James Mitchell White

Experimental studies on the stability of Newtonian Taylor–Couette flow in the presence of viscous heating

The dramatic effects of viscous dissipation on the stability of Newtonian Taylor–Couette (TC) flows are studied experimentally using flow visualization techniques. Viscous heating, parameterized by the Nahme–Griffith number Na , drives a transition to a new, oscillatory mode of instability when coupled with the effects of centrifugal destabilization. This instability, consisting of travelling axisymmetric vortices, only occurs when viscous heating and centrifugal destabilization are both present. Step tests in cylinder velocity show that the time following initiation of shearing required for onset of instability scales well with the time for the fluid to reach a steady temperature profile under the action of viscous heating. The onset time can be dramatically reduced at fixed Na by increasing the centrifugal destabilization through the addition of co-rotation of the outer cylinder. The onset time can also be reduced while holding the centrifugal destabilization constant by increasing the amount of viscous heating (i.e. holding Reynolds number Re constant while increasing Na ). The effects of viscous heating on the critical conditions of Newtonian TC flows are also quantified using ramp tests in cylinder velocity. These tests reveal the large extent to which viscous heating is destabilizing; at Na ≈ 2, a transition occurs at a critical Re that is less than 5% of the isothermal value.

Experimental studies on the effect of viscous heating on the hydrodynamic stability of viscoelastic Taylor–Couette flow

Experimental results on the hydrodynamic stability of three dilute polymer solutions (polyisobutylene-based Boger fluids) in Taylor–Couette flow are presented. We demonstrate that viscous heating causes significant destabilization relative to the isothermal viscoelastic case, and we quantify the effect of viscous heating on the critical conditions. Experiments in which the shear rate was stepped to a steady value indicate that the onset time for instability scales with the product of the polymeric relaxation time and the time for the fluid to reach a steady temperature profile under the influence of viscous heating. This time scale was used to perform quasistatic ramp tests to determine the critical Deborah number (De) as a function of the Nahme number, or the magnitude of viscous heating. At low Nahme and Peclet numbers, the critical De remains essentially constant and the disturbance flow is nonaxisymmetric and oscillatory. As the Nahme number (Na) and Peclet number (Pe) are increased, the disturbance flow changes to an axisymmetric and stationary vortex flow similar to Taylor vortices, and the critical De decreases dramatically. At Pe≈108 000 and Na≈0.1, corresponding to a maximum temperature increase in the gap of 1.6 K, the critical Deborah number decreases to a value that is 12% of the plateau value of Dec observed at low Na and Pe. These observations are in agreement with linear stability predictions by Al-Mubaiyedh and co-workers (1999, 2000) of viscoelastic Taylor–Couette flow for a multimode Oldroyd-B fluid in which viscous heating is present.Experimental results on the hydrodynamic stability of three dilute polymer solutions (polyisobutylene-based Boger fluids) in Taylor–Couette flow are presented. We demonstrate that viscous heating causes significant destabilization relative to the isothermal viscoelastic case, and we quantify the effect of viscous heating on the critical conditions. Experiments in which the shear rate was stepped to a steady value indicate that the onset time for instability scales with the product of the polymeric relaxation time and the time for the fluid to reach a steady temperature profile under the influence of viscous heating. This time scale was used to perform quasistatic ramp tests to determine the critical Deborah number (De) as a function of the Nahme number, or the magnitude of viscous heating. At low Nahme and Peclet numbers, the critical De remains essentially constant and the disturbance flow is nonaxisymmetric and oscillatory. As the Nahme number (Na) and Peclet number (Pe) are increased, the disturbance f...