The Carreau fluid flow in an infinite pipe, caused by a time-dependent pressure gradient, is studied theoretically. The problem is axisymmetric in space and reduces to a nonlinear parabolic equation for the axial velocity. This equation has no analytical solution in the general case of different Carreau numbers. In the present paper, it is proved that the velocity and its gradient, as well as their differences from the similar Newtonian solution, are bounded by explicitly found constants, which depend on the Carreau number and on the other parameters of the viscosity rheological model. These estimates are also discussed for the special case of oscillatory pressure gradient using some numerical examples at different Carreau numbers.

The interaction between oscillatory blood flow and an abdominal aorta aneurysm (AAA) is numerically modeled using the fluid-structure interaction (FSI) module of software ANSYS. The AAA is modelled as an elastic tube with a symmetric or asymmetric sac. For both geometrical cases, the laminar or turbulent flow regimes depend on the elasticity modulus of the artery wall. The influence of both types of aneurysms on the flow regimes is shown in correspondence with the similar flow regimes for a straight tube (without aneurysm).

The present paper studies the oscillatory flow of Carreau fluid in a channel at different Womersley and Carreau numbers. At high and low Womersley numbers, asymptotic expansions in small parameters, connected with the Womersley number, are developed. For the intermediate Womersley numbers, theoretical bounds for the velocity solution and its gradient, depending on the problem parameters, are proven and explicitly given. It is shown that the Carreau number changes the type of the flow velocity to be closer to the Newtonian velocity corresponding to low or high shear or to have a transitional character between both Newtonian velocities. Some numerical examples for the velocity at different Carreau and Womersley numbers are presented for illustration with respect to the similar Newtonian flow velocity.

The deformation behaviour of an elastic tube possessing a Gaussian defected profile is discussed depending on the inlet pulsatile fluid flow, as an opportunity to imitate the interaction between abdominal aortic aneurysm (AAA) and blood flow. The numerical simulations are performed using the fluid-structure interaction (FSI) of ANSYS software. Three deformation regimes of the tube wall are established depending on the wall elasticity and average fluid pressure. Some stable and unstable deformed shapes of the defected part are found together with the corresponding distributions of displacements and von Misses stresses in the wall zone.

The cardiovascular diseases depend directly on the blood flow dynamics. The mathematical modeling and numerical simulations are expected to play an important role to predict the genesis of the atherosclerosis and the formation and rupture of the aneurysms. In the present work the numerical solutions for the oscillatory flow velocity due to the Newtonian and the non-Newtonian (Carreau) model are constructed for a straight long tube and for a tube (artery) with a model aneurysm. The numerical solutions are obtained by the finite-difference method (FDM) for the straight tube and by the software ANSYS/FLUENT for both geometries. The numerical results obtained by the ANSYS/FLUENT for a straight long tube are validated by the analytical and numerical solutions using the FDM for the Newtonian and Carreau models for different Womersley numbers, correspondent to different tube radii. The obtained peak wall shear stresses from the oscillatory flow in the straight long tube are lower than those in the tube with the model aneurysm, which can be used as an indicator for further clinical examinations.

The two-dimensional Newtonian and non-Newtonian (Carreau viscosity model used) oscillatory flows in straight tubes are studied theoretically and numerically. The corresponding analytical solution of the Newtonian flow and the numerical solution of the Cancan viscosity model flow show differences in velocity and shear rate. Some estimates for the velocity and shear rate differences are theoretically proved. As numerical examples the blood flow in different type of arteries and the polymer flow in pipes are considered.

The analysis of the blood flow dynamics (hemodynamics) in tubes is crucial when investigating the rupture of different types of aneurysms. The blood viscosity nonlinear dependence on the flow shear rate creates complicated manifestations of the blood pulsations. Although a great number of studies exists, experimental and numerical, this phenomenon is still not very well understood. The aim of the present work is to propose a numerical model of the oscillatory blood flow in a tube on the basis of the Carreau model of the blood viscosity (nonlinear model with respect to the shear rate). The obtained results for the flow velocity and tangential stress on the tube wall are compared well with other authors' results.

