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This thesis is intended to fulfill the requirements of the Math and Physics departments at Harvey Mudd College. We begin with a brief introduction to the study of surfactant dynamics followed by some background on the experimental framework our work is related to. We then go through a derivation of the model we use, and explore in depth the nature of the Equation of State (EoS), the relationship between the surface tension on a fluid and the surfactant concentration. We consider the effect of using an empirical equation of state on the results of the simulations and compare the new results against the results produced using a multilayer (EoS) as well as experimental observations. We find that the empirical EoS leads to two new behaviors - preserving of large gradients of surfactant concentration and the occurrence of dynamics in distinct regimes. These behaviors suggest that the empirical EoS improves the agreement of the model’s prediction with experiment.

This thesis presents detailed investigations of the effect of end wall profiling on the secondary flow in a large scale, linear cascade with nozzle guide vanes. The purpose of this project is to look into the secondary flow structure in the linear cascade and the influence of the shaped end wall on the secondary flow. By applying the non-axisymmetric end wall, the secondary flow is reduced compared to the flat end wall data. The yaw angle variation at the exit of the blade passage is reduced. The cascade was designed according to the nozzle guide vane from ALSTOM Energy Ltd. It was manufactured and connected to the low speed wind tunnel in the Thermo- Fluids Lab in Durham. The data acquisition system was designed and commissioned. Five hole probes were designed and calibrated according to the cascade test condition. The flow field with the flat end wall in the cascade was investigated using five hole probes through different traverse slots. Flow visualisations were conducted as well. The secondary flow structure and the loss development in the cascade are understood. Transitional trips were put on the blade surfaces and their effects on the secondary flow were observed. The CFD code was modified to fit the cascade case. It was validated against the Durham standard case and the flat end wall results. Different numerical schemes and turbulence models were evaluated. Different shaped end walls were systematically tested by the CFD code. The best end wall profile was selected and manufactured. It was then tested in the cascade. Detailed investigations by five hole probes, flow visualisation and wall static pressure measurements were conducted. The results were compared to the flat end wall results and the CFD prediction. The secondary flow and the total pressure loss were reduced. The test data in the cascade will supply the evidence and data for the real turbine design. The chosen end wall profile will hopefully be tested in a test turbine.

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