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  • 1.
    Holmberg, N.A.
    et al.
    Luleå tekniska universitet.
    Åkerstedt, Hans
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Analysis of the motion of a flat jet in a direct strip casting feeding system1998In: Steel Research International, ISSN 1611-3683, E-ISSN 1869-344X, Vol. 69, no 1, p. 17-21Article in journal (Refereed)
    Abstract [en]

    The motion and shape of a vertically falling flat rectangular jet of liquid metal issuing from an inclined plane is analysed numerically and analytically. The jet is affected by surface tension and gravity. The main interest in this problem originates from the technological application of the direct strip casting process, which is a novel process to cast steel strips in a thickness range from 2 to 15 mm with a minimum or no hot-rolling. In this process the liquid metal is fed onto a single endless horizontal belt that runs between two rollers. The bottom of the belt is cooled by water. One of the techniques to feed the liquid metal is down an inclined plane Due to disturbances in the flow, for instance slag in the liquid metal, the jet issuing from the inclined plane may split into two or several jets. The large convergence of the individual jets causes an unfavourable non uniform distribution of the liquid metal over the belt. In the analysis of the present paper it is shown, using an expansion in the inverse Froude number, that the convergence of a single jet depends to zero order on the inverse square root of the Weber number We'[l/2]= (y/(p[wo][2] lt))[1/2]. Small convergence of the jet is found for large Weber numbers, which can be accomplished with a large initial velocity w[o].

  • 2.
    Holmstedt, Elise
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Åkerstedt, Hans
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Lundström, Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Högberg, Sofie
    Sandvik Materials Technology.
    Modeling Transport and Deposition Efficiency of Oblate and Prolate Nano- and Micro-particles in a Virtual Model of the Human Airway2016In: Journal of Fluids Engineering - Trancactions of The ASME, ISSN 0098-2202, E-ISSN 1528-901X, Vol. 138, no 8, article id 81203Article in journal (Refereed)
    Abstract [en]

    A model for the motion and deposition of oblate and prolate spheroids in the nano- and microscale was developed. The aim was to mimic the environment of the human lung, but the model is general and can be applied for different flows and geometries for small nonspherical particle Stokes and Reynolds numbers. A study of the motion and orientation of a single oblate and prolate particle has been done yielding that Brownian motion disturbs the Jeffery orbits for small particles. Prolate microparticles still display distinguishable orbits while oblate particles of the same size do not. A statistical study was done comparing the deposition efficiencies of oblate and prolate spheroids of different size and aspect ratio observing that smaller particles have higher deposition rate for lower aspect ratio while larger particles have higher deposition rates for large aspect ratio.

  • 3.
    Holmstedt, Elise
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Åkerstedt, Hans O.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Lundström, Staffan T.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Modelling transport and deposition of non-spherical micro- and nano-particles in composites manufacturing2018In: Journal of reinforced plastics and composites (Print), ISSN 0731-6844, E-ISSN 1530-7964, Vol. 37, no 8, p. 507-519Article in journal (Refereed)
    Abstract [en]

    In liquid moulding processes, a fabric is impregnated with a fluid that may contain particles aimed at giving the final product additional and possible smart properties. It is therefore interesting to be able to reveal how the distribution and orientation of such particles are affected by the processing condition. During the manufacturing of the fabric, relatively large channels are formed between bundles of fibres where the impregnating fluid may flow. There are also micro-channels within the bundle that are impregnated by the fluid in the larger channels mainly by capillary action. With focus on fibre bundles along the main flow direction, three main stages of the flow are the flow is leading within the bundles, the flow is moving at equal rate within the bundles and between them and the flow is leading in the channels between the bundles. The latter one of these is in focus in this study, and the capillary action from the larger channels to the micro-channels is modelled as a constant radial velocity. Brownian, gravitational and hydrodynamic forces acting on the particles are studied. The introduction of a radial velocity component drastically increases the deposition rate, and it is clear that while particle shape has a great influence on deposition rates in a flow moving strictly in the direction of the channel, when a radial flow component is introduced the differences seem to disappear.

  • 4.
    Holmstedt, Elise
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Åkerstedt, Hans O.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Lundström, T. Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Simulation of the movements and deposition rates of oblate and prolate nano- and microparticles in a virtual model of the human airways2014Conference paper (Refereed)
  • 5. Högberg, Sofie
    et al.
    Åkerstedt, Hans
    Lundström, Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Deposition av nanopartiklar i luftvägarna: analys med CFD2007In: Svenska Mekanikdagar 2007: Program och abstracts / [ed] Niklas Davidsson; Elianne Wassvik, Luleå: Luleå tekniska universitet, 2007, p. 125-Conference paper (Other academic)
  • 6. Högberg, Sofie
    et al.
    Åkerstedt, Hans
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Lundström, Staffan
    Nanoparticle transport and deposition in human lung2009In: Interdisciplinary transport phenomena: fluid, thermal, biological, materials, and space sciences ; [result of a conference entitled "Interdisciplinary Transport Phenomena V: Fluid, Thermal, Biological, Materials, and Space Sciences", held on October 14 - 19, 2007 in Bansko, Bulgaria], Boston, Mass.: Blackwell Munksgaard, 2009, p. ITP-07-17-Chapter in book (Refereed)
    Abstract [en]

    Transport and deposition properties of micro- and nanoparticles in human lung are of great importance in health risk assessments on potentially toxic matter, such as carbon nanotubes. The risks largely depend on the extent of exposure; thus if effects upon inhalation are considered, it is crucial to clarify the differences in transport mechanics between nano- and microparticles. In this work, we examined deposition properties of spherical particles (r = 1950 kg/m3), 15 nm - 50 mm in diameter, in a multiply bifurcated asymmetric 3D model, extending from trachea to the segmental bronchi. Steady, laminar flow was studied for inhalation flow rates of 0.1 and 0.5 l/s, and Computational Fluid Dynamics was used for analysis. Most 50 mm particles were captured near the first bifurcation, whereas particles 1-10 mm were less efficiently, but more uniformly, deposited. The nanoparticles essentially followed the streamlines, unaffected of the deposition mechanisms modeled. Deposition efficiency for microparticles was in the same order of magnitude as reported in previously published work when regarded on generation level, except in trachea. Our model added new information by predicting distribution of deposited particles in every bifurcation unit (two daughter branches and preceding transition zone), and site of deposition was more or less affected by geometric asymmetry. In conclusion, our results indicate that nanoparticle deposition is negligible in the larger airways, thus transport to the distal airways can be assumed extensive. Further, distribution of deposited particles was influenced by the airway asymmetry. However, more work and validating experiments are required before the model can be used as a tool in particle risk assessments.

