الفهرس 
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Abstract
The U-bend is used in several engineering applications as connected the cooling paths in gas turbines blades. The cooling of the gas turbine blade is highly demanded (Using a serpentine path in it is the regular way to cool it from inside). These paths have a huge loss which reflect on the output power. The pressure DROP and the heat transfer in eight different U-bend geometries are investigated using the power of the computational fluid dynamics at Reynolds number equal to 25000. Through different geometries convex extended vane showed better results. The pressure DROP is reduced reaching about 53% of the baseline U-bend with relatively small reduction in the heat transfer of about 8% of the baseline.
Another approach, adjoint optimization, is applied to reduce the pressure DROP by changing the geometrical shape according to restricted boundaries. The optimal geometry achieved the best result according to pressure DROP observable (about 44% of the baseline). The erosion in S-bend is also studied and compared with optimized one. The adjoint method showed its power in different applications and off designed conditions.
The Latin hypercube sampling type is used to apply design of experiments on U-bend to save the cost and time in studying the effect of different variables (the position and the radius of U-vane) on the objectives (pressure DROP and heat transfer). Genetic algorithm is used to get optimized shapes of U-bend using a surrogate model created by using the radial basis function neural network. The optimal geometry achieved pressure DROP reduction about 9%. while for the heat transfer objective the optimal geometry heat transfer rate increased about 17% of the reference case. Finally, Pareto front is used to do a multi-objective optimization to get different operating options to choose from.
Gas turbines are used to produce power as it is the heart or the prime mover of a lot of industries, aircrafts, and other machines. Raising the maximum temperature of the cycle will lead to higher thermal efficiencies and consequently higher output, but this is limited with melting point of the material and the stresses it can withstand at high temperature. So cooling is a must in the gas turbines to achieve a safe running and long life for the blades.
This study concerned about the internal cooling, serpentine type, trying to overcome its biggest issue of pressure loss through its internal passages. In this type the 180○ turns cause a high pressure DROP reaching about 25% of the losses in the cooling system. Due to the losses more power is needed for transporting extra air mass flow rate which leads to the main problem of the output power. Reducing the pressure DROP in the U-bend is the main purpose of the study and how that will affect the heat transfer which is the goal of these serpentines. Modified new shapes of U-bend equipped with new guiding vanes shape are investigated. Two optimization approaches are used, adjoint solver shape optimization, and parametric shape optimization based on a surrogate model. As fluid transport is one of the main process in each industry (pipeline infrastructure, fuel transport, water transport, heat exchangers, power plants, and airplanes) in whole the world. This study also little concerned on multiphase transport.
1.3 Outline This thesis consists of five chapters aiming to present in details the achieved work. The first chapter is the (Introduction) which explains the problem and its effect. The rest of this thesis is organized as follows:
In chapter 2, the most relevant literature are reviewed to identify the gap to be filled in the field.
In chapter 3, the mathematical modelling used for solving the problem is explained, and the different optimization methods are discussed.
In chapter 4, the results obtained are analyzed and discussed with comparison between the different approaches.
In chapter 5, the conclusions of the study and recommendation for future are stated.