Three-dimensional topology optimization of heat exchangers with the level-set method

We design heat exchangers using level-set method based topology optimization. The heat exchange between two fluids in separate channels is maximized while constraining the pressure drop across each channel. The flow is modeled by an incompressible Navier-Stokes-Brinkmann equation and the heat transfer is modeled by a convection-diffusion equation with high Peclet number. Each fluid region is subject to its own set of Navier-Stokes-Brinkmann equations where the Brinkmann term models the other fluid as solid, thereby preventing mixing. A level-set defines the interface that separates the two fluids. The Hamilton-Jacobi equation advects the level-set, allowing for topological changes of the channels. The velocity of the Hamilton-Jacobi equation is defined by the shape derivatives of the cost and constraint functions with respect to normal interface perturbations. We present results in three-dimensions with different heat exchanger configurations and operating conditions.