  • 7. Högberg, Sofie
    et al.
    Åkerstedt, Hans
    Lundström, Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Nanoparticle transport and deposition in the large conducting airways using CFD2006In: Proceedings of the International Conference on Nanotechnology Occupational and Environmental Health and Safety: Research to Practice, 2006Conference paper (Refereed)
  • 8. Högberg, Sofie
    et al.
    Åkerstedt, Hans
    Lundström, Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Freund, Jonathan
    University of Illinois at Urbana-Champaign.
    Numerical model for fiber transport and deposition in the respiratory airways2008In: 2008 AAAR Annual Conference Abstracts, American Association for Aerosol Research , 2008Conference paper (Other academic)
    Abstract [en]

    Health hazards associated with inhalation of toxic particles depend on the extent of exposure. Thus, knowledge of transport and deposition properties of aerosol particles in lung flows is essential. Spherical particles may potentially cause adverse health effects when inhaled, and fibers may cause additional harm due to their specific shape. Asbestos is a well-known example of hazardous fibrous materials, and more recently this has also called for concern on the extended use of nanotubes. A numerical model is developed for transport and deposition of fibrous particles in the respiratory airways. Fibers are represented by prolate spheroids, and expressions from Jeffery(1922) are used for the fluid dynamic torque. Transport of non-spherical particles includes both translational and rotational motion. In the past, Euler angles have frequently been used to describe the resulting fiber orientation, but the Euler angles bring problems with singular terms for certain angles and thus are not suited for rigid motion simulations for fibers undergoing full rotations. Here, the evolvement of fiber orientation with time is calculated with quaternions, which have well-behaved equations of motion. The model is valid for arbitrary Stokes flows at low particle concentrations. Forces included are fluid dynamic drag, gravity and Brownian diffusion, making the model applicable for fibers with diameters ranging from nano- to microscale. Results so far show that fibers with larger aspect ratios are transported further before being deposited on the airway walls. This implies that the potential for a fiber to reach the distal airways increases with increased fiber aspect ratio, regardless of particle size.

  • 9. Högberg, Sofie
    et al.
    Åkerstedt, Hans
    Lundström, Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Freund, Jonathan
    University of Illinois at Urbana-Champaign.
    Numerical model for fiber transport in the respiratory airways2008In: Proceedings of the 19th International Symposium on Transport Phenomena (ISTP-19): Reykjavik, Iceland, August 17-21, 2008 / [ed] Sigurdur Brynjolfsson; Olafur Petur Palsson; Jong H. Kim, University of Iceland, Faculty of Industrial Engineering, Mechanical Engineering and Computer Science , 2008Conference paper (Refereed)
    Abstract [en]

    A numerical model is developed for fiber transport in the respiratory airways. Fibers are represented by prolate spheroids and fiber orientation is computed with quaternions. The model is valid for arbitrary Stokes flows at low particle concentrations. Forces included are fluid dynamic drag, gravity and Brownian diffusion, making the model applicable for fibers with diameters ranging from nano- to microscale. The results suggest that the potential for a fiber to reach the distal airways increases with increased fiber aspect ratio, regardless of particle size.

  • 10. Högberg, Sofie
    et al.
    Åkerstedt, Hans O.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Holmstedt, Elise
    Lundström, T. Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Sandström, Thomas
    Umeå universitet.
    Time-dependent deposition of micro- and nanofibers in straight model airways2012In: Journal of Fluids Engineering - Trancactions of The ASME, ISSN 0098-2202, E-ISSN 1528-901X, Vol. 134, no 5, p. 051208-1Article in journal (Refereed)
    Abstract [en]

    In this paper, we increase the understanding of the influence of the breathing pattern on the fate of inhaled non-spherical micro and nanoparticles and examine the accuracy of replacing the cyclic flow field with a quasi-steady flow. This is done with new analysis and numerical simulations on straight model airways using a previously developed discrete model for fiber motion. For the conditions studied, maximum deposition is obtained when fibers are released at the start of the inspiratory cycle, and minimum is received at the peak of inhalation. A quasi-steady solution generally provides a relatively good approximation to cyclic flow if an average velocity over one residence time of the particles moving with the mean fluid velocity is used. For a batch type, supply of particles deposition is favored in light activity breathing as compared to heavy breathing and the inclusion of a short pause after the inhalation results in an increased deposition in the terminal bronchiole. During zero-flow over the time of a breathing pause, spherical 10 nm particles experience considerable deposition in the distal airways, whereas only a few percent of larger and/ or fibrous nanoparticles were deposited. Hence, size and shape are crucial variables for deposition for no flow conditions. Common for all breathing parameters examined was that minimum deposition was obtained for the spherical 1 µm-particles and the fibrous 100 nm-particles. The former is expected from studies on spherical particles, and the latter is in agreement with results from a recent publication on steady inspiration.

