摘要
针对动导数计算工程应用亟需的高效、高精度发展目标,提出求解非定常雷诺平均Navier-Stokes(RANS)方程的时间谱方法(TSM)的全隐格式,以改善采样点数较大时的数值稳定性,并将TSM离散推广到Menter剪切应力输运(SST)湍流模型,以提高TSM的工程实用性。将TSM应用于数值模拟NACA0015强迫振荡,所得计算结果与试验数据和双时间步(DTS)方法的计算结果均能较好地吻合,验证了TSM对周期运动的模拟能力。采用发展的TSM对高超声速HBS标模和超声速Finner标模进行计算,并分析研究攻角和马赫数对动导数的影响规律。结果表明:对于周期运动,具有与DTS方法相当的计算精度,但TSM的计算效率会随来流马赫数的增大而提高,其效率优势在高超声速范围时可达一个量级以上。
The engineering application requires the solver of periodic unsteady flows to be of high efficiency and precision. Based on solving the Reynolds-averaged Navier-Stokes （RANS） equations, a fully implicit version of the time spectral method （TSM） is established and the stability problem that occurs as the sampling number grows is improved. The Menter shearstress transport （SST） turbulence model is discretized with the TSM, which makes the TSM more applicable to practical engineering problems. The TSM is applied to simulate the forced oscillation of NACA0015. The calculated results are in good agreement with the experimental data and the results of the dual time stepping （DTS） method, validating the ability of the TSM to simulate the periodic motion. The hypersonic HBS and the supersonic Finner are taken as typical examples of computing dynamic derivatives using the TSM. Influences of the angle of attack and Mach number on dynamic derivatives are analyzed. Results show that the TSM can acquire the same order of accuracy compared with the DTS method. But the relative efficiency of the TSM improves as the Mach number increases. The efficiency advantage in hypersonic range could be up to an order of magnitude.
出处
《航空学报》
EI
CAS
CSCD
北大核心
2015年第6期2016-2026,共11页
Acta Aeronautica et Astronautica Sinica
基金
国家自然科学基金(11372040)~~
关键词
时间谱方法
动导数
RANS
强迫振荡
傅里叶变换
time spectral method
dynamic derivatives
RANS
forced oscillation
Fourier transformation
