Konrad Bajer

Accelerated diffusion in the centre of a vortex

The spiral wind-up and diffusive decay of a passive scalar in circular streamlines is considered. An accelerated diffusion mechanism operates to destroy scalar fluctuations on a time scale of order P1/3 times the turn-over time, where P is a Peclet number. The mechanism relies on differential rotation, that is, a non-zero gradient of angular velocity. However if the flow is smooth, the gradient of angular velocity necessarily vanishes at the centre of the streamlines, and the time scale becomes greater. The behaviour at the centre is analysed and it is found that scalar there is only destroyed on a time scale of order P1/2. Related results are obtained for magnetic field and for weak vorticity, a scalar coupled to the stream function of the flow. Some exact solutions are presented.

From feathers to syngas - technologies and devices.

The poultry waste produced by industrial slaughterhouses typically contains not only feathers, but also a mixture of animal entrails, nails, blood, beaks and whole carcasses. Economical utilisation of this mixture, varying strongly in composition and moisture content, is, in general, difficult. We demonstrate that this awkward material can be successfully used for gasification in a simple, fixed-bed gasifier. The method of gasification, which we developed, enables control of the gasification process and ensures its stability in the operational regime of a working poultry processing plant. The installation, which has been working in Poland for 2 years, utilises 2 tons of feathers per hour and produces syngas of stable composition and fairly high quality. The syngas is burnt in the combustion chamber adjacent to the gasifier. Heat is recuperated in a boiler producing 3.5 tons per hour of technological steam continuously used for the operation of the slaughterhouse. The whole process complies with the stringent emission standards. In the paper we present the end-use device for feather utilisation and describe the underlying gasification and syngas combustion processes. Key elements of the whole installation are briefly discussed. The environmental impacts of the installation are summarized.

Cascade of vortex loops initiated by a single reconnection of quantum vortices

We demonstrate that a single reconnection of two quantum vortices can lead to the creation of a cascade of vortex rings. Our analysis involves localized induction approximation, high-resolution Biot-Savart and Gross-Pitaevskii simulations. The latter showed that the rings cascade starts on the atomic scale, with rings diameters orders of magnitude smaller than the characteristic line spacing in the tangle. Vortex rings created in the cascades may penetrate the tangle and annihilate on the boundaries. This provides an efficient decay mechanism for sparse or moderately dense vortex tangle at very low temperatures.

The magnetoelliptic instability of rotating systems

We address the question of stability of the Euler flow with elliptical streamlines in a rotating frame, interacting with uniform external magnetic field perpendicular to the plane of the flow. Our motivation for this study is of astrophysical nature, since many astrophysical objects, such as stars, planets and accretion discs, are tidally deformed through gravitational interaction with other bodies. Therefore, the ellipticity of the flow models the tidal deformations in the simplest way. The joint effect of the magnetic field and the Coriolis force is studied here numerically and analytically in the limit of small elliptical (tidal) deformations (ζ � 1), using the analytical technique developed by Lebovitz & Zweibel (Astrophys. J., vol. 609, 2004, pp. 301–312). We find that the effect of background rotation and external magnetic field is quite complex. Both factors are responsible for new destabilizing resonances as the vortex departs from axial symmetry (ζ � 1); however, just like in the non-rotating case, there are three principal resonances causing instability in the leading order. The presence of the magnetic field is very likely to destabilize the system with respect to perturbations propagating in the direction of the magnetic field if the basic vorticity and the background rotation have opposite signs (i.e. for anticyclonic background rotation). We present the dependence of the growth rates of the modes on various parameters describing the system, such as the strength of the magnetic field (h), the inverse of the Rossby number (Rv), the ellipticity of the basic flow (� ) and the direction of propagation of modes (ϑ). Our analytical predictions agree well with the numerical calculations.