  • 11. Högberg, Sofie
    et al.
    Åkerstedt, Hans O.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Lundström, Staffan
    Deposition av nanofibrer i rör motsvarande luftvägarna2009In: Svenska mekanikdagarna: Södertälje 2009, Stockholm: Svenska nationalkommittén för mekanik , 2009, p. 92-Conference paper (Other academic)
  • 12.
    Högberg, Sofie
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics.
    Åkerstedt, Hans O.
    Lundström, Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Freund, Jonathan
    University of Illinois at Urbana-Champaign.
    Respiratory deposition of fibers in the non-inertial regime: development and application of a semi-analytical model2010In: Aerosol Science and Technology, ISSN 0278-6826, E-ISSN 1521-7388, Vol. 44, no 10, p. 847-860Article in journal (Refereed)
    Abstract [en]

    A semi-analytical model describing the motion of fibrous particles ranging from nano- to micro scale was developed, and some important differences in respiratory tract transport and deposition between fibrous particles of various sizes and shapes were elucidated. The aim of this work was to gain information regarding health risks associated with inhalation exposure to small fibers such as carbon nanotubes. The model, however, is general in the sense that it can be applied to arbitrary flows and geometries at small fiber Stokes and Reynolds numbers. Deposition due to gravitational settling, Brownian motion and interception was considered, and results were presented for steady, laminar, fully developed parabolic flow in straight airways. Regarding particle size, our model shows that decrease in particle size leads to reduced efficiency of sedimentation but increased intensity of Brownian diffusion, as expected. We studied the effects due to particle shape alone by varying the aspect ratios and diameters of the microfibers simultaneously, such that the effect of particle mass does not come into play. Our model suggests that deposition both due to gravitational settling and Brownian diffusion decreases with increased fiber aspect ratio. Regarding the combined effect of fiber size and shape, our results suggest that for particles with elongated shape the probability of reaching the vulnerable gas-exchange region in the deep lung is highest for particles with diameters in the size range 10-100 nm and lengths of several micrometers. Note that the popular multi-walled carbon nanotubes fall into this size-range

  • 13.
    Jansson, Ida
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Åkerstedt, Hans
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    The dynamics of cylinder in a confined swirling flow with constant vorticity2015In: European journal of mechanics. B, Fluids, ISSN 0997-7546, E-ISSN 1873-7390, Vol. 54, p. 98-104Article in journal (Refereed)
    Abstract [en]

    In this work, we present a rigid body dynamics model that accounts for phenomena earlier studied both within hydrodynamic stability theory and the area of fluid-induced vibrations. The model captures the transverse dynamics of a rigid cylinder in a confined swirling flow. We show that a linear inviscid stability analysis of the whole system with respect to two-dimensional disturbances could be decomposed intoa solution governing rotational disturbances with homogeneous boundary conditions and a solution governing irrotational disturbances with inhomogeneous boundary conditions. This implies that the continuous stable spectrum of rotational disturbances is unchanged by the supposition of a free boundary. Moreover, the time-dependence of irrotational disturbances is governed by the disturbance of the rigid cylinder. Consequently, a rigid body dynamics model suffices to determine the time evolutionof irrotational disturbances. The model is based on the definition of a merged homogeneous state in which the solid mass of the rigid cylinder equals the displaced fluid mass and the flow is in solid body rotation. A departure from this merged homogeneous state yields an imbalance of the fictitious Coriolis and centrifugal force of the rigid cylinder and the counterbalancing motion-induced fluid forces. Thisimbalance makes the fluid flow support propagation of waves and may render a concentric position of the body unstable. A non-uniform distribution of the angular velocity delays the onset of instability so that the rigid cylinder can maintain a concentric position even though it is denser than the fluid.

  • 14.
    Jansson, Ida
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Åkerstedt, Hans O.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Hur en cylinders egensvängningar beror av en omgivande fluids rörelse2011Conference paper (Refereed)
  • 15.
    Jansson, Ida
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Åkerstedt, Hans O.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Aidanpää, Jan-Olov
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Lundström, T. Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    The effect of inertia and angular momentum of a fluid annulus on lateral transversal rotor vibrations2012In: Journal of Fluids and Structures, ISSN 0889-9746, E-ISSN 1095-8622, Vol. 28, p. 328-342Article in journal (Refereed)
    Abstract [en]

    An extensive amount of work exists on experimental and theoretical analysis of unsteady flow phenomena in hydraulic turbines. Still, resonance phenomena and self-excited vibrations of the rotor of hydropower machines are not considered as a major problem during normal operation conditions. Nevertheless, in development and research it is not sufficient to rely on earlier experience. An accurate predictive rotor model is crucial in risk assessment of rotor vibrations of hydraulic generator units. This paper discusses the effects of inertia and the rotational energy of the fluid in the turbine on lateral transversal shaft vibrations of hydraulic generator units. There is a lack of agreement among engineers upon how fluid inertia of the turbine should be included in rotor models. The rotational energy of the fluid has a potential risk of feeding self-excited vibrations. A fluid-rotor model is presented that captures the effect of inertia and angular momentum of a fluid annulus on vibrations of an inner rigid cylinder. The purpose of the model is to gain physical understanding of the phenomena at work and it is not applicable to specific turbines. The linearized equation of motion of the cylinder surrounded by a fluid annulus is solved for by one single complex equation. The constrained cylinder has two degrees of freedom in the plane perpendicular to its axis. By the assumption of irrotational cyclic flow, the fluid motion is described by a complex potential function. The motion of the cylinder is described by three parameters. Two surfaces are defined that splits the parameter space into regions with different qualitative behaviour. One surface defines the limit of stability whereas the other defines a limit when the eigenvalues have opposite signs or are both positive. The response to an external periodic rotating force is visualized by the magnitude of the inverse of the complex dynamic stiffness.

  • 16.
    Jansson, Ida
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Åkerstedt, Hans O.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Lundström, Staffan
    Aidanpää, Jan-Olov
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Fluidinducerade reaktionskrafter för vertikalaxlade vattenkraftturbiner och dess betydelse för axelns laterala egensvängningar2009In: Svenska mekanikdagarna: Södertälje 2009, Stockholm: Svenska nationalkommittén för mekanik , 2009, p. 97-Conference paper (Other academic)
  • 17.
    Löfgren, Hans B.
    et al.
    Luleå tekniska universitet.
    Åkerstedt, Hans
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Damping mechanisms of perturbations in electromagnetically braked horizontal film flows2000In: Fluid Dynamics Research, ISSN 0169-5983, E-ISSN 1873-7005, Vol. 26, no 1, p. 53-68Article in journal (Refereed)
    Abstract [en]

    The stability of shear and surface modes in an electromagnetically braked free surface liquid metal flow over a horizontally moving boundary is considered. The main objective is to investigate the stabilizing effect of a transverse magnetic field of the film flow appearing in connection with the horizontal belt strip casting. The flow is two-dimensional and the upper boundary is a free surface. In the stability analysis the film flow is approximated as parallel and is therefore based on the MHD-modified Orr-Sommerfeld equation. Numerical calculations present the linear growth rate for shear and surface mode instabilities. A transverse magnetic field is found to have two damping mechanisms. For low Hartmann numbers the main mechanism is due to the braking of the flow, reducing the shear stress. The other mechanism is due to dissipation by the Joule effect.

