The Subgrid-Scale Approach for Modeling Impingement Cooling Flow in the Combustor Pedestal Tile

Abstract

The widely used gas turbine combustor double-walled cooling scheme relies on very small pedestals. In a combustor it is impractical for computational fluid dynamics (CFD) to resolve each pedestal individually as that would require a very large amount of grid points and consequent excessive computation time. These pedestals can be omitted from the mesh and their effects captured on the fluid via a pedestal subgrid-scale (SGS) model. The aim is to apply the SGS approach, which takes into account the effects on pressure, velocity, turbulence, and heat transfer, in an unstructured CFD code. The flow inside a two-dimensional (2D) plain duct is simulated to validate the pedestal SGS model, and the results for pressure, velocity, and heat transfer are in good agreement with the measured data. The conjugate heat transfer inside a three-dimensional (3D) duct is also studied to calibrate the heat source term of the SGS model due to the pedestals. The resolved flow in the combustor pedestal tile geometry is numerically investigated using Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) in order to first assess the viability of the RANS and LES to predict the impinging flow and second to provide more validation data for the development of the SGS pedestal correlations. It is found that the complexity of such a flow, with high levels of curvature, impingement, and heat transfer, poses a challenge to the standard RANS models. The LES provides more details of the impinging flow features. The pedestal model is then applied to the complete tile to replace the pedestals. The results are close to both the fully resolved CFD and the measurements. To improve the flow features in the impingement zone, the first two rows were resolved with the mesh and combined with the SGS modeling for the rest of the tile; this gave optimum results of pressure, velocity, and turbulence kinetic energy (TKE) distribution inside the pedestal cooling tile.

Implicit Hybrid Quantum-Classical CFD Calculations using the HHL Algorithm

“…Since the eigen-expansions of both the HHL and GSL solutions are available, the effect of the discrepancy in the first two eigen coefficients can be used to create a corrected HHL solution as shown in Equation (15).…”

“…The 8x8 Toeplitz matrix studied by [12] needed only two real numbers to define all the non-zero entries. In previous work [13], the author considered a real world CFD test case and studied the Poisson type pressure correction matrix common to many CFD solvers that use the SIMPLE algorithm and its derivatives [14,15]. Matrices with up to 288 entries, of which 176 were unique, were analysed using an emulated HHL algorithm [16].…”