Fluid dynamics considers the physics of liquids and gases. This is a branch of classical physics and is totally based on Newton's laws of motion. Nevertheless, the equation of fluid motion, Navier-Stokes equation, becomes very complicated to solve even for very simple configurations. This thesis treats mainly analytical vortex solutions to Navier-Stokes equations. Vorticity is usually concentrated to smaller regions of the flow, sometimes isolated objects, called vortices. If one are able to describe vortex structures exactly, important information about the flow properties are obtained. Initially, the modeling of a conical vortex geometry is considered. The results are compared with wind-tunnel measurements, which have been analyzed in detail. The conical vortex is a very interesting phenomenaon for building engineers because it is responsible for very low pressures on buildings with flat roofs. Secondly, a suggested analytical solution to Navier-Stokes equation for internal flows is presented. This is based on physical argumentation concerning the vorticity production at solid boundaries. Also, to obtain the desired result, Navier-Stokes equation is reformulated and integrated. In addition, a model for required information of vorticity production at boundaries is proposed. The last part of the thesis concerns the examples of vortex models in 2-D and 3-D. In both cases, analysis of the Navier-Stokes equation, leads to the opportunity to construct linear solutions. The 2-D studies are, by the use of diffusive elementary vortices, describing experimentally observed vortex statistics and turbulent energy spectrums in stratified systems and in soapfilms. Finally, in the 3-D analysis, three examples of recent experimentally observed vortex objects are reproduced theoretically. First, coherent structures in a pipe flow is modeled. These vortex structures in the pipe are of interest since they appear for Re in the range where transition to turbulence is expected. The second example considers the motion in a viscous vortex ring. The model, with diffusive properties, describes the experimentally measured velocity field as well as the turbulent energy spectrum. Finally, a streched spiral vortex is analysed. A rather general vortex model that has many degrees of freedom is proposed, which also may be applied in other configurations.

Both experimental and numerical investigations of converging shock waves have been performed. In the experiments, a shock tube was used to create and study converging shock waves of various geometrical shapes. Two methods were used to create polygonally shaped shocks. In the first method, the geometry of the outer boundary of the test section of the shock tube was varied. Four different exchangeable shapes of the outer boundary were considered: a circle, a smooth pentagon, a heptagon, and an octagon. In the second method, an initially cylindrical shock wave was perturbed by metal cylinders placed in various patterns and positions inside the test section. For three or more regularly spaced cylinders, the resulting diffracted shock fronts formed polygonal shaped patterns near the point of focus. Regular reflection was observed for the case with three cylinders and Mach refection was observed for cases with four or more cylinders. When the shock wave is close to the center of convergence, light emission is observed. An experimental investigation of the light emission was conducted and results show that the shape of the shock wave close to the center of convergence has a large influence on the amount of emitted light. It was found that a symmetrical polygonal shock front produced more light than an asymmetrical shape. The shock wave focusing was also studied numerically using the Euler equations for a gas obeying the ideal gas law with constant specific heats. Two problems were analyzed; an axisymmetric model of the shock tube used in the experiments and a cylindrical shock wave diffracted by cylinders in a two dimensional test section. The results showed good agreement with the experiments. The temperature field from the numerical simulations was investigated and shows that the triple points behind the shock front are hot spots that increase the temperature at the center as they arrive there. As a practical example of shock wave focusing, converging shocks in an electrohydraulic lithotripter were simulated. The maximum radius of a gas bubble subjected to the pressure field obtained from the lithotripter was calculated and compared for various geometrical shapes and materials of the reflector. Results showed that the shape had a large impact while the material did not influence the maximum radius of the gas bubble. / QC 20100706

QC 20100726

A turbulent two-phase flow model using kinetic theory of granularflows for the particle phase is developed and implmented in afinite element code. The model can be used for engineeringapplications. However, in this thesis it is used to investigateturbulent gas-particle flows through numerical simulations.  The feedback from the particles on the turbulence and the meanflow of the gas in a vertical channel flow is studied. In particular,the influence of the particle response time, particle volumefraction and particle diameter on the preferential concentration ofthe particles near the walls, caused by the turbophoretic effect isexplored. The study shows that when particle feedback is includedthe accumulation of particles near the walls decreases. It is also foundthat even at low volume fractions particles can have a significant impacton the turbulence and the mean flow of the gas. The effect of particles on a developing turbulent vertical upward pipeflow is also studied. The development length is found to substantiallyincrease compared to an unladen flow. To understand what governs thedevelopment length a simple estimation was derived, showing that itincreases with decreasing particle diameters in accordance with themodel simulations. A model for the fluctuating particle velocity in turbulentgas-particle flow is derived using a set of stochastic differentialequations taking into account particle-particle collisions. Themodel shows that the particle fluctuating velocity increases whenparticle-particle collisions become more important and that increasingparticle response times reduces the fluctuating velocity. The modelcan also be used for an expansion of the deterministic model for theparticle kinetic energy. / QC20100726