  • 18.
    Löfgren, Hans B.
    et al.
    Luleå tekniska universitet.
    Åkerstedt, Hans
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Electromagnetic braking of the flow of a liquid metal with a free surface1998In: Fluid Dynamics Research, ISSN 0169-5983, E-ISSN 1873-7005, Vol. 23, no 1, p. 1-25Article in journal (Refereed)
    Abstract [en]

    The electromagnetic braking of liquid metal flowing over a moving boundary is considered. The flow is two dimensional and the upper boundary is a free surface. The main interest of this flow originates from the application of horizontal belt strip casting. In this process, the liquid metal is fed onto a single endless horizontal belt that runs between two rollers. The bottom of the belt is cooled by water and the liquid is fed onto the belt through a slit. This results in a flow that can be modelled as a flat free jet impinging onto a horizontally moving boundary. The flow after the impingement region is analysed using the boundary layer equations. Here, the flow depends on the Reynolds number R, the Froude number F, the Hartman number M, and the ratio of the belt velocity to jet velocity, β. For βF-2/3, there is no hydraulic jump and the film thickness grows smoothly into the final state with constant thickness and uniform velocity. The braking length for the case without hydraulic jump is shown to be of order O(F2/3Ra/2) without magnetic field and of order O(M-2Ra/2) with magnetic field, where a is the jet width. Thus, the magnetic field decreases the braking distance considerably. This result is favourable for both the stability of the flow and for the solidification process in the horizontal belt strip casting process.

  • 19.
    Löfgren, Hans B.
    et al.
    Luleå tekniska universitet.
    Åkerstedt, Hans
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Initial solidification in liquid metal film flow over a moving bondary2001In: International Journal of Heat and Mass Transfer, ISSN 0017-9310, E-ISSN 1879-2189, Vol. 44, no 4, p. 837-842Article in journal (Refereed)
    Abstract [en]

    The initial solidification problem of a two-dimensional liquid metal film flow over a heat extracting moving boundary is studied. Analytical solutions in the limit of large Peclet numbers are found. It is shown that the point of initial solidification depends on the Peclet number, the Biot number and the superheat. The initial growth of the solidified phase is found to have a quadratic dependence of the distance from the point of initial solidification. The results are applicable to continuous strip casters.

  • 20.
    Löfgren, Hans B.
    et al.
    Luleå tekniska universitet.
    Åkerstedt, Hans
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    The laminar stagnation-point flow against a solidifying moving shell2000In: Acta Mechanica, ISSN 0001-5970, E-ISSN 1619-6937, Vol. 142, no 1-4, p. 33-46Article in journal (Refereed)
    Abstract [en]

    This paper considers the two-dimensional laminar stagnation-point flow due to a jet impinging onto a solidifying moving boundary. The flow is of interest in connection with the horizontal belt strip casting process. An exact solution to the Navier-Stokes equations is found that is shown to depend on a single ordinary differential equation. The solution is useful in the study of morphological and hydrodynamic instabilities within the impingement region. Solutions for the steady-state shape of the initial stages as well as the asymptotic behavior of the solidifying interface are also discussed in a perturbative manner.

  • 21.
    Nycander, J.
    et al.
    National Defence Research Establishment.
    Pavlenko, V.P.
    Department of Technology, Euratom–NFR Fusion Association, Uppsala University.
    Åkerstedt, Hans O.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Response to ``Comment on `Three-dimensional stability of drift vortices'1996In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 3, no 11, p. 4292-Article in journal (Other academic)
  • 22.
    Westerberg, Lars-Göran
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Vedin, Jörgen
    Umeå university.
    Ekenbäck, Andreas
    Swedish Institute of Space Physics / Institutet för rymdfysik.
    Åkerstedt, Hans
    Three-dimensional flow near a reconnection site at the dayside magnetopause: analytical solutions coupled with MHD simulations: 3D solar wind flow2007In: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 73, no 6, p. 811-819Article in journal (Refereed)
    Abstract [en]

    We present a coupling between an analytical three-dimensional model covering the plasma flow behaviour through the magnetopause transition layer near a reconnection site, with results from a global MHD simulation describing the plasma flow in the magnetosheath. The structure of the plasma flow near a reconnection site at the dayside terrestrial magnetopause is investigated, together with the development of the magnetopause transition region.

  • 23.
    Westerberg, Lars-Göran
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Åkerstedt, Hans
    Hall effects on the steady structure of the rotational layer at the dayside magnetopause2007In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 14Article in journal (Refereed)
    Abstract [en]

    The influence of the Hall term in the generalized Ohm's law on the large-scale plasma flow during conditions of ongoing magnetic reconnection at the dayside magnetopause (MP) is investigated. Of special interest is the plasma flow behavior during the transition of the MP transition layer as the Hall effect grows in proportion to the viscous-resistive effects. The governing equations are solved approximately by an ordinary perturbation expansion in orders of large Reynolds and Lundqvist numbers. It is shown that the flow pattern is strongly dependent on the magnitude of the Hall parameter; as it approaches zero, the viscous-resistive solution is obtained, while for an ordering of the same magnitude as the resistivity/viscosity, the Hall effect begins to affect the flow structure severely. For an increasing value on the Hall parameter, oscillations are brought into the system, an effect that is enhanced with the magnitude of the Hall parameter. Furthermore, it is shown that as the Hall effect begins to dominate, the transition layer thickens.

