输运概率密度函数(transported probability density function,TPDF)方法在湍流燃烧模拟中颇受重视,其优势是可以精确处理方程中的非线性化学源项。将这种方法应用于由一维随机Burgers方程控制的Burgers湍流。首先,从带非线性随机强迫...输运概率密度函数(transported probability density function,TPDF)方法在湍流燃烧模拟中颇受重视,其优势是可以精确处理方程中的非线性化学源项。将这种方法应用于由一维随机Burgers方程控制的Burgers湍流。首先,从带非线性随机强迫项的一维Burgers方程出发推导一个精确的单点速度PDF输运方程,并分别用两个模型封闭该方程中的条件对流项和条件扩散项,获得模化PDF输运方程。然后分别用基于网格的Monte Carlo随机粒子法、原始积分矩法和文章发展的线性积分矩法等3种数值解法求解模化PDF输运方程。数值实验表明,所发展的输运概率密度函数方法可用于研究B.urgers湍流的统计特性。3种数值解法中,线性积分矩法和原始积分矩法均可获得和直接数值模拟相似的结果,且线性积分矩法比原始积分矩法的计算效率更高。Monte Carlo方法的计算结果在带随机外力项的Burgers方程算例中不太理想,这或许和该方法为保持单位网格内颗粒数不变而频繁地增删粒子从而引入数值扰动有关。展开更多
The angular deviations and influential factors of Burgers orientation relationship(BOR)in Ti-6Al-4V and Ti-6.5Al-2Zr-1Mo-1V alloys were investigated by optical microscope(OM),scanning electron microscope(SEM),electron...The angular deviations and influential factors of Burgers orientation relationship(BOR)in Ti-6Al-4V and Ti-6.5Al-2Zr-1Mo-1V alloys were investigated by optical microscope(OM),scanning electron microscope(SEM),electron backscattered diffraction(EBSD)and high-angle annular dark-field scanning transmission electron microscope(HAADF-STEM).A spherical center angle model was introduced to calculate the angular deviations from the ideal BOR between α and β phases.The results indicate thatαand β phases in α colonies of both alloys do not follow the perfect BOR during β→α phase transformation,with angular deviation values less than 3°.Through detailed microstructure characterization,the broad face of α/β interfaces viewed along two different electron incident directions shows the atomic-scale terrace-ledge structure,and many dislocations are observed within α and β phases and near α/β interfaces.Further studies reveal that the angular deviations mainly originate from lattice distortions caused by dislocations in α and β phases and lattice mismatches at α/β interfaces.展开更多
文摘输运概率密度函数(transported probability density function,TPDF)方法在湍流燃烧模拟中颇受重视,其优势是可以精确处理方程中的非线性化学源项。将这种方法应用于由一维随机Burgers方程控制的Burgers湍流。首先,从带非线性随机强迫项的一维Burgers方程出发推导一个精确的单点速度PDF输运方程,并分别用两个模型封闭该方程中的条件对流项和条件扩散项,获得模化PDF输运方程。然后分别用基于网格的Monte Carlo随机粒子法、原始积分矩法和文章发展的线性积分矩法等3种数值解法求解模化PDF输运方程。数值实验表明,所发展的输运概率密度函数方法可用于研究B.urgers湍流的统计特性。3种数值解法中,线性积分矩法和原始积分矩法均可获得和直接数值模拟相似的结果,且线性积分矩法比原始积分矩法的计算效率更高。Monte Carlo方法的计算结果在带随机外力项的Burgers方程算例中不太理想,这或许和该方法为保持单位网格内颗粒数不变而频繁地增删粒子从而引入数值扰动有关。
基金supported by the National Natural Science Foundation of China(Nos.51971009,12002013,51831006)the Natural Science Foundation of Zhejiang Province,China(No.LZ23E010004).
文摘The angular deviations and influential factors of Burgers orientation relationship(BOR)in Ti-6Al-4V and Ti-6.5Al-2Zr-1Mo-1V alloys were investigated by optical microscope(OM),scanning electron microscope(SEM),electron backscattered diffraction(EBSD)and high-angle annular dark-field scanning transmission electron microscope(HAADF-STEM).A spherical center angle model was introduced to calculate the angular deviations from the ideal BOR between α and β phases.The results indicate thatαand β phases in α colonies of both alloys do not follow the perfect BOR during β→α phase transformation,with angular deviation values less than 3°.Through detailed microstructure characterization,the broad face of α/β interfaces viewed along two different electron incident directions shows the atomic-scale terrace-ledge structure,and many dislocations are observed within α and β phases and near α/β interfaces.Further studies reveal that the angular deviations mainly originate from lattice distortions caused by dislocations in α and β phases and lattice mismatches at α/β interfaces.
