Vapor chamber is a phase change based heat spreader broadly used for thermal management of electronics due to its high equivalent thermal conductivity. Vapor chamber performance depends on various factors such that optimization by experiment is time and cost consuming. Therefore, a steady numerical model is helpful for such optimization purposes. However, phase change at the liquid-vapor interfaces is complex and the numerical stability often suffers from the fluctuation of the pressure, temperature, and density inside vapor core. Therefore, ignoring the compressibility effect and temperature variation in the vapor core while predefined phase change (either condensation or evaporation) on the specified location at liquid-vapor interfaces becomes a practical approach. These assumptions might be helpful but insufficient for vapor chambers with high input heat flux, large geometry, or small heating area, and when the pillars are presented. This study developed a steady numerical model for the vapor chamber by implementing the source terms derived from the Lee model in the single-phase flow through the ghost fluid method. At the same time, the flow compressibility and the temperature variation within the vapor core are considered without any predefined phase change location at the liquid-vapor interfaces. Furthermore, this proposed numerical model is used to optimize the thermal performance of pillar-reinforced vapor chambers in terms of pillar pitch, porosity, and diameter. The results show that this proposed numerical model agrees with the experimental data well. Under a wide range of heat input (50 W to 350 W), the average relative temperature error ranges from 5.5\% to 8.0\% and from 1.4\% to 3.0\% for the evaporator and condenser sides, respectively, while for the heating area, the error ranges from 3.0\% to 5.0\%. Although the temperature accuracy is not exceptional compared to the works shown in the literature, this proposed numerical model exhibits good numerical stability, fast convergence (fewer than 500 iterations with over four million elements), and fewer assumptions needed. In addition, the temperature and flow characteristics agree with the phase change behaviors, making it suitable for vapor chamber design and optimization. The design optimization results show that a smaller pillar pitch, lower pillar porosity, and larger pillar diameter can reduce the thermal resistance significantly but result in higher temperature differences on the condenser side. At the same time, a small pillar pitch and large pillar diameter can enhance the critical heat flux by lowering the liquid pressure drop. However, the thermal resistance of the vapor chamber starts to increase when the contact area ratio between the pillar and heating area is higher than 50\%. Therefore, it is suggested that the pillar-reinforced vapor chamber works best at the pillar pitch of 10 mm, the pillar porosity of 0.3, and the pillar diameter of 6 mm.

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