Taylor Vortices–Induced Instability (Transition Flow) versus “Turbulence” in Concentric Cylinders Separated by Microscale Clearances

Abstract

This paper is concerned with the relationship between the onset and the development of the Taylor instabilities and their treatment as turbulent flows in the most accepted turbulence models (Constantinescu (1); Ng-Pan (2); Hirs (3)) used with the Reynolds equation, in the range of 41.3√R/C < Re < 2000. The authors show that in between these limits there is a transition regime where the velocity and pressure profiles are fundamentally different from either a Couette flow or a fully developed turbulent flow. Thus the issue under consideration is whether the flow formations observed during Taylor instability regimes should be simulated using the widely accepted turbulence models as they presently are modeled in microscale clearance flows. We are considering the flow of light silicone oil in gaps varying from 3.302 mm (0.13 in.) to 0.127 mm (0.005 in.) between two concentric cylinders, with the inner cylinder rotating. The computational engine used in this study is a well-established and a tried software package: CFD-ACE+. It was found that the Taylor vortices (cells) begin to form at certain, but different, “critical” speeds, function of clearance size, and as the speed grows, the vortices become fully developed and evolve further into wavy vortices. Calculations show that both the 1st and 2nd critical Taylor numbers and Reynolds numbers are functions of the clearance size. The Taylor numbers decrease, while the Reynolds numbers increase with the decrease in clearance size. The onset of both instabilities is clearly characterized by the discontinuities in the Torque-√Ta (or Torque – Re) curve slope. The calculations presented here show that the slope changes in the above-mentioned graphs are due to the changes in the average velocity gradient on the outer cylinder and not to a change in the actual viscosity as it is implemented by the turbulence models mentioned above. Finally a comparison is made between present calculations and the data of Roberts (4), Cole (5), Walowit et al. (6), Weinstein (7), Koschmieder (8), and DiPrima (9).

KEY WORD:

• Flow Instability
• Transition Flow
• Reynolds Equation
• Turbulence

Acknowledgments

Presented at the STLE Annual Meeting in Las Vegas, Nevada May 15-19, 2005

Review led by Jane Wang