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A harmonic balance method for the analysis of nonlinear unsteady flow around oscillating cascades is developed to improve computational efficiency for the simulation of periodic flow in turbomachinery. The periodic unsteady flow parameters can be represented by a Fourier series. In this way, the unsteady problem can be solved using conventional computational fluid dynamic method for steady problem. The analysis exploits the fact that, calculated results by harmonic balance are in good agreement with those from dual-time stepping method and linear method, and present method is highly efficient; it is about one order of magnitude faster than conventional dual-time stepping method in the present computation. The effects of the number of harmonics are also studied. It shows that lower order harmonic balance methods are sufficient to simulate periodic unsteady flow accurately except the flow fields including serious separated domain. So, lower order harmonic balance methods could be adopted to analysis unsteady flow in turbomachinery to reduce the computational cost. In addition, the characteristic of unsteady flow around a compressor cascade is investigated, and the mechanism of generation of separated vortex and the vortex shedding frequency are also analyzed. [ABSTRACT FROM AUTHOR]

When the high-order discretization scheme is applied for solving the hyperbolic conservation laws, the Gibbs oscillations emerging around the discontinuities may cause the fields to take unphysical values, which could result in the undesired interruption of calculation process. This problem is especially severe for the discontinuous Galerkin scheme. Therefore, suitable limiting calculators are supposed to be designed in order to damp the appearance of unphysical oscillations. However, the existed limiters for the discontinuous Galerkin scheme originate mostly from the finite volume methods, thus for the unstructured grids they can only limit the spatial solutions of the solutions, namely the lower-order derivatives, rather than offer an general criterion for the higher order derivatives. Due to this background, the discontinuous finite element solutions are firstly processed into general Fourier expansion series for the realization of spectral decomposition in different frequency domains. Afterwards, a modal coordinate system is originally proposed, describing the changing patterns of the directional derivatives in different orders in a new form. Finally, after the combination of the information of the current mode and its adjacent mode, and the limitation of the directional derivatives in different orders for different levels, the unphysical solutions are successfully damped. Based on this method, the Euler equations are solved for the numerical simulations of the 2-D Riemann problems, the flow field of the wind-tunnel with a front step, the reflection of shockwaves in the inner field of scramjet engines as well as the subsonic and transonic flow surrounding airfoils. The obtained results demonstrate that the new limiter is relatively reliable and it can be generalized to high-order schemes. [ABSTRACT FROM AUTHOR]

A method of rotor wake stability analysis in hovering state by Fourier method is established. By the present method, the interval of harmonic wavelength is given when any disturbance on the rotor wake is separated into Fourier series, by which the theoretical foundation of rotor wake stability analysis is improved. Furthermore, a methodology, which can extend the stability analysis for single collocation point to the whole rotor wake by extracting and analyzing the upper and lower bound of the divergence rate relative to the vortex age, has been presented. Taking the rotor of H-34 helicopter in hovering state as a numerical example, the influence of the number of wakes (blades), distribution of vortex core and distortion of wake on rotor wake stability is investigated by this method. The results show that, as for a single collocation point on the rotor wake, it is intrinsically unstable, while as for the whole rotor wake, its stability relative to the vortex age is affected by many factors and exhibits some variation characteristics. Moreover, by comparing with the experimental data of a periodicity of the hovering rotor wake, it is proved that this method can effectively predict the growth characteristics of any disturbance on the rotor wake. [ABSTRACT FROM AUTHOR]

The unsteady flow around helicopter rotor in forward flight is simulated by using harmonic balance method based on Euler equations. For the periodical characteristics in forward flight, the flow variables can be represented by Fourier series in time. Thus, the unsteady governing equations in time domain can be converted to steady equations in frequency domain, so the well-developed steady computational fluid dynamics(CFD) techniques can be used to solve the steady equations in frequency domain, and the unsteady solution is obtained. The main advantage of the present method is that only one blade needs to be simulated by implementation of the periodical condition. Compared with the traditional dual-time stepping method, harmonic balance method improves unsteady calculation efficiency greatly. The calculated pressure distributions and thrust coefficients agree well with the results of experimental data or dual-time stepping method. Message passing interface(MPI) parallel computing technique is utilized to improve the computational efficiency further. [ABSTRACT FROM AUTHOR]