One of the biggest unsolved problems of modern physics is the turbulence phenomena in fluid flow. The appearance of turbulence in a flow system is regularly determined by velocity and length scales of the system. If those scales are small the motion of the fluid is laminar, but at larger scales, disturbances appear and grow, leading the flow field to transition to a fully turbulent state. The prediction of transitional flow is critical for many complex fluid flow applications, such as aeronautical, aerospace, biomedical, automotive, chemical processing, heating and cooling systems, and meteorology. For example, in some cases the flow may remain laminar throughout a significant portion of a given domain, and fully turbulent simulations may produce results that can lead to inaccurate conclusions or inefficient design, due to an inability to resolve the details of the transition process. This work aims to develop, implement, and test a new model concept for the prediction of transitional flows using a linear eddy-viscosity RANS approach. The effects of transition are included through one additional transport equation for v2 as an alternative to the Laminar Kinetic Energy (LKE) framework. Here v2 is interpreted as the energy of fully turbulent, three-dimensional velocity fluctuations. This dissertation presents two new single-point, physics-based turbulence models based on the transitional methodology mentioned above. The first one uses an existing transitional model as a baseline which is modified to accurately capture the physics of fully turbulent free shear flows. The model formulation was tested over several boundary layer and free shear flow test cases. The simulations show accurate results, qualitatively equal to the baseline model on transitional boundary layer test cases, and substantially improved over the baseline model for free shear flows. The second model uses the SST k-w fully turbulent model and again the effects of transition are included through one additional transport equation for v2. An initial version of the model is presented here. Simplicity of the formulation and ease of extension to other baseline models are two potential advantages of the new method.

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This thesis contains an exposition of the new strongly polynomial algorithm for the generalized flow problem by Laszlo Vegh (2013). It has been a long-standing open question whether such an algorithm exists, until it was resolved by Vegh in 2013. Generalized flows have many applications in economic problems, such as transportation of goods and foreign currency exchange. The main presentation follows Vegh's paper, but this exposition contains some simplifications and differences in the algorithm and its analysis. The main difference is that we consider the running time of the strongly polynomial algorithm up to one arc contraction before starting fresh on a smaller network. This increases the running time of the algorithm slightly, but the analysis becomes easier.

This work is concerned with the interaction between condensing aerosol dynamics and hydrodynamic mixing within ow configurations in which aerosol particles form (nucleate) from a supersaturated vapor and supersaturation is induced by the mixing of two streams (a saturated stream and a cold one). Two canonical hydrodynamic configurations are proposed for the investigation. The First is the steady one-dimensional opposed-ow configuration. The setup consists of the two (saturated and cold) streams owing from opposite nozzles. A mixing layer is established across a stagnation plane in the center where nucleation and other aerosol dynamics are triggered. The second is homogeneous isotropic turbulence in a three-dimensional periodic domain. Patches of a hot saturated gas mix with patches of a cold one. A mixing layer forms across the growing interface where the aerosol dynamics of interest occur. In both configurations, a unique analogy is observed. The results reveal a complex response to variations in the mixing rates. Depending on the mixing rate, the response of the number density falls into one of two regimes. For fast mixing rates, the maximum reached number density of the condensing droplets increases with the hydrodynamic time. We refer to this as the nucleation regime. On the contrary, for low mixing rates, the maximum reached number density decreases with the hydrodynamic time. We refer to this as the consumption regime. It is shown that vapor scavenging by the aerosol phase is key to explaining the transition between these two regimes.

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