Transfer Function Based Optimization of Film Hole Sizes With Conjugate Heat Transfer Analysis

With the improvements of 3D metal printing of turbine components, it is now feasible to produce ready to use production quality parts without casting and conventional machining. This new manufacturing technique has opened up new frontiers in cooling optimizations that could not be practiced before. For example, it is possible to have unconventional diameter of the film holes and the hole sizes can also be changed based on the cooling demands.

This paper seeks to optimize each film hole diameter at the leading edge of a turbine. The technique developed can be used in both stationary and rotating airfoils and will also work on other parts of the airfoil; but our current analysis is limited to the leading edge region of an airfoil. To apply this work to other regions, the corresponding heat transfer coefficients need to be adjusted to address a specific component, The underlying optimization technique stays the same. Any optimization technique needs the cost and benefit criteria. The cost is minimized to get maximum benefit. In gas-turbine heat transfer, there is a floor constraint that must be satisfied. This study minimizes the coolant flow with satisfying the constraint on maximum metal temperature that limits the life of the component.

The temperature distribution in the leading edge of a gas turbine vane is first learnt through the adjustment of film hole diameters. A design of Experiments provided the hole diameters needed to be tested to build a database of temperature distribution. The numerical simulations assumed uniform impingement cooling across the internal face of the vane, film holes are assumed round, and cooling inside the film holes are modeled with three zones of heat pickup, and external film cooling is applied with film effectiveness. The change in film hole diameter is simulated by scaling while the finite element model is kept the same. The film cooling is also scaled to accommodate variations on a fixed model. The external film cooling contains spanwise variations in film effectiveness, vertical change in temperature profile due to film hole spacings, and spanwise variations in convective heat transfer coefficient as transition of hot-gas flow develops on the leading edge.

As the foundation of this work is numerical simulations, the influence of varying diverse set of parameters are possible, such as impingement and film hole diameters, pressure drop in the film hole, external gas flow conditions, and the profile of film effectiveness on the external face. These changes are implemented through ANSYS based finite element model. Test mode outputs are processed to create transfer function using Python and that model is used for optimization. The parameter selection is limited by the mean and standard deviation and available correlations. A convex optimization technique is adopted to minimize coolant flowrate by varying film hole diameters.

List of Parameters considered for this study:

§  Multi-jet Impingement, diameter of impingement holes, S/D and H/D of impingement holes

§  External flow, surface roughness, turbulence, and supply temperature

§  Supply and dump pressure, and thus the corresponding overall pressure drop

§  Film hole diameters, range of these diameters and internal roughness

§  Profile of film effectiveness for film cooling on leading edge and curved surfaces