Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Mechanical Engineering


Leylek, James H


Computational fluid dynamics and heat transfer (CFD) has become a viable, physics-based analysis tool for complex flow and/or heat transfer problems in recent years due, in large part, to rapid advances in computing power. CFD based on the Reynolds-averaged Navier-Stokes (RANS) equations is starting to enter the mainstream design environment in certain industries where rapid and reliable predictive capability is necessary. One such application is the gas turbine industry, where thermal management of airfoils at extremely high temperatures is one of the most critical components in engine design for reliability. The problem is complicated by the need for advanced airfoil cooling techniques, which typically includes internal convection cooling.
Current turbine aerothermal design practice involves separate simulations or empirical correlations for the airfoil external aerodynamics and heat transfer, the internal heat transfer, and conduction in the metal part. This approach is time-consuming and quite inefficient when design iterations are required, and accuracy is lost in the decoupling of the heat transfer modes. The physically-realistic approach is a single CFD simulation in which the convective heat transfer (fluid zones) and heat diffusion in the solid are fully coupled. This is known as the conjugate heat transfer (CHT) method, and it is ideally suited to the rigors of design. An obstacle to the adoption of the CHT method is difficulty in the accurate prediction of heat transfer coefficients on both external and internal surfaces, which is usually attributed to performance of the turbulence models used to close the RANS equations. The present study develops a comprehensive, 'best-practice' RANS-based conjugate heat transfer methodology for application to the aerothermal problem of an internally-cooled gas turbine airfoil at realistic operating conditions. With the design environment in mind, attention is given to high-quality mesh generation, efficient solution initialization, and solution-based adaption for grid-independence. Matching the conditions of the only experimental test case available in the literature, the simulations consist of a linear cascade of C3X vanes cooled by air flowing radially through ten smooth-walled cooling channels. Initially, popular 'off-the-shelf' k-e turbulence models are employed. Predictions for vane external surface temperature distribution at the midspan generally agree well with experimental data. The only exception is along a portion of the suction (convex) surface of the airfoil, where the predicted temperature is significantly greater than measured. This indicates an overprediction in the local heat transfer coefficient, and it corresponds to the region of strong curvature of the surface.
In an effort to correct the excessive heat transfer coefficients predicted on the vane suction surface, a new eddy-viscosity-based turbulence model is developed to include correct sensitivity to the effects of streamline curvature (and, by analogy, system rotation). The novel feature of the model is the elimination of second derivatives in the formulation of the eddy-viscosity, making it much more robust than other curvature-sensitive models when implemented in general-purpose solvers with unstructured meshes. A new dynamic two-layer near-wall treatment is included for integration of the flow to the wall. The new model is proven to exhibit physically-accurate results in several fundamental test cases. When the C3X vane conjugate heat transfer simulation is revisited with the new model, the heat transfer coefficients in the region of strong convex curvature are correctly attenuated, and the wall temperature predictions are much closer to measurements.
Cooling channels in many hot-section turbine airfoils have ribs machined on their walls to augment heat transfer, and they make multiple passes through the airfoil, meaning sharp turns are present. In order to extend the CHT methodology to these more complex internal cooling configurations, work is also conducted on the prediction of heat transfer in ribbed channels and in channel 180-deg-turns. In the two ribbed-channel cases studied, the use of steady simulations with popular turbulence models result in a significant underprediction of Nusselt numbers on the ribbed walls. Predictions improve significantly with unsteady (time-accurate) RANS simulations using another new in-house turbulence model, which is designed to promote and sustain small-scale unsteady motions. The results clearly show the importance of capturing the unsteady shear layer breakup into roller vortices aft of the ribs. In a simulation of a channel of square cross-section making a sharp 180-deg-turn, the new curvature-sensitive turbulence model gives Nusselt number predictions that are superior to existing k-e models. With the added capability to handle complex internal cooling configurations, the conjugate heat transfer methodology becomes a versatile gas turbine aerothermal design tool.