Periodic Unsteady Transonic Compressible Flow Simulation using Fourier-Based Algorithm

Document Type : Original Article

Authors

• M.R. Mohaghegh
• M. Malek Jafarian

10.22067/fum-mech.v25i2.40479

Abstract

The present research simulates time-periodic unsteady transonic flow around pitching airfoils via the solution of unsteady Euler and Navier-Stokes equations, using Time Spectral Method (TSM) and compares it with the traditional methods such as BDF and Explicit Structured Adaptive Grid Method. The TSM uses a Fourier representation in time and hence solves for the periodic state directly according to physics of flow. Mathematical tools used here are discrete Fourier transformations. The TSM has been validated with 2D external aerodynamics test cases. These test cases are NACA 64A010 (CT6) and NACA 0012 (CT1 and CT5) pitching airfoils. Because of turbulence nature of flow, Baldwin-Lomax turbulence model has been used in viscous flow analysis with large oscillation amplitude (CT5 type). The results presented by the TSM are compared with experimental data and the two other methods. By enforcing periodicity and using Fourier representation in time that has a spectral accuracy, tremendous reduction of computational cost has been obtained compared to the conventional time-accurate methods. Results verify the small number of time intervals per pitching cycle (just four time intervals) required to capture the flow physics with small oscillation amplitude (CT6) and large oscillation amplitude (CT5) as compared to two other methods.

Keywords

• Time Spectral Method
• Unsteady transonic flow
• Pitching airfoil
• Discrete Fourier transform
• Baldwin-Lomax turbulence model

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