## 4 Discussion  
ATHs are indispensable tools in modern dental treatment. While previous studies have focused primarily on enhancing ATH performance metrics such as rotational speed, torque, and power [9; 12; 15; 23; 24], this study exclusively investigates the aeroacoustic noise mechanisms that directly impact the patient experience. Although steady-state analyses of ATH aerodynamics have been conducted in prior research [12; 13; 15], such approaches are fundamentally inadequate for capturing transient pressure fluctuations for noise generation. This study is the first to simulate transient flow to assess aeroacoustic noise. When detailed analysis of time-dependent effects is required to understand aerodynamic flow and noise during rotation or to optimize control strategies, transient modeling is essential. However, transient calculation introduces complexities such as initial conditions, time step schemes, and convergence, making the setup and analysis more challenging. More computational resources and time are required for managing its multiple time steps and transient data. Our novel CFD framework for transient conditions addresses these challenges. By generating a highly refined mesh near the complex impeller geometry (Figures 1 and 2) and computing over 100 million mesh cells in a few minutes, compared to the several days required by traditional unstructured grid methods, this approach significantly improves computational efficiency. This numerical framework is a suitable architecture for running CFD on supercomputers, enabling simulations at the computational scale of hundreds of millions of cells. The pressure fluctuation magnitude around the ATH was approximately 100 times smaller than the dominant pressure generated by the rotational speed at the airfoil tip of the impeller. The successful capture of these subtle acoustic phenomena demonstrates the high numerical accuracy of our developed framework in resolving acoustic field fluctuations. Figure 7: Time-resolved pressure fluctuation contours showing aeroacoustic wave propagation from the air turbine handpiece (ATH). Snapshots are shown from 5 us to 60 us at 5 us intervals. Periodic concentric wavefronts originate in front of the ATH, forming a wave pattern consistent with the third harmonic frequency observed in the simulated spectrum. Experimental spectral analyses of noise emitted by different ATHs with similar rotation speeds have reported pronounced peaks at approximately 5-6 kHz and their harmonic frequencies [10]. Several studies have explored the relationship between the acoustic properties of sound emitted by ATHs and patient emotions, finding that these prominent frequencies contribute to anxiety and discomfort [10; 11]. It has been shown that teenagers are more sensitive to high-frequency components and therefore rate dental drill sounds as more unpleasant than older individuals do [11]. These findings suggest that frequency-specific acoustic design must be adapted to the auditory profiles of different patient groups. Validated against experimental data, our framework accurately captured specific noise frequencies associated with patient anxiety [2; 3; 11; 25; 26]. Unlike previous studies [12; 13; 14] that focused only on the steady internal flow within the ATH, we employed a comprehensive approach considering both internal flow dynamics and the surrounding acoustic environment. This approach enabled the successful simulation of the complex 3D airflow in an ATH, which is crucial for understanding the mechanisms of sound source generation and accurately predicting noise propagation. Overall, this framework demonstrates a numerical precision that accurately models the sound field. This study provides valuable insights; however, there are opportunities for further refinement. First, a slightly coarser resolution may have contributed to differences in sound pressure at certain frequencies between the simulation and the experiment.