engleski

Harmonic Balance Method for Unsteady Periodic Flows

Harmonic Balance method for unsteady periodic flows is presented in this study. Assumption of a time periodic flow allows us to formulate 2n + 1 coupled steady state problems. By solving 2n + 1 steady state problems, we obtain a transient flow field. Fourier series expansion is the core of the Harmonic Balance method, therefore the accuracy of the method depends on the number of harmonics specified, n. Accuracy of the method also depends on the periodic nature of the problem. The method was first derived for a passive scalar transport and implemented in OpenFOAM. Validation has been carried out on 4 test cases concerning forced periodic behaviour at the inlet of the rectangular 2D domain. The first test case was a sine wave, which was fully resolved with 1 harmonic. The second case was a linear combination of sine and cosine waves with different frequencies, resolved with 2 harmonics. After successful validation of harmonic waves, robustness and accuracy test was carried out on two square waves. Square waves are numerically more difficult and more demanding, which was also shown in the convergence study carried out using 3, 5, 7 and 10 harmonics. Harmonic Balance method results were compared to transient simulation for all of the test cases. After validation of the passive scalar transport, the Harmonic Balance pressure-velocity system was derived and implemented. Preliminary validation of NACA2412 pitching airfoil was presented together with performance comparison between transient solver and Harmonic Balance.

Harmonic Balance; Unsteady Periodic Flow; Fourier Series; Scalar Transport; p-U Coupling; OpenFOAM

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