The Effects of Flexion and Torsion on a Fluid Flow Through a Curved Pipe

Fluid flow through a helical pipe

“…Before proceeding, it should be mentioned that the first idea was to write the equations in the pair of basis (a i , a i ), as in [10], [21], [23], and [33]. However, covariant basis in our case depends on the small parameter ε in an inconvenient way (i.e.…”

“…We use the similar tools as in [23] but adapted to our complex geometry (see Appendix). We start by proving an a priori estimate for the velocity gradient: Proposition 1.…”

“…The formal computation was done by W.R.Dean in 1927 [7] (see also [8]), using a curvilinear co-ordinate system. However a rigorous justification of such approximation and an analysis of its error, in case of small and moderate Reynolds number, was done more then 70 years later in [23]. Dean's result was applied to the case of helical pipes at the beginning of 80's by C.Y.Wang [33] and particularly by M.Germano [10], [11].…”

“…If both κ and τ are of order one, then such situation has been rigorously treated in [23]. Indeed, in [23] the case of general curve has been addressed, with no assumptions on its curvature or torsion and helical central curve would only be a special case. Another situation covered by Wang's and Germano's result is the case when both κ and τ tend to zero with the same rate of convergence.…”

Asymptotic Behavior of Micropolar Fluid Flow Through a Curved Pipe

“…We consider an incompressible micropolar fluid flowing through a very thin (or a very long) curved pipe with an arbitrary (smooth) central curve and circular cross-section. In [9] and [10] it was proved that flexion and torsion of the pipe affect the flow profile of the fluid in the case of the classical Navier-Stokes model. The goal of this paper is to investigate those effects in the case of micropolar flow via rigorous asymptotic analysis.…”