Numerical solutions turbulent pipe flow

Flow through resistive porous elements has been studied by many in the particle filtration community to determine basic relations and empirical correlations (Ergun, 1952 Jones and Krier, 1982 Laws and Livesey, 1978 Munson, 1988 Brundrett, 1993 Olbricht, 1996 Sodre and Parise, 1997 Wakeland and Keolian, 2003 Wu et al 2005 Valli et al 2009). A detailed and rigorous review of previous analytical and numerical solutions in porous pipe, annulus, and channel flow is reserved in Appendix F only highlights are presented here. Porous channel flow is classified by the size of flow within the channel (laminar or turbulent), the number of porous walls (one or two), the size (small, large, arbitrary), and nature (uniform or variable) of injection into the porous element, the type of transverse and axial boundary conditions at the porous surface (suction or injection), and whether or not there is heat transfer and/or electrical or magnetic component, where the injection Reynolds number is defined as ... 

---