航空学报 > 2014, Vol. 35 Issue (3): 736-743   doi: 10.7527/S1000-6893.2013.0256

谐波平衡法在非定常流场中的应用

陈琦1,2, 陈坚强2, 谢昱飞2, 袁先旭2   

  1. 1. 中国空气动力研究与发展中心 空气动力学国家重点实验室, 四川 绵阳 621000;
    2. 中国空气动力研究与发展中心 计算空气动力研究所, 四川 绵阳 621000
  • 收稿日期:2013-04-01 修回日期:2013-05-12 出版日期:2014-03-25 发布日期:2013-07-20
  • 通讯作者: 陈坚强,Tel.:0816-2463009 E-mail:jq-chen@263.net E-mail:jq-chen@263.net
  • 作者简介:陈琦 博士研究生,助理研究员。主要研究方向:非定常计算空气动力学。Tel:0816-2463157 E-mail:chenqi@mail.ustc.edu.cn;陈坚强 男,博士,研究员,博士生导师。主要研究方向:计算流体力学方法及复杂流动数值模拟等。Tel:0816-2463009 E-mail:jq-chen@263.net
  • 基金资助:

    国家自然科学基金(11172315)

Application of Harmonic Balance Method to Unsteady Flow Field

CHEN Qi1,2, CHEN Jianqiang2, XIE Yufei2, YUAN Xianxu2   

  1. 1. State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, China;
    2. Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China
  • Received:2013-04-01 Revised:2013-05-12 Online:2014-03-25 Published:2013-07-20
  • Supported by:

    National Natural Science Foundation of China (11172315)

摘要:

谐波平衡法(HBM)适用于模拟周期性非定常流场。求解这类问题时,只需要一个周期中几个等距时刻的流场解,即可重建整个周期流动的时间历程,计算效率较高;同时还采用谱算子精确求解流场变量对物理时间的导数项,保障了算法的计算精度。鉴于此,详细介绍了谐波平衡法的原理和实现过程,并给出了如何在现有计算程序下实现谐波平衡法的流程。取跨声速翼型和超声速钝锥两个周期性强迫俯仰振荡绕流为例,以双时间步方法为参考,对谐波平衡法的效率和精度作了详细的考核和分析。计算结果表明,谐波平衡法的内存消耗较大,谐波数NH=2时约为双时间步方法的4倍,但谐波平衡法取得与双时间步方法相近结果的计算时间仅为后者的1/5。因此,谐波平衡法是一种有应用前景的工程实用方法。对于长周期问题,谐波平衡法的优势更加明显。

关键词: 谐波平衡法, 双时间步方法, 非定常流动, 强迫俯仰振荡, 数值模拟

Abstract:

The harmonic balance method (HBM) is adapted in this paper to solve periodic unsteady flow problems. For these problems, this method has a high computational efficiency because it can rebuild the time history of a complete periodic flow with only computations at several equally spaced time intervals. The order of accuracy of the algorithm is guaranteed by employing a spectral operator to accurately solve the derivatives of the flow variables against the physical time. The mechanism and realization of the harmonic balance method are introduced in detail, and the process of modifying the existing code is presented. Two periodically forced pitching oscillation test cases are used to demonstrate the efficiency and accuracy of the harmonic balance method, including an airfoil in subsonic flow and a bluntcone configuration in hypersonic flow.A comparison is made with the dual time stepping method, and the results show that the harmonic balance method requires considerably more CPU memory, with the memory in NH=2 case being four times that of the dual time-stepping method. Yet it can reduce the computing time greatly with only about 1/5 in NH=2 case of that needed by the dual time-stepping method to obtain similar results. Therefore the harmonic balance method is an engineeringly applicable method with bright prospects. For problems with a long period, it has a more obvious advantage.

Key words: harmonic balance method, dual time stepping method, unsteady flow, forced pitching motion, numerical simulation

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