Fully developed viscous and viscoelastic flows in curved pipes

摘要: Some h-p finite element computations have been carried out to obtain solutions for fully developed laminar flows in curved pipes with curvature ratios from 0.001 0.5. An Oldroyd-3-constant model is used represent the viscoelastic fluid, which includes upper-convected Maxwell (UCM) and Oldroyd-B as special cases. With this we can examine separately effects of fluid inertia, first second normal-stress differences. From analysis global torque force balances, three criteria are proposed problem estimate errors computations. Moreover, accurately confirmed by perturbation Robertson & Muller (1996) cases small Reynolds/Deborah numbers.Our numerical an order-of-magnitude governing equations elucidate mechanism secondary flow absence difference. For Newtonian flow, pressure gradient near wall region driving flow; creeping combination large axial normal stress streamline curvature, so-called hoop wall, promotes a same direction inertial despite adverse there; case both larger smaller inertia promote flow.For fluids volumetric fluxes per unit work consumption flux increase then decrease number increases; behaviour should be interest engineering applications.Typical negative values difference drastically suppress ratios, make approximate corresponding Poiseuille straight pipe. The viscoelasticity causes drag enhancement compared flow. Adding typical produces reductions ratio δ = 0.01; however, 0.2, although also attenuated difference, resistance remains considerably higher than flow.It was observed that UCM models, limiting Deborah numbers met our steady solution calculations obey scaling criterion McKinley et al. elastic instabilities; present intriguing on relation between Newton iteration linear stability analyses.