3D Wavy Channel Flow

The flow in channels with a variable cross section is of fundamental interest and of great technical importance, in particular for heat exchangers. Novel applications of wavy channel flow range from micro heat exchangers and catalytic converters to membrane blood oxygena-tors. Since the performance of these devices is mainly determined by the flow and the vortex structures in the channel the fluid mechanics is of prime importance for the efficiency of heat and mass transfer, a reduction of noise emissions, or a reduction of the mechanical stresses acting on biomaterial processed in the channel. 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 shown that qualitatively different flow states can exist in wavy channels. They depend on the channel geometry and the magnitude and time-dependence of the applied pressure gradient. The different flow regimes occur due to flow instabilities which are associated with the loss of certain symmetries, like time invariance or translation invariance in transverse direction. It is well known that full numerical simulations of the flow close to the linear stability boundary may need long computation times, owing to the phenomenon of critical-slowing down. A lin-ear stability analysis does not suffer from this deficit. It is one of the most powerful methods to accurately determine the stability boundaries. In this project the instability of two-dimensional steady and pulsatile flow through sinusoi-dally-walled channels is investigated numerically. The numerical calculations will be based on a combined Fourier-Chebyshev spectral method. Coordinate mapping is used to transform the wavy into a straight channel. After having calculated the two- dimensional flow, a linear temporal stability analysis will be made. The focus will be on the bifurcations from two- to three-dimensional flow. Critical stability boundaries are to be obtained as functions of the geometry parameters, i.e. the wave number, the amplitudes, and the relative phase of the sinu-soidal boundaries, and as functions of the flow parameters which are the Reynolds number for the mean flow, the flow-rate oscillation amplitude, and the frequency of the latter (Strouhal number). The instabilities found will be analyzed regarding their physical mechanisms by evaluating the local rate of change of kinetic energy and by application of other instability criteria. Comparisons will be made with instabilities known to occur in other fluid systems. Finally, the implications for an improved heat and mass transfer will be investigated.

Transition of laminar to turbulent flow is an important issue in everyday life as in many technical applications. The present project focuses on the details of this transition, which is still not fully understood. During transition to turbulence complex patterns and structures can arise in fluid flows. These patterns, that finally lead to turbulence, are investigated by numerical calculations. The model system is a channel with wavy boundaries. The main objective is to clarify the dependence of pattern formation on the flow parameters and the geometrical data. In the project the basic flow, including the formation of recirculation regions, has been calculated and validated. During the development of a new calculation code for the investigation of hydrodynamical instabilities fundamental difficulties in the implementation of the problem occurred. Commercial software packages for computational fluid dynamics (CFD) are currently not capable of calculating the formation of instabilities. By implementing codes for the investigation of particular model systems, important experience can be gained. The aim is the calculation of the formation of instabilities and the responsible physical mechanisms for arbitrary geometries and systems. Knowledge of these hydrodynamical instabilities is not only necessary for the design of technical and medical applications (heat exchanger, membrane blood oxygenator), but can also be an important step towards active flow control that will help reduce fuel consumption and suppress noise generation of aircraft in future.