Konrad Bajer - Academia.edu (original) (raw)
Papers by Konrad Bajer
Journal of Fluid Mechanics, 1990
The low Reynolds number flow between two concentric steadily rotating spheres is considered. The ... more The low Reynolds number flow between two concentric steadily rotating spheres is considered. The pattern of streamlines is explained in terms of an adiabatic invariant. It is shown that, when the two rotation vectors are not parallel, the streamlines become chaotic when the Reynolds number Re is increased and the onset of global chaos occurs near Re = 20.
Journal of Fluid Mechanics, 1997
Experiments and numerical simulations of fully developed turbulence reveal the existence of elong... more Experiments and numerical simulations of fully developed turbulence reveal the existence of elongated vortices whose length is of the order of the integral scale of turbulence while the diameter is somewhere between the Kolmogorov scale and the Taylor microscale. These vortices are embedded in quasi-irrotational background flow whose straining action counteracts viscous decay and determines their cross-sectional shape. In the present paper we analyse the effect of a stretched vortex of this kind on a uni-directional magnetic flux tube aligned with vorticity in an electrically conducting fluid. When the magnetic Prandtl number is large, P m & 1, the field is concentrated in a flux tube which, like the vortex itself, has elliptical cross-section inclined at 45 • to the principal axes of strain. We focus on the limit P m 1 when the magnetic flux tube has radial extent much larger than that of the vortex, which appears like a point vortex as regards its action on the flux tube. We find the steady-state solution valid in the entire plane outside the vortex core. The solution shows that the magnetic field has a logarithmic spiral component and no definite orientation of the inner contours. Such magnetized vortices may be expected to exist in MHD turbulence with weak magnetic field where the field shows a tendency to align itself with vorticity. Magnetized vortices may also be expected to exist on the solar surface near the corners of convection cells where downwelling swirling flow tends to concentrate the magnetic field.
We develop an asymptotic theory of the steady state of a rectilinear vortex in linear straning fl... more We develop an asymptotic theory of the steady state of a rectilinear vortex in linear straning flow. In the special case of axisymmetric strain the solution is the familiar Burgers vortex. In the more general, non-axisymmetric situation the asymptotic theories were developed for low Reynolds number (Robinson & Saffman 1984) and for high Reynolds number (Moffatt, Kida & Ohkitani 1994). In the present paper we develop a new expansion in the parameter X which characterises the departure from axisymmetry. Hence we obtain an expansion valid uniformly for all Reynolds numbers and thus bridgeing the gap between the low and the high Reynolds number theories. In practice the new expansion is useful when the nonaxisymetric deformation of the vortex is not too large.
Journal of Physics: Conference Series, 2011
ABSTRACT A new auxiliary clear-air turbulence (CAT) predictor based on a triggering mechanism for... more ABSTRACT A new auxiliary clear-air turbulence (CAT) predictor based on a triggering mechanism for clear-air turbulence, namely short (500m-20000m) gravity waves excited by shallow convection is considered. Case studies are presented in which the predictor is compared with other widely used CAT indices. One case is based on NWP (numerical weather prediction) model and other on on real sounding. Also comparison of real life sounding results with model generated ones is performed.
The ultrafast aircraft thermometer is an airborne device designed for measuring temperature in cl... more The ultrafast aircraft thermometer is an airborne device designed for measuring temperature in clouds with centimeter spatial resolution. Its sensor consists of 5mm long and 2.5μm thick thermo-resistive wire protected against impact of cloud droplets by a shield in the form of a suitably shaped rod, placed upstream. However the disturbances of airflow around this rod result in noise in the temperature record. Suction applied through slits located on both sides of the rod reduces the noise generated by vortices shed from the rod and lowers the probability of droplet-wire collisions. Our recent theoretical analysis and numerical simulations led to optimization of this device and additionally clarified the role of the sampling method in processing of the analogue output of the thermometer. In this paper we try to deepen our understanding of the nature of the noise as well as to improve calculations of the corrections connected with the dynamic heating. For this purpose we have done extensive three-dimensional numerical simulations of the airflow around the protective rod and the sensing wire, which permitted precise computation of dynamic heating and showed how applying the suction removes the thermal boundary layer from the rod and damps the sources of the noise.
