Toward Quieter Dental Devices: Transient CFD Simulation of Airflow and Noise in Air Turbine Handpieces

Abstract

High-pitched noise generated by dental air turbine handpieces (ATHs) causes discomfort and anxiety, discouraging dental visits. Understanding the time-dependent noise generation mechanism associated with compressed airflow in ATHs is crucial for effective noise reduction. However, the direct investigation of airflow dynamics within ATHs is challenging. The transient-state modeling of computational fluid dynamics (CFD) simulations remains unexplored owing to the complexities of high rotational speeds and air compressibility. This study develops a novel CFD framework for transient (time-dependent) modeling under high-speed rotational conditions. Simulations were performed using a three-dimensional model reconstructed from a commercial ATH. Simulations were conducted at 320,000 rpm using a novel framework that combines the immersed boundary and building cube methods. A fine 0.025 mm mesh spacing near the ATH, combined with supercomputing resources, enabled the simulation of hundreds of millions of cells. The simulation results were validated using experimental noise measurements. The CFD simulation revealed transient airflow and aeroacoustic behavior inside and around the ATH that closely matched the prominent frequency peaks from the experimental data. This study is the first to simulate the transient airflow of ATHs. The proposed CFD model can accurately predict aeroacoustics, contributing to the future development of quieter and more efficient dental devices.

1. Introduction

In dental clinics, the environment is filled with various sounds [1], particularly the high-pitched discomforting noise of dental drills. Studies show that over half the patients feel uneasy due to this noise, which is closely linked to heightened levels of dental anxiety [2,3]. This anxiety can result in patients avoiding dental visits, ultimately compromising their oral health [2,3]. Addressing dental drill noise is therefore crucial for improving patient experience and promoting better oral health outcomes [2,3].

The dental high-speed air turbine handpiece (ATH), a prominent source of high-pitched sound in dental clinics, is defined by ISO standards as a dental drill operating at 160,000 rotations per minute (rpm) or higher, powered by compressed air [4]. Structurally, an ATH consists of a rotor housed in the drill head body, which includes an impeller, bearings, and a spindle [5,6]. When high-pressure compressed air enters the ATH, the impeller rotates rapidly, causing the cutting diamond bar inserted into the spindle to rotate. Given that tooth enamel is the toughest substance in the human body [7], ATHs can sometimes reach speeds of up to 400,000 rpm for effective drilling [6,8,9]. At such high rotational speeds, airflow inside and around the ATH generates complex fluid dynamics, producing noise. The characteristic frequency components of the noise generated by ATHs are primarily determined by the drill’s rotational speed [10,11]. The noise generated during ATH idling is different in timbre from the sound of drilling teeth and dental metal, but their frequency components are closely related [10]. Psychoacoustic experiments and acoustic physical measurements have strongly linked both sound pressure levels and high-frequency noise components to patient discomfort caused by ATH noise [10,11]. Therefore, understanding the aeroacoustic mechanisms of ATH noise generation is essential for developing solutions to mitigate these unpleasant sounds from devices and improve patient experiences.

Computational fluid dynamics (CFD) has been widely applied for numerical analysis in various industries, including aerospace, automotive, construction, and chemical engineering. While previous CFD studies on ATHs have focused on torque and rotational speed [12,13,14], they have been limited to steady-state modeling. Although these studies provide useful insights, steady-state simulations assume fluid properties remain constant over time, which may not capture the transient behaviors critical to aeroacoustic phenomena. Therefore, in systems where transient effects are significant, this approach may lead to incomplete or misleading results. In contrast, transient simulation accurately captures dynamic behavior, transients, and temporal variations, providing a more precise representation of time-sensitive systems and improving the reliability of results. To our knowledge, no previous work has conducted a full transient CFD simulation of ATHs with compressible flow modeling.

Using CFD to assess the transient state for aeroacoustic noise presents unique challenges in simulating airflow in ATHs. The high rotational speed (up to 320,000 rpm), complex small geometry, and significant scale differences in pressure [ranging from 303,975 Pa (3.0 atm) at the inlet of ATHs to 100 Pa for noise fluctuations] demand a compressible flow solver and fine computational resolution. Additionally, transient simulations are essential for accurately predicting decibel levels and evaluating noise impacts on patients, requiring supercomputing resources. These challenges have historically limited research on non-steady airflow and aeroacoustics in ATHs.

