Viscoelastic turbulent

Beris, A.N. Dimitropoulos, C.D. Sureshkumar, R. Handler, R.D. Direct numerical simulations of polymer-induced drag reduction in viscoelastic turbulent channel flows. Proceedings of the International Congress on Rheology, Cambridge, U.K., Aug 20-25 British Society of Rheology Glasgow, 2000 Vol. 2, 190-192. 

A. N. Direct numerical simulation of viscoelastic turbulent channel flow exhibiting drag reduction effect of the variation of rheological parameters. J. Non-Newton. Fluid 1998, 79 (2-3), 433-468. 

S. Berti, A. Bistagnino, G. Boffetta, A. Celani, and S. Musacchio. Small-scale statistics of viscoelastic turbulence. Europhys. Lett., 76 63-69, 2006. 

Note that in viscoelastic turbulent flows, because of the shear thinning effect [3 5,79], we have to distinguish between two different types of wall units. One is based on the zero shear properties and the other, applicable for channel and boundary layer... 

Housiadas, K.D. and Beris, A.N. (2005) Direct Numerical Simulations of viscoelastic turbulent channel flows at high drag reduction. Korea-Aust. RheoLj, 17 (3), 131-140. 

Housiadas, K.D., Wang, L., and Beris, A.N. (2010) A new method preserving the positive definiteness of a second order tensor variable in flow simulations with application to viscoelastic turbulence. Comput. Fluids, 39,... 

Samanta, G., Beris, A.N., Handler, R.A., and Housiadas, K.D. (2009) Velocity and conformation statistics based on reduced Karhunen-Loeve projection data from DNS of viscoelastic turbulent channel flow. J. Non-Newtonian Fluid Mech., 160, 55-63. 

The transition to turbulent flow begins at Re R in the range of 2,000 to 2,500 (Metzuer and Reed, AIChE J., 1, 434 [1955]). For Bingham plastic materials, K and n must be evaluated for the condition in question in order to determine Re R and establish whether the flow is laminar. An alternative method for Bingham plastics is by Hanks (Hanks, AIChE J., 9, 306 [1963] 14, 691 [1968] Hanks and Pratt, Soc. Petrol. Engrs. J., 7, 342 [1967] and Govier and Aziz, pp. 213-215). The transition from laminar to turbulent flow is influenced by viscoelastic properties (Metzuer and Park, J. Fluid Mech., 20, 291 [1964]) with the critical value of Re R increased to beyond 10,000 for some materials. 

Reynolds numbers from 10,000 to 25,000, at which strong evidence exists that under certain conditions, a viscoelastic fluid thread can interact with turbulence eddies and reduce the overall flow friction in the pipe... 

Deviation from laminar shear flow [88,89],by calculating the material functions r =f( y),x12=f( Y),x11-x22=f( y),is assumed to be of a laminar type and this assumption is applied to Newtonian as well as viscoelastic fluids. Deviations from laminar flow conditions are often described as turbulent, as flow irregularities or flow instabilities. However, deviation from laminar flow conditions in cone-and-plate geometries have been observed and analysed for Newtonian and viscoelastic liquids in numerous investigations [90-95]. Theories have been derived for predicting the onset of the deviation of laminar flow between a cone and plate for Newtonian liquids [91-93] and in experiments reasonable agreements were found [95]. 

This classification of material behavior is summarized in Table 3-1 (in which the subscripts have been omitted for simplicity). Since we are concerned with fluids, we will concentrate primarily on the flow behavior of Newtonian and non-Newtonian fluids. However, we will also illustrate some of the unique characteristics of viscoelastic fluids, such as the ability of solutions of certain high polymers to flow through pipes in turbulent flow with much less energy expenditure than the solvent alone. 

Figure 13 plots an example of the processed PIV frame. The turbulent velocity field and its boundaries, solid wall, and liquid-free surface are simultaneously shown in Figure 13. The turbulence structures such as the coherent vortical structure near the bottom wall and its modification after release from the no-slip boundary condition near the free surface of the open-channel flow, and the evolvement of the free-surface wave can be seen in Figure 13. This simultaneous measurement technique for free-surface level and velocity field of the liquid phase using PIV has been successfully applied to the investigation of wave-turbulence interaction of a low-speed plane liquid wall-jet flow (Li et al., 2005d), and the characteristics of a swirling flow of viscoelastic fluid with deformed free surface in a cylindrical container driven by the constantly rotating bottom wall (Li et al., 2006c).

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