Abstract:An Aeroelastic-Harmonic Balance (A-HB) formulation of the Euler flow equations using a high-order spatial discretization scheme coupled with structural dynamic equations is proposed. The main objective of this new approach is to drammatically reduce the computational cost required to predict unsteady, periodic problems such as limit cycle oscillations (LCO). To this end, a new solver based on the Monotonicity Preserving limiter together with the AUSM +-up flux function is developed for the harmonic balance equ… Show more
“…Therefore, this article studies the transonic regime up to Mach number 0.9. However, similar to other studies, 11,39,40,43,44 this study also shows rational results for low amplitude oscillation.…”
“…22 The present investigation considers inviscid flow around the NACA0012 airfoil with a linear structure and at zero incidence. Many researchers 11,14,39,40 use Euler equations for their aerodynamic part. Since this study solves Euler equations for the aerodynamic part, the only source of nonlinearity is the compressibility effects in the transonic regime.…”
The present study presents a new nonlinear unsteady aerodynamic model to investigate the aeroelastic behavior of a self-sustained oscillating rigid airfoil. Here the unsteady Euler equations are considered simulating inviscid compressible transonic flow over an oscillating airfoil. In regard to providing boundedness criteria, a high-order technique based on a normalized variable diagram scheme has been presented. Since using dynamic mesh for simulating flow over a dynamic airfoil is too complex and requires many computational efforts, the current paper proposes a nonorthogonal and static mesh with oscillation of flow boundary. The results are compared with both well-validated numerical methods and experimental data. A time-marching method is employed to determine system responses. The predicted flutter boundary for NACA0012 airfoil at different free-stream Mach numbers is in fair agreement with direct flutter tools of the Hopf bifurcation points. Finally, the influences of the center of mass and elastic axis position on the system aeroelastic behavior are examined.
“…They have demonstrated that accurate results can be obtained efficiently with the harmonic balance method.  In this article, the harmonic balance method is applied to investigate the unsteady flow field in a full-annulus multi-stage axial compressor. First, the numerical method and the model used in this work are introduced.…”
To improve the understanding of unsteady flow in modern advanced axial compressor, unsteady simulations on full-annulus multi-stage axial compressor are carried out with the harmonic balance method. Since the internal flow in turbomachinery is naturally periodic, the harmonic balance method can be used to reduce the computational cost. In order to verify the accuracy of the harmonic balance method, the numerical results are first compared with the experimental results. The results show that the internal flow field and the operating characteristics of the multi-stage axial compressor obtained by the harmonic balance method coincide with the experimental results with the relative error in the range of 3%. Through the analysis of the internal flow field of the axial compressor, it can be found that the airflow in the clearance of adjacent blade rows gradually changes from axisymmetric to non-axisymmetric and then returns to almost completely axisymmetric distribution before the downstream blade inlet, with only a slight non-axisymmetric distribution, which can be ignored. Moreover, the slight non-axisymmetric distribution will continue to accumulate with the development of the flow and, finally, form a distinct circumferential non-uniform flow field in latter stages, which may be the reason why the traditional single-passage numerical method will cause certain errors in multi-stage axial compressor simulations.
“…The results showed that the coupled vortex‐induced vibration dynamics and the frequency lock‐in phenomenon are accurately captured, while the overall computational cost is significantly reduced. Yao and Marques presented a high‐order HB method for a transonic aerofoil forced motion with a moving normal shock wave . Dimitriadis provided a thorough discussion of the harmonic balance method and its several variants .…”
“…Yao and Marques presented a high-order HB method for a transonic aerofoil forced motion with a moving normal shock wave. 14 Dimitriadis provided a thorough discussion of the harmonic balance method and its several variants. 15 In his work, the harmonic balance method was applied to a nonlinear aeroelastic model of a transport aircraft with nonlinear stiffness in the control surface.…”
A reduced‐order model (ROM) is presented based on Fourier method for flow to predict aerodynamic forces of blades subjected to periodic time‐varying upstream wakes. In the method, a time‐varying wake is decomposed into harmonic waves by fast Fourier transformation. Using the Fourier method for flow and neglecting the cross‐coupling between harmonics, the aerodynamic forces caused by the wake are represented by a linear combination of harmonics with the same frequencies as the wake. The coefficients of the aerodynamic force harmonics are interpolated at the per‐fitted curves of the normalized Fourier coefficients (coefficients of aerodynamic forces harmonics corresponding to a unit simple harmonic excitation)–frequency relationship. A blade example is used to show the ability of the proposed method. The results indicate that the ROM method can predict the aerodynamic forces of blades caused by wakes efficiently and accurately. The amplitude levels of wakes have a linear impact on the accuracy of the ROM. Neglecting the higher‐order cross‐coupling between the harmonics in the ROM method is acceptable.
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