Journal of Atmospheric and Oceanic Technology, 2005
We modeled damaged-irradiated carbon plasma facing component PFCs by graphite surfaces with vacan... more We modeled damaged-irradiated carbon plasma facing component PFCs by graphite surfaces with vacancies. We combined theoretical and experimental investigations with a view to building tools to make a better assignment of the observed defects from the scanning tunneling microscope (STM) images. The theoretical part of this work is based on periodic density functional theory calculations. The electronic structure is calculated and the density of state along with the electronic density near the Fermi level are plotted. STM images are further simulated and their features are interpreted. On the experimental side, we performed scanning tunneling microscopy (STM) imaging at low bias voltage in order to probe the electronic modifications of the graphite surface induced either by H + (or D + ) ion bombardment and/or atomic H (respectively D) adsorption. A connection between STM images and the reactivity of defective graphite surfaces towards H is also proposed.
Small-scale inhomogeneities of the atmospheric temperature field are caused by air turbulence and... more Small-scale inhomogeneities of the atmospheric temperature field are caused by air turbulence and result in refractive index fluctuations, which in turn influence the propagation of optical beams. Understanding small density fluctuations in the atmosphere is important for the free-space laser communication and for high-resolution imaging through the atmosphere. The ultra-fast aircraft resistance thermometer constructed in the Institute of Geophysics, Warsaw University, measures the temperature of cloudless air and of warm clouds with 10 kHz sampling frequency. During a flight at the speed of 100 m/s, at low altitudes up to 2 km, this corresponds to the spatial resolution of the order of one centimeter. This resolution is sufficient for studying small density fluctuations in the atmospheric boundary layer. A streamlined shield protects the sensing wire of the thermometer from cloud droplets and other small particles suspended in the air but introduce aerodynamic disturbances in the form of vortices. The thermometer records the resulting fluctuations of temperature as noise. The shield sucks air and water collected on its surface through the suction slits. This suction also suppresses the disturbances. In this paper we analyze how the temperature measurements are influenced by: (i) turbulence generated behind the shield placed in front of the sensing wire; (ii) suction of air through the shield slits; (iii) cloud droplets of various space distributions, masses and velocities. We have carried out the 2D numerical simulations of the time-dependent, incompressible, viscous flow (the Navier-Stokes equation) around the shield placed in a uniform stream. We solved the particle path equations for an ensamble of droplets in the Stokes approximation. All the simulations are oriented toward optimization of the shield shape in order to (i) reduce noise in measurements at low and high altitudes and (ii) protect the sensing wire against ice crystals in flights at high altitudes.
Journal of Physics: Conference Series, 2011
ABSTRACT The PDF contains the preface and other editorial material.
Journal of Physics: Conference Series, 2011
ABSTRACT In this work we focus on the simulation of the process of biomass syngas combustion in t... more ABSTRACT 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.
Journal of Physics: Conference Series, 2011
ABSTRACT Simulations of the chemically reacting mixing layer were performed. Especially the early... more ABSTRACT Simulations of the chemically reacting mixing layer were performed. Especially the early stage of the flow transition, when the coherent Kelvin-Helmholtz vortices can be recognized, was studied. This is a physical problem of great importance in many industrial and environmental systems. Simple passive reaction of the second order is considered. Its effective rate is analysed for different values of the Damköhler number. The results are compared to the case of the steady, laminar shear flow. It is found that slow and fast reactions respond in different ways to the fluctuations of the reactant concentration. Faster reactions appeared to be much more sensitive to the character of mixing. Moreover a buffer layer of product of fast reactions forms in the system and separates the substrates what influence the effective reaction rate.
