研究RESEARCH研究专题RESEARCH TOPIC
谐波平衡法在气动声学计算问题中的研究及应用Harmonic Balance Methods for Aeroacoustics
科学问题QUESTION
传统时域方法需要经历较长瞬态过程，未充分利用气动声学问题中的周期性。
Conventional time marching spends substantial effort on transients and does not fully exploit periodicity in aeroacoustic problems.
研究方法METHOD
将周期非定常问题转化为多个时刻的全耦合定常问题，实现时间与空间并行。
Transform a periodic unsteady problem into coupled steady solutions at multiple phases, enabling parallelism in both time and space.
验证证据EVIDENCE
应用于阵风—机翼相互作用，分析不同来流马赫数和频率下的压力与速度扰动。
Apply the method to gust–airfoil interaction and examine pressure and velocity disturbances across Mach numbers and frequencies.
我们如何研究How we investigate
时域方法在时间方向上顺序求解控制方程，直到流动达到周期性稳定状态。其思想简单，适合各种非定常流动的求解，故广泛用于气动声学研究中。然而时域方法没有利用声学计算问题中普遍存在的周期性特征，瞬态计算时间较长，计算效率偏低。
谐波平衡法（Harmonic Balance Method，HBM）是一种高效的周期性流动频域计算方法。其优势在于将非定常周期性流动数值求解转化为N个时刻的全耦合定常流场的求解，实现了时间与空间的同时并行计算，在保证计算精度的前提下大幅提高了计算效率，对于求解气动声学问题具有很大的优势。
目前谐波平衡法已经成功应用于阵风与机翼作用向外辐射噪声的研究中，并对不同来流马赫数和频率的影响做了计算和分析。
结合对流单极子声源、频域阵风激励与无反射边界条件，使用单极子、俯仰翼型、阵风—翼型及阵风—叶栅算例评估谐波平衡方法。
Time-domain methods march the governing equations sequentially until the flow reaches a periodic state. They are broadly applicable but do not exploit the periodic structure common in aeroacoustics, so long transient integrations can limit efficiency.
The harmonic balance method is an efficient frequency-domain approach for periodic flows. It converts an unsteady periodic solution into fully coupled steady flow fields at a finite number of phases, enabling parallel computation in time and space while retaining predictive accuracy.
The method has been applied to noise radiation from gust–airfoil interaction, including numerical analysis of the effects of incoming Mach number and gust frequency.
Convective monopoles, frequency-domain gust excitation and nonreflecting boundaries support harmonic-balance tests for monopoles, pitching airfoils, gust–airfoil and gust–cascade interactions.
计算与分析图像Computational evidence