To address these challenges, we developed a novel transient CFD framework for ATH noise analysis. By analyzing the flow field of an ATH at high rotational speeds during dental treatment, we aimed to identify the cause of acoustic noise and explore potential improvements. In this study, we simulate transient noise by performing numerical calculations using a novel CFD framework on a supercomputer equipped with a 2.2 GHz, 48-core A64FX multi-core processor. Additionally, comparing the CFD simulation and experimental results, we evaluated the validity of the new transient model in CFD.

2. Materials and Methods

2.1. Physical Model of an ATH for Numerical Calculations

The ATH used in the experiment (TwinPower Turbine, J. MORITA MFG. CORP., Kyoto, Japan) is shown in Figure 1a. To assess the capabilities of the developed framework, we intentionally selected an ATH with a more complex impeller shape among the commercial products, rather than the star-shaped impellers commonly used in numerous dental drill studies [12,13,15]. A three-dimensional (3D) model of the ATH was obtained (Figure 1b) by scanning the realistic geometry of a commercially available ATH. The intricate geometry of the impeller in the rotary is shown in Figure 1b. To obtain geometry data for CFD, we performed the computed tomography (CT) imaging of the body and rotor cartridge separately using a microfocus CT scanner (phoenix v|tome|x m300, Baker Hughes, Houston, TX, USA) [16]. The 3D data were reconstructed by defining a reference plane in the tomographic images. The 3D data of both components were then superimposed and converted into a standard triangulated language (STL) data format. As shown in Figure 1b, the complex 3D shapes of the ATH body and rotor cartridge were accurately reproduced. We adopted the building cube method (BCM) [17,18,19] to generate the computational grid. The BCM has been proven to be a suitable architecture for running CFD on supercomputers [20]. The concept of BCM is straightforward, as shown in Figure 1c. The computational domain is divided into units called cubes, where each cube is assigned an equal number of cells. By distributing the same number of cubes to each processing rank, high load balancing can be easily achieved. Additionally, the BCM structure offers advantages such as continuous memory access, which enhances the overall computational efficiency.

2.2. Numerical Simulation Method

2.2.1. Governing Equation

To capture the aeroacoustic sound, pressure and density fluctuations were calculated using the 3D Navier–Stokes equations while considering compressibility:

$${\displaystyle \frac{\partial U}{\partial t}}+{\displaystyle \frac{\partial F_1}{\partial x_1}}+{\displaystyle \frac{\partial F_2}{\partial x_2}}+{\displaystyle \frac{\partial F_3}{\partial x_3}}=0,$$

(1)

where U is the conservative form and F_i is the flux term. Denoting the density of the fluid by ρ, U and F_i are expressed as

$$U=\left(\begin{array}{c}\rho \\ \rho u_1\\ \rho u_2\\ \rho u_3\\ \rho e\end{array}\right)$$

(2)

and

$$F_i=\left(\begin{array}{l}\rho u_i\\ \rho u_i{u}_1+p{\delta }_{i1}-\mu A_{i1}\\ \rho u_i{u}_2+p{\delta }_{i2}-\mu A_{i2}\\ \rho u_i{u}_3+p{\delta }_{i3}-\mu A_{i3}\\ (\rho e+p)u_i-\mu A_{ij}{u}_j-k\partial T/\partial x_i\end{array}\right), \forall i=1,2,3,$$

(3)

where $A_{ij}=\partial u_i/\partial x_j+\partial u_j/\partial x_i-2/3(\nabla \cdot u){\delta }_{ij}$. The pressure p is given by the ideal gas equation:

$$p=\rho RT.$$

(4)

The dynamic viscosity and thermal conductivity of the fluid at temperature T are based on Sutherland’s law:

$$\mu (T)={\mu }_0{(T/T_0)}^{3/2}[(T_0+110)/(T+110)],$$

(5)

$$k(T)=\mu (T)\gamma R/[(\gamma -1)Pr],$$

(6)

where ${\rho }_0=1.1842\hspace{0.33em}{\mathrm{kg}/\mathrm{m}}^3$, ${\mu }_0=1.85\times {10}^{-5}\hspace{0.33em}\mathrm{N}\cdot {\mathrm{s}/\mathrm{m}}^2$, $T_0=298.06\hspace{0.33em}\mathrm{K}$, $\gamma =1.4$, $R=287\hspace{0.33em}\mathrm{J}/\mathrm{kg}/\mathrm{K}$, and $Pr=0.72$.

