This work presents a comparison of thin film gauge (TFG) and infrared (IR) thermography measurement techniques to simultaneously determine heat transfer coefficient and film cooling effectiveness. The first comparison was with an uncooled vane where heat transfer coefficient was measured at Mex=0.77 and Tu=16%. Relatively good agreement was found between the results of the two methods and the effect of recovery temperature and data reduction time was analyzed. Improvements were made to the experimental set up for the next comparison, a showerhead film cooled vane. This geometry was tested at BR=0, 2.0, Mex=0.76 and Tu=16%. The TFG and IR results did not compare well for heat transfer coefficient or film cooling effectiveness. The effects of measured and calculated recovery temperature were analyzed as well as the respective data reduction methods, though the analysis could not account for the effectiveness trend seen on the suction surface. Finally, a vane with showerhead and shaped film cooling holes were presented at BR=0, 1.7, 2.0, 2.8, Mex=0.85, and Tu=13% to assess a new film cooling geometry measured with the IR technique. Similarities on the suction surface trend between the different film cooled geometries tested with IR indicate a flaw in the experiment that will require further analysis, changes and testing to complete the comparison with TFG. / Master of Science

In the drive to increase cycle efficiency, gas turbine designers have increased turbine inlet temperatures well beyond the metallurgical limits of engine components. In order to prevent failure and meet life requirements, turbine components must be cooled well below these hot gas temperatures. Film cooling is a widely employed cooling technique whereby air is extracted from the compressor and ejected through holes on the surfaces of hot gas path components. The cool air forms a protective film around the surface of the part. Accurate numerical prediction of film cooling performance is extremely difficult so experiments are required to validate designs and CFD tools. In this study, a first stage turbine vane with five rows of showerhead cooling was instrumented with platinum thin-film gauges to experimentally characterize film cooling performance. The vane was tested in a transonic vane cascade in Virginia Tech's heated, blow-down wind tunnel. Two freestream exit Mach numbers of 0.76 and 1.0—corresponding to exit Reynolds numbers based on vane chord of 1.1x106 and 1.5x106, respectively—were tested at an inlet freestream turbulence intensity of two percent and an integral length scale normalized by vane pitch of 0.05. The showerhead cooling scheme was tested at blowing ratios of 0 (no cooling), 1.5, and 2.0 and a density ratio of 1.35. Midspan Nusselt number and film cooling effectiveness distributions over the surface of the vane are presented. Film cooling was found to augment heat transfer and reduce adiabatic wall temperature downstream of injection. In general, an increase in blowing ratio was shown to increase augmentation and film cooling effectiveness. Increasing Reynolds number was shown to increase heat transfer and reduce effectiveness. Finally, comparing low turbulence measurements (Tu = 2%) to measurements performed at high freestream turbulence (Tu = 16%) by Nasir et al. [13] showed that large-scale high freestream turbulence can reduce heat transfer coefficient downstream of injection. / Master of Science

The objective of this work is to examine the flow structure and heat transfer distribution of a squealer tip rotor blade with purge flow cooling and provide a comparison with a basic flat tip rotor blade without purge flow cooling, under transonic conditions and high inlet free stream turbulence intensity. The blade design was provided by Solar Turbines Inc., and consists of a double squealer around the pressure and suction sides, two purge flow blowing holes located downstream of the leading edge and mid-chord, four ribs in the mid-chord region and a trailing edge bleeder exiting on the pressure side. Blade cavity depth is 2.29 mm (0.09 in.) and the total blade turning angle is 107.5°. Tests were performed in a blow-down facility at a turbulence intensity of 12%, in a seven bladed 2-D linear cascade at transonic conditions. Experiments were conducted at isentropic exit Mach numbers of 0.85 and 1.05, corresponding to Reynolds numbers based on axial chord of 9.75x10^5 and 1.15x10^6, respectively, and tip clearance gaps of 1% and 2% of the scaled engine blade span. A blowing ratio of 1.0 was used in the squealer tip experiments. Detailed heat transfer coefficient and film cooling effectiveness distributions were obtained using an infrared thermography technique, while oil flow visualization was used to investigate the flow patterns in the blade tip region. With the addition of a squealer tip, leakage flow was found to decrease, as compared to a flat tip blade. With increasing tip clearance gap, the heat transfer coefficients within the cavity and along the squealer rim were found to decrease and increase, respectively. Film cooling effectiveness decreased with increasing tip clearance gap and was mainly observed within the squealer cavity. The maximum heat transfer coefficient was observed on the leading edge, however, comparatively large values were observed on the mid-chord ribs. The presence of the ribs, greatly affected the flow structure and heat transfer distributions within the cavity and downstream towards the trailing edge. / Master of Science

Ph. D.

An inverse method for the design of exhaust nozzles with a specified transonic pressure distribution is presented. A problem of mixed Neumann and Dirichlet boundary condition is solved. A successive line relaxation process is used to solve the array of velocity potentials in the entire flow field. The streamlines are then displaced to produce boundaries which match a desired pressure distribution. Various cases are tested to verify the reliability of the method. The design calculation proves to be efficient and accurate. / M.S.

