Lia Tong-ji, Pu Qun. An Exact Solution for Incompressible Flow Through a Two-Dimensional Laval Nozzle[J]. Applied Mathematics and Mechanics, 1986, 7(6): 487-495.
 Citation: Lia Tong-ji, Pu Qun. An Exact Solution for Incompressible Flow Through a Two-Dimensional Laval Nozzle[J]. Applied Mathematics and Mechanics, 1986, 7(6): 487-495.

An Exact Solution for Incompressible Flow Through a Two-Dimensional Laval Nozzle

• Publish Date: 1986-06-15
• A careful examination of the variation of the velocity along the centerline and the contour of a Laval nozzle in the physical plane shows that either the upper or the lower half of the Laval nozzle assumes the same form of a slitted thick airfoil with tandem trailing edges. These two airfoils lie on different Ricmann sheets in the hodograph plane. The interior of the airfoil is then mapped onto an infinite strip in the complex potential plane. Making use of these results, we obtained an exact solution for the incompressible potential flow through a two-dimensional Laval nozzle. The solution is applicable for nozzles with any given contraction ratio n1 expansion ratio n2 and throat wall radius R*. As examples of the method, various nozzle contours, the velocity distribution of the flow, and the locations of the fluid particles at different time intervals are presented.
•  [1] Lin, T, C, and L, G, Witehead, The St, Venant torsion problem for the hyperbolic airfoil cross section, Bulletin, Experimental Station, Univ, of Wash,,Seattle, Wash,,U, S, A,,118 (1951) 103-111. [2] 浦群、林同骥,二元拉伐尔喷管中的亚、跨声速流动,力学学报, 16. 6 (1984) 535-545. [3] Lin, T.C.,Ducts for accelerated flow, Proc, of the Second U, S, National Congress of Applied Mechanics (1954).

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