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The streamsheet thickness variation obtained from a meridionalplane solu tion is required as input for a bladetoblade solution.




 The present paper is devoted to the search for variational principles for the direct aerodynamic problem of channels and aerofoil cascades (with prescribed distributed mass injection or/and suction along the profile contours for blade cooling or boundary layer control) on an arbitrary stream sheet of revolution and aimed mainly at providing a rigkms and sound theoretical basis for introducing and widely applying the finite element method to computational aerodynamics of turbomachines. Three generalized... The present paper is devoted to the search for variational principles for the direct aerodynamic problem of channels and aerofoil cascades (with prescribed distributed mass injection or/and suction along the profile contours for blade cooling or boundary layer control) on an arbitrary stream sheet of revolution and aimed mainly at providing a rigkms and sound theoretical basis for introducing and widely applying the finite element method to computational aerodynamics of turbomachines. Three generalized variational principles (among which two are for homoentropic flow, and the other for nonhomoentropic flow) are developed first, and then from them three families of variational principles are derived respectively by means of successive transformations. Furthermore, for homoentropic subsonic flows a pair of dual extremum principles are also shown to exist.Special attention is payed to taking full advantage of 2 effective means: "natural boundary conditions" and "artificial boundaries", in order to greatly simplify the numerical treatment of various boundary conditions characterizing the complexitg of the cascade problem. So in all variational principles all boundary conditions have been converted to natural ones.The variational principles presented here can be used to advantage as basis also for variationalfinite difference method and for various direct variational methods (e.g. Ritz's method, Kantorovich's method etc.).  本文致力于任意旋成面叶栅和流道气动正命题(沿叶面可有气体喷人或吸出,例如边界层控制、气膜式或发汗式冷却等)的变分原理的探索研究,为在叶轮机气动计算领域中引进和推广有限元法提供一个较严密的理论基础.结果有:1.对均熵流动,建立了两条广义变分原理,并从它们派生出两族亚广义变分原理,包括亚声速下的一对互偶极值原理;2.对非均熵流动,建立了一条广义变分原理,并由此派生出一族亚广义变分原理.文中着重充分发挥自然边界条件和人工界面的有力作用,以简化叶栅复杂多样的边界条件的处理.除用于有限元法外,它们也为变分一差分法和各种变分直接解法创造了有利条件.  The paper shows that the streamsurface theory does not take account of the actions of secondary flow induced by the disturbance blade force. Based on the streamsurface, the generalised equation of such a secondary flow in an axialturbomachine is deduced. Compressibility of flow is corrected with the local Much number of the primary flow to avoid the errors which are brought out by using only Much number upstream or a given average Much number in the traditional linearlized theory. The existance... The paper shows that the streamsurface theory does not take account of the actions of secondary flow induced by the disturbance blade force. Based on the streamsurface, the generalised equation of such a secondary flow in an axialturbomachine is deduced. Compressibility of flow is corrected with the local Much number of the primary flow to avoid the errors which are brought out by using only Much number upstream or a given average Much number in the traditional linearlized theory. The existance of the primary flow vorticity reflects in a socalled streamsheet thickness 6 of the S2 stream surface of the primary flow. The b=1 represents an irrotational primary flow or the case in which the primary flow vortex is negligible small. The b=0 is a limiting case which represents that the vorticity of the primary flow becomes infinite. Then an attempt to approach the secondary flow problem of large shear and large disturbance flow is tested.The paper also shows the equations deduced from generalised equation under the conditions of the compressible axisymmetric axialinlet flow and the incompressible 2D plane cascade flow. Then it shows that the generalised equation is appropriate for correcting the effects of the secondary flow on the stream surface flow after comparing with the equations in the reference [10], [11] and [12] when the assumptions of lifting line theory are adopted.  本文论证了流面理论未能计及由举力场的扰动所诱导的二次流的影响,并以流面为基础,推导了轴流式涡轮机械中此类二次流场所遵循的一般方程式。流场的可压缩性用当地的基本流场M数来校正,避开了通常的线性化理论中用叶排上游M数或某个平均M数所带来的误差。基本流场的旋度影响用基本流场5_2中心流面的流片厚度b来代表。b=1代表了基本流场无旋或旋度影响可忽略的情形,b=0的极限情况代表了基本流场的旋度为无穷大的情况。从而为探索解决大剪切大扰动流场中的二次流问题提供了一种可能的途径。文中分析了一般方程在不可压平面叶栅流动和可压缩轴对称轴向进气流动中所具有的形式,并指出,在举力线理论的假设前提下,它们和文献[10—12]中的基本方程的形式相同,从而证明了本方程的适用性。  In this part Ⅱ, another type "B" of the hybrid problem of airfoil cascades on a general stream sheet of revolution, in which the profile thickness distribution and the aerodynamic loading distribution [i. e. the pressure diffcrence distribution on the suctionand pressure sides (PpPs)] along the profile chord are prescribed, is formulated and studied, in order to meet various practical requirements of turbomachinery blade design more closely and flexibly. Two families of variational principles and generalized... In this part Ⅱ, another type "B" of the hybrid problem of airfoil cascades on a general stream sheet of revolution, in which the profile thickness distribution and the aerodynamic loading distribution [i. e. the pressure diffcrence distribution on the suctionand pressure sides (PpPs)] along the profile chord are prescribed, is formulated and studied, in order to meet various practical requirements of turbomachinery blade design more closely and flexibly. Two families of variational principles and generalized variational principles are developed for this hybrid problem B in terms of the moment function Ω and arzimuthal angular function introduced in part I formerly. Full advantage has been taken of two powerful means——natural boundary conditions and artificial interfaces——in order to facilitate the handling of various boundary conditions of complex character. As a result, in every variational principle all boundary conditions appear as natural ones.This part Ⅱ is also aimed at providing a broader and sound theoretical foundation for introducing the finite element method, variationaldifference method or direct variational methods into computational aerodynamics of turbomachinery as well as providing some new rational ways for cascade design.  在这第Ⅱ部分里,我们将专门研究下列一种杂交型命题:给定叶型厚度分布和叶型的气动负荷(即叶型凹、凸面上的压差)分布。我们为这种杂交型命题建立了相应的两族变分原理与广义变分原理,旨在为将有限元法、变分一差分法以及变分直接解法引进和推广到叶轮机叶栅气动问题中去提供一个更广泛、完密的理论基础,同时也为叶栅气动设计提供一些新的合理途径。在诸变分原理中充分发挥了自然边界条件和人工分界面的有力作用,已将全部边界条件都化成自然边界条件,以简化边界条件的处理。   << 更多相关文摘 
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