Two strategies extended the single-cascade methods from a compressible three-dimensional inverse method for radial and mixed flow turbomachines to two three-dimensional multi-cascade co-design methods for single-stage...Two strategies extended the single-cascade methods from a compressible three-dimensional inverse method for radial and mixed flow turbomachines to two three-dimensional multi-cascade co-design methods for single-stage centrifugal compressors.These two three-dimensional methods and a typical quasi-threedimensional streamline curvature through-flow inverse method were employed to design the same subsonic high-speed single-stage centrifugal compressors.The compressor performances were simulated by a commercial Reynolds averaged Navier-Stokes(RANS) equations solver.The studies show that two three-dimensional codesign methods are reasonable and feasible.It was found that : firstly the blade camber angle designed by the three-dimensional methods was larger than that designed by the quasi-three-dimensional method;and secondly with regard to two three-dimensional methods with different boundary conditions,the co-design result differences between the diffusers were small,but those between the deswirlers were relatively large.展开更多
We review the irreducible representation of an angular momentum vector operator constructed in terms of spinor algebra. We generalize the idea of spinor approach to study the coupling of the eigenstates of two indepen...We review the irreducible representation of an angular momentum vector operator constructed in terms of spinor algebra. We generalize the idea of spinor approach to study the coupling of the eigenstates of two independent angular momentum vector operators. Utilizing the spinor algebra, we are able to develop a simple way for calculating the SU(2) Clebsch-Gordan(CG) coefficients. The explicit expression for the SU(2) CG coefficients is worked out, and some simple physical examples are presented to illustrate the spinor approach.展开更多
本文主要对Hessian度量诱导的截面曲率展开分析。首先阐述Hessian度量和与之相关的Christoffor符号和曲率张量公式。接着介绍当定义域U为锥时,齐次函数的相关概念,以及Clebsch covariant S(f)和截面曲率的联系。利用R3中开子集U和超平面...本文主要对Hessian度量诱导的截面曲率展开分析。首先阐述Hessian度量和与之相关的Christoffor符号和曲率张量公式。接着介绍当定义域U为锥时,齐次函数的相关概念,以及Clebsch covariant S(f)和截面曲率的联系。利用R3中开子集U和超平面M = {f = 1}相切2-平面上一点处的截面曲率可由S(f)和Hessian行列式H(f)表示,其中f为R3上的齐次多项式,得到不变量S(f)为零与Witten-Dijkgraaf-Verlinde-Verlinde (WDVV)方程等价的条件,即f可以表示为两种特殊的形式。This paper primarily analyzes the sectional curvature induced by the Hessian metric. It begins by detailing the Hessian metric and its associated Christoffel symbols and curvature tensor formulas. It then introduces the concept of homogeneous functions when the domain U is a cone, as well as the relationship between the Clebsch covariant S(f) and the sectional curvature. Using an open subset U in R3 and a hypersurface M = {f = 1}, the sectional curvature at a point on a 2-plane tangent to M can be expressed in terms of S(f) and the Hessian matrix H(f), where f is a homogeneous polynomial on R3. The condition for the invariant S(f) to be zero is equivalent to the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations, which implies that f can be represented in two specific forms.展开更多
多晶体的晶粒取向分布可通过取向分布函数(orientation distribution function,ODF)表示,取向分布函数(ODF)可在Wigner D函数基下展开,其展开系数称为织构系数。利用Clebsch-Gordan表达式可推导出立方晶粒多晶体材料的弹性张量显表达式...多晶体的晶粒取向分布可通过取向分布函数(orientation distribution function,ODF)表示,取向分布函数(ODF)可在Wigner D函数基下展开,其展开系数称为织构系数。利用Clebsch-Gordan表达式可推导出立方晶粒多晶体材料的弹性张量显表达式。对于立方晶粒正交板材,其弹性张量中包含3个材料常数和3个织构系数,根据这3个织构系数与超声波速间的关系式,通过超声波实验来测出这3个织构系数。展开更多
基金Programme of Introducing Talents of Discipline to Universities(B08009)
文摘Two strategies extended the single-cascade methods from a compressible three-dimensional inverse method for radial and mixed flow turbomachines to two three-dimensional multi-cascade co-design methods for single-stage centrifugal compressors.These two three-dimensional methods and a typical quasi-threedimensional streamline curvature through-flow inverse method were employed to design the same subsonic high-speed single-stage centrifugal compressors.The compressor performances were simulated by a commercial Reynolds averaged Navier-Stokes(RANS) equations solver.The studies show that two three-dimensional codesign methods are reasonable and feasible.It was found that : firstly the blade camber angle designed by the three-dimensional methods was larger than that designed by the quasi-three-dimensional method;and secondly with regard to two three-dimensional methods with different boundary conditions,the co-design result differences between the diffusers were small,but those between the deswirlers were relatively large.
基金Supported by the National Natural Science Foundation of China under Grant No.11475016by the Scientific Research Foundation for Returned Scholars,Ministry of Education of China
文摘We review the irreducible representation of an angular momentum vector operator constructed in terms of spinor algebra. We generalize the idea of spinor approach to study the coupling of the eigenstates of two independent angular momentum vector operators. Utilizing the spinor algebra, we are able to develop a simple way for calculating the SU(2) Clebsch-Gordan(CG) coefficients. The explicit expression for the SU(2) CG coefficients is worked out, and some simple physical examples are presented to illustrate the spinor approach.
文摘本文主要对Hessian度量诱导的截面曲率展开分析。首先阐述Hessian度量和与之相关的Christoffor符号和曲率张量公式。接着介绍当定义域U为锥时,齐次函数的相关概念,以及Clebsch covariant S(f)和截面曲率的联系。利用R3中开子集U和超平面M = {f = 1}相切2-平面上一点处的截面曲率可由S(f)和Hessian行列式H(f)表示,其中f为R3上的齐次多项式,得到不变量S(f)为零与Witten-Dijkgraaf-Verlinde-Verlinde (WDVV)方程等价的条件,即f可以表示为两种特殊的形式。This paper primarily analyzes the sectional curvature induced by the Hessian metric. It begins by detailing the Hessian metric and its associated Christoffel symbols and curvature tensor formulas. It then introduces the concept of homogeneous functions when the domain U is a cone, as well as the relationship between the Clebsch covariant S(f) and the sectional curvature. Using an open subset U in R3 and a hypersurface M = {f = 1}, the sectional curvature at a point on a 2-plane tangent to M can be expressed in terms of S(f) and the Hessian matrix H(f), where f is a homogeneous polynomial on R3. The condition for the invariant S(f) to be zero is equivalent to the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations, which implies that f can be represented in two specific forms.
文摘多晶体的晶粒取向分布可通过取向分布函数(orientation distribution function,ODF)表示,取向分布函数(ODF)可在Wigner D函数基下展开,其展开系数称为织构系数。利用Clebsch-Gordan表达式可推导出立方晶粒多晶体材料的弹性张量显表达式。对于立方晶粒正交板材,其弹性张量中包含3个材料常数和3个织构系数,根据这3个织构系数与超声波速间的关系式,通过超声波实验来测出这3个织构系数。
