© 2018 Elsevier B.V. In this work the fully-developed steady channel flow of the homogeneous polymer solution studied in [4] is revisited and a completely new analytical solution is proposed which is devoid of the limitations of the previous solution (β3ɛDeκ 2≤2/27), i.e., it is valid for the complete range of the rheological parameters. The viscoelastic fluid is described by the simplified Phan–Thien and Tanner model with linear stress coefficient function for the polymer contribution plus a Newtonian solvent. The solution is also valid if the polymer contribution is described by the finitely extensive non-linear elastic model with the Peterlin approximation for the average spring force (FENE-P model).

© 2018 The Japan Society of Fluid Mechanics and IOP Publishing Ltd. The evolution of viscoelastic turbulent models, in the last years, has been significant due to the direct numeric simulation (DNS) advances, which allowed us to capture in detail the evolution of the viscoelastic effects and the development of viscoelastic closures. New viscoelastic closures are proposed for viscoelastic fluids described by the finitely extensible nonlinear elastic-Peterlin constitutive model. One of the viscoelastic closure developed in the context of isotropic turbulent models, consists in a modification of the turbulent viscosity to include an elastic effect, capable of predicting, with good accuracy, the behaviour for different drag reductions. Another viscoelastic closure essential to predict drag reduction relates the viscoelastic term involving velocity and the tensor conformation fluctuations. The DNS data show the high impact of this term to predict correctly the drag reduction, and for this reason is proposed a simpler closure capable of predicting the viscoelastic behaviour with good performance. In addition, a new relation is developed to predict the drag reduction, quantity based on the trace of the tensor conformation at the wall, eliminating the need of the typically parameters of Weissenberg and Reynolds numbers, which depend on the friction velocity. This allows future developments for complex geometries.

An experimental investigation was carried out to characterize the flow field in a liquid impinging jet confined by inclined plane walls at an angle of 12° relative to the plate and emanating from a rectangular duct for two non-Newtonian fluids and a Newtonian reference fluid. The nozzle-to-plate distance (D) was kept constant at D/. H=0.8. The experiments were complemented by a numerical investigation for purely viscous generalized Newtonian fluids. Detailed measurements of mean flow fields were carried out by laser-Doppler anemometry at inlet duct Reynolds numbers of 200 pertaining to laminar flow regime and all flow fields were found to be symmetric relative to the x- y and x-z center planes. The two non-Newtonian fluids were aqueous solutions of xanthan gum (XG) and polyacrylamide (PAA) at weight concentrations of 0.2% and 0.125% respectively. A characteristic three-dimensional helical flow was seen to exist inside the recirculation, starting at the symmetry plane and spiraling to the flat side walls, which eliminated the separated flow region near these side walls, as previously found for Newtonian fluids [5]. Upon reaching the flat side wall region, the fluid in helical motion exits the recirculation and joins the main flow stream creating near-wall jets which were enhanced by the non-Newtonian fluid nature. The PAA solution, which was more elastic than the XG solution, was found to be subject to larger decelerations than the XG solution in the vicinity of the impinging plate. The numerical simulations investigated the roles of shear-thinning and inertia on the main flow characteristics for purely viscous fluids at Reynolds numbers between 10 and 800. The length of the recirculation (L R) is constant in the central portion of the channel and decays to zero before reaching the flat side walls. At high Reynolds numbers a slight increase in L R at the edge of the core of the flow is apparent. As expected, inertia increases the length of the recirculation as for Newtonian fluids, but somewhat surprisingly it also increases the three-dimensional nature of the flow by reducing the extent of the central core. Shear-thinning enhances the role of inertia especially at high Reynolds numbers, whereas at low Reynolds numbers the opposite behavior is observed. © 2011 Elsevier B.V.

An experimental and numerical investigation was carried out to characterize the isothermal laminar flow of a liquid impinging jet confined by inclined plane walls and emanating from a rectangular duct, where the flow was allowed to become fully-developed. The rectangular duct has an aspect ratio of 13, the plane walls opposite to the impinging jet have an inclination of 12°and the nozzle-to-plate distance (D) is very short, D/H = 0.8. The presence of the impact plate is felt upstream the nozzle, inside the rectangular duct, up to x/H = -0.4. The flow in the cell is symmetric relative to the x-y and x-z center planes and near the inclined walls the flow separates for Reynolds numbers higher than 208, except close to the side walls where the flow remains attached. The length of the separated flow region, LR, measured along the inclined wall, is constant in the central portion of the channel with L R/H = 0.35 for Re = 275 and dropping to zero before reaching the side walls. The recirculation length increases with the Reynolds number and with the thickness of the outlet channel. There is a three-dimensional effect associated with the finite slenderness of the geometry. It consists of spiraling secondary motions away from the central symmetry plane and toward the side walls, where the fluid merges with the main flow creating a local wall jet, as is discussed in detail. © 2012 Elsevier Masson SAS. All rights reserved.

An extensive numerical investigation was carried out to assess the influences of shear-thinning intensity and Reynolds number on the steady flow of power law fluids within an impinging jet cell, and in particular, on the pressure loss and the size and strength of the recirculation region formed along the sloping surfaces of the cell. Some comparisons with experiment are reported. The size and strength of this recirculation increases with Reynolds number and three-dimensional effects due to the finite aspect ratio of the geometry are reported. The end walls are shown to eliminate the recirculation in their vicinity and create a spiralling motion inside the recirculation. Shear-thinning enhances these effects. There is also a linear dependence between the pressure loss coefficient and the Reynolds number studied. © 2008 American Institute of Physics.