广义矩阵法在求油气输送积分方程中的应用

Generalized Matrix Method and Its Applications to Integral Equations in Oil-gas Transportation

基于建立在非笛卡儿张量分析的广义矩阵法,根据选择的任意曲线坐标系和基,在非正交的一般曲线坐标系中,提出了三维空间中油或气单相输送及油气两相输送的动量传递和能量传递的一系列积分方程的张量式和广义矩阵式。利用这些公式,在任意的、不均匀螺距的螺旋线-笛卡儿坐标系中,导出了油或气单相输送及油气两相输送的质量守恒、动量守恒和能量守恒的积分方程。

A series of integral equations for momentum or energy transfer in tensorial and generalized matrix form in the industry of oil-gas transportation is derived in non-orthogonal or orthogonal general curvilinear coordinates, according to arbitrary curvilinear coordinates and bases and using generalized matrix method based upon non-Cartesian tensor analysis. The integral equations of mass conservation, momentum conservation and energy conservation in an arbitrary curvilinear coordinate system are developed in an arbitrary inhomogeneous pitch. The results of the derivation of these integral equations show their agreements with the references in transactions of ASME.