Journal of Fluid Mechanics, 1990
The low Reynolds number flow between two concentric steadily rotating spheres is considered. The ... more The low Reynolds number flow between two concentric steadily rotating spheres is considered. The pattern of streamlines is explained in terms of an adiabatic invariant. It is shown that, when the two rotation vectors are not parallel, the streamlines become chaotic when the Reynolds number Re is increased and the onset of global chaos occurs near Re = 20.
Journal of Fluid Mechanics, 1997
Experiments and numerical simulations of fully developed turbulence reveal the existence of elong... more Experiments and numerical simulations of fully developed turbulence reveal the existence of elongated vortices whose length is of the order of the integral scale of turbulence while the diameter is somewhere between the Kolmogorov scale and the Taylor microscale. These vortices are embedded in quasi-irrotational background flow whose straining action counteracts viscous decay and determines their cross-sectional shape. In the present paper we analyse the effect of a stretched vortex of this kind on a uni-directional magnetic flux tube aligned with vorticity in an electrically conducting fluid. When the magnetic Prandtl number is large, P m & 1, the field is concentrated in a flux tube which, like the vortex itself, has elliptical cross-section inclined at 45 • to the principal axes of strain. We focus on the limit P m 1 when the magnetic flux tube has radial extent much larger than that of the vortex, which appears like a point vortex as regards its action on the flux tube. We find the steady-state solution valid in the entire plane outside the vortex core. The solution shows that the magnetic field has a logarithmic spiral component and no definite orientation of the inner contours. Such magnetized vortices may be expected to exist in MHD turbulence with weak magnetic field where the field shows a tendency to align itself with vorticity. Magnetized vortices may also be expected to exist on the solar surface near the corners of convection cells where downwelling swirling flow tends to concentrate the magnetic field.
We develop an asymptotic theory of the steady state of a rectilinear vortex in linear straning fl... more We develop an asymptotic theory of the steady state of a rectilinear vortex in linear straning flow. In the special case of axisymmetric strain the solution is the familiar Burgers vortex. In the more general, non-axisymmetric situation the asymptotic theories were developed for low Reynolds number (Robinson & Saffman 1984) and for high Reynolds number (Moffatt, Kida & Ohkitani 1994). In the present paper we develop a new expansion in the parameter X which characterises the departure from axisymmetry. Hence we obtain an expansion valid uniformly for all Reynolds numbers and thus bridgeing the gap between the low and the high Reynolds number theories. In practice the new expansion is useful when the nonaxisymetric deformation of the vortex is not too large.
Journal of Physics: Conference Series, 2011
ABSTRACT A new auxiliary clear-air turbulence (CAT) predictor based on a triggering mechanism for... more ABSTRACT A new auxiliary clear-air turbulence (CAT) predictor based on a triggering mechanism for clear-air turbulence, namely short (500m-20000m) gravity waves excited by shallow convection is considered. Case studies are presented in which the predictor is compared with other widely used CAT indices. One case is based on NWP (numerical weather prediction) model and other on on real sounding. Also comparison of real life sounding results with model generated ones is performed.
The ultrafast aircraft thermometer is an airborne device designed for measuring temperature in cl... more The ultrafast aircraft thermometer is an airborne device designed for measuring temperature in clouds with centimeter spatial resolution. Its sensor consists of 5mm long and 2.5μm thick thermo-resistive wire protected against impact of cloud droplets by a shield in the form of a suitably shaped rod, placed upstream. However the disturbances of airflow around this rod result in noise in the temperature record. Suction applied through slits located on both sides of the rod reduces the noise generated by vortices shed from the rod and lowers the probability of droplet-wire collisions. Our recent theoretical analysis and numerical simulations led to optimization of this device and additionally clarified the role of the sampling method in processing of the analogue output of the thermometer. In this paper we try to deepen our understanding of the nature of the noise as well as to improve calculations of the corrections connected with the dynamic heating. For this purpose we have done extensive three-dimensional numerical simulations of the airflow around the protective rod and the sensing wire, which permitted precise computation of dynamic heating and showed how applying the suction removes the thermal boundary layer from the rod and damps the sources of the noise.
