Over the previous summer I studied mixing of a passive tracer by flow in a straight cylindrical pipe, under the supervision of prof. Bernoff. The mixing process can be thought of as the successive action of advection by the fluid flow and diffusion modeled by random walks. With this method we were able to distinguish three different regimes. For short times, diffusion is more relevant than advection and we observed a Gaussian longitudinal distribution of the concentration. In an intermediate regime, advection by the shear is dominant over longitudinal diffusion and we observed a distinctively asymmetric distribution which spread much faster than would be expected by the action of diffusion alone. Finally when the tracer had completely mixed across the pipe’s cross- section, we recovered the classical Taylor regime with a longitudinal Gaussian distribution. In each regime we have analytical prediction of tracer distribution, confirmed by numerical calculation. The object of this thesis is to extend our results to curved pipes; we will start by considering curved planar pipes and helical pipes. We will try to determine if mixing in these geometries displays the same three distinctive regimes of mixing. The pipe’s curvature introduces a secondary flow in the form of a transverse recirculation with a dipolar form, discovered by Dean (1928). We believe this transverse flow should enhance mixing, which explains why curved pipes are used in cooling systems and other situations where heat exchange is relevant. Our object is to first understand existing analytical approximations to the flow in a curved pipe due to Dean and others and then to study analytically and numerically the spread of a passive scalar in these flows.

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This thesis is motivated by the necessity to understand the flow structure of turbulent flows in bends encountered in many technical applications such as heat exchangers, nuclear reactors and internal combustion engines. Flows in bends are characterised by strong secondary motions in terms of counter-rotating vortices (Dean cells) set up by a centrifugal instability. Specifically the thesis deals with turbulent flows in 90° curved pipes of circular cross-section with and without an additional motion, swirling or pulsatile, superposed on the primary flow.  The aim of the present thesis is to study these complex flows in detail by using time-resolved stereoscopic particle image velocimetry to obtain the three-dimensional velocity field, with complementary hot-wire anemometry and laser Doppler velocimetry measurements. In order to analyse the vortical flow field proper orthogonal decomposition (POD) is used. The so called ``swirl-switching'' is identified and it is shown that the vortices instantaneously, ``rock'' between three states, viz. a pair of symmetric vortices or a dominant clockwise or counter-clockwise Dean cell. The most energetic mode exhibits a single cell spanning the whole cross-section and ``rolling'' (counter-)clockwise in time. However, when a honeycomb is mounted at the inlet of the bend, the Dean vortices break down and there is strong indication that the ``swirl-switching'' is hindered. When a swirling motion is superimposed on the incoming flow, the Dean vortices show a tendency to merge into a single cell with increasing swirl intensity. POD analysis show vortices which closely resemble the Dean cells, indicating that these structures co-exist with the swirling motion. In highly pulsating turbulent flow at the exit of a curved pipe, the vortical pattern is diminished or even eliminated during the acceleration phase and then re-established during the deceleration. In order to investigate the effect of pulsations and curvature on the performance of a turbocharger turbine, highly pulsating turbulent flow through a sharp bend is fed into the turbine. Time-resolved pressure and mass-flow rate measurements show that the hysteresis loop in the pressure-ratio-mass-flow plane, may differ significantly between straight and curved inlets, however the mean operating point is only slightly affected. / <p>QC 20140523</p>

The thesis deals with the flow in pipe bends and radial turbines geometries that are commonly found in an Internal Combustion Engine (ICE). The development phase of internal combustion engines relies more and more on simulations as an important complement to experiments. This is partly because of the reduction in development cost and the shortening of the development time. This is one of the reasons for the need of more accurate and predictive simulations. By using more complex computational methods the accuracy and predictive capabilities are increased. The disadvantage of using more sophisticated tools is that the computational time is increasing, making such tools less attractive for standard design purposes. Hence, one of the goals of the work has been to contribute to assess and improve the predictive capability of the simpler methods used by the industry. By comparing results from experiments, Reynolds Averaged Navier-Stokes (RANS) computations, and Large Eddy Simulations (LES) the accuracy of the different computational methods can be established. The advantages of using LES over RANS for the flows under consideration stems from the unsteadiness of the flow in the engine manifold. When such unsteadiness overlaps the natural turbulence the model lacks a rational foundation. The thesis considers the effect of the cyclic flow on the chosen numerical models. The LES calculations have proven to be able to predict the mean field and the fluctuations very well when compared to the experimental data. Also the effects of pulsatile exhaust flow on the performance of the turbine of a turbocharging system is assessed. Both steady and pulsating inlet conditions are considered for the turbine case, where the latter is a more realistic representation of the real flow situation inside the exhaust manifold and turbine. The results have been analysed using different methods: single point Fast Fourier Transforms (FFT), probe line means and statistics, area and volume based Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD). / Denna avhandling behandlar flödet i rörkrökar och radiella turbiner som vanligtvis återfinns i en förbränningsmotor. Utvecklingsfasen av förbränningsmotorer bygger mer och mer på att simuleringar är ett viktigt komplement till experiment. Detta beror delvis på minskade utvecklingskostnader men även på kortare utevklningstider. Detta är en av anledningarna till att man behöver mer exakta och prediktiva simuleringsmetoder. Genom att använda mer komplexa beräkningsmetoder så kan både nogrannheten och prediktiviteten öka. Nackdelen med att använda mer sofistikerade metoder är att beräkningstiden ökar, vilket medför att sådana verktyg är mindre attraktiva för standardiserade design ändamål. Härav, ett av målen med projektet har varit att bidra med att bedöma och förbättra de enklare metodernas prediktionsförmåga som används utav industrin. Genom att jämföra resultat från experiment, Reynolds Averaged Navier-Stokes (RANS) och Large Eddy Simulations (LES) så kan nogrannheten hos de olika simuleringsmetoderna fastställas. Fördelarna med att använda LES istället för RANS när det gäller de undersökta flödena kommer ifrån det instationära flödet i grenröret. När denna instationäritet överlappar den naturligt förekommande turbulensen så saknar modellen en rationell grund. Denna avhandling behandlar effekten av de cykliska flöderna på de valda numeriska modellerna. LES beräkningarna har bevisats kunna förutsäga medelfältet och fluktuationerna väldigt väl när man jämför med experimentell data. Effekterna som den pulserande avgasströmning har på turboladdarens turbin prestanda har också kunnat fastställas. Både konstant och pulserande inlopps randvillkor har används för turbinfallet, där det senare är ett mer realistiskt representation av den riktiga strömningsbilden innuti avgasgrenröret och turbinen. Resultaten har analyserats på flera olika sätt: snabba Fourier transformer (FFT) i enskilda punkter, medelvärden och statistik på problinjer, area och volumsbaserade metoder så som Proper Orthogonal Decomposition (POD) samt Dynamic Mode Decomposition (DMD). / <p>QC 20140919</p>