By Eric Ricci* and William J. Kelly, Villanova University, Villanova, PA

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Mixing tanks are typically used in the production of viscous fluids such as petroleum, plastics, paints, paper, cosmetics, and food. The mechanical agitation of fluid in these vessels can significantly increase the rate of heat transfer between the process and cooling fluids. Since the 1950s, a number of authors have explored heat transfer for Newtonian fluids in a variety of agitated vessel configurations. There has been a limited amount of research performed, however, for heat transfer to non-Newtonian (power law) fluids.

Flow patterns between the impeller and coils at Re=650

In an ongoing research project at Villanova University, CFD has been used to understand how power law fluid rheology affects the local heat transfer coefficients at helical coils in a stirred tank operating in the transitional flow regime. With the use of FLUENT 6.0, it was possible to observe spatially varying phenomena in both the fluid flow and heat transfer in the tank. With limited technology, previous investigations could, at best, make only general approximations about this kind of process.

The numerical simulations were designed to investigate whether non- Newtonian behavior, defined by the index n (pseudoplasticity) in the Metzner- Otto viscosity method, is sufficiently reflected in the Reynolds number in existing correlations for the Nusselt number. The Metzner-Otto method characterizes the fluid viscosity in the high shear region of the impeller, and not in the film where heat transfer is actually taking place. To better account for the n dependency, three new correlations were proposed, each with a different approach to predicting the Nusselt number.

Steady-state temperature profile in the mixing tank

The computational grid for the CFD simulations was strategically decomposed in GAMBIT 2.0 to allocate a large number of cells in the impeller region and around the heat transfer surfaces. The model consisted of a hexagonal and tetrahedral mesh of 497,000 cells, with a concentration of cells in the boundary layer around the coil surface (10 cells within 2 mm) that was designed to capture local temperature and velocity gradients. The non-Newtonian flow was modeled as laminar, and a multiple reference frames (MRF) approach was used to solve the discretized equations of energy and motion in one-quarter of a baffled tank driven by a Lightnin A200 pitched blade turbine.

The recommended correlation takes the form of the Sieder-Tate type equation (Nu = CRe^xPr^y), where the geometrical constant, C, and Reynolds number exponent, x, are functions of pseudoplasticity (n). The average difference between the correlation-predicted Nusselt numbers and those generated by FLUENT was 8% over the entire range of n values. The difference slightly increases as the fluid becomes more pseudoplastic (low n).

High density grid captures the thermal boundary layer at the coil surface

The research has led to an alternative coil design that may provide more efficient heat transfer (i.e. less area and power consumption) for mixing tanks with pitched blade turbines in the transitional flow regime. By analyzing the CFD-generated flow patterns and understanding how the impeller discharge angle directs flow in the vessel, it was found that moving the top three coils to a location where they would be in direct contact with (and closer to) the impeller plume over a Reynolds number range of 450-850 would result in higher heat transfer coefficients.

Using GAMBIT and FLUENT, it is possible to change other geometrical factors in the mixing tank (i.e. coil spacing, tube size, coil bank diameter, impeller diameter and position, etc.) to evaluate how these additional parameters affect heat transfer to pseudoplastic fluids. Design engineers in the chemical process industry can then model specific tank configurations with a variety of fluids under a wide range of mixing situations to determine the optimal heat transfer.

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