• Institute of Fluid Mechanics and Heat Transfer

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Stability of flows in sinusoidally-walled channels

The viscous flow in channels with a variable cross section is of fundamental interest and of great technical importance, in particular for heat exchangers. Other applications range from micro heat exchangers and catalytic converters to membrane blood oxygenators. For optimum operation, these devices should provide a heat or mass transfer as high as possible. Since the heat and mass transfer is mainly convective for moderate to high Reynolds numbers, the flow and vortex structures in the channel are essential for the transport properties in the device. For biomedical applications an efficient mixing and a high mass transfer at low shear rates is required to minimize the damage to shear- sensitive biomaterial. Hence, the local rate of strain is of crucial importance. On the other hand, the flow at low to moderate Reynolds numbers is of considerable interest for a reduction of noise emissions and the requirement to reduce the mechanical stresses if biomaterials are processed. This is particularly true for micro heat exchangers where the reduced length scales prevent high Reynolds numbers.

In order to identify the optimum operating conditions, the properties of the flow must be known as functions of the external controlling parameters. Previous investigations have demonstrated that qualitatively different flow states can exist in wavy channels. They depend on the channel geometry and the magnitude and time-dependence of the pressure gradient. However, a comprehensive and coherent understanding is still lacking.

The present investigation is aimed at a comprehensive classification of the qualitatively different regimes of wavy-channel flows driven by a steady and an oscillatory pressure gradient. This goal is achieved by an efficient linear-stability analysis of the fundamental two-dimensional flow (basic flow). This method allows to accurately detect the linear-stability boundaries at which the flow becomes three-dimensional, unsteady, or both. Besides providing the critical data the analysis also enables a theoretical understanding of the instability mechanisms.