Performance and accuracy of high-order accurate large-eddy simulations for gas turbine combustor aerodynamics

The doctoral work compares two numerical approaches, the second-order finite-volume method and a newer high-order (HO) element-based method, for performing scale resolving simulations of industrially-relevant gas turbine combustor (GTC) flow fields. The overarching objective is to provide recommendations to the industrial partner on next-generation combustor simulation methods.

Computational fluid dynamics (CFD) plays an important role in physical understanding, design and development of industrial flow devices such as GTCs. The GTCs feature highly unsteady flow features and therefore require computationally-demanding scale resolving simulations for accurate results. In practice, these simulations are predominantly performed using the existing finite-volume (FV) solvers,

which are at most second-order accurate and therefore can be considerably inaccurate or expensive. As an alternative, the HO accurate methods are gaining popularity in engineering flow simulations due to their promise of higher accuracy for a given computational cost, or lower cost for a required accuracy. The HO solvers are particularly advantageous for scale resolving simulations of unsteady,

vortex dominated flows. This becomes relevant for GTCs where the combustion performance is dominated by the unsteady flow features (similar features are encountered in many other engineering scenarios such as bluff body wakes, high-lift wing configurations and rotor blades). The challenge, however, is that the HO methods are relatively complicated to implement and use for complex industrial geometries on affordable under-resolved grids. Recently, implementations of element-based HO methods, such as spectral-hp and flux-reconstruction, have been developed that are capable of handling complex geometry via hybrid meshes. However, their application to realistic flow cases using under-resolved meshes is still rare. Furthermore, very few studies could be found that evaluate the accuracy vs cost of these methods for practical scale resolving large-eddy simulation (LES). To address this gap, the present work objectively evaluates and analyses the accuracy vs cost of the element-based HO solvers against standard second-order FV solvers for LES of GTC relevant geometries. This quantification may facilitate the use of better methods in industry and academia for not only GTCs but a broader range of vortex-dominated flow applications.

The second-order FV and HO LES solvers are compared for fixed cost/accuracy under industrially relevant conditions (complex geometry and under-resolution). The representative open-source packages are employed– the second-order FV solver derives from the OpenFoam framework and the HO solver from the spectral-hp Nektar++ framework. The key differences are in the numerical accuracy and the subgrid scale treatment. The evaluation of accuracy vs cost is undertaken on four cases, two fundamental (inviscid vortex advection, Taylor-Green vortex) and two combustor-related advanced cases. The vortex advection test suggests that polynomial order 4 (P4) provides a good balance of accuracy, cost and numerical stability within the HO solver. Further, under-resolved P4 LES on the Taylor-Green vortex case shows that HO solver is at least 7 times computationally cheaper for a given accuracy level, and 2.5 to 10 times more accurate for a given cost as compared to the second-order solver. In addition, switching to coarser and unstructured meshes is found to lower the HO benefits. The combustor cases focus on two relevant flow features: port flow and swirling flow with mixing. Here, the flow parameters such as Reynolds numbers, flow split and Swirl number are representative of realistic combustors. For both cases, the unsteady data shows that the HO P4 simulations resolve a much broader range of turbulent scales and reproduce the instantaneous flow state better than the second-order simulations for a given cost. This feeds into the mean and rms velocity statistics and the P4 run matches the reference experimental data better in the majority of flow domain. However, the accuracy improvement in mean results of the advanced cases is not always as distinctive as the Taylor-Green vortex case. It is estimated that for a given accuracy, a second-order FV run may cost 3-8 times more as compared to a P4 run. In the swirling flow case, it is additionally found that the HO benefit is higher with hybrid meshes compared to the hexahedral meshes (relevant to industry). For each case, the differences observed in the flow-fields are explained using a kinetic energy dissipation rate analysis. It is found that the improvement from HO solver is mainly due to lower numerical dissipation and the subgrid scale treatment plays a secondary role.

As a first step towards combustion simulations, a passive scalar transport equation is solved in the swirler case (the scalar mimics a conserved quantity such as the mixture fraction). The solvers are extended to incorporate this additional equation. The improvement from the HO solver in scalar field results is less significant as compared to that of the velocity field. This shortfall is partly attributed

to the high Schmidt number (∼3000) from the reference experiment, for which the current scalar stabilisation technique in the high-order solver needs further improvement. Nevertheless, it is likely that for gaseous mixing (where Schmidt number is around unity) there would be considerable benefit from HO in mixing and reacting flow LES due to better resolution of small turbulent scales.

The work shows that adopting HO methods for practical turbulent combustion system applications is highly likely to provide considerable accuracy/cost benefits. It also highlighted that improvements in high-order mesh generation and scalar boundedness would be required to mature the HO solvers for realistic combustion configurations.