M. Bourouis et M. Prevost, NUMERICAL STUDY OF FULLY-DEVELOPED FLOW A RRANGEMENT IN A WAVY-WALLEDPIPE UNDER LAMINAR CONDITIONS, Chemical engineering journal and the biochemical engineering journal, 55(1-2), 1994, pp. 15-25
This study treats the influence of the wavy wall geometry on the inter
nal hydrodynamics and the flow arrangement for the case of fully devel
oped flow in a pipe under laminar conditions. The Navier-Stokes equati
ons are established, for the case of isothermal and axisymmetric liqui
d flow in a pipe characterized by a sinusoidal wall profile. The discr
etization of these equations is based on a finite difference method. F
or the case with vorticity and stream function as variables, the selec
ted method is an algebraic transformation of the non-orthogonal coordi
nates. In addition, an orthogonal mathematical field is obtained from
a complex physical field. The calculation process is controlled by use
of the Neumann limiting conditions and a comparison is made with the
results found in the literature (flow conditions without remixing). Th
e present work is also carried out to predict the best sinusoidal wall
profile to obtain a large remixing effect. It is noted that the wavy
wall geometry directly affects the flow arrangement: the fluid flow is
fully disturbed along the radial direction for weak hydrodynamic cond
itions (Re < 100), whereas for stronger conditions (Re greater-than-or
-equal-to 100) this influence is only noticed near to the wavy wall. T
hese results define the area of application of this wall geometry if a
recirculating effect is required.