航空学报2025，Vol.46Issue(17)：59-70,12.DOI:10.7527/S100-6893.2025.31713
BOS测量密度场泊松方程源项快速计算方法
Fast calculation method of Poisson equation source term for BOS measuring density field
摘要
Abstract
Background-Oriented Schlieren(BOS)is a vital non-intrusive method for measuring fluid density field.The finite difference method is employed to solve the Poisson equation for calculating the projected density field.However,existing approaches for computing the source term of the Poisson equation(which mainly includes the first-order partial derivatives of the light deflection angle at the grid nodes)are time-consuming and poor precision at discontinuities with abrupt changes.To address this issue,a fast calculation method of Poisson equation source term for BOS measuring density field is proposed.A Hash function between the point coordinates and the light deflection angle field data is pre-sented to rapidly locate the BOS measurement points,their deflection angles in a local area centered around a given point,and the interpolation-based derivative formula for this local area are constructed.A region division method is proposed for areas with abrupt changes in light deflection angle,where first-order partial derivatives are computed separately using Hash tables and local interpolation.Simulation results show a 56.66%reduction in residuals and a 75.8%decrease in peak error near abrupt changes.For a cavity wind tunnel model,the method yields a finer density field and achieves a 411.85 speedup over existing Poisson source term methods.Two supersonic wind tunnel tests,on a 7° cone-cylinder and a sonic boom model,validate the method,with weak head shock waves closely matching theory and a maximum density ratio error of only 3.9%.The method proposed in this paper therefore improves the rapid and accuracy of the density field measurement,and can capture weak shock waves,offering substantial applica-tion value.关键词
密度场重建/光线偏折角/背景纹影/泊松方程/哈希函数Key words
density field reconstruction/light deflection angle/background-oriented schlieren/Poisson equation/Hash function分类
航空航天引用本文复制引用
张建,张征宇,杨洋,钱丰学,李小霞,王材钢,罗家杰..BOS测量密度场泊松方程源项快速计算方法[J].航空学报,2025,46(17):59-70,12.基金项目
国家自然科学基金(11872069) National Natural Science Foundation of China(11872069) （11872069）
