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Modern gas turbine engines operate at temperatures well above the melting point of the metal components. This has driven manufactures to develop sophisticated cooling methods which minimise the use of coolant to maximise engine efficiency by enabling further increases in operating temperature. This thesis investigates the cooling performance of engine representative mid-chord internal cooling passages for turbine blades. The work forms part of a larger E.C. FP7 project ERICKA (Engine Representative Internal Cooling Knowledge Applications).This thesis provides detailed maps of heat transfer coefficient (HTC) under a number of conditions, new experimental techniques, and has lead to a better understanding of the impact HTC distributions have on the thermal performance of a turbine blade at engine conditions. Transient liquid crystal experiments have been conducted on a large scale model of an engine representative internal cooling passage at three aspect ratios (width:height (chord length:spanwise length), 1:2, 1:3 and 1:4). Spatially resolved maps of Nusselt number have been produced for the full surface of the internal cooling passages. Little information exists in the literature for more engine representative geometries, and it is rare for spatial measurements to be presented over the full surface. The detailed maps provide validation data for CFD within the ERICKA programme. A novel method which produces spatially resolved maps in areas with highly non-one-dimensional heat transfer has been developed and validated. This method couples transient finite element analysis and data from transient liquid crystal experiments. Applied to the ribbed passage geometry, this produced spatially resolved maps of HTC over the rib surface. To the author’s best knowledge this is the first time spatial HTC maps have been presented for an engine representative rib. Industry best practice methods for internal cooling passage design typically apply averaged values of HTC, in part due to lack of spatially resolved data. To determine the significance of this approximation on blade design and life, experimental measurements have been applied to finite element (FEA) models at typical engine conditions. Application of a 3D HTC distribution to a FEA model of a section of ribbed wall demonstrated a significant under prediction (up to 58%) of localised thermal gradients when an average value is applied compared to a spatially resolved profile. This work demonstrated good agreement between distributions taken from experimental data and CFD predictions, indicating that CFD distributions may be more appropriate than bulk values in the design process. A 2D FEA study was undertaken to quantify the impact of HTC distribution approximations and aspect ratio on cooling of a generic turbine section. This study considered multiple adjacent internal cooling passages. It was confirmed that multi-pass arrangements offer greater heat removal for a given mass flow rate. Also a symmetric heat transfer profile with a higher HTC on the ribbed wall is the most desirable distribution. Use of average values significantly impacted the metal temperature, causing an underprediction up to 13◦C and 8◦C in the maximum and average values respectively. Based on the experimental HTC data, the 1:3 aspect ratio passage offered the lowest metal temperatures. Applying HTC distributions from CFD data (calculated with using the centreline temperature) showed, in general, good agreement, with the lowest metal temperatures (by up to 8◦C) in the 1:4 aspect ratio passage. Use of and HTC distribution provided by CFD prediction based on the mixed bulk temperature, produced average and peak metal temperatures 16◦C and 17◦C, respectively, lower in the 1:4 aspect ratio passage than the next best design. This highlights the need for appropriate and consistent method to be used in the analysis. As expected, reducing the passage aspect ratio led to increases in both thermal gradient and total pressure loss.

This manuscript demonstrates the well-posedness (existence, uniqueness, and regularity of solutions) of the Cauchy problem for simplified equations of nematic liquid crystal hydrodynamic flow in three dimensions for initial data that is uniformly locally L3(R3) integrable (L3U(R3)). The equations examined are a simplified version of the equations derived by Ericksen and Leslie. Background on the continuum theory of nematic liquid crystals and their flow is provided as are explanations of the related mathematical literature for nematic liquid crystals and the Navier–Stokes equations.

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Aniline Black, a polymer containing p-benzoquinodiimine groups, was synthesized chemically or electrochemically by the oxidation of aniline. The polymer salts showed the conductivity of 10⁻¹-10⁻³ ohm⁻¹cm⁻¹. Polymers containing anthroquinodiimine units were also prepared by polycondensations. The syntheses of model compounds containing p-benzoquinodiimine were attempted. Multiazobisphenol monomers were synthesized. 4,4'-(3,3'-Dimethyl-4,4'-biphenylenebisazo) bisphenol 7, 4,4'-[azobis(p-phenyleneazo)] bisphenol 8, and 4,4'-(2-methoxy-1,4-phenylenebisazo) bisphenol 10 displayed liquid crystal (l.c.) properties, while model derivatives of 7, 8, and 4,4'-(4,4'-stilbenebisazo) bisphenol 9 did likewise. Monomers and derivatives of 4-[(4-hydroxyphenyl)azo]-1-naphthol 5, and 4,4'- [oxybis(p-phenyleneazo)] bisphenol 6 showed no l.c. behavior. New thermotropic polyesters based on these multiazobisphenols were synthesized. Sebacates of 5, 6, 7, 8, and 10 showed l.c. behavior, while polymers based on isophthalic or 5-t-butylisophthalic acid did not do so. Polyformals were also synthesized from these momoners, only that of 4 showed weak l.c. behavior. The correlation between the structure of these polymers and their tractabilities, electrical properties, liquid crystal behaviors was studied. Polymers and copolymers containing p-azoarylene and p-azoxyarylene groups were synthesized by oxidative coupling of various aromatic diamines. Films were cast directly from the reaction mixtures or from the polymer solution. The films were n-doped by sodium naphthalide or p-doped by iodine. They showed electrical conductivities of 10⁻⁴ to 10⁻⁵ ohm⁻¹cm⁻¹. AB monomers containing dipolar p-phenyleneazo groups were synthesized: 4-(4-hydroxy-2-methoxyphenylazo) benzoic acid 21, 4-[4-(4-hydroxy-2-methoxyphenylazo)-2-methoxyphenylazo] benzoic acid 22, and 4-(4-hydroxy-2-methoxyphenylazo)-3-nitrobenzoic acid 23. The monomers were polymerized by direct polycondensations. The polyester synthesized from 21 formed a red, transparent film. A polymethacrylate containing dipolar p-phenyleneazo groups in the side chains was also prepared by the free radical polymerization of 1- [3-methoxy-4-(p-nitrophenylazo)-phenoxy] hexyl methacrylate 28.

In this work, using the idea of an electrically conducting "functional unit," monomers and polymers with possible electronic and electro-optic applications were synthesized. The synthesis and polymerizations were, in many cases, novel and non-trivial. Dithiafulvene (1,3-dithiole) and variations of this functional unit were synthesized and incorporated into new condensation polymers. Polyesters, polyamides and polyhydrazones were all successfully synthesized and could be cast into films. These new polymers might be applicable as processable conducting materials if compatible dopants are employed or by themselves in the area of third order non-linear optics. Using a (meth)acrylate backbone, a spacer group of six methylene units, and a phenyl-CO₂-phenyl mesogen, linked by an ester group to a strongly polar optically active center containing a methoxy group, three new novel monomers and polymers were designed to exhibit smectic C* liquid-crystal phases. The polymers exhibited liquid crystalline behavior as was shown in differential scanning calorimetry and optical microscopy. Further studies and investigations in the synthesis of pure (meth)acrylate esters and their homopolymers yielded surprising results with regard to the Schotten-Baumann reaction. Interestingly, the use of meth(acryloyl) chloride in this scheme leads to (meth)acrylic anhydride, which is not easily isolable from distillable products. This anhydride is responsible for gelation in the polymerization of glycolate esters, and cannot be removed by work-up with various nucleophiles without disrupting desired ester functions. An S(N)2 method is recommended in this work.

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