prandtl number Pr < Prc =0 :018. For such a small Pr no alignment of the critical perturbation with a spanwise magnetic eld is possible, and the critical Marangoni number can be increased almost directly with the strength of the magnetic eld without limit.

Boundary-Integral method for calculating poloidal axisymmetric AC magnetic fields

This paper presents a boundary-integral equation (BIE) method for the calculation of poloidal axisymmetric magnetic fields applicable in a wide range of ac frequencies. The method is based on the vector potential formulation, and it uses the Greens functions of Laplace and Helmholtz equations for the exterior and interior of conductors, respectively. The paper focuses on a calculation of axisymmetric Greens function for the Helmholtz equation which is both simpler and more accurate than previous approaches. We use three different techniques for calculation of Greens function, depending on the parameter range. For low and high ac frequencies, we use a power series expansion in terms of elliptical integrals and an asymptotic series in terms of modified Bessel functions of second kind, respectively. For the intermediate frequency range, we use Gauss-Chebyshev-Lobatto quadratures. We verify the accuracy of the method by comparing its results with the analytical solution for a sphere in a uniform external ac field. We illustrate the application of the method by analyzing a composite model inductor containing an external secondary circuit.

Modelling of electromagnetic levitation – consequences on non-contact physical properties measurements

Electromagnetic levitation of electrically conductive droplets by alternating magnetic fields is a technique used to determine the physical properties of liquid metallic alloys such as surface tension, viscosity, heat capacity and thermal diffusivity/1/. To improve accuracy, it is mandatory to reduce electromagnetic stirring and shaping of the droplet, therefore experiments are conducted in microgravity. Properties are deduced from direct measurements of position or temperature using specific models. Our purpose is to check various assumptions on which those models are built by the use of adapted numerical codes. We first compare experimental and numerical results concerning the shape and mass centre oscillation frequencies of electromagnetically levitated Nickel droplets. Axisymmetric numerical model yields equilibrium shapes and positions of the droplets in a good agreement with experiment. Then, fluid flow effects on the measurement precision of surface tension and viscosity by comparing expecte and calculated properties values are charcterized. We determine critical values of initial droplet distortion or magnetic field intensity which can lead to an overestimate of the value of viscosity. We also calculate flow effects of heat capacity and thermal conductivity values.

Edge pinch instability of liquid metal sheet in a transverse high-frequency ac magnetic field

We analyze the linear stability of the edge of a thin liquid metal layer subject to a transverse high-frequency ac magnetic field. The layer is treated as a perfectly conducting liquid sheet that allows us to solve the problem analytically for both a semi-infinite geometry with a straight edge and a thin disk of finite radius. It is shown that the long-wave perturbations of a straight edge are monotonically unstable when the wave number exceeds the critical value k(c) = F0/(gamma l0), which is determined by the linear density of the electromagnetic force F0 acting on the edge, the surface tension gamma, and the effective arclength of edge thickness l0. Perturbations with wavelength shorter than critical are stabilized by the surface tension, whereas the growth rate of long-wave perturbations reduces as similar to k for k --> 0. Thus, there is the fastest growing perturbation with the wave number k max = 2/3 k(c). When the layer is arranged vertically, long-wave perturbations are stabilized by the gravity, and the critical perturbation is characterized by the capillary wave number k(c) = square root of (g rho/gamma), where g is the acceleration due to gravity and rho is the density of metal. In this case, the critical linear density of electromagnetic force is F(0,c) = 2k(c)l0 gamma, which corresponds to the critical current amplitude I(0,c) = 4 square root of (pi k(c) l0L gamma/mu 0) when the magnetic field is generated by a straight wire at the distance L directly above the edge. By applying the general approach developed for the semi-infinite sheet, we find that a circular disk of radius R0 placed in a transverse uniform high-frequency ac magnetic field with the induction amplitude B0 becomes linearly unstable with respect to exponentially growing perturbation with the azimuthal wave number m = 2 when the magnetic Bond number exceeds Bm(c) = B(0)2 R(0)2 / (2 mu 0 l0 gamma) = 3 pi. For Bm > Bm(c), the wave number of the fastest growing perturbation is m(max) = [2Bm/(3 pi)]. These theoretical results agree well with the experimental observations.

Stability of an electromagnetically levitated spherical sample in a set of coaxial circular loops

This paper presents a theoretical study of oscillatory and rotational instabilities of a solid spherical body, levitated electromagnetically in axisymmetric coils made of coaxial circular loops. We apply our previous theory to analyze the static and dynamic stability of the sample depending on the ac frequency and the position of the sample in the coils for several simple configurations. We introduce an original analytical approach employing a gauge transformation for the vector potential. First, we calculate the spring constants that define the frequency of small-amplitude oscillations. For static stability, the spring constants must be positive. Dynamic instabilities are characterized by critical ac frequencies that, when exceeded, may result either in a spin-up or oscillations with increasing amplitude. We found that the critical frequencies increase with the nonuniformity of the field. We show that for a spherically harmonic field, the critical frequency for the spin-up instability in a field of degree l coincides with the critical frequency for the oscillatory instability in a field of degree l+1.

Kontaktlose Durchflussmessung in Metallschmelzen

Zusammenfassung Bis zum heutigen Zeitpunkt gibt es bezogen auf die Strömungs- und Durchflussmessung elektrisch leitfähiger Metallströmungen nahezu keine kommerziell verfügbare Lösungen. Eines der wichtigsten Einsatz- oder Aktionsfelder ist die metallverarbeitende Industrie. Eisen- und Nichteisenmetalle werden durch den technologisch anspruchsvollen Prozess des Gießens in die Form von weiterverarbeitbaren Halbzeugen oder in aufwendige Endformen gebracht. Wichtige Automationsparameter sind dabei Durchflussrate und Geschwindigkeit, ohne deren Kenntnis und Kontrolle keine Prozessführung möglich ist. Zwei weitere, wichtige Anwendungsfelder für kontaktlos operierende Durchfluss- und Strömungssensoren ergeben sich aus der Notwendigkeit des Verständnisses der thermohydraulischen Vorgänge bezüglich des Energie- und Massentransportes in metallgekühlten Reaktorsystemen sowie in künftig geplanten Transmutationssystemen. Abgesehen von der auf dem Markt etablierten, kontaktbehafteten Durchflussmesstechnik stehen derzeit kaum Alternativen der Durchflussbestimmung in flüssigen Metallen zur Verfügung. Der folgende Beitrag stellt zwei innovative, kontaktlose Messverfahren vor, die in zahlreichen Tests untersucht wurden. Ein Verfahren wird in Kürze auf dem Markt kommerziell verfügbar sein. Abstract