Christian Morsbach

The trend towards higher bypass ratios and downsized cores in modern compressors leads to locally reduced Reynolds numbers, intensifying flow separation and unsteadiness, which limits the reliability of RANS models and motivates the use of LES as a feasible and attractive high-fidelity approach for these conditions. In this paper, we assess the capabilities of low- and high-fidelity numerical tools for predicting the effects of varying incidence angles for a linear compressor cascade at a Reynolds number of 150,000 and a Mach number of 0.6 based on the inflow conditions. The comparison is supported by experiments carried out at the Transonic Cascade Wind Tunnel at the DLR in Cologne, which feature an incidence angle variation of plus/minus 5 degrees. Particular emphasis is put on the numerical setup to reproduce the cascade experiment, discussing the effects of spanwise domain size, axial-velocity density ratio and inflow turbulence. The effects of the incidence angle variation are studied on the basis of instantaneous and mean flow quantities with a focus on separation, transition and loss mechanisms.

In the second part of this three-paper series, high-fidelity simulations of the transonic cascade TEAMAero at the aerodynamic design point with Rein=1.35×106 and Main=1.21 are presented. A high-order discontinuous Galerkin spectral element method with finite-volume subcell shock capturing is employed to simulate the flow based on an implicit large eddy simulation (LES) scheme and advanced over several buffeting cycles to reliably capture the shock unsteadiness. A study on the spanwise domain size shows that the shock oscillation amplitude decreases with increasing span, although its frequency and mean location remain fixed through the simulations. By comparing high- and low-resolution LES results, it is further presented that deviations from under-resolution are mostly limited to the separated region past the shock, where the high-fidelity results match experimental results more closely. In addition to the LES, low-fidelity unsteady Reynolds-averaged Navier–Stokes is shown to capture the shock unsteadiness correctly, but at a reduced amplitude and fails to match the force distributions on the blade surface. Through examination of instantaneous flow features, space–time relations and spectral proper orthogonal decomposition, a basic analysis of the shock–boundary layer interaction is presented and indicates that velocity perturbations travel upstream through the subsonic boundary layer and periodically cause oblique shock waves, transporting the information from the boundary layer into the passage.

In this paper, we quantify the turbulence modeling uncertainty for the transonic Technische Universität Darmstadt (TUDa) compressor. The present work applies the Eigenspace Perturbation Framework (EPF) as it is the only published physics-based framework capable of addressing the model-form uncertainty in turbulence closure modeling. To sample from the possible solution space and obtain the modeling uncertainty, we perform simulations perturbing the eigenvalues of the Reynolds stress tensor in addition to simulations using an unperturbed turbulence model. We show that the shape of the Reynolds stress tensor ellipsoid has significant impact on the evolution of turbulence, flow separation, vortex systems, shock-boundary layer interaction, and finally the overall performance of the compressor. We compare the estimated uncertainties with available measurements and transitional Delayed Detached-Eddy Simulations (DDES). This allows us to assess the confidence of the chosen turbulence model and to evaluate the sharpness and coverage of the resulting uncertainty bounds. Thus, the EPF is comprehensively validated and suggestions for its future applicability with respect to turbomachinery components are made.

We investigate the unsteady behavior of an in-line jet impingement array of nine jets at a Reynolds number of 10,000 in a narrow channel subjected to a developing cross flow of up to 25% of the bulk jet velocity. To this end, we present an improved version of a previously published large eddy simulation (LES) now with resolved turbulence at the inflow boundaries. After a careful analysis of the transient behavior and statistical convergence of the LES, we discuss the time-averaged heat transfer characteristics of the configuration compared to numerical references of similar configurations. We then show how the large-scale unsteadiness increases from jet to jet. Both space-only and spectral proper orthogonal decompositions (POD and SPOD) are used to discuss the large-scale organization of single jets and multiple jets in combination. The latter shows a qualitative change in the unsteady behavior of the temperature footprint on the impingement wall with increasing cross flow.

The accurate prediction of transitional flows is crucial for the industrial turbomachinery design process. While a Reynolds-averaged Navier–Stokes approach inherently brings conceptual weaknesses, large-eddy simulation will still be too expensive in the near future to affordably analyze complex turbomachinery configurations. We introduce a transitional delayed detached-eddy simulation (DDES) model, namely, DDES-[ ], and analyze the numerical results of the compressor cascade V103. A comparison with the fully turbulent DDES approach emphasizes the benefit of coupling DDES with a transition model. Issues with undesired decay of modeled turbulent kinetic energy in the freestream are improved when running DDES-[ ] in combination with the synthetic turbulence generator method. The best results for DDES-[ ] are obtained when changing the inviscid flux solver blending from dynamic to constant mode. We show that DDES-[ ] is capable of predicting the transitional flow through a linear compressor cascade, but we also critically discuss the general concept and results.

In this paper, a reduced order film cooling model previously investigated on single cylindrical and laid back fan-shaped cooling holes is extended with a model variant for trailing edge cooling slots. The extended model is evaluated on a modern HPT NGV combining these cooling features and paired with either an eddy viscosity model or a differential RSM. To simulate a worst-case scenario during the maximum take-off operating point, a hot streak from the combustion chamber with a maximum temperature of about 2230 K is directly impinging on this NGV. Compared to resolved RANS simulations, the model performs better on the NGV than on single holes. In particular, the grid dependency is significantly reduced. The model error and grid dependence peak at the leading edge and decrease downstream of the showerhead. When an average film cooling efficiency is considered, three cells per cooling hole diameter were sufficient to approach grid convergence. A more accurate turbulence model also reduced the model error of the film cooling model, with an absolute error in the averaged film cooling effectiveness of 0.2 at the leading edge and 0.1 at the suction and pressure sides of the NGV.

We revisit recently published high-fidelity implicit large eddy simulation datasets obtained with a high-order discontinuous Galerkin spectral element method and analyse them using Proper Orthogonal Decomposition (POD) as well as Spectral Proper Orthogonal Decomposition (SPOD). The first configuration is the MTU T161 low-pressure turbine cascade with resolved end wall boundary layers in a clean version and one with incoming turbulent wakes. We focus on the behaviour of the laminar separation bubble and the secondary flow system and how these phenomena are affected by incoming wakes. The second configuration is a transonic compressor cascade in which we analyse the unsteady behaviour of the shock wave boundary layer interaction. Throughout the paper, we try to discuss not only the flow physics but also insights into how the modal decomposition techniques can help facilitate understanding and where their limitations are.

Aerospace design is increasingly incorporating design under uncertainty-based approaches to lead to more robust and reliable optimal designs. These approaches require dependable estimates of uncertainty in simulations for their success. The key contributor of predictive uncertainty in computational fluid dynamics (CFD) simulations of turbulent flows are the structural limitations of Reynolds-averaged Navier–Stokes models, termed model-form uncertainty. Currently, the common procedure to estimate turbulence model-form uncertainty is the eigenspace perturbation framework (EPF), involving perturbations to the modeled Reynolds stress tensor within physical limits. The EPF has been applied with success in design and analysis tasks in numerous prior works from the industry and academia. Owing to its rapid success and adoption in several commercial and open-source CFD solvers, in-depth verification and validation of the EPF is critical. In this work, we show that under certain conditions, the perturbations in the EPF can lead to Reynolds stress dynamics that are not physically realizable. This analysis enables us to propose a set of necessary physics-based constraints, leading to a realizable EPF. We apply this constrained procedure to the illustrative test case of a converging-diverging channel, and we demonstrate that these constraints limit physically implausible dynamics of the Reynolds stress tensor, while enhancing the accuracy and stability of the uncertainty estimation procedure.