Flow through tubes with sinusoidal axial variations in diameter

Abstract

An iteration technique has been developed to solve the equations of motion for flow of an incompressible Newtonian fluid through a circular tube with a radius which varies sinusoidally in the axial direction. The iteration is essentially geometric; one proceeds from a solution for flow through a tube in which the wavelength of diameter change in the axial direction is arbitrarily large to a solution for the wavelength and amplitude of interest. Theoretical predictions of inception of secondary flow are in good agreement with experiments.

Instability in pipe flow

“…For regions of parameter space in which the use of zeroth order continuation is unable to converge to a solution, first order continuation (23) is used. To validate the base flow code, comparison was made to previous numerical results (9,14,15,22), where authors have shown that the higher the wall corrugation amplitude, the earlier the vortex formation in the bulge region, that the vortex initially forms on the upstream portion of the bulge region, and that as the Reynolds number increases, the vortex core migrates toward the downstream boundary of the bulge region. These features of the base flow are consistent with the current results (see Fig.…”

Effect of helical corrugations on the low Reynolds number flow in a tube

“…These optimum geometries do not coincide. The error of both flow rate and rotation rate are of order 4 . Our analysis does not include the singular case of n ϭ 0 (transverse corrugations) because averaging with respect to requires n 0.…”

“…2 In the case of transversely corrugated tubes (corrugations perpendicular to the tube axis), the Navier-Stokes equations essentially reduce to a biharmonic equation in terms of a stream function. Methods include approximations by assuming long wavelengths, [3][4][5][6] small amplitudes, 7 or numerical integration. [8][9][10][11][12][13][14] The present work is the first theoretical attempt to quantify the effect of helical striations on flow in a tube.…”

The creeping motion of immiscible drops through a converging/diverging tube

“…andRe defined in terms of rHP· Data for the wavy-wall tube expressed in terms ofj andRe are shown in figure 3; they coincide precisely with the Hagen-Poiseuille law for a straight-wall tube with radius rffp, thus demonstrating the relevance of rHP as a lengthscale of the flow under present conditions. Detailed velocity and pressure fields for flow through periodically constricted tubes of a variety of shapes have been calculated by Payatakes, Tien & Turian (1973), Payatakes & Neira (1977), Neira & Payatakes (1979), Fedkiw & Newman (1977), Deiber & Schowalter (1979) and Payatakes & Tilton (1983). These results consistently show that a log-log plot of an appropriately defined friction factor versus Re yields a linear relationship as shown in figure 3, at least up to the value of Re at which either flow separation or turbulence occurs.…”