Numerical Modeling of Biomass Pyrolysis—Heat and Mass Transport Models

We consider the pyrolysis of robinia pseudoacacia, which is a common material for biomass gasifiers. We formulate three models of the process, with increasingly detailed physics, best suited for different spatial scales from large to small. For each model, we perform numerical simulations of adaptable complexity and compare the results with the thermogravimetric analysis (TGA) experiments.

Theoretical and Experimental Characterization of the Ultrafast Aircraft Thermometer: Reduction of Aerodynamic Disturbances and Signal Processing

Abstract The ultrafast aircraft thermometer, built for measuring temperature in clouds at flight speeds up to 100 m s−1, employs a 2.5-μm-thick platinum-coated tungsten wire as a sensing element. When temperature increases, the wire resistance increases. The changes are amplified by an electronic system. Temperature measurements made in a wind tunnel and during flights show noise that is related to the von Karman vortex street generated behind the shield that protects the sensing element against the impact of cloud droplets. To reduce both the level of turbulence and the amount of water collected on the shield, suction is applied through the slits in its sides. The effect of suction on the flow field is twofold. First, at the Reynolds numbers that the thermometer is operated suction eliminates aerodynamic disturbances. Second, suction diverts the inner part of the boundary layer into the slit. This inner part is a region of strong shear and, therefore, a region where intensive viscous heating takes place....

Numerical simulations of industrial-scale combustion chamber - LES versus RANS

In this work we focus on the simulation of the process of biomass syngas combustion in the industrial combustion chamber directly linked with gasification chamber, where this gas is continuously producing from the biomass. Conflicting demands from the engineers to have rapid results and hints how to ensure the best conditions for combustion of this particular fuel and to lower the emission of pollutants, with simultaneously deep view inside the process and its stability motivates us to use both the RANS and LES techniques of turbulence modelling, compare it and take their advantages. We designed and performed series of 3D numerical simulations of both cold flow and combustion in complex geometry of industrial burner. It seems to us that the proper approach for modelling of biomass syngas combustion is steady flamelets model. Simulations performed with RANS closure are used as the initialisation of LES models, but their main goal is to predict the long-time oscillation of pressure and temperature observed in the working combustion chamber. On the other hand the main goal of the simulations with LES closure is to predict the proper level of short-time behaviour of the flame and local phenomena.

A class of solutions of the Einstein–Maxwell equations

We present all the exact solutions of the Einstein–Maxwell equations for a special case of the Robinson–Trautman metric form. Gaussian curvature of the angularlike part of the chosen metric form is equal to zero. The solutions are of the Petrov types D or II. Eight of them are probably new.

Pyrolysis and gasification of single biomass particle – new openFoam solver

We present a new solver biomassGasificationFoam that extended the functionalities of the well-supported open-source CFD code OpenFOAM. The main goal of this development is to provide a comprehensive computational environment for a wide range of applications involving reacting gases and solids. The biomassGasificationFoam is an integrated solver capable of modelling thermal conversion, including evaporation, pyrolysis, gasification, and combustion, of various solid materials. In the paper we show that the gas is hotter than the solid except at the centre of the sample, where the temperature of the solid is higher. This effect is expected because the thermal conductivity of the porous matrix of the solid phase is higher than the thermal conductivity of the gases. This effect, which cannot be considered if thermal equilibrium between the gas and solid is assumed, leads to precise description of heat transfer into wood particles.

Vortex motion in a weak background shear flow

A point vortex is introduced into a weak background vorticity gradient at finite Reynolds number. As the vortex spreads viscously so the background vorticity becomes wrapped around it, leading to enhanced diffusion of vorticity, but also giving a feedback on the vortex and causing it to move. This is investigated in the linear approximation, using a similarity solution for the advection of weak vorticity around the vortex, at finite and infinite Reynolds number. A logarithmic divergence in the far field requires the introduction of an outer length scale L and asymptotic matching. In this way results are obtained for the motion of a vortex in a weak vorticity field modulated on the large scale L and these are confirmed by means of numerical simulations.