Hitting cold surfaces, such as aircraft ones, supercooled water droplets may freeze immediately. However, glaze ice may also be formed under some conditions: a part of the droplets may freeze, while the rest remains liquid, flowing on the substrate as a film. This paper proposes a model of a film created by the impact of supercooled droplets on a cylindrical obstacle. The film is a mixture of water and frazil ice, viz. a slurry. The film thickness and volume fraction of ice in the water are expressed by simple analytical formulas obtained from the mass and enthalpy balance laws in the presence of different phenomena responsible for film cooling. The results are compared with the data of existing experiments.

In the present work the dynamics of a non-isothermal thin viscous film, with fully mobile interfaces, is studied in the case when the inertial, viscous, capillary, van der Waals and thermocapillary forces are important. The film is laterally bounded by a frame, whose temperature is higher than the environmental one. The stability of the static film shapes is examined numerically by a linear and non-linear analysis. The results show that the film rupture is mostly governed by the dynamics, but it could be delayed or enhanced by the thermocapillary convection and the heat transfer with the surrounding environment.

The paper review key results [1-14] of the joint researches conducted by IMech and IUSTI. In the First part, we review models and experimental results on the linear and nonlinear instability of a capillary jet including both axisymmetric and nonaxisymmetric disturbances. In the Second part, results on draw resonances, occurring during a glass fibre process are reviewed, as well as the unique optical models and methods developed to perform these studies.

Abstract The paper review key results [1-14] of the joint researches conducted by IMech and IUSTI. In the First part, we review models and experimental results on the linear and nonlinear instability of a capillary jet including both axisymmetric and nonaxisymmetric disturbances. In the Second part, results on draw resonances, occurring during a glass fibre process are reviewed, as well as the unique optical models and methods developed to perform these studies.

After impact of a viscous liquid drop on a dry wall surrounded by a gas, the drop surface is highly deformed, leading to the formation of an axisymmetrical lateral lamella along the wall. A local asymptotic model for the potential flow and unsteady boundary layer flow is developed to describe the lamella dynamics at early stages after impact. The second-order potential flow displaced by the unsteady boundary layer is taken into account. The lamella shape, its velocity and pressure are calculated with this model in parametrical forms. The three model parameters are evaluated here by fitting with recent experimental findings.

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.

Drop impact has various applications like supercooled drops freezing when hitting aircrafts or electrical power lines, spray cooling, soldering, ink jet printing. When a drop hits a solid surface, a circular wall jet appears, which may spread and/or splash afterwards. The modeling of this jet is still an open problem. In the present paper we propose an axisymmetric dynamic model of the jet appearance, as an inviscid fluid, and its evolution in time towards a thin viscous film, as a boundary layer develops from the wall. Typical values of the drop diameter considered here are 0(1 nun) and typical values of the impact velocity are O(1m/s). Numerical results for the jet thickness and lateral velocity are shown for some typical process parameters and are compared with experimental data obtained with a rapid shutter video camera.

The nonlinear instability of a compound jet consisting of a liquid core and immiscible coaxial liquid layer is studied. The equations of motion for both liquids (phases) are used in one-dimensional (1-D) approximation similar to that known for one-layer jet.A numerical method is proposed for calculation the radiuses of both interfaces and axial velocities of the core and outer layer. The method is tested for determining the typical forms of compound jet disintegration.

A kinetic problem of mass transfer in a model porous body in the process of intense evaporation (condensation) and vapour escape into a vacuum is considered. Two computational methods have been used: the mean free path method and the method of direct statistical simulation. With the aid of the first method the location of the condensation zone within a porous body is determined as a function of the evaporating surface-to-porous layer temperature difference and also of the condensation coefficient. The second method is employed in a one-dimensional case to obtain (without condensation) the density, velocity and temperature distributions for a gas in a porous layer and in a gas medium behind the porous body. It is shown that the agreement between the parameters obtained by both methods for the gas flow escaping the porous layer is quite satisfactory