COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 44 (1984) 49-65 NORTH-HOLLAND THE COMPUTATION OF FLOW IN A SPIRALLY FLUTED TUBE A. BARBA zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPON Department of M echanical Engineering, UMIST, Manchester M60 lQD, U.K. G. BERGELES National Technical University of Athens, Athens, Greece I. DEMIRDZIC and A.D. GOSMAN Imperial College, London, U.K. B.E. LAUNDER Department of M echanical Engineering, UMIST, Manchester M60 lQD, U.K. Received 7 March 1983 Revised manuscript received 27 December 1983 The paper describes the development and application of a computational procedure for calculating the velocity field in fully-developed flow through spirally fluted tubes. Topics covered include the choice of coordinate system, the resultant form of the governing equations, the validation of the accuracy of the procedure by comparison with known analytical solutions and a discussion of the results of applying the procedure to the spirally fluted tube flow itself. The computations indicate that the effectiveness of the flutes in imparting swirl to the flow increases markedly with the number of flutes. The swirling motion and the turning over of fluid within the flute region produces very little increase in drag; indeed, when friction factor and Reynolds number are based on hydraulic diameter, the drag is less than for a smooth tube. 0. Nomenclature AX b f fP h hg, k,, hr cross-stream area, Hl27~7 friction factor, (-dp/dz)4A,l(~p~ZP), friction factor, (-dp/dz)2W(bW2), height of flute, magnitudes of base vectors, es, e,, e,, spiral pitch, number of flutes, pressure, axial pressure gradient, perimeter of the fluted tube, radial coordinate, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA H n P dpldz P r RI & Re R% zyxwvutsrqponmlkjihgfedcbaZYXWVUTS S flute S u V zyxwvutsrqponmlkjihgfedcbaZYXWVUTSR W w 2 inner radius of the solution domain, mean radius of the fluted tube, Reynolds number based on con- ventional equivalent diameter, W4&/( VP), Reynolds number based on mean diameter, 2 w&/v, perimeter of the flute = P/n, = hdb, velocity in 5 direction, velocity in n direction, axial velocity in z direction, bulk mean axial velocity, axial direction. 004.57825/84/$3.00 @ 1984, Elsevier Science Publishers B.V. (North-Holland)