Secondary Flows in Eccentric-Annular Tubes

In this paper, transversal flow field of nonlinear viscoelastic fluids abiding by the modified-Phan-Thien-Tanner (MPTT) constitutive model in straight tubes of eccentric-annular cross-section is investigated. An analytical solution is developed based on an asymptotic expansion in terms of the Weissenberg number coupled with the shape factor method a one-to-one mapping taking the circular cross-section into the eccentric annular cross section. The analysis reveals the formation of transversal flows due to elasticity and to the eccentricity parameter. The number of vortices in the cross-section depends on the ratio of the diameters in addition to the eccentricity parameter. The effect of these parameters on the vortical structure is explored for different values of the material parameters.

Investigation and Analysis of the Flow Field Induced by a Symmetrical Suction Elbow at the Pump Inlet

The pump inlet casing deflects the fluid flow from the inlet pipe, mainly arranged normally to the axis, into the axial direction. The pump inlet casing can take a large variety of geometrical shapes from curved pipes to three-dimensional elbows. The hydrodynamic field induced by symmetrical suction elbow (SSE) at the pump inlet is experimentally investigated in order to quantify it effects at the pump inlet. The pump test rig and the experimental setup are detailed. A SSE model is installed at the pump inlet. Laser Doppler Velocimetry (LDV) measurements are performed on the annular cross section located at the pump inlet. As a result, the map of the velocity field is determined quantifying the non-uniformities induced by SSE. Next, the full 3D turbulent numerical investigation of the flow in the SSE is performed. The numerical results on the annular cross section are qualitatively and quantitatively validated against LDV data. A good agreement between numerical results and experimental data is obtained. The hydrodynamic flow structure with several pairs of vortices is identified examining the vorticity field. However, two pairs of vortices with largest contribution to the flow non-uniformity are examined. Three parameters are considered to quantify the evolution of each vortex center: two geometrical quantities (e.g. the radial and angular coordinates) and one hydrodynamic (the magnitude of vorticity). The largest values of the vorticity magnitude are identified in the center of both vortices located behind the shaft. The 3D distribution of the vortex core filaments is visualized. As a result, the 3D geometry of the SSE and the pump shaft are identified as the main sources of the flow non-uniformity at the pump inlet. This deep analysis of the 3D flow field induced by the SSE paves the way towards an improved geometry with practical applications to real pump and pump-turbines.