Theoretical Analysis of Pressure Drop in the Laminar Flow of Fluid in a Coiled Pipe

Larrain, J.; Bonilla, C.F.

doi:10.1122/1.549184

Cited by 46 publications

(20 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The WSS produces a result that at first seems counter-intuitive: the maximum WSS occurs at the inner wall (figure 17). The same phenomenon is seen in Dean flow at very low Reynolds numbers (see Larrain & Bonilla 1970;Murata et al 1976). It is due to the geometrical effect of curvature upon the basic Poiseuille flow, which is dominant if the convective inertia is sufficiently small.…”

Section: Resultsmentioning

confidence: 58%

Flow in pipes with non-uniform curvature and torsion

Gammack

Hydon

2001

J. Fluid Mech.

View full text Add to dashboard Cite

This paper describes steady and unsteady flows in pipes with small, slowly varying curvature and torsion. Four new pipe shapes are studied, using Germano's extension of the Dean equations. Analytic and numerical solutions are obtained for flows driven by a steady pressure gradient. Oscillatory flows in pipes with non-uniform curvature are obtained by numerical methods. The effects of the non-uniformities in curvature and torsion are discussed, with particular reference to wall shear stress.

show abstract

Section: Resultsmentioning

confidence: 58%

Flow in pipes with non-uniform curvature and torsion

Gammack

Hydon

2001

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…Considerable experimental work has been done by Grindley (1908), Eustice (1910), White (1929), Keulegan andBeij (1937), %ban andMcLaughlin (1963), Kubair and Kuloor ( 1963), Schmidt ( 1967), Ito ( 1969), and Larrain and Bonilla ( 1970) to establish a pressure-drop relationship. The first reliable resistance law was determined by…”

Section: Conclusion and Significancementioning

confidence: 99%

“…Several theoretical attempts have been made by Dean ( 1927Dean ( , 1928, Topakoglu ( 1967), McConalogue and Srivastava (1968), Truesdell and Adler (1970), Larrain andBonilla (1970), andAkiyama andCheng (1971) to solve the equations of fluid motion for the case of toroidal flow. The first classical work is attributed to Dean (1927Dean ( , 1928 Akiyama and Cheng (1971) also utilized the vorticity concept but restricted their solution to very large ciirvature ratios and could not obtain solutions beyond a Dean number of 300.…”

Section: Page 86mentioning

confidence: 99%

Fully developed viscous flow in coiled circular pipes

1973

View full text Add to dashboard Cite

The Navier-Stokes equations in stream-function/vorticity form were solved numerically by over-relaxation for the case of steady state, fully developed, isothermal, incompressible viscous Newtonian flow within a rigorously treated toroidal geometry. Solutions were obtained for curvature ratios ranging from 5 to 100 and for Dean numbers as low as 1 and as high as 1000. The Dean number was demonstrated to be the principal parameter to characterize toroidal flow; however, a second-order dependence upon the curvature ratio above that expressed in the Dean number was observed. Comparisons of the numerically computed axial-velocity profiles were made with experimental data. The cross-sectional pressure distribution was calculated, and a correlation is presented for a diametral pressure drop in terms of the Dean number. Curved configurations of circular tubes-such as partial coils, single coils, helical coils, and spiral coils-have received far less attention in the literature despite their frequent use in heat exchangers, chemical reactors, rocket engines, and other apparatus, equipment, or devices. In some cases, the use of curved tubes is necessitated because of geometrical restrictions. However, it is also becoming increasingly apparent that the nature of the complex primary (axial direction) and secondary (normal to primary) flow patterns in curved tubes makes possible some definite advantages of this configuration over straight tubes for a number of situations. In fully developed curved-tube viscous flow, the primary-flow-velocity profile is distorted from its parabolic straight-tube-flow counterpart, a secondary flow is established that consists of two vortices, and the resultant combined primary and secondary flow patterns cause a fluid element to have a screw-like motion. At one instant, a fluid element may be traveling near the very center of the tube cross section. After a short period of time and a short axial distance downstream, the same fluid element may be found very near the outside wall of the tube. The nature of curved-tube viscous-fluid motion, as compared with simple straight-tube parabolic flow, causes a higher axial-pressure gradient, a higher critical Reynolds number for transition to turbulent Row, a diametral-pressure gradient, a fluid-element residence-time distribution that more closely approximates plug flow, relatively high average heat-transfer and mass-transfer rates per unit axial pressure drop, especially for high-handtlnumber and high-Schmidt-number fluids, and significant peripheral distributions of the transport rates. The latter effect can be utilized to advantage in applications where the peripheral boundary conditions are asymmetrical.Of fundamental interest to the development of a complete understanding of viscous-flow phenomena in curved or coiled tubes is the nature of the velocity and pressure distributions in the fully-developed flow region. In studies by previous investigators, these profiles have been found to depend strongly on the Dean number N D , where N D , = NRe(R/Rc)'...

show abstract

“…We call the calculation procedure for (15) the &sweep, that for (16) Owing to the presence of a boundary layer for large R,, in which velocity changes rapidly for both the main and secondary flows, a co-ordinate stretching is advisable near the wall, such that fine grid lines are clustered near r = 1 and equidistance is maintained in the computational domain. To do this we introduce an r-co-ordinate stretching function ln(sy/II + 1) ln(s + 1)…”

Section: Numerical Formulationmentioning

confidence: 99%

Fully developed flow in a curved pipe of arbitrary curvature ratio

Soh

Berger

1987

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYIt is generally assumed in curved pipe flow analyses that the curvature ratio, 6, of the pipe is very small, in which case the flow depends on a single parameter, the Dean number. This is not the case if 6 is not very small. To determine the importance of this effect we have numerically solved the full Navier-Stokes equations, in primitive variable form, for arbitrary values of 6. A factored AD1 finite-difference scheme has been used, employing Chorin's artificial compressibility technique. The results show that the central-difference calculation on a staggered grid is stable, without adding artificial damping terms, due to coupling between pressure and velocity. A spatially variable time step is used with a fixed Courant number.

show abstract

Theoretical Analysis of Pressure Drop in the Laminar Flow of Fluid in a Coiled Pipe

Cited by 46 publications

References 0 publications

Flow in pipes with non-uniform curvature and torsion

Flow in pipes with non-uniform curvature and torsion

Fully developed viscous flow in coiled circular pipes

Fully developed flow in a curved pipe of arbitrary curvature ratio

Contact Info

Product

Resources

About