The effect of global warming due to increased level of greenhouse gas emissions from coal fired thermal power plants and crisis of reliable energy resources has profoundly increased the importance of natural gas based power generation as a major alternative in the last few decades. Although gas turbine propulsion system had been primarily developed and technological advancements over the years had focused on application in civil and military aviation industry, use of gas turbine engines for land based power generation has emerged as the most promising candidate due to higher thermal efficiency, abundance of natural gas resources, development in generation of hydrogen rich synthetic fuel (Syngas) using advanced gasification technology for further improved emission levels and strict enforcement in emission regulations on installation of new coal based power plants. The fundamental thermodynamic principle behind gas turbine engines is Brayton cycle and higher thermal efficiency is achieved through maximizing the Turbine Inlet Temperature (TIT). Modern gas turbine engines operate well beyond the melting point of the turbine component materials to meet the enhanced efficiency requirements especially in the initial high pressure stages (HPT) after the combustor exit. Application of thermal barrier coatings (TBC) provides the first line of defense to the hot gas path components against direct exposure to high temperature gases. However, a major portion of the heat load to the airfoil and passage is reduced through injection of secondary air from high pressure compressor at the expense of a penalty on engine performance. External film cooling comprises a significant part of the entire convective cooling scheme. This can be achieved injecting coolant air through film holes on airfoil and endwall passages or utilizing the high pressure air required to seal the gaps and interfaces due to turbine assembly features. The major objective is to maximize heat transfer performance and film coverage on the surface with minimum coolant usage. Endwall contouring on the other hand provides an effective means of minimizing heat load on the platform through efficient control of secondary flow vortices. Complex vortices form due to the interaction between the incoming boundary layer and endwall-airfoil junction at the leading edge which entrain the hot gases towards the endwall, thus increasing surface heat transfer along its trajectory. A properly designed endwall profile can weaken the effects of secondary flow thereby improving the aerodynamic and associated heat transfer performance. This dissertation aims to investigate heat transfer characteristics of a non-axisymmetric contoured endwall design compared to a baseline planar endwall geometry in presence of three major endwall cooling features – upstream purge flow, discrete hole film cooling and mateface gap leakage under transonic operating conditions. The preliminary design objective of the contoured endwall geometry was to minimize stagnation and secondary aerodynamic losses. Upstream purge flow and mateface gap leakage is necessary to prevent ingestion to the turbine core whereas discrete hole cooling is largely necessary to provide film cooling primarily near leading edge region and mid-passage region. Different coolant to mainstream mass flow ratios (MFR) were investigated for all cooling features at design exit isentropic Mach number (0.88) and design incidence angle. The experiments were performed at Virginia Tech's quasi linear transonic blow down cascade facility. The airfoil span increases in the mainstream flow direction in order to match realistic inlet/exit airfoil surface Mach number distribution. A transient Infrared (IR) thermography technique was employed to measure the endwall surface temperature and a novel heat transfer data reduction method was developed for simultaneous calculation of heat transfer coefficient (HTC) and adiabatic cooling effectiveness (ETA), assuming a 1D semi-infinite transient conduction. An experimental study on endwall film cooling with endwall contouring at high exit Mach numbers is not available in literature. Results indicate significant benefits in heat transfer performance using the contoured endwall in presence of individual (upstream slot, discrete hole and mateface gap) and combined (upstream slot with mateface gap) cooling flow features. Major advantages of endwall contouring were observed through reduction in heat transfer coefficient and increase in coolant film coverage by weakening the effects of secondary flow and cross passage pressure differential. Net Heat Flux Reduction (NHFR) analysis was carried out combining the effect of heat transfer coefficient and film cooling effectiveness on both endwall geometries (contoured and baseline) where, the contoured endwall showed major improvement in heat load reduction near the suction side of the platform (upstream leakage only and combined upstream with mateface leakage) as well as further downstream of the film holes (discrete hole film cooling). Detailed interpretation of the heat transfer results along with near endwall flow physics has also been discussed. / Ph. D.

In transonic flow, the aerodynamic interference that occurs on a strut-braced wing airplane, pylons, and other applications is significant. The purpose of this work is to provide relationships to estimate the interference drag of wing-strut, wing-pylon, and wing-body arrangements. Those equations are obtained by fitting a curve to the results obtained from numerous Computational Fluid Dynamics (CFD) calculations using state-of-the-art codes that employ the Spalart-Allmaras turbulence model. In order to estimate the effect of the strut thickness, the Reynolds number of the flow, and the angle made by the strut with an adjacent surface, inviscid and viscous calculations are performed on a symmetrical strut at an angle between parallel walls. The computations are conducted at a Mach number of 0.85 and Reynolds numbers of 5.3 and 10.6 million based on the strut chord. The interference drag is calculated as the drag increment of the arrangement compared to an equivalent two-dimensional strut of the same cross-section. The results show a rapid increase of the interference drag as the angle of the strut deviates from a position perpendicular to the wall. Separation regions appear for low intersection angles, but the viscosity generally provides a positive effect in alleviating the strength of the shock near the junction and thus the drag penalty. When the thickness-to-chord ratio of the strut is reduced, the flowfield is disturbed only locally at the intersection of the strut with the wall. This study provides an equation to estimate the interference drag of simple intersections in transonic flow. In the course of performing the calculations associated with this work, an unstructured flow solver was utilized. Accurate drag prediction requires a very fine grid and this leads to problems associated with the grid generator. Several challenges facing the unstructured grid methodology are discussed: slivers, grid refinement near the leading edge and at the trailing edge, grid convergence studies, volume grid generation, and other practical matters concerning such calculations. / Ph. D.

