Despite being one of the oldest and most widely-used turbulence models in engineering computational fluid dynamics(CFD),the k-ωmodel has not been fully understood theoretically because of its high nonlinearity and co...Despite being one of the oldest and most widely-used turbulence models in engineering computational fluid dynamics(CFD),the k-ωmodel has not been fully understood theoretically because of its high nonlinearity and complex model parameter setting.Here,a multi-layer analytic expression is postulated for two lengths(stress and kinetic energy lengths),yielding an analytic solution for the k-ωmodel equations in pipe flow.Approximate local balance equations are analyzed to determine the key parameters in the solution,which are shown to be rather close to the empirically-measured values from the numerical solution of the Wilcox k-ωmodel,and hence the analytic construction is fully validated.The results provide clear evidence that the k-ωmodel sets in it a multilayer structure,which is similar to but different,in some insignificant details,from the Navier-Stokes(N-S)turbulence.This finding explains why the k-ωmodel is so popular,especially in computing the near-wall flow.Finally,the analysis is extended to a newlyrefined k-ωmodel called the structural ensemble dynamics(SED)k-ωmodel,showing that the SED k-ωmodel has improved the multi-layer structure in the outer flow but preserved the setting of the k-ωmodel in the inner region.展开更多
将食用植物油中的脂肪酸转化为相应的脂肪酸甲酯,并采用立体结构参数Steric and Electronic Descriptors(SEDs)表征其分子结构,然后运用多元线性回归(MLR)方法,建立了预测食用植物油中脂肪酸(甲酯)的定量结构-色谱保留相关(QSRR)模型,...将食用植物油中的脂肪酸转化为相应的脂肪酸甲酯,并采用立体结构参数Steric and Electronic Descriptors(SEDs)表征其分子结构,然后运用多元线性回归(MLR)方法,建立了预测食用植物油中脂肪酸(甲酯)的定量结构-色谱保留相关(QSRR)模型,同时采用内部及外部双重验证的方法对所建模型的稳定性能和预测能力进行了分析和验证。建模计算值、留一法(LOO)交互检验(CV)预测值和外部样本预测值的相关系数R、R LOO、Q2ext分别为0.9990、0.9970、0.9860。结果表明,SEDs参数能较好地表征食用植物油中的脂肪酸甲酯分子的结构信息,所建立的QSRR模型具有良好的稳定性和预测能力,为间接分析鉴定食用植物油中脂肪酸提供了一种方便有效的新途径。展开更多
基金the National Numerical Wind Tunnel(No.NNW2019ZT1-A03)the National Natural Science Foundation of China(Nos.91952201,11372008,and 11452002)。
文摘Despite being one of the oldest and most widely-used turbulence models in engineering computational fluid dynamics(CFD),the k-ωmodel has not been fully understood theoretically because of its high nonlinearity and complex model parameter setting.Here,a multi-layer analytic expression is postulated for two lengths(stress and kinetic energy lengths),yielding an analytic solution for the k-ωmodel equations in pipe flow.Approximate local balance equations are analyzed to determine the key parameters in the solution,which are shown to be rather close to the empirically-measured values from the numerical solution of the Wilcox k-ωmodel,and hence the analytic construction is fully validated.The results provide clear evidence that the k-ωmodel sets in it a multilayer structure,which is similar to but different,in some insignificant details,from the Navier-Stokes(N-S)turbulence.This finding explains why the k-ωmodel is so popular,especially in computing the near-wall flow.Finally,the analysis is extended to a newlyrefined k-ωmodel called the structural ensemble dynamics(SED)k-ωmodel,showing that the SED k-ωmodel has improved the multi-layer structure in the outer flow but preserved the setting of the k-ωmodel in the inner region.
文摘将食用植物油中的脂肪酸转化为相应的脂肪酸甲酯,并采用立体结构参数Steric and Electronic Descriptors(SEDs)表征其分子结构,然后运用多元线性回归(MLR)方法,建立了预测食用植物油中脂肪酸(甲酯)的定量结构-色谱保留相关(QSRR)模型,同时采用内部及外部双重验证的方法对所建模型的稳定性能和预测能力进行了分析和验证。建模计算值、留一法(LOO)交互检验(CV)预测值和外部样本预测值的相关系数R、R LOO、Q2ext分别为0.9990、0.9970、0.9860。结果表明,SEDs参数能较好地表征食用植物油中的脂肪酸甲酯分子的结构信息,所建立的QSRR模型具有良好的稳定性和预测能力,为间接分析鉴定食用植物油中脂肪酸提供了一种方便有效的新途径。
