Dr. Haim Bau | CURRENT RESEARCH:  Micro and Nano Fluidics | Active Control of Flow Patterns | Molecular Motions
   

Active Control of Flow Patterns

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Active Control of Flow Patterns:

Thermal Convection Loops


The thermal convection loop consists of a liquid filled torus standing in the vertical plane. The lower half of the torus is heated and the upper half of the torus is cooled. The thermal convection loop is a relatively simple experimental paradigm that exhibits complex dynamic behavior. As the heating rate increases, the flow in the loop undergoes a sequence of bifurcations from a motionless state to time-independent convection to chaotic flow. The loop provides a convenient platform for studying chaotic dynamics and evaluating and comparing various control strategies. In prior experimental and theoretical investigations, Singer, Wang & Bau (1991), Singer & Bau (1991), Wang, Singer & Bau (1992), Yuen & Bau (1996), Yuen (1997), and Yuen and Bau (1998) used various linear and nonlinear control strategies to alter the bifurcation structure of the convective motion in a thermal convection loop. For example, with the aid of a controller, they were able to delay the transition from a no-motion to a motion state, laminarize the naturally occurring chaotic motion in the loop, stabilize otherwise non-stable periodic orbits embedded in the chaotic attractor, render subcritical bifurcations supercritical, and induce chaos under conditions in which the flow normally would be laminar.

 
FIG. 2: The experimentally observed temperature difference between positions 3 and 9 o'clock is depicted as a function of time. The Rayleigh number is three times the critical Rayleigh number when chaos is first observed.


FIG. 3: Experimental observations of the flow in the controlled thermal convection loop. The conditions are similar to the ones in Fig. 2. The temperature difference between positions 3 and 9 o'clock (a), the temperature difference between positions 6 and 12 o'clock (b), and the power fluctuations (c) are depicted as functions of time. Witness that the controller requires relatively small power modulations.  

 

  

PUBLICATIONS

  • Bau, H. H., 1991, On Controlling a Chaotic System, Modern Physics Letters B, 5, 1489-1497.
  • Singer J., & Bau, H. H., 1991, Active Control of Convection, Physics of Fluids A, 3 (12), 2859-2865.
  • Wang Y-Z, & Bau, H. H., 1992, Thermal Convection Loop with Heating from Above, Int. J. Heat and Mass Transfer, 35, 111-120.
  • Wang Y., Singer J., and Bau, H. H., 1992, Controlling Chaos in a Thermal Convection Loop, J. Fluid Mechanics, 237, 479-498.
  • Yuen, P. K., & Bau, H. H., Rendering Subcritical Hopf Bifurcation Supercritical, J. Fluid Mechanics, 317, 91-109, 1996.
  • Yuen, P. K., & Bau, H. H., Controlling Chaotic Convection Using Neural Nets - Theory and Experiments, Neural Networks, 11, 557 - 569, 1998.
  • Yuen, P., K., & Bau, H. H., 1999, Optimal and Adaptive Control of Chaotic Convection - Theory and Experiments, Physics of Fluids, 11, Issue 6, 1435-1448.