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数学
FLUID FLOW IN A HELICAL PIPE
<正> Without simplifying the N-S equations of Germano's, we study theflow in a helical circular pipe employing perturbation method. A third perturbationsolution is fully presented. The first- second- and third-order effects of curvature кand torsion т on the secondary flow and axial velocity are discussed in detail. Thefirst-order effect of curvature is to form two counter-rotating cells of the secondaryflow and to push the maximurn axial velocity to the outer bend. The two cells arepushed to the outer bend by the pure second-order effect of curvature. The combinedhigher-order (second-, third-) effects of curvature and torsion, are found to be anenlargement of the lower vortex of the secondary flow at expense of the upper oneand a clockwise shift of the centers of the secondary vortices and the location ofmaximum axial velocity. When the axial pressure gradient is small enough or thetorsion is sufficiently larger than the curvature, the location of the maximal axialvelocity is near the inner bend. The equation of the volume flux is obtained from integrating the perturbationsolutions of axial velocity. From the equation the validity range of the perturbationsolutions in this paper can be obtained and the conclusion that the three terms oftorsion have no effect on the volume flux can easily be drawn. When the axial pressuregradient is less than 22.67, the volume flux in a helical pipe is larger than that in astraight pipe.
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Acta Mechanica Sinica
1999年04期
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