A ground structure based topology optimization method for thermofluid problems

Abstract

In this thesis, a ground structure based thermofluid topology optimization (TO) method is presented which is applicable to problems with creeping flow. Fluid channels with creeping flow are found in a variety of engineering applications, primarily in the field of microfluidics. Current fluid channel TO is typically done with density-based TO and Darcy-Stokes flow. While this approach can improve the performance of cooling devices, certain benefits can be achieved by using a ground structure representation of the fluid channels. By confining the flow to a Poiseuille flow pipe network, a significant reduction (up to a factor 13 in 3-D) in the number of degrees of freedom can be obtained compared to an FEM discretization of the Darcy-Stokes equations, thus reducing computation time. Other benefits of this approach are related to the increased control of explicit geometry features such as channel minimum/maximum width, channel to channel angles, or the number of channel branches at junctions. The presented method, named the Ground Structure Projection (GSP) method, uses a projection step to map the channel geometry and flow onto an Ersatz material model. Performance is subsequently evaluated using an FEM discretization of the advection-diffusion equation. The modeling is validated with comparisons against a trusted commercial FEM package. For Reynolds numbers in the range of Re < 20, the GSP method shows fluid and thermal results within 5% accuracy of an FEM solution. Afterwards, a number of numerical optimization cases are analyzed including a multi-objective (pressure drop + average temperature) optimization of a cooling device. It is shown that the GSP method can achieve improved cooling performance with good objective convergence.

In the second part of this thesis, the GSP method is applied to an industrial case concerning the reduction of optical aberration of a Projection Optics Box (POB) mirror in an EUV photolithography machine from ASML. Extreme precision is required in EUV photolithography machines and hence any unwanted optical aberration of the POB mirrors must be minimized. However, the mirrors absorb some EUV radiation resulting in thermomechanical deformation and consequent optical aberration. By optimizing the cooling channel layout to maximize surface temperature uniformity, an attempt is made to reduce optical aberration. A hybrid 2-D/3-D model is created to evaluate the optimization objective. It is shown that for a dipole and a circular heat load the temperature uniformity is improved significantly against a reference fluid channel layout. To check how well the chosen objective translates to reduced thermomechanical deformation, an optimized design is transferred to a commercial FEM package and analyzed. Since the optical systems in the EUV machine can compensate for some optical distortion, a second order surface polynomial is fitted to the FEM deformed mirror surface. The residual root mean square (RMS) error of the FEM deformed surface and the polynomial fit serves as a measure for optical performance. The optimized design performs 20% better than the reference design with a residual RMS of 3.14 µm versus 3.91 µm respectively.