Stefan Völker

A Model for Cylindrical Hole Film Cooling—Part II: Model Formulation, Implementation and Results

A model to simulate flows ejected from cylindrical film cooling holes in 3D-CFD without meshing the cooling hole geometry has been developed. It uses a correlation-based prediction of the complete three-dimensional flow field in the vicinity of a film hole exit based on characteristic film cooling parameters that is presented in part I of this two-part paper. The model describes the film-jet in terms of its shape and the distribution of temperature and velocity components within the film-jet body. For example, the characteristic counter-rotating vortex pair in the film-jet is modeled. Adding source terms to the transport equations for mass, momentum, and energy locally, the correlation-based prediction of the film-jet flow field is imposed onto a 3D-CFD simulation. Source terms are specified in the vicinity of a film hole exit, within a region representative of the volume occupied by the film jet. Each node within this source volume is treated individually in order to model the complex flow structure of the film-jet. The model has successfully been implemented in a commercial CFD code. Its general applicability has been tested and proven. The model’s predictive capability is compared to detailed CFD calculations and experimental investigations. A grid requirement study has been conducted, showing that the film cooling model delivers reasonable predictions of the surface temperature distributions downstream of the ejection location using relatively coarse grids. A minimum grid resolution requirement has been identified.

Multi-Fidelity Surrogate Models for Predicting the Aerodynamic Performance of Turbine Airfoils

In recent years, turbine designers have relied more and more on 3D-CFD to come up with new and innovative airfoil designs. While individual CFD simulations are quite affordable nowadays, especially when used in aero optimization, where often thousands of CFD runs are required, the overall cost is still significant. In comparison, 2D-CFD simulations (Low Fidelity, LoFi) on multiple radially stacked airfoil sections (quasi-3D) are much faster, but less accurate because secondary flow effects are neglected. However, if HiFi and LoFi re-sults (e.g. aerodynamic efficiency) are reasonably well correlated, multi-fidelity surrogate models, which are constructed from a small number of HiFi and LoFi results, can offer a good compromise. Once the surrogate model is available, it allows to approximate HiFi results representing for example different geometry variations based on the correspond-ing LoFi results, thereby eliminating the need for further HiFi computations. Thus the multi-fidelity approach can be used to speed up airfoil optimization. In this paper the applicability of (gappy) proper orthogonal decomposition (POD, GPOD) for building a multi-fidelity surrogate model is presented and compared to the widely-used kriging based surrogate models from a industrial point of view. As the name suggests, GPOD is based on the decomposition of the HiFi and LoFi computational domain into orthogonal basis functions. In contrast, kriging based surrogate models are built based on the differences in the output values (e.g. efficiency) from the HiFi and LoFi simulations. Both methods are compared in terms of accuracy of the predicted HiFi output values. In addition, the dependency between the accuracy of prediction and the number of HiFi simulations required for creating the surrogate model is given. The ideal surrogate method would provide a high level of accuracy while requiring only few HiFi evaluations. The surrogate models are evaluated for different geometry variations that are not included in the set used for building the surrogate models. The analysis is carried out for a number of turbine airfoils subject to different flow regimes, namely a gas turbine second and fourth stage vane and blade. It is found, that for the examined cases, the GPOD method gives better predictions while requiring fewer HiFi simulations for creating the surrogate model.

Applicability of Quasi-3D Blade Design Methods to Profile Shape Optimizaton of Turbine Blades

The performance of gas turbine airfoils is continually improved by creating advanced aerodynamic and thermal designs. Optimization methods are used to handle the increasing complexity of such a design. However, optimization is expensive when performed based on 3D CFD calculations. Therefore, an optimization strategy based on simpler, less expensive analysis methods is desirable.Oftentimes, a so-called quasi-3D (Q3D) approach is used, where 2D calculations are carried out on multiple, radially stacked meridional blade sections. This paper investigates the applicability of such an approach for optimization with regard to blade profile loss.Obviously, certain physical effects are neglected using this approach, leading to errors in the predicted blade performance. Still, optimization based on Q3D calculations might be possible if the error is consistent, i.e. not random.For this purpose, a design of experiment (DOE) was carried out to compare and correlate loss predictions from Q3D calculations and high-fidelity 3D CFD calculations for gas turbine blades. It is shown that the total pressure loss coefficients found with both the Q3D and 3D calculations correlate well (75–90%) to warrant the use of a Q3D method for profile shape optimization. Subsequently, an optimization is performed to demonstrate the applicability of the method.Copyright

Aerodynamic Optimization of Turbine Airfoils Using Multi-fidelity Surrogate Models

For many applications numerical simulations are available in varying degrees of fidelity and computational expense. On the one hand, in an accurate and time-consuming high-fidelity (HiFi) version, that is used as a reference for design and optimization, and on the other hand, in a low-fidelity (LoFi) version that is faster but less accurate. In computational fluid dynamics (CFD) of turbine airfoils an accurate 3D solver accounts for the HiFi model and a faster 2D solver for the LoFi model. Assuming the LoFi model captures the fundamental physics reasonably well, many inexpensive LoFi computations may be coupled with a few expensive HiFi computations to enhance the accuracy of a surrogate model based solely on the HiFi data. In this way multi-fidelity surrogate models can be used to speed up the optimization.