Stefan Radev

Freezing of a supercooled spherical droplet with mixed boundary conditions

The freezing of a supercooled droplet occurs in two steps: recalescence, that is, a rapid return to thermodynamic equilibrium at the freezing temperature leading to a liquid–solid mixture and a longer stage of complete freezing. The second freezing step can be modelled by the one-phase Stefan problem for an inward solidification of a sphere, assuming the droplet to be spherical. A convective heat transfer with the ambient immiscible fluid is modelled by a mixed boundary condition on the outer surface of the droplet. This condition depends on the Biot number (ratio of the heat transfer resistances inside the droplet and at its surface). A novel asymptotic solution is developed for a small Stefan number and an arbitrary Biot number. Applying the method of matched asymptotic expansions, uniformly valid solutions are obtained for the temperature profile and freezing front evolution in the whole stage of complete freezing. For an infinite Biot number, that is, for a fixed temperature at the droplet outer boundary, known solutions are recovered. In parallel, numerical results are obtained for an arbitrary Stefan number using a finite-difference scheme based on the enthalpy method. The asymptotic and numerical solutions are in good agreement.

A computational approach for the earthquake response of cable-braced reinforced concrete structures under environmental actions

A numerical treatment for the seismic response of reinforced concrete structures containing cable elements is presented. The cable behaviour is considered as nonconvex and nonmonotone one and is described by generalized subdifferential relations including loosening, elastoplastic - fracturing etc. effects. The problem is treated incrementally by double discretization: in space by finite elements and piece-wise linearization of cable - behaviour, and in time by the Newmark method. Thus, in each time - step an incremental linear complementarity problem is solved with a reduced number of problem unknowns.

Approximation of the oscillatory blood flow using the Carreau viscosity model

The analysis of non-Newtonian flows in tubes is very important when studying the blood flow in different types of arteries. Usually the blood viscosity is defined by shear-dependent models, for example by the Carreau model, which represents the viscosity as a non-linear function of the shear-rate. In this paper the unsteady (oscillatory) 2D model of the blood flow in a straight tube is discussed theoretically and numerically. The solution of the quasilinear parabolic equation for the velocity is constructed using appropriate analytical functions. Further the corresponding numerical solution is approximated by similar analytical functions.

Physical-optics approximation of near-critical-angle scattering by spheroidal bubbles

A first-order approximation is derived for the near-critical-angle scattering of a large spheroidal bubble illuminated by a plane wave propagating along the bubble axis of symmetry. The intensity of the far-field scattering pattern is expressed as a function of the relative refractive index and the two radii of curvature of the spheroidal bubble at the critical impact point.

Optical measurement of the drawing tension of small glass fibres

This work introduces the principle of a simple interferometric method to measure the drawing tension (F ≈ 10−3–10−4 N) of a small glass fibre (D ≈ 7–30 µm) during its forming process. Because of the industrial process and the complexity of the light scattering properties of small glass fibres, mechanical methods or optical methods based on birefringence measurements are not suitable to measure this tension. The method we propose uses the principle of the phase Doppler technique to determine the fibre size and simultaneously, the fibre tension, with the vibrating string method. No calibration is required with the proposed technique, and it is thought to be applicable to other types of fibres (polymer, carbon, metallic, etc).

Application of the Carreau viscosity model to the oscillatory flow in blood vessels

When studying the oscillatory flow in different types of blood vessels it is very important to know what type of the blood viscosity model has to be used. In general the blood viscosity is defined as a shear-thinning liquid, for which there exist different shear-dependent models, for example the Carreau model, which represents the viscosity as a non-linear function of the shear-rate. In some cases, however, the blood viscosity could be regarded as constant, i.e., the blood is treated as Newtonian fluid. The aim of the present work is to show theoretically and numerically some approximate limits of the Newtonian model application, when the blood vessel is assumed as a 2D straight tube. The obtained results are in agreement with other authors’ numerical results based on similar blood viscosity models.

Pounding Effects on the Earthquake Response of Adjacent Reinforced Concrete Structures Strengthened by Cable Elements

Abstract A numerical approach for estimating the effects of pounding (seismic interaction) on the response of adjacent Civil Engineering structures is presented. Emphasis is given to reinforced concrete (RC) frames of existing buildings which are seismically strengthened by cable-elements. A double discretization, in space by the Finite Element Method and in time by a direct incremental approach is used. The unilateral behaviours of both, the cable-elements and the interfaces contact-constraints, are taken strictly into account and result to inequality constitutive conditions. So, in each time-step, a non-convex linear complementarity problem is solved. It is found that pounding and cable strengthening have significant effects on the earthquake response and, hence, on the seismic upgrading of existing adjacent RC structures.

Tall RC Buildings Environmentally Degradated and Strengthened by Cables Under Multiple Earthquakes: A Numerical Approach

A numerical investigation is presented for the seismic analysis of tall reinforced concrete (RC) Civil Engineering structures, which have been degradated due to extreme environmental actions and are strengthened by cable elements. The effects of multiple earthquakes on such RC building frames are computed. Damage indices are estimated in order to compare the seismic response of the structures before and after the retrofit by cable element strengthening, and so to elect the optimum strengthening version.

Freezing of a Suspended Supercooled Droplet with a Heat Transfer Mixed Condition on Its Outer Surface

The problem of water droplets freezing before or after their impact on solid surfaces is of major importance when modeling the aircrafts icing in wind tunnels. The object in this study is to estimate the freezing time of a suspended supercooled droplet in an air flow. It is known that freezing occurs into two steps: a short stage of rapid return to thermodynamic equilibrium, when the droplet becomes a water‐ice mixture and a longer stage of its complete freezing. Mathematically, the second freezing step can be modeled by the one‐phase Stefan problem. A convective heat transfer with ambient air is modeled here by a mixed boundary condition on the droplet outer surface. Assuming a spherical droplet, an asymptotic solution is developed for small Stefan numbers, while for arbitrary Stefan numbers a numerical solution based on the enthalpy method is constructed. Both solutions are compared. The numerical solution is also compared with other authors experimental results.

A computational approach for the seismic damage response under multiple earthquakes excitations of adjacent RC structures strengthened by ties

Civil Engineering systems of adjacent reinforced concrete (RC) structures, which have been environmentally degraded, are considered in order to be seismically strengthened by cable-elements (ties). A numerical approach for estimating the effects of pounding (seismic interaction) on the response of such adjacent structures under multiple earthquakes excitation is presented. For the system of the governing partial differential equations (PDE) a double discretization, in space by the Finite Element Method and in time by a direct incremental approach, is used. The unilateral behaviors of both, the cable-elements and the interfaces contact-constraints, are strictly taken into account and result to inequality constitutive conditions. So, in each time-step, a non-convex linear complementarity problem is solved. The decision for the optimal cable-strengthening scheme is obtained on the basis of computed damage indices. It is found that pounding and cable strengthening have significant effects on the earthquake response and, hence, on the seismic upgrading of existing adjacent RC structures.