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- Lintzén, Nina, 1978-
(författare)
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Properties of snow with applications related to climate change and skiing
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Snow has been a subject of research since the mid-20th century. Research on mechanical properties of snow started as an off-shoot of soil mechanics, where methods, tools and instruments used often are the same. However, during the last decades the winter business industry has been growing requiring a number of new fields of research. The aim with this PhD thesis is to investigate and contribute to solutions of some of the new research problems appearing in this area. Machine-made snow is commonly used for buildings and artwork of snow. Only minor scientific studies of machine-made snow and its properties have been published. Therefore, mechanical properties of machine-made snow were investigated. Strength and deformation properties were evaluated through uniaxial compressive tests where cylindrical test specimens were subjected to different constant deformation rates. Creep deformation, bending strength and ultimate load were also evaluated through beam tests. The results showed that the deformation rate is crucial if the snow will deform plastically or if brittle failure will occur. The grain size and structure of the snow had a strong influence on the strength properties. Snow is a constantly changing material with a large variety of grain sizes and shapes. Therefore it is of importance to classify snow. Classication of snow can be done using different methods depending on the property that is to be investigated. Several non-contact detection methods to evaluate snow properties exist. In this thesis, spectral reflectance measurements were performed to investigate liquid water content in snow using two different systems, a spectrometer and an optical sensor called Road Eye. The Road Eye sensor was also used to classify snow in cross-country ski tracks. This method enables a fast classication of a complete track where different types of snow can be distinguished. The properties of a ski track and the characteristics of the snow determine the type of skis that should be selected for optimum sliding properties. Cross-country skis have different mechanical properties, which to a large extent can be evaluated from the span curve of the ski. Depending on the skiing style, the skier's skills, terrain and track conditions different ski properties are required, which is particularly important for competitive skiing. Span curves of cross-country skis were measured using a digital instrument called Skiselector. Results from the investigations showed that skis within the same pair may have signicantly different properties. Moreover, temperature influences the span curve and thus the mechanical properties of the skis. Therefore, skis should be measured at a temperature close to where they are aimed to be used. Field tests of skis with similar span curves but different ski base topography were tested during wet and cold snow conditions. The results indicate that different topographies are preferable during different snow conditions. Due to the climate change, winters have become shorter and warmer with less natural snow. To compensate for the lack of natural snow, ski resorts and other stakeholders produce machinemade snow in order to run their business. Storing snow in insulated piles is an alternative and sometimes a complement to snow production. Studies on stored snow show that the surface area of the pile should be minimized in order to reduce the melt rate. Furthermore, the pileshould be covered with a suciently thick insulating layer, preferably with good evaporation properties. Theoretical calculations can be used to estimate the amount of snow that melts and to predict the efficiency of different materials as thermal insulation on snow. These calculations coincide well with experiments performed in northern Sweden where snow melt was measured. This PhD thesis consists of five publications and an introduction to this area which in particular puts these publications into a more general frame.
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| 2. |
- Tsandzana, Afonso Fernando, 1969-
(författare)
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Homogenization of some new mathematical models in lubrication theory
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We consider mathematical modeling of thin film flow between two rough surfaces which are in relative motion. For example such flows take place in different kinds of bearings and gears when a lubricant is used to reduce friction and wear between the surfaces. The mathematical foundations of lubrication theory is given by the Navier--Stokes equation, which describes the motion of viscous fluids. In thin domains several approximations are possible which lead to the so called Reynolds equation. This equation is crucial to describe the pressure in the lubricant film. When the pressure is found it is possible to predict vorous important physical quantities such as friction (stresses on the bounding surfaces), load carrying capacity and velocity field.In hydrodynamic lubrication the effect of surface roughness is not negligible, because in practical situations the amplitude of the surface roughness are of the same order as the film thickness. Moreover, a perfectly smooth surface does not exist in reality due to imperfections in the manufacturing process. Therefore, any realistic lubrication model should account for the effects of surface roughness. This implies that the mathematical modeling leads to partial differential equations with coefficients that will oscillate rapidly in space and time. A direct numerical computation is therefore very difficult, since an extremely dense mesh is needed to resolve the oscillations due to the surface roughness. A natural approach is to do some type of averaging.In this PhD thesis we use and develop modern homogenization theory to be able to handle the questions above. Especially, we use, develop and apply the method based on the multiple scale expansions and two-scale convergence. The thesis is based on five papers (A-E), with an appendix to paper A, and an extensive introduction, which puts these publications in a larger context.In Paper A the connection between the Stokes equation and the Reynolds equation is investigated. More precisely, the asymptotic behavior as both the film thickness and wavelength of the roughness tend to zero is analyzed and described. Three different limit equations are derived. Time-dependent equations of Reynolds type are obtained in all three cases (Stokes roughness, Reynolds roughness and high frequency roughness regime). In paper C we extend the work done in Paper A where we compare the roughness regimes by numeric computations for the stationary case.In paper B we present a mathematical model that takes into account cavitation, surfaces roughness and compressibility of the fluid. We compute the homogenized coefficients in the case of unidirectional roughness.In the paper D we derive a mathematical model of thin film flow between two close rough surfaces, which takes into account cavitation, surface roughness and pressure dependent density. Moreover, we use two-scale convergence to homogenize the model. Finally, in paper E we prove the existence of solutions to a frequently used mathematical model of thin film flow, which takes cavitation into account.
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