This thesis presents models and simulations of dielectrophoretic separation of micro and nano particles. The fluid dynamics involved and the dielectric properties of water inside single-walled carbon nanotube are studied as well. Based on the effective dipole moment method, the particle dynamic model focuses on the translational motions of micro particles. The hydrodynamic force between the particles and the particle-particle electrostatic interactions are considered as well. By comparing the dimensionless parameters, the dominating force can be determined. Based on a simplified version of the particle dynamic model, two numerical simulations are carried out to predict the efficiency of dielectrophoretic separation of micro size particles. The first calculation suggests a strategy to improve the trapping efficiency of E.coli bacteria by applying superimposed AC electric fields. The second calculation discusses the concept of mobility and improves the separation rate of particles by a multi-step trapping-releasing dielectrophoresis strategy. The model is extended down scale to calculate the separation of metallic and semiconducting single-walled carbon nanotubes by the modified effective dipole moment method for prolate ellipsoids. The steeply changed gradient of electric field results in the local joule heating therefore creates gradient of dielectric properties in the solution. As a result, certain pattern of fluid flow with a considerable strength is created and affects the motion of carbon nanotubes especially close to the electrode gap, which indicates that the so-called electrothermal flow should be considered in designing the experiment to separate single-walled carbon canotubes. When the length scale of particles is comparable to that of the electrodes, the calculation of dielectrophoretic force by the effective dipole moment is considered not to be accurate since only the electric field in the center point is taken into account. Hence in the thesis a new method based on distributed induced charge is suggested. By approximating a straight slender body as a prolate ellipsoid, the electric field of multiple points along the centerline are all considered in the calculation and the interaction between particles could be concurrently taken care. This method is expected to be an improved method to calculate the dielectrophoretic force of rod-like virus, DNA, nanowires and carbon nanotubes. The dielectric property of water confined in carbon nanotubes is expected to be dramatically different from that of bulk water. The thesis also contains a molecular dynamics study to reveal the difference also a dependence on the diameter of carbon nanotubes. The results show that along the axial direction, both the static permittivity and the relaxation time are larger than the isotropic bulk water, and in the cross-section plane it is opposite. When the radius of the carbon nanotubes increases, the properties of water inside become closer to the bulk water. / QC 20100820

Simulation and modelling of turbulent flows under influence of streamline curvature and system rotation have been considered. Direct numerical simulations have been performed for fully developed rotating turbulent channel flow using a pseudo-spectral code. The rotation numbers considered are larger than unity. For the range of rotation numbers studied, an increase in rotation number has a damping effect on the turbulence. DNS-data obtained from previous simulations are used to perform a priori tests of different pressure-strain and dissipation rate models. Furthermore, the ideal behaviour of the coefficients of different model formulations is investigated. The main part of the modelling is focused on explicit algebraic Reynolds stress models (EARSMs). An EARSM based on a pressure strain rate model including terms that are tensorially nonlinear in the mean velocity gradients is proposed. The new model is tested for a number of flows including a high-lift aeronautics application. The linear extensions are demonstrated to have a significant effect on the predictions. Representation techniques for EARSMs based on incomplete sets of basis tensors are also considered. It is shown that a least-squares approach is favourable compared to the Galerkin method. The corresponding optimality aspects are considered and it is deduced that Galerkin based EARSMs are not optimal in a more strict sense. EARSMs derived with the least-squares method are, on the other hand, optimal in the sense that the error of the underlying implicit relation is minimized. It is further demonstrated that the predictions of the least-squares EARSMs are in significantly better agreement with the corresponding complete EARSMs when tested for fully developed rotating turbulent pipe flow. / QC 20100825