Continuous adjoint methods and optimal control theory are applied to a pressure-matching inverse design problem of quasi 1-D nozzle flows. Pontryagin’s Minimum Principle is used to derive the adjoint system and the reduced gradient of the cost functional. The properties of adjoint variables at the sonic throat and the shock location are studied, revealing a logarithmic singularity at the sonic throat and continuity at the shock location. A numerical method, based on the Steger-Warming flux-vector-splitting scheme, is proposed to solve the adjoint equations. This scheme can finely resolve the singularity at the sonic throat. A non-uniform grid, with points clustered near the throat region, can resolve it even better. The analytical solutions to the adjoint equations are also constructed via Green’s function approach for the purpose of comparing the numerical results. The pressure-matching inverse design is then conducted for a nozzle parameterized by a single geometric parameter. In the second part, the adjoint methods are applied to the problem of minimizing drag coefficient, at fixed lift coefficient, for 2-D transonic airfoil flows. Reduced gradients of several functionals are derived through application of a Lagrange Multiplier Theorem. The adjoint system is carefully studied including the adjoint characteristic boundary conditions at the far-field boundary. A super-reduced design formulation is also explored by treating the angle of attack as an additional state; super-reduced gradients can be constructed either by solving adjoint equations with non-local boundary conditions or by a direct Lagrange multiplier method. In this way, the constrained optimization reduces to an unconstrained design problem. Numerical methods based on Jameson’s finite volume scheme are employed to solve the adjoint equations. The same grid system generated from an efficient hyperbolic grid generator are adopted in both the Euler flow solver and the adjoint solver. Several computational tests on transonic airfoil design are presented to show the reliability and efficiency of adjoint methods in calculating the reduced (super-reduced) gradients. / Ph. D.

The unsteady interaction of shock waves emerging from the trailing edge of modern turbine nozzle guide vanes and impinging on downstream rotor blades is modeled in a linear cascade. The Reynolds number based on blade chord and exit conditions (5*10^6) and the exit Mach number (1.2) are representative of modern engine operating conditions. The relative motion of shocks and blades is simulated by sending a shock wave along the leading edges of the linear cascade instead of moving the blades through an array of stationary shock waves. The blade geometry is a generic version of a modern high turning rotor blade with transonic exit conditions. The blade is equipped with a showerhead film cooling scheme. Heat flux, surface pressure and surface temperature are measured at six locations on the suction side of the central blade. Pressure measurements are taken with Kulite XCQ-062-50a high frequency pressure transducers. Heat flux data is obtained with Vatell HFM-7/L high speed heat flux sensors. High speed heat flux and pressure data are recorded during the time of the shock impact with and without film cooling. The data is analyzed in detail to find the relative magnitudes of the shock effect on the heat transfer coefficient and the recovery temperature or adiabatic wall temperature (in the presence of film cooling). It is shown that the variations of the heat transfer coefficient and the film effectiveness are less significant than the variations of recovery temperature. The effect of the shock is found to be similar in the cases with and without film cooling. In both cases the variation of recovery temperature induced by the shock is shown to be the main contribution to the overall unsteady heat flux. The unsteady heat flux is compared to results from different prediction models published in the literature. The best agreement of data and prediction is found for a model that assumes a constant heat transfer coefficient and a temperature difference calculated from the unsteady surface pressure assuming an isentropic compression. / Ph. D.

Numerical optimization procedures have been employed for the design of airfoils in transonic flow based on the transonic small-disturbance (TSD) and Euler equations. A sequential approximation optimization technique was implemented for solving the design problem of lift maximization with wave drag and area constraints. A simple linear approximation was utilized for the approximation of the lift. Accurate approximations for sensitivity derivatives of the wave drag were obtained through the utilization of Nixon's coordinate straining approach. A modification of the Euler surface boundary conditions was implemented in order to efficiently compute design sensitivities without recreating the grid. Our design procedures experienced convergence problems for some TSD solutions, where the wave drag was found not to vary smoothly with the design parameters and consequently create local optimum problems. A procedure interchanging the role of the objective function and constraint, initially minimizing drag with a constraint on the lift was found to be effective in producing converged designs, usually in approximately 10 global iterations. This procedure was also shown to be robust and efficient for cases where the drag varied smoothly, such as with the Euler solutions. The direct lift maximization with move limits which were fixed absolute values rather than fractions of the design variables, was also found to be a reliable and efficient procedure for designs based upon the Euler equations. / Ph. D.