Calculation of turbulent flows in a compressor/turbine cascade is a challenging task due to the complicated flow field and high computational costs. In the current study, the turbulent flow in a compressor cascade is calculated by using a new simulation method developed by the author, i.e., parameter extension simulation (PES). A typical PES calculation is composed of three consecutive steps: Set up an asymptotic relationship between the exact solution of the Navier-Stokes equations and the reference solution for the initial parameter values, calculate the reference solution and the necessary asymptotic coefficients, and extend the reference solution to the parameter values to produce the exact solution. A controlled-eddy simulation (CES) method has been developed to calculate the reference solution and the asymptotic coefficients. The CES method is a special case of large-eddy simulation (LES), in which a weighting coefficient and an artificial force distribution are used to damp part of the turbulent motions. The artificial force distribution is modeled with the help of eddy viscosity. The reference weighting coefficient can be determined empirically or in a convergence study.

The developed method is used to calculate the turbulent flows in a compressor cascade made of NACA0065-009 airfoils. The Reynolds number 3.82x10^5^  and the attack angles from 0^o^ to 4^o^ are accounted for in the study. The effects of end-wall, the attack angle, and the tripping band on the turbulent flows are analyzed.

Tripping bands are used in the experiments to remove the difficulty of simulating the laminar–turbulence transition, which, nevertheless, can be directly resolved from the PES solution without any difficulty. To compare with experimental data, the simulations are first carried out with the tripping bands accounted for. The effects of the tripping bands are modeled by adding the Darcy’s term to the momentum equation. The PES results are compared intensively with the experimental data as well as the LES results using the Smagorinsky and k-equation-transport subgrid models. The secondary flows including the horseshoe and passage vortices are clearly identified from the reference CES results. The PES results for the pressure coefficient at the airfoil surface and the total pressure loss coefficient downstream the airfoil are in good accordance with the experimental data. When the same mesh resolution is used, the PES results are more accurate than the other LES results.

The simulation was repeated without the tripping bands. Unlike a Reynolds-average Navier-Stokes simulation (RANS) or detached-eddy simulation (DES) method, the PES method can capture the laminar-turbulence transition at the suction surface of airfoil directly without introducing any transition model. The PES results show that the transition leads to a jump of the pressure coefficient. This is in accordance with the experimental observation. The CES solution also shows the perturbation of instantaneous dissipation rate close to the transition region.

The numerical study shows that the PES solution can identify more flow details than a RANS or DES solution. In addition, the PES requires a lower mesh resolution than a traditional LES method. These characteristics make the PES a potential method for simulating flows in turbomachinery that are characterized by complex geometry and high Reynolds number.


Parameter Extension Simulation of Turbulent Flows in a Compressor Cascade With a High Reynolds Number

Division / Sponsor:
International Gas Turbine Institute (IGTI)

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2020/volume/84058

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