Boundary layer separation is an unwanted phenomenon in most technical applications, as for instance on airplane wings, ground vehicles and in internal flow systems. If separation occurs, it causes loss of lift, higher drag and energy losses. It is thus essential to develop methods to eliminate or delay separation.In the present experimental work streamwise vortices are introduced in turbulent boundary layers to transport higher momentum fluid towards the wall. This enables the boundary layer to stay attached at  larger pressure gradients. First the adverse pressure gradient (APG) separation bubbles that are to be eliminated are studied. It is shown that, independent of pressure gradient, the mean velocity defect profiles are self-similar when the scaling proposed by Zagarola and Smits is applied to the data. Then vortex pairs and arrays of vortices of different initial strength are studied in zero pressure gradient (ZPG). Vane-type vortex generators (VGs) are used to generate counter-rotating vortex pairs, and it is shown that the vortex core trajectories scale with the VG height h and the spanwise spacing of the blades. Also the streamwise evolution of the turbulent quantities scale with h. As the vortices are convected downstream they seem to move towards a equidistant state, where the distance from the vortex centres to the wall is half the spanwise distance between two vortices. Yawing the VGs up to 20° do not change the generated circulation of a VG pair. After the ZPG measurements, the VGs where applied in the APG mentioned above. It is shown that that the circulation needed to eliminate separation is nearly independent of the pressure gradient and that the streamwise position of the VG array relative to the separated region is not critical to the control effect. In a similar APG jet vortex generators (VGJs) are shown to as effective as the passive VGs. The ratio VR of jet velocity and test section inlet velocity is varied and a control effectiveness optimum is found for VR=5. At 40° yaw the VGJs have only lost approximately 20% of the control effect. For pulsed VGJs the pulsing frequency, the duty cycle and VR were varied. It was shown that to achieve maximum control effect the injected mass flow rate should be as large as possible, within an optimal range of jet VRs. For a given injected mass flow rate, the important parameter was shown to be the injection time t1. A non-dimensional injection time is defined as t1+ = t1Ujet/d, where d is the jet orifice diameter. Here, the optimal  t1+ was 100-200. / QC 20100825

This thesis deals with Large Eddy Simulation (LES) of impinging air jets. The impinging jet configuration features heated circular jets impinging onto a flat plate. The problem addressed here is of generic nature, with applications in many engineering devices, such as cooling of components in gas turbines, in cars and electronic devices. The flow is inherently unsteady and contains relatively slowly varying coherent structures. Therefore, LES is the method of choice when the Reynolds number is large enough to exclude Direct Numerical Simulations (DNS). The present LES model is a basic model without explicit Sub-Grid-Scale (SGS) modeling and without explicit filtering. Instead, the numerical scheme is used to account for the necessary amount of dissipation. By using the computational grid as a filter the cutoff wavenumber depends explicitly on the grid spacing. The underlying computational grid is staggered and constructed in a Cartesian coordinate system. Heat transfer is modeled by the transport equation for a passive scalar. This is possible due to the negligible influence of buoyancy which implies constant density throughout the flow field. The present method provides accurate results for simple geometries in an efficient manner. A great variety of inlet conditions have been considered in order to elucidate how the dynamics of the flow and heat transfer are affected. The considered studies include top-hat and mollified mean velocity profiles subjected to random and sinusoidal perturbations and top-hat profiles superimposed with solid body rotation. It has been found that the shape of the mean inlet velocity profile has a decisive influence on the development of the flow and scalar fields, whereas the characteristics of the imposed artificial disturbances (under consideration) have somewhat weaker effect. In order to obtain results unequivocally comparable to experimental data on turbulent impinging jets both space and time correlations of the inflow data must be considered, so also the spectral content. This is particularly important if the region of interest is close to the velocity inlet, i.e. for small nozzle-to-plate spacings. Within this work mainly small nozzle-toplate spacings are considered (within the range of 0.25 and 4 nozzle diameters), which emphasizes the importance of the inflow conditions. Thus, additional to the basic methods also turbulent inflow conditions, acquired from a precursor pipe simulation, have been examined. Both for swirling and non-swirling flows. This method emulates fully developed turbulent pipe flow conditions and is the best in the sense of being well defined, but it demands a great deal of computing power and is also rather inflexibility. In case of the basic randomly perturbed methods the top-hat approach has been found to produce results in closest agreement with those originating from turbulent inlet conditions. In the present simulations the growth of individual instability modes is clearly detected. The character of the instability is strongly influenced by the imposed boundary conditions. Due to the lack of correlation random superimposed fluctuations have only a weak influence on the developing flow field. The shape of the mean profile, on the other hand, influences both the growth rate and the frequency of the dominant modes. The top-hat profile yields a higher natural frequency than the mollified. Furthermore, for the top-hat profile coalescence of pairs of vortices takes place within the shear-layer of the axial jet, whereas for the mollified profile (for the considered degree of mollification) it takes place within the wall jet. This indicates that the transition process is delayed for smoother profiles. The amount of wall heat transfer is directly influenced by the character of the convective vortical structures. For the mollified cases wall heat transfer originates predominantly from the dynamics of discrete coherent structures. The influence from eddy structures is low and hence Reynolds analogy is applicable, at least in regions of attached flow. The top-hat and the turbulent inflow conditions yield a higher rate of incoherent small scale structures. This strongly affects the character of wall heat transfer. Also the applied level of swirl at the velocity inlet has significant influence on the rate of heat transfer. The turbulence level increases with swirl, which is positive for heat transfer, and so also the spreading of the jet. The latter effect has a negative influence on wall heat transfer, particularly in the center most regions. This however depends also on the details of the inflow data. / QC 20100831

