In modern engineering design and manufacturing, topology optimization is widely employed to produce high-performance, lightweight structures. However, the resulting optimized geometries often contain internal enclosed voids, which not only undermine structural integrity and functional performance, but also trap residual material in additive manufacturing processes, thereby reducing overall material efficiency. Although existing methods, such as the Virtual Temperature Method (VTM) and approaches based on an auxiliary eigen problem, can detect the presence and number of enclosed voids, yet both suffer from critical limitations: VTM relies on empirically chosen temperature thresholds that lack a clear physical foundation, and the eigen problem-based approach may struggles with determining the second eigenvalue of the characteristic equation. To overcome this limitation, the present study incorporates a linear partial differential equation into the topology optimization framework. They enables the strict control of void volumes during the iterative optimization process. Numerical results show that the proposed method not only meets the lightweight and high-performance criteria, but also effectively eliminates the formation of internal enclosed voids. Consequently, it provides a more reliable and efficient technical pathway for structural design and quality assurance within the manufacturing domain, including additive manufacturing.