Improved Models for Thermal Fluid Topology Optimization

Thermal-fluid cooling systems are commonly used in many industrial applications due to their capability to handle high heat loads. An example is the cooling of electronic devices. For the new generations of processors, the continuously increasing power density is a bottleneck in guaranteeing their functional performance. This poses serious challenges to the cooling system design. To optimize the performance of these liquid-cooled heat sinks therein, recent research has resorted to the use of topology optimization, in which the complete topology of the cooling channels is left as design freedom for the optimizer. With topology optimization, the number and the distribution of the cooling channels in the heat sink can be optimized simultaneously, greatly expanding the design freedom compared to sizing or shape optimization. In this way, better cooling performance can be obtained, and the resulting complex designs can be manufactured with modern manufacturing techniques. However, topology optimization for such a thermal-fluid system is not yet mature. In particular, due to the complex designs and conjugate heat transfer in these devices, an accurate and reliable optimization is computationally extremely challenging. This work focuses on the analysis and improvement of the models used for thermal-fluid topology optimization. By examining deficiencies currently encountered in both hydraulic and thermal-fluid topology optimization, it is shown that the widely used Darcy penalty model suffers from an issue with accuracy, in particular when used for topology optimization involving conjugate heat transfer. This issue stems from an inaccurate approximation of the no-slip condition at the solid-fluid interface and a leakage flow tolerated in the solid with this model, and is especially problematic in thermal-fluid problems. On the one hand, the leakage velocity leads to artificial advection cooling in the solid and any fluid stopped by the blocked structure. On the other hand, the slip velocity tolerated by the model at the solid-fluid interface introduces artificial advection cooling in the channel flow at the interface. These different kinds of artificial cooling are the most likely reason that the impractical optimized results with disconnected channels are obtained in the previous work. In this PhD work, an error analysis framework is established to rigorously disentangle modeling and numerical errors in the models used for topology optimization. Based on a unit channel-fin study case, the errors introduced by the Darcy penalized hydraulic model are studied in detail. A posterior error analysis is presented with the help of the analytical solutions derived from this study case. It is shown that the model error decreases only with order 0.5 w.r.t. an increase in the Darcy penalization factor, requiring strong penalization factors to achieve acceptable accuracy. With this error analysis, the Darcy force's penalty parameter can be effectively selected to achieve sufficient model accuracy when the original model is employed. Besides, the Darcy penalty term introduces a thin leakage boundary layer on the solid side of the solid-fluid interface, whose thickness decreases with increasing Darcy penalty term. It is shown that this leads to a conflict between computational cost and accuracy in topology optimization problems using this model. To tackle these issues, an improved hydraulic model is proposed that considers the viscosity in de Darcy penalty model to be a function of the porosity. The model error of this improved model converges with an order of 1 with increasing penalty. Moreover, by a proper scaling of the penalization parameters in the new model, the leakage boundary layer thickness can be kept constant, thereby resolving the conflict between the computational cost and the accuracy. Flow topology optimization with this improved model shows very promising results in several classical benchmarks. Also a second hydraulic model is proposed, in which the no-slip condition can be exactly satisfied in the solid. This removes the remaining issue of a virtual leakage flow through the solid and associated overcooling effects from the Darcy penalty models. This model is implemented in an in-house finite volume solver on a staggered mesh. Although the implementation of this idea in the finite element framework needs further investigation, the forward simulation and preliminary optimization results show good potential. Thermal-fluid topology optimization for heat sink design is studied with the improved Darcy penalty model. Due to the complex interaction of fluid flow and heat transfer near the solid-fluid interface, thermal-fluid problems impose a much stricter requirement on the accuracy of the no-slip condition. The thermal-hydraulic model is further improved to eliminate the effect of virtual advection cooling in the solid material by multiplying the advection term in the heat transfer model with the porosity. To study the grid independency in thermal-fluid topology optimization, also a superelement method is employed to constrain the minimal structure size. With a state-of-the-art 2-layer heat sink model, the improved performance obtained with the new model in terms of accuracy and computational efficiency is verified. A straight microchannel heat sink layout is considered to evaluate the impact of modeling accuracy on the grid independency. Grid independent temperatures and optimized designs are obtained once the thermal boundary layer is well resolved. In contrast, with the original Darcy penalty model more computational cost is still wasted on resolving the leakage boundary layer, and grid independency is difficult to achieve. It is shown that the grid independency is clearly improved with the improved models, in both 1D and 2D topology optimization of straight microchannel heat sinks.

Jaar van publicatie:2021

Toegankelijkheid:Open