Accelerating the Convergence of Favre-Averaged Non-Linear Harmonic Method for Efficient Modeling of Unsteady Turbomachinery Flows

Core Concepts

This paper develops a unified numerical procedure to accelerate the convergence of the Favre-averaged Non-Linear Harmonic (FNLH) method, which efficiently couples the mean flow and its finite-amplitude periodic perturbations for compressible flows in the frequency domain. The proposed approach explores the similarity of the sparse linear systems in FNLH to enable both explicit and implicit schemes, and the memory consumption is independent of the number of harmonics computed.

Abstract

The paper presents a convergence acceleration procedure for the Favre-Averaged Non-Linear Harmonic (FNLH) method, which is a computational framework for efficiently modeling unsteady flows in turbomachinery.
Key highlights:

The FNLH method couples the mean flow and its finite-amplitude periodic perturbations in the frequency domain, avoiding the need for global time-stepping.
The authors develop a unified formulation to solve the sparse linear systems of FNLH using both explicit and implicit schemes.
The implicit scheme is shown to yield better convergence and be 7-10 times more computationally efficient than the explicit scheme with 4 levels of multigrid.
The implicit scheme also consumes only around 50% of the memory used by the explicit scheme.
Compared to full annulus unsteady RANS simulations, the implicit FNLH scheme produces comparable results with two orders of magnitude lower computational time and memory consumption.
The parallel implementation of the implicit scheme is discussed, showing that the convergence rate has a weak dependence on the number of processors used.
The effectiveness of the approach is demonstrated through two test cases: a compressor rotor-rotor interaction and a turbine hot streak migration.

Stats

Compared to full annulus unsteady RANS simulations, the implicit FNLH scheme produces comparable results with two orders of magnitude lower computational time and memory consumption.

Quotes

None

Key Insights Distilled From

Convergence Acceleration of Favre-Averaged Non-Linear Harmonic Method

by Feng Wang,Ku... at arxiv.org 04-03-2024

https://arxiv.org/pdf/2404.01407.pdf

Deeper Inquiries

How could the limitations of the FNLH method, such as the assumption of known periodic disturbance frequencies and the neglect of interactions between stochastic and periodic perturbations, be addressed in future work

In future work, the limitations of the FNLH method could be addressed by developing techniques to handle unknown periodic disturbance frequencies. One approach could involve using data-driven methods, such as machine learning algorithms, to identify and adaptively adjust the frequencies of the periodic disturbances based on the flow field characteristics. This would allow for a more flexible and accurate representation of the unsteady flow phenomena. Additionally, the interactions between stochastic and periodic perturbations could be addressed by incorporating more advanced turbulence models that can capture the coupling between these different types of disturbances. By enhancing the modeling capabilities of the FNLH method in these aspects, the accuracy and applicability of the method could be significantly improved.

What other convergence acceleration techniques, beyond the implicit scheme presented here, could be explored to further improve the efficiency of the FNLH method

Beyond the implicit scheme presented in the context, other convergence acceleration techniques could be explored to further enhance the efficiency of the FNLH method. One potential approach is to investigate the use of adaptive mesh refinement strategies to dynamically adjust the grid resolution based on the flow features and the convergence behavior. This adaptive refinement can help concentrate computational resources in regions of interest, leading to faster convergence and reduced computational cost. Additionally, exploring advanced iterative solvers, such as preconditioned Krylov subspace methods or domain decomposition methods, could offer alternative ways to accelerate convergence and improve the overall efficiency of the FNLH method.

How could the FNLH method be extended to handle more complex flow phenomena, such as flow separation, transition, and combustion, that are typically challenging for frequency-domain methods

To extend the FNLH method to handle more complex flow phenomena, such as flow separation, transition, and combustion, several modifications and enhancements could be considered. For handling flow separation, incorporating advanced turbulence models, such as detached eddy simulation (DES) or large eddy simulation (LES), could provide a more accurate representation of the unsteady flow behavior near separation regions. Transition modeling could be addressed by integrating transition models into the FNLH framework to capture the laminar-to-turbulent transition process. For combustion applications, coupling the FNLH method with combustion models, such as flamelet models or detailed chemical kinetics solvers, would enable the simulation of reactive flows and combustion processes. By integrating these advanced modeling techniques, the FNLH method could be extended to tackle a wider range of complex flow phenomena with improved accuracy and fidelity.