2.2.2. Numerical Method

To overcome the challenges in simulating ATH aeroacoustics, we developed an innovative numerical framework that combines the immersed boundary method (IBM) with the BCM [20] in a rotational framework. This approach efficiently handles complex geometry and high-speed rotational dynamics by integrating an adaptively switched time stepping (ASTS) scheme [21], thereby enhancing computational stability and precision in capturing transient aeroacoustic phenomena. By addressing the limitations of existing methods, such as grid generation issues and instability at high Courant–Friedrichs–Lewy numbers, our framework provides an unprecedented capability to simulate both internal and external flow fields of ATHs.

Table 1. Numerical scheme.

Equation Term	Algorithm	Numerical Method
Time advancement	Implicit	Adaptively switched time stepping
Convective terms	Roe scheme	Low Mach fix Roe [22]
Reconstruction	MUSCL	5th order (without limiter)
Viscous terms	Central difference	2nd order

summarizes the numerical scheme adopted; detailed technical implementations and mathematical formulations are provided in the Appendix A.

2.2.3. Computational Setting

To optimize computational efficiency, we conducted simulations using a supercomputer. Our computational domain included both the interior and surrounding environment. The computational parameters are listed in

Table 2. Computation parameter settings.

Category	Parameter	Value
Geometry	Body diameter	9 mm
	Length of the body	13.0 mm
	Impeller diameter	8.1 mm
	Length of the rotor	10.7 mm
	Stage 1 impeller blade count	18
	Stage 1 blade length (axial)	2.0 mm
	Stage 1 blade height (radial)	0.6 mm
	Stage 2 impeller blade count	18
	Stage 2 blade length (axial)	1.2 mm
	Stage 2 blade height (radial)	0.7 mm
Numerical setup	Atmospheric pressure P0	101,300.0 Pa
	Inlet pressure	3.06 atm
	Outlet pressure	1.15 atm
	Rotational speed	320,000 rpm
	Velocity of the air turbine at impeller tip	135 m/s
	Computational time step (development phase)	4 × 10−6 s flow under development
	Computational time step (after steady state)	2 × 10−7 s after quasi steady state
Mesh	Finest cell size	0.025 mm
	Cell number	104,767,488

, and key geometric dimensions of the ATH are shown in Figure 2. The inlet pressure was set to 3.06 atm and the rotational speed was fixed at 320,000 rpm, representing the actual operating conditions observed in the dental clinic. Using the BCM, we generated the computational grid for large-scale simulations within minutes. The simulation conditions were matched to the experimental setup to accurately reflect actual operational conditions, including inlet/outlet pressures and rotational speed. A fine mesh with a spacing of 0.025 mm was applied near the ATH to capture complex flow details. The total mesh cell count reached 100 million, offering precise information on critical regions, such as the gap between the head body and rotor and the region near the airfoil of the impeller (Figure 1c). Although a full grid independence study was not performed due to the high computational cost associated with the mesh size (>100 million cells), the fine spatial and temporal resolutions were validated by the excellent agreement between simulated and experimental results (as discussed in Section 3.3). The time step size was set to 2 × 10⁻⁷ s to satisfy the CFL condition for numerical stability near the impeller region, allowing a Nyquist frequency of 2.5 MHz, which is significantly higher than the highest observed acoustic frequency (~21 kHz). This confirms the adequacy of the chosen computational settings for resolving relevant aeroacoustic phenomena.

To prevent reflections from affecting result accuracy at the boundaries of the computational domain, we adopted an absorbing boundary condition for low-speed flow. Additionally, to accommodate the computational scale of hundreds of millions of cells, we utilized the Supercomputer Fugaku (RIKEN Center for Computational Science, Kobe, Hyogo, Japan). The simulations were performed using the powerful 2.2 GHz, 48-core A64FX processors developed by Fujitsu. Message-passing interface libraries were used to establish communication between neighboring processors. Furthermore, we employed open multi-processing and single-instruction multiple data methods to enhance computational performance.

2.3. Experimental Setting

To validate the CFD simulations, we conducted measurements in a quiet dental clinical room outside of clinic hours at Osaka University Dental Hospital with low noise levels. The background noise level of the clinical room was measured using a sound level meter and was found to be 42 dB. The experimental setup is illustrated in Figure 3. The same ATH model (TwinPower Turbine, J. MORITA MFG. CORP.) and operating conditions were used for both CFD simulations and measurements. Air pressure and rotational speed were regulated using a pressure gauge and a non-contact handheld digital tachometer designed for high-speed measurements (