Developing Turbulent Flow in a U-Bend of Circular Cross-Section: Measurement and Computation

Abstract

Laser-Doppler measurements of the longitudinal and circumferential velocity components are reported for developing turbulent flow in a strongly curved 180 deg pipe and its downstream tangent. In the bend, the mean longitudinal velocity component changes little after θ = 90 deg, but the circumferential component never achieves a fully-developed state. Similar behavior is observed in the normal stresses, with large levels of flow anisotropy arising everywhere in the bend and downstream tangent. Between θ = 90 deg and X/D = 5, the circumferential velocity profiles display reversals of the secondary flow which are essentially independent of the Reynolds number. Predictions of the flow development are presented based on a “semi-elliptic” truncation of the Reynolds equations in the main part of the flow with the standard k-ε effective viscosity model used to approximate the turbulent stress field. In the immediate vicinity of the wall a simpler treatment, PSL, is adopted that allows the inclusion of the very fine mesh needed to resolve the viscous sublayer without excessive computer storage. The calculated behavior displays reasonably good agreement with the measurements in the bend, including the secondary flow reversals. Downstream of the bend, however, the rate of recovery of the flow is too slow, which points to the same weakness in the turbulence model as found in the recovery region of the flow over a backward-facing step.