Journal of Atmospheric and Oceanic Technology, 2005
We modeled damaged-irradiated carbon plasma facing component PFCs by graphite surfaces with vacan... more We modeled damaged-irradiated carbon plasma facing component PFCs by graphite surfaces with vacancies. We combined theoretical and experimental investigations with a view to building tools to make a better assignment of the observed defects from the scanning tunneling microscope (STM) images. The theoretical part of this work is based on periodic density functional theory calculations. The electronic structure is calculated and the density of state along with the electronic density near the Fermi level are plotted. STM images are further simulated and their features are interpreted. On the experimental side, we performed scanning tunneling microscopy (STM) imaging at low bias voltage in order to probe the electronic modifications of the graphite surface induced either by H + (or D + ) ion bombardment and/or atomic H (respectively D) adsorption. A connection between STM images and the reactivity of defective graphite surfaces towards H is also proposed.
Small-scale inhomogeneities of the atmospheric temperature field are caused by air turbulence and... more Small-scale inhomogeneities of the atmospheric temperature field are caused by air turbulence and result in refractive index fluctuations, which in turn influence the propagation of optical beams. Understanding small density fluctuations in the atmosphere is important for the free-space laser communication and for high-resolution imaging through the atmosphere. The ultra-fast aircraft resistance thermometer constructed in the Institute of Geophysics, Warsaw University, measures the temperature of cloudless air and of warm clouds with 10 kHz sampling frequency. During a flight at the speed of 100 m/s, at low altitudes up to 2 km, this corresponds to the spatial resolution of the order of one centimeter. This resolution is sufficient for studying small density fluctuations in the atmospheric boundary layer. A streamlined shield protects the sensing wire of the thermometer from cloud droplets and other small particles suspended in the air but introduce aerodynamic disturbances in the form of vortices. The thermometer records the resulting fluctuations of temperature as noise. The shield sucks air and water collected on its surface through the suction slits. This suction also suppresses the disturbances. In this paper we analyze how the temperature measurements are influenced by: (i) turbulence generated behind the shield placed in front of the sensing wire; (ii) suction of air through the shield slits; (iii) cloud droplets of various space distributions, masses and velocities. We have carried out the 2D numerical simulations of the time-dependent, incompressible, viscous flow (the Navier-Stokes equation) around the shield placed in a uniform stream. We solved the particle path equations for an ensamble of droplets in the Stokes approximation. All the simulations are oriented toward optimization of the shield shape in order to (i) reduce noise in measurements at low and high altitudes and (ii) protect the sensing wire against ice crystals in flights at high altitudes.
Journal of Physics: Conference Series, 2011
ABSTRACT The PDF contains the preface and other editorial material.
Journal of Physics: Conference Series, 2011
ABSTRACT In this work we focus on the simulation of the process of biomass syngas combustion in t... more ABSTRACT 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.
Journal of Physics: Conference Series, 2011
ABSTRACT Simulations of the chemically reacting mixing layer were performed. Especially the early... more ABSTRACT Simulations of the chemically reacting mixing layer were performed. Especially the early stage of the flow transition, when the coherent Kelvin-Helmholtz vortices can be recognized, was studied. This is a physical problem of great importance in many industrial and environmental systems. Simple passive reaction of the second order is considered. Its effective rate is analysed for different values of the Damköhler number. The results are compared to the case of the steady, laminar shear flow. It is found that slow and fast reactions respond in different ways to the fluctuations of the reactant concentration. Faster reactions appeared to be much more sensitive to the character of mixing. Moreover a buffer layer of product of fast reactions forms in the system and separates the substrates what influence the effective reaction rate.