CFD-based investigation on the flow of Bingham plastic fluids through $$90^\circ$$ bends

Abstract

In this paper, CFD-based results are presented on the estimation of losses in bends with validated numerical models for single-phase, incompressible Bingham fluids. Five fittings were investigated: $$90^\circ$$ 90 ∘ bends of different R/D ratios between 1 and 10. Bingham plastic fluids were studied with Hedström numbers in the wide range from 1 to $$10^9$$ 10 9 . Loss coefficients are given as the function of the generalized Reynolds number ($${\textrm{Re}_\textrm{gen}}=$$ Re gen = 0.1–17 800) and the generalized Dean number ($${\textrm{De}_\textrm{gen}}=$$ De gen = 0.1–12 600). The paper presents friction factors as well that were consistent with the literature. It was shown that at low generalized Dean numbers of $${\textrm{De}_\textrm{gen}}< 40$$ De gen < 40 , the losses of the bends were caused purely by the wall friction and can be estimated from the $${\textrm{De}_\textrm{gen}}$$ De gen . In a broad range of higher $${\textrm{Re}_\textrm{gen}}$$ Re gen and $${\textrm{De}_\textrm{gen}}$$ De gen numbers, the loss coefficients were separated at the basis of the Hedström numbers. This phenomenon was mainly observable in the case of high curvature and was attributed to the flow patterns. Our study investigated this range with the bend of $$R/D=1$$ R / D = 1 in detail: flow patterns in the bend and at the upstream side of the fitting were examined. An approximating equation and the fitting parameters were also given for loss coefficients.