  • 24.
    Westerberg, Lars-Göran
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Åkerstedt, Hans
    Modeling of solar wind transport into the terrestrial magnetosphere2008In: Proceedings of the 19th International Symposium on Transport Phenomena (ISTP-19): Reykjavik, Iceland, August 17-21, 2008 / [ed] Sigurdur Brynjolfsson; Olafur Petur Palsson; Jong H. Kim, University of Iceland, Faculty of Industrial Engineering, Mechanical Engineering and Computer Science , 2008Conference paper (Refereed)
    Abstract [en]

    In this study we have combined a 2D viscous/resistive reconnection model of the plasma flow through the magnetopause boundary, with solutions for the outer magnetosheath flow based on the same methodology as by Petschek in his classical model treating fast magnetic reconnection. The objective is to put the 2D model into the context of a well established reconnection model, and also to investigate the influence of the reconnection process onto the magnetosheath flow. The ideal MHD equations governing the magnetosheath flow; Ohm's law, the MHD equation of motion, and the divergence free property of the magnetic field and the plasma velocity, are solved approximately using an expansion along uniform fields. Considering solutions up to the order O(E) for the outer magnetosheath flow, we obtain a class of solutions which are matched with the 2D viscous/resistive solutions in the transition layer. It is shown that a Petschek-like solution is obtained when the velocity gradient and the uniform velocity is zero. Having non-zero values on these parameters dramatically changes the topology of the magnetic field line- and plasma streamline pattern. The reconnection rate is also modified substantially, leading to a shut off when the velocity reaches the Alfvén velocity.

  • 25.
    Westerberg, Lars-Göran
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Åkerstedt, Hans
    Solar wind flow near a reconnection site at the dayside magnetopause: development of an existing three-dimensional model2007In: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 73, no 2, p. 145-151Article in journal (Other academic)
    Abstract [en]

    An improvement of an existing three-dimensional analytical model describing the solar wind flow near a reconnection site at the dayside magnetopause is reported. Introducing an arbitrary orientation of the reconnection line, general solutions for the plasma velocity and magnetic field during the transition of the magnetopause are presented, together with the development of the magnetopause transition layer away from the reconnection site.

  • 26. Westerberg, Lars-Göran
    et al.
    Åkerstedt, Hans
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Nilsson, Hans
    Swedish Institute of Space Physics / Institutet för rymdfysik.
    Solar wind flow near a reconnection site at the dayside magnetopause: cluster multi-spacecraft observations coupled with a three-dimensional theoretical analysis2006Conference paper (Other academic)
  • 27.
    Westerberg, Lars-Göran
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Åkerstedt, Hans
    Nilsson, Hans
    Swedish Institute of Space Physics / Institutet för rymdfysik.
    Rème, Henri
    CESR, Toulouse.
    Balogh, Andre
    Imperial College.
    3D MHD reconnection model coupled with Cluster multi-spacecraft data: 3D reconnection model2008In: Journal of Geophysical Research, ISSN 0148-0227, E-ISSN 2156-2202, Vol. 113Article in journal (Refereed)
    Abstract [en]

    We present a model where a three-dimensional viscous/resistive analytical model of the large scale plasma flow in the outflow region about a reconnection site at the dayside magnetopause, is coupled with multi-spacecraft measurements from the Cluster satellite armada. A total of ten magnetopause crossings have been analyzed during the period 10:29-11:05 UT January 26, 2001, where nine are shown to be suitable to be coupled with the analytical model. Five of these nine reconnection events results in a successful coupling. By fitting the analytical expressions of the plasma velocity and magnetic field behaviour during the transition of the magnetopause, with data from the Cluster spacecraft we obtain estimates of the location of the X-line together with estimates on the anomalous transport coeffcients of kinematic viscosity (v) and magnetic diffusivity (ηd). We also obtain the development of the magnetopause transition layer away from the X-line. It is shown that the distance from the spacecraft to the X-line varies between 0.01 and 1 Earth radii, while v + ηd have a value between 4 . 104 km2/ s and 4 . 106 km2/ s. Furthermore it is shown that the transition layer thickness follows the analytical pattern where it grows proportional to the square root of the distance from the reconnection site. The estimated thickness obtained from each spacecraft is shown to follow the analytical structure well.

  • 28.
    Westerberg, Lars-Göran
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Åkerstedt, Hans O.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics.
    2D solutions to the compressible solar wind flow near a reconnection site at the dayside magnetopause2005In: Neue Wege der Multiphysik Simulation: FEMLAB Konferenz 2005 ; 02. - 04. November 2005, Arabella Sheraton Grand Hotel, Frankfurt ; proceedings, Göttingen: FEMLAB , 2005Conference paper (Refereed)
  • 29.
    Westerberg, Lars-Göran
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Åkerstedt, Hans O.
    A three-dimensional analysis of the flow past an open terrestrial magnetopause2006In: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 72, no 3, p. 359-382Article in journal (Refereed)
    Abstract [en]

    We present a three-dimensional analysis covering an investigation of the behavior of the magnetosheath plasma velocity and the magnetic field during the transfer from the magnetosheath to the magnetosphere. magnetic reconnection is assumed to occur at an arbitrary line parallel to the $y$-axis, located in a region along the magnetopause stretching from the sub-solar point to the north. we do not focus on the process itself, but on its implications for the plasma flow and the magnetic field outside the diffusion region. viscosity and resistivity are included in the magnetohydrodynamic equation of motion as non-ideal effects. the governing equations are solved approximately using the method of asymptotic expansions, with expansion in orders of large reynolds and lundquist numbers. we present two classes of solutions describing the properties north and south of the reconnection line, respectively. results are presented for two locations of the reconnection line at distances of two and seven earth radii from the sub-solar point correspondingly. it is shown that the velocity increases faster north of the reconnection line, and that the effect intensifies as the location of the reconnection line moves further away from the sub-solar point. it is also shown for this case, that there is less variation of the magnetic field and an increase in the field strength.

  • 30.
    Westerberg, Lars-Göran
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Åkerstedt, Hans O.
    A two dimensional analysis of the compressible flow near a reconnection site at the dayside magnetopause2007In: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 73, no 1, p. 89-115Article in journal (Refereed)
    Abstract [en]

    An improvement of an existing three-dimensional analytical model describing the solar wind flow near a reconnection site at the dayside magnetopause is reported. Introducing an arbitrary orientation of the reconnection line, general solutions for the plasma velocity and magnetic field during the transition of the magnetopause are presented, together with the development of the magnetopause transition layer away from the reconnection site.

