On the structure of the floating zone in melting

Floating zone melting is used in crystal growth and purification of high melting materials. The use of a reduced gravity environment will remove the constraint imposed on the length of the zone by the hydrostatic pressure. The equilibrium of the fioatmg zone may involve, (1)Hydrostatic forces, when the zone rotates as a whole. (2)Convective driving forces, when the zone is stationary but fluid property gradients appear.(3) Hydrodynamic forces, when some parts of the zone are set into motion with respect to others. The last effects are considered in this paper. The flow pattern of a floating zone held between two discs in relative motion is complicated, and thence the solution of the problem is difficult even assuming a constant property-newtonian liquid Nevertheless, when a small parameter appears m the problem, the complete flow field can be split into zones where simple solutions are found. To illustrate this approach, the spin up from rest of an initially cylindrical floating zone is considered with detail. Here the small parameter is the time elapsed from the impulsive starting of motion. Since the problem which has been considered, as well as some others which can be tackled by use of similar methods, concern the viscous layer close to either plate, they can be simulated experimentally in the ground laboratory with short floating zones. Procedures to produce these zones are indicated.

A regular perturbation approach to surface tension driven flows

Surface tension induced convection in a liquid bridge held between two parallel, coaxial, solid disks is considered. The surface tension gradient is produced by a small temperature gradient parallel Co the undisturbed surface. The study is performed by using a mathematical regular perturbation approach based on a small parameter, e, which measures the deviation of the imposed temperature field from its mean value. The first order velocity field is given by a Stokes-type problem (viscous terms are dominant) with relatively simple boundary conditions. The first order temperature field is that imposed from the end disks on a liquid bridge immersed in a non-conductive fluid. Radiative effects are supposed to be negligible. The second order temperature field, which accounts for convective effects, is split into three components, one due to the bulk motion, and the other two to the distortion of the free surface. The relative importance of these components in terms of the heat transfer to or from the end disks is assessed

Effect of the pulse trajectory on ultrasonic fluid velocity measurement

In a general situation a non-uniform velocity field gives rise to a shift of the otherwise straight acoustic pulse trajectory between the transmitter and receiver transducers of a sonic anemometer. The aim of this paper is to determine the effects of trajectory shifts on the velocity as measured by the sonic anemometer. This determination has been accomplished by developing a mathematical model of the measuring process carried out by sonic anemometers; a model which includes the non-straight trajectory effect. The problem is solved by small perturbation techniques, based on the relevant small parameter of the problem, the Mach number of the reference flow, M. As part of the solution, a general analytical expression for the deviations of the computed measured speed from the nominal speed has been obtained. The correction terms of both the transit time and of the measured speed are of M 2 order in rotational velocity field. The method has been applied to three simple, paradigmatic flows: one-directional horizontal and vertical shear flows, and mixed with a uniform horizontal flow.

Application of the Boundary Method to the determination of the properties of the beam cross-sections

Using the 3-D equations of linear elasticity and the asylllptotic expansion methods in terms of powers of the beam cross-section area as small parameter different beam theories can be obtained, according to the last term kept in the expansion. If it is used only the first two terms of the asymptotic expansion the classical beam theories can be recovered without resort to any "a priori" additional hypotheses. Moreover, some small corrections and extensions of the classical beam theories can be found and also there exists the possibility to use the asymptotic general beam theory as a basis procedure for a straightforward derivation of the stiffness matrix and the equivalent nodal forces of the beam. In order to obtain the above results a set of functions and constants only dependent on the cross-section of the beam it has to be computed them as solutions of different 2-D laplacian boundary value problems over the beam cross section domain. In this paper two main numerical procedures to solve these boundary value pf'oblems have been discussed, namely the Boundary Element Method (BEM) and the Finite Element Method (FEM). Results for some regular and geometrically simple cross-sections are presented and compared with ones computed analytically. Extensions to other arbitrary cross-sections are illustrated.

Performance metrics for small-signal stability assessment of DC-distributed power-system-architecture comparisons

The objective of this paper is to provide performance metrics for small-signal stability assessment of a given system architecture. The stability margins are stated utilizing a concept of maximum peak criteria (MPC) derived from the behavior of an impedance-based sensitivity function. For each minor-loop gain defined at every system interface, a single number to state the robustness of stability is provided based on the computed maximum value of the corresponding sensitivity function. In order to compare various power-architecture solutions in terms of stability, a parameter providing an overall measure of the whole system stability is required. The selected figure of merit is geometric average of each maximum peak value within the system. It provides a meaningful metrics for system comparisons: the best system in terms of robust stability is the one that minimizes this index. In addition, the largest peak value within the system interfaces is given thus detecting the weakest point of the system in terms of robustness.