Orthogonal Decomposition Methods for Turbulent Heat Transfer Analysis with Application to Gas Turbines



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Gas turbine engines are the main propulsion source for world wide aviation and are also used for power generation. Even though they rely mainly on fossil fuel and emit climate active gasses, their importance is not likely to decrease in the future. But more efficient ways of using finite resources and hence reducing emissions have to be found. Thus, the interest to improve engine efficiency is growing. Considering the efficiency of the underlying thermodynamic cycle, an increase can be achieved by raising the turbine inlet temperature or compression ratio. Due to the complex nature of the underlying flow physics, however, the aero-thermal processes are still not fully understood. For this reason, one needs to perform research at high spatial and temporal resolution, in turn creating the need for effective means of postprocessing the large amounts of data.

This dissertation addresses both sides of the problem - using high-scale, high resolution simulations as well as effective post processing techniques. As an example for the latter, a temporal highly resolved data set from wall pressure measurements of a transonic compressor stage is analyzed using proper orthogonal decomposition. The underlying experiments were performed by collaborators at Technical University Darmstadt. To decompose signals into optimal orthogonal basis functions based on temporal correlations including temperature, a formal mathematical framework is developed. A method to rank the reduced order representations with respect to heat transfer effectiveness is presented. To test both methods, a Reynolds-averaged Navier-Stokes (RANS) simulation and large eddy simulation (LES) are performed on turbulent heat transfer in a square duct with one single row of pin fins. While the LES results show closer agreement to experiments, both simulations unveil flow parts that do not contribute to heat transfer augmentation and can be considered wasteful. From the most effective mode, a wall contour for the same domain is derived and applied. In the wall contoured domain, energy in wasteful modes decreased, heat transfer increased and the temperature fluctuations at the wall decreased.

Another stagnating boundary layer flow is examined in a direct numerical simulation of a first stage stator vane. Elevated levels of free stream turbulence and integral length scale are generated to simulate the features of combustor exit flow. The horseshoe vortex dynamics cause an increase in endwall heat transfer upstream of the vane. The link between energy optimal orthogonal basis functions and flow structures is examined using this data and the reduced order heat transfer analysis shows high energy modes with comparatively low impact on turbulent heat transfer. The analysis further shows that there are multiple horseshoe vortices that oscillate upstream of the blade, vanish, regenerate and can also merge. There is a punctual correlation of intense vortex dynamics and peaks in the orthogonal temperature basis function.

For all data considered, the link between the energy optimal orthogonal basis functions and flow structures is neither guaranteed to exist nor straightforward to establish. The orthogonal expansion locks onto flow parts with high fluctuating kinetic energy - which might or might not be the ones that are looked for. The heat transfer ranking eliminates this problem and is valid independently of how certain basis functions are interpreted.