  • 31.
    Westerberg, Lars-Göran
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Åkerstedt, Hans O.
    A two-dimensional analysis of the flow past an open terrestrial magnetopause2005In: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 71, no 5, p. 537-562Article in journal (Refereed)
    Abstract [en]

    A study of the two-dimensional incompressible flow of the solar wind past an open terrestrial magnetosphere is presented. The plasma is described by the magnetohydrodynamic (MHD) equations including non-ideal effects such as resistivity and viscosity. The theoretical analysis is based on an ordinary perturbation technique with expansion in orders of large Reynolds and Lundqvist numbers. Magnetic reconnection is assumed to occur at an arbitrary point along a region of the magnetopause, stretching from the sub-solar point to the north. From the analysis we find analytical solutions describing the transition layers north and south of a reconnection point. It is shown that the transition layer north of the reconnection point is thinner than the layer on the south side. It is also shown that in order for steady reconnection to occur, the velocity at the reconnection point must be less than the Alfvén velocity. Using the method of matched asymptotic expansions, we match the transition layer solution with a potential flow solution describing the flow and magnetic field in the exterior magnetosheath.

  • 32.
    Westerberg, Lars-Göran
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Åkerstedt, Hans
    Taavola, J. Henric
    Effects of varying magnetosheath flow and dissipation on the two-dimensional reconnection structure at the magnetopause2009In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 16, no 5, p. 052902-1Article in journal (Refereed)
    Abstract [en]

    The stationary Riemann problem including dissipation in form of resistivity and viscosity for the reconnection structure at the dayside magnetopause is considered. Including tangential velocity shear and gradients across the complete reconnection structure from the magnetosheath side into the magnetosphere, it is shown how dissipation affects the thickness of the intermediate shock wave in the vicinity of a reconnection site. We present how plasma flow structure undergoes a significant change for a nonzero uniform plasma velocity and velocity gradient. It is also shown how the reconnection rate changes and leads to a cutoff when the velocity becomes Alfvénic.

  • 33. Åkerstedt, Hans
    Analytic solutions of a fourth-order differential equation with a second-order turning point1989In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 30, no 2, p. 343-344Article in journal (Refereed)
    Abstract [en]

    Analytic solutions of a certain fourth-order differential equation with a second-order turning point are given. The solutions can be expressed in terms of products of the well-known parabolic-cylinder functions, and the equation might therefore be useful as a comparison equation in the theory of asymptotic expansions of ordinary differential equations.

  • 34. Åkerstedt, Hans
    Corrigendum1989In: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 42, p. 531-532Article in journal (Other academic)
  • 35.
    Åkerstedt, Hans
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Damping of transient energy growth of three-dimensional perturbations in hydromagnetic pipe flow1995In: Fluid Dynamics Research, ISSN 0169-5983, E-ISSN 1873-7005, Vol. 15, no 5, p. 295-312Article in journal (Refereed)
    Abstract [en]

    The stability of infinitesimal three-dimensional perturbations in hydromagnetic pipe flow where the applied magnetic field is in the streamwise direction is considered. The study is limited to the case of small magnetic Reynolds numbers and the main objective of the paper is to study the transient evolution of the kinetic energy. A general effect of the magnetic field is to increase the damping of the eigenvalues of the individual perturbation modes. For the case of infinitely long perturbations, which in the non-magnetic case has been found to have the largest transient growth, the magnetic field perturbations are decoupled from the flow and there is no effect on the stability properties of the flow. For shorter waves, and for moderate values of the interaction parameter (I = RmA2 ≈ 1-3) the hydromagnetic damping effect on the transient energy growth is, however, substantial, especially for small azimuthal mode numbers n. (Here Rm is the magnetic Reynolds number and A is the Alfvén number.) This parameter range has been found in experiments to give significantly higher transitional Reynolds numbers (Fraim and Heiser, 1968). Since the hydromagnetic damping effect is weak for long waves and large for shorter waves, the implications of the results to ordinary pipe flow is that the energy growth found for short waves may be more crucial as a mechanism for transition than the corresponding growth for longer waves.

  • 36. Åkerstedt, Hans
    Drift-kinetic stability analysis of z–pinches1989In: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 41, no 41, p. 45-59Article in journal (Refereed)
  • 37. Åkerstedt, Hans
    The motion of a finite plasma slab across a transverse magnetic field1981In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 24, no 4, p. 775-784Article in journal (Refereed)
  • 38. Åkerstedt, Hans
    Velocity shear instabilition associated with plasma motion across a magnetic field1984In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 29, no 1, p. 75-86Article in journal (Refereed)
    Abstract [en]

    Velocity shear instabilition associated with plasma motion across a magnetic fie .a{background-color: #ffff88}.h{background-color: #ffff00}.b{background-color: #ccccff}.i{background-color: #3333ff}.c{background-color: #ffcccc}.j{background-color: #ff3333}.d{background-color: #bbffff}.k{background-color: #00ffff}.e{background-color: #ffdd77}.l{background-color: #ff6600}.f{background-color: #ccffaa}.m{background-color: #33ff00}.g{background-color: #ffccff}.n{background-color: #ff00ff} a:link {color: #0000ff} a.oa:link {color: #00a000} a:visited {color: #4000a0} a.oa:visited {color: #006666} a:hover {color: #ff0000} a.oa:hover {color: #cc33cc} The stability of stationary Vlasov equilibria simulating the motion of plasma across a transverse magnetic field has been analyzed. The stability analysis is based on the Vlasov-Poisson equations together with an assumption of finite larmor radius ordering. Especially the instabilities associated with velocity shear transitions separating plasmas moving in opposite directions have been considered. Two extreme cases of such velocity shear transitions are studied, one where the confining current is only due to ions and one where the containing current is only due to electrons.

