Optimal shape design of pressure-driven microchannels using adjoint variable method

The shape of microchannels is an important design variable to achieve the desired performance. Since most microchannels are, at present, designed by trial and error, a systematic optimal shape design method needs to be established. Computational fluid dynamics (CFD) is often used to rigorously examine the influence of the shape of microchannels on heat and mass transport phenomena in the flow field. However, the rash combination of CFD and the optimization technique based on evaluating gradients of the cost function requires enormous computation time when the number of design variables is large. Recently, the adjoint variable method has attracted the attention as an efficient sensitivity analysis method, particularly for aeronautical shape design, since it allows one to successfully obtain the shape gradient functions independently of the number of design variables. In this research, an automatic shape optimization system based on the adjoint variable method is developed using C language on a Windows platform. To validate the effectiveness of the developed system, pressure drop minimization problems of a 180 degrees curved microchannel and a branched microchannel in incompressible flows under constant volume conditions are solved. These design examples illustrate that the pressure drop of the optimally designed microchannels is decreased by about 20 % similar to 40 % as compared with that of the initial shape.