Two-dimensional dendritic growth at arbitrary Peclet number

Velocity selection in two-dimensional dendritic growth caused by anisotropy of the surface energy is considered. In the limit of low anisotropy the integro-differential equation for the velocity spectrum is reduced to a differential equation. The solution of this equation, corresponding to the maximal velocity, is stable, whereas the other solutions have unstable modes. A differential equation for the spectrum of growth rates is also derived. The growth velocity v ~ α3/4. f(pα1/2), where p is the Peclet number, α <<; 1 is a small anisotropy parameter. At pα1/2 ∼ 1 the function f is calculated numerically. The growth rates of the unstable modes Ω ~ α3/2 g (pα1/2). At pα1/2 <<; 1 the function g ~ (pα1/2)3, and in the opposite limit g ~ (pα1/2)-4/5.La sélection de vitesse due à l'anisotropie de l'énergie de surface dans la croissance dendritique à deux dimensions est considérée. Dans la limite de petite anisotropie, l'équation intégro-différentielle du spectre de vitesse se réduit à une équation différentielle. La solution de cette équation correspondant à la vitesse maximale est stable alors que les autres solutions présentent des modes instables. Une équation différentielle pour le spectre des taux de croissance est également dérivée. La vitesse de croissance v se comporte comme α3/4 f(pα1/2) où p est le nombre de Péclet et α <<; 1, un petit paramètre d'anisotropie. Pour pα1/2 ∼ 1, la fonction f est calculée numériquement. Les taux de croissance des modes instables Ω se comportent comme α3/2 g (pα1/2). Pour pα1/2 <<; 1, g se comporte comme (pα 1/2)3 et comme (pα1/2)- 4/5 dans le cas contraire

The study of ultrasonic reflex-radar waveguide coolant level gage for a nuclear reactor

Results of experimental study of operation of ultrasonic reflex-radar waveguide level gage in water coolant at elevated parameters with pressure up to 18MPa and temperature up to 350°C are examined. In contrast to the known waveguide level gages, traveltime of acoustic pulses along the waveguide from the radiator to the subsurface layer and back is measured in the level gage under study. Waveguide consists of two acoustically isolated waveguides – the radiating waveguide and the receiving waveguide. Waveguides of zero-order flexural waves and piezoelectric transformers operated at frequency of ∼800kHz are applied. Processing of received signals is performed by microprocessor-based electronic circuit. Measurement uncertainty does not exceed ±10mm. Description of the experimental setup and the experimental methodology is provided. The instrument works reliably and does not require introducing corrections of readings when coolant thermal physical properties change. The measurement instrument is intended for application in heat exchanging equipment in thermal and nuclear power generation