  • 39.
    Åkerstedt, Hans
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Jansson, Ida
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    The stability of a flexibly mounted rotating cylinder in turbulent annular flow2015In: Journal of Fluids and Structures, ISSN 0889-9746, E-ISSN 1095-8622, Vol. 58, p. 152-172Article in journal (Refereed)
    Abstract [en]

    In this paper, we determine the inviscid linear stability with respect to two-dimensional disturbances of a fluid flow between two concentric cylinders. The inner rigid cylinder rotates with the angular velocity Ω0 and is fixed on elastic hinges at each end in the transverse direction. The outer cylinder does not rotate and is rigidly fixed. We assume that the fluid flow has an inner core that rotates as a solid body with angular velocity Ω0/2 and outside the core there are turbulent boundary layers. The velocity profile of the turbulent boundary layers satisfies the viscous Camassa−Holm equations. The perturbed fluid flow is derived from Rayleigh’s equation. The analysis yields an equation of motion of the cylinder equivalent to previous work without boundary layers and a basic flow of constant angular vorticity. The analysis is not restricted to a small gap between the cylinders. The results are compared with the results by Antunes et al. (1996), who consider a similar problem with uniform velocity profile and the limit of small gap. For ρc/ρf<1ρc/ρf<1 the results disagree in that the present analysis shows stability whereas Antunes et al. find instability. For ρc/ρf>1ρc/ρf>1 both theories predict stability and for larger values of ρc/ρfρc/ρf the agreement is good especially for small gap.

  • 40.
    Åkerstedt, Hans
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Lundström, Staffan
    Högberg, Sofie
    Electrostatic filtration of air-borne nano-particles2007In: Journal of Nanostructured Polymers and Nanocomposites, ISSN 1790-4439, Vol. 3, no 4, p. 111-115Article in journal (Other academic)
    Abstract [en]

    Due to potential danger of nanoparticles for human health it is necessary to have control of their motion in air. Mechanical filtering is tricky since the particles are very small and alternative means to guide and collect them, need to be developed. Hence, in this paper clusters of carbon nanotubes are allowed to move through an electrical field generated by two parallel electrodes and it is shown that the tubes are strongly affected by this field and move swiftly towards the electrodes. Once hitting one of them most of the clusters leave towards the other electrode, the procedure is repeated and very few particles are collected. By putting an electrically insulating layer on one plate the particles however get stuck. This implies that the method investigated is an efficient method to collect air-borne carbon nanotubes

  • 41.
    Åkerstedt, Hans O.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Deposition of charged nano-particles in the human airways including effects from cartilaginous rings2011In: Natural Science, ISSN 2150-4091, E-ISSN 2150-4105, Vol. 3, no 10, p. 885-888Article in journal (Refereed)
    Abstract [en]

    This paper presents a numerical study of the deposition of spherical charged nano-particles caused by convection, Brownian diffusion and electrostatics in a pipe with a cartilaginous ring structure. The model describes the deposition of charged particles in the different generations of the tracheobronchial tree of the human lung. The upper airways are characterized by a certain wall structure called cartilaginous rings which modify the particle deposition when compared to an airway with a smooth wall. The problem is defined by solving Naver-Stokes equations in combination with a convective-diffusion equation and Gauss law for electrostatics. Three non- dimensional parameters describe the problem, the Peclet number Pe = 2ūa/D , the Reynolds number Re = ūa/v and an electrostatic parameter α=α2c0q2/(4ε0κT) . Here U is the mean velocity, a the pipe radius and D the diffusion coefficient due to Brownian motion given by D=κTCu/3πμd , where Cu is the Cunningham-factor Cu=1+λ/d(2.34+1.05exp(-0.39d/λ)) Here d is the particle diameter and λ the mean free path of the air molecules. Results are provided for generations G4-G16 of the human airways. The electrostatic parameter is varied to model different concentrations and charge numbers

  • 42.
    Åkerstedt, Hans O.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Deposition of submicron charged particles in turbulent pipe flow with an application to trachea2018In: The International Journal of Multiphysics, ISSN 1750-9548, E-ISSN 2048-3961, Vol. 12, no 1, p. 9-25Article in journal (Refereed)
    Abstract [en]

    The paper presents a study of the deposition of submicron charged spherical particles caused by convection, Brownian and turbulent diffusion in a pipe with a smooth wall and with a cartilaginous ring wall structure. The model is supposed to describe deposition of charged particles in generation 0 (trachea) of the human respiratory airways. The flow is modeled with a SST-turbulence model combined with a convective-diffusion equation including electric field migration for the particles, and Poisson’s equation for the determination of the electrostatic potential in terms of the space-charge density of the particles. An approximate analytical solution is derived for the case of a smooth pipe which is used to verify the numerical solutions obtained from using the commercial software Comsol Multiphysics. Numerical results of deposition rates are also provided for the case of a pipe with a cartilaginous ring wall structure.

  • 43. Åkerstedt, Hans O.
    Finite larmor radius effects on the stability properties of internal modes of a Z-pinch1988In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 37, no 1, p. 117-130Article in journal (Refereed)
    Abstract [en]

    From the Vlasov-fluid model a set of approximate stability equations describing the stability of a cylindrically symmetric z-pinch is derived. The equations are derived in the limit of small gyroradius and include first order kinetic effects such as finite ion Larmor radius effects and resonant ion effects. Neglecting the resonant ion terms, we explicitly solve this set of equations for a constant current density profile leading to a dispersion relation. FLR effects are shown for the case of m = 1 internal mode to be stabilizing and for large wavenumbers k, using a trial function approach, absolute stabilization is found.

  • 44. Åkerstedt, Hans O.
    Gyrokinetic stability theory of z–pinches1990In: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 44, p. 137-149Article in journal (Refereed)
    Abstract [en]

    From the Vlasov-fluid model a set of approximate stability equations describing the stability of the pure z–pinch is derived. The equations are valid for equilibria with small gyroradius compared with the pinch radius, but the perturbation wavenumber k may be of the order of the gyroradius ρi, δ = kρi = 0(1) - so-called gyrokinetic ordering. The equations are used to study the stability of the m = 0 and m = 1 internal modes of the z–pinch. In the limit of zero gyroradius δ → 0 we recover previously obtained results. For δ ≠ 0 we find that increasing δ at first gives a rapidly decreasing growth rate, and for δ ≈ l the growth rate compared with perpendicular MHD is γ/γMHD ≈ 0·09. For larger δ however, the growth rate increases to a quite large value. For the m = O mode we find, provided that drift resonances can be neglected, a stability criterion for δ ≥ 1, which is fulfilled both for the Bennett equilibrium and the constant-current-density equilibrium.

  • 45. Åkerstedt, Hans O.
    Kinetic effects on the ideal Alfvén continuum1990In: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 44, p. 507-516Article in journal (Refereed)
    Abstract [en]

    Kinetic effects such as those of finite Larmor radius (FLR) and. wave–particle resonances on the ideal Alfvén-wave continuum in a z-pinch geometry are investigated. The effect of FLR increases the order of the equations and is therefore treated as a singular perturbation. Similar eigenvalue curves are found as for the case when the non-ideal effect is resistivity, with a bifurcation of a global-mode branch into a boundary-mode branch and an internal-mode branch.

  • 46. Åkerstedt, Hans O.
    Some kinetic equilibria and their stability1985Doctoral thesis, comprehensive summary (Other academic)
  • 47.
    Åkerstedt, Hans O.
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Eller, Sebastian
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Lundström, Staffan T.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Numerical Investigation of Turbulent Flow through Rectangular and Biconvex Shaped Trash Racks2017In: Engineering, ISSN 1947-3931, E-ISSN 1947-394X, Vol. 9, no 5, p. 412-426, article id 76642Article in journal (Refereed)
    Abstract [en]

    Turbulent flow through a trash rack of bars of rectangular and biconvex shapes is considered. A trash rack is composed of an array of bars fitted into a hydro-electric power station to prevent debris and fish to enter the waterway towards the turbine. The work is directed towards modeling a large number of bars for which the flow turn out to have a periodic structure. It is here shown that this case can be simplified with the flow past a single bar together with periodic boundary conditions. Using this approach the head loss is derived for different angles of attack α and blockages P for two shapes of the rack, a rectangular bar and an aerodynamically shaped biconvex bar. It is found that overall loss of the biconvex bars is in general about 15% of the loss for the rectangular case for small angles of attack. For large angle of attack this difference diminishes. Of interest for the biconvex bars is also a local minimum in the head loss for angles approximately greater than 20˚ and for a blockage P around 0.35. This combination of parameters gives a low loss together with an efficient barrier for debris and fishes.

  • 48.
    Åkerstedt, Hans O.
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Högberg, Sofie
    Lundström, Staffan
    Sandström, Tomas
    Umeå universitet.
    The effect of cartilaginous rings on particle deposition by convection and Brownian diffusion2010In: Natural Science, ISSN 2150-4091, E-ISSN 2150-4105, Vol. 2, no 7, p. 769-779Article in journal (Refereed)
    Abstract [en]

    A finite volume method for the numerical solution of viscoelastic flows is given. The flow of a differential upper-convected Maxwell (UCM) fluid through a contraction channel has been chosen as a prototype example. The conservation and constitutive equations are solved using the finite volume method (FVM) in a staggered grid with an upwind scheme for the viscoelastic stresses and a hybrid scheme for the velocities. An enhanced-in-speed pressure-correction algorithm is used and a method for handling the source term in the momentum equations is employed. Improved accuracy is achieved by a special discretization of the boundary conditions. Stable solutions are obtained for higher Weissenberg number (We), further extending the range of simulations with the FVM. Numerical results show the viscoelasticity of polymer solutions is the main factor influencing the sweep efficiency.

  • 49.
    Åkerstedt, Hans O.
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Högberg, Sofie
    Lundström, T. Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics.
    An asymptotic approach of Brownian deposition of nanofibres in pipe flow2013In: Theoretical and Computational Fluid Dynamics, ISSN 0935-4964, E-ISSN 1432-2250, Vol. 27, no 5, p. 561-575Article in journal (Refereed)
    Abstract [en]

    An asymptotic approach is considered for the transport and deposition of nanofibres in pipe flow. Convection and Brownian diffusion are included, and Brownian diffusion is assumed to be the dominant mechanism. The fibre position and orientation are modelled with a probability density function for which the governing equation is a Fokker-Planck equation. The focus is set on dilute fibres concentrations implying that interaction between individual fibres is neglected. At the entrance of the pipe, a fully developed velocity profile is set and it is assumed that the fibres enter the pipe with a completely random orientation and position. A small parameter {Mathematical expression} is introduced, where l is the fibre half-length and a is the pipe radius. The probability density function is expanded for small {Mathematical expression} and the solution turns out to be multi-structured with three areas, consisting of one outer solution and two boundary layers. For the deposition of fibres on the wall, it is found that for parabolic flow, and for the lowest order, the deposition can be obtained with a simplified angle averaged convective-diffusion equation. It is suggested that this simplification is valid also for more complex flows like when the inflow boundary condition yields a developing velocity profile and flows within more intricate geometries than here studied. With the model fibre, deposition rates in human respiratory airways are derived. The results obtained compare relatively well with those obtained with a previously published model

  • 50.
    Åkerstedt, Hans O.
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Löfgren, Hans B
    Luleå tekniska universitet.
    Free surface magnetohydrodynamic flow with solidification2003In: European journal of mechanics. B, Fluids, ISSN 0997-7546, E-ISSN 1873-7390, Vol. 22, no 6, p. 581-601Article in journal (Refereed)
    Abstract [en]

    The paper considers an analysis of a liquid metal flow, occurring in the horizontal belt strip casting process. The liquid metal flows over a moving copper belt with a growing solidifying phase beneath the melt. The effect of applying a transverse magnetic field is investigated. A set of three-dimensional shallow water equations is derived. Supercritical flow is assumed and the shallow water equations are solved numerically using a shock-capturing method, which automatically takes care of the possibility of oblique hydraulic jumps.It is shown that non-uniform conditions introduced in the feeding region give a pattern of steady hydraulic jumps, which propagate downstream and are reflected at the sidewalls. The effect of the magnetic field is to brake the flow and damp the standing hydraulic jump pattern. Different feeding methods are compared and it is shown that the magnetic field erases the initial differences in liquid distribution using different feeding techniques

12 1 - 50 of 51
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