The separating turbulent flow in a plane asymmetric diffuser with 8.5 degrees opening angle is investigated experimentally and computationally. The considered flow case is suitable for fundamental studies of separation, separation control and turbulence modelling. The flow case has been studied in a specially designed wind-tunnel under well controlled conditions. The average velocity and fluctuation fields have been mapped out with stereoscopic particle image velocimetry (PIV). Knowledge of all velocity components allows the study of several quantities of interest in turbulence modelling such as the turbulence kinetic energy, the turbulence anisotropy tensor and the turbulence production rate tensor. Pressures are measured through the diffuser. The measured data will form a reference database which can be used for evaluation of turbulence models and other computational investigations. Time-resolved stereoscopic PIV is used in an investigation of turbulence structures in the flow and their temporal evolution. A comparative study is made where the measured turbulence data are used to evaluate an explicit algebraic Reynolds stress turbulence model (EARSM). A discussion regarding the underlying reasons for the discrepancies found between the experimental and the model results is made. A model for investigations of separation suppression by means of vortex generating devices is presented together with results from the model in the plane asymmetric diffuser geometry. A short article on the importance of negative production-rates of turbulent kinetic energy for the reverse flow region in separated flows is presented. A detailed description of the experimental setup and PIV measurement procedures is given in a technical report. / QC 20100923

För ett genomsnittligt småhus i Sverige idag går ca 5000 kWh till hushållsel. Av dessa 5000 kWh går 7% till att driva diskmaskiner. Effektiviseringen av diskmaskiner har framförallt strävat efter en låg vatten- och energianvändning, en kort processtid samt en effektiv rening av disken. Det finns dock gränser för hur effektiva diskmaskinerna kan göras med traditionell teknik. Därför har producenter under de senaste åren börjat se sig om efter mindre traditionella metoder som till exempel bruket av en värmepump för att få ned energiförbrukningen. Syftet med det här examensarbetet har varit att ta fram systemlösningar för värmepump i diskmaskin samt att utvärdera energibesparingspotentialen i denna tillämpning. Målet har varit att ta fram och beskriva de möjliga systemlösningar som uppstår vid en idégenerering. Att välja ut två lösningar för närmare undersökning, att bestämma en lämplig kompressoreffekt samt att beräkna energibesparingen dessa lösningar ger. En litteraturstudie har gjorts av teknik och tillämpningar inom området, som till exempel värmeväxlaranvändning i diskmaskiner samt användandet av värmepumpar i andra vitvaror. Denna litteraturstudie följdes upp av en idégenerering, som tar hänsyn till möjliga värmekällor och –sänkor. Idégenereringen gav upphov till två systemlösningar som modellerades i MATLABs Simulink för att en lämplig kompressoreffekt och storleken på energibesparingen skulle bestämmas. De två utvalda lösningarna ifrån idégenereringen var utomhusluftlösningen, där värme hämtas från uteluften och energilagerlösningen, där värme hämtas ur ett energilager. I båda lösningarna överförs värmen till det kalla ingående vattnet. Energiåtgången för utomhusluftlösningen var beroende av köldmediets förångningstemperatur och modellering av lösningen visade att energiåtgången var 0,25 kWh vid en förångningstemperatur på -10°C, och 0,18 kWh vid 5°C. Vid modellering av energilagerlösningen påvisades en energiåtgång på 0,23 kWh. Slutsatsen som drogs var att kompressorn vid energilagerlösningen skall leverera en effekt på 240 W till köldmediet. / For an average detached house in Sweden today about 5000 kWh are used for household electricity. Of these 5000 kWh 7% are used to run dishwashers. The streamlining of dishwashers has above all strived for a lower water and energy use, a short process time along with a more efficient cleaning of the dishes. There are however limits for how efficient the dishwashers can be made with traditional technology and acceptable costs. Therefore producers have, during recent years, started looking for less traditional methods, for example the use of a heat pump to reduce the energy use. The purpose of this examination work has been to find system solutions for an application of a heat pump in a dishwasher and to evaluate the possible energy saving for each solution. The goal has been to find and describe possible system solutions, which came up during the idea generation. To choose some of these for a closer investigation, to decide a fitting mechanical power for the compressor and to calculate the energy saving these solutions give rise to. The method has consisted of a literature study, an idea generation, which takes the heat sources and sinks in consideration and a modelling in MATLAB’s Simulink of the selected solutions from the idea generation, which has been used to fit a mechanical power for the compressor. The result of the idea generation was two solutions, an outdoor air solution, which collects heat from the outdoor air and gives it to the cold water which enters the machine and a energy storage solution, which collect heat from a heat stock to give to the cold entering water. A modelling of these show an energy usage of 0,24 respectively 0,17 kWh for the outdoor air solution, with a heat source temperature at 10 °C respectively 5°C and a energy usage of 0,22 kWh for the energy storage solution for one round. The conclusion that was drawn was that the compressor of the energy storage solution should deliver a mechanical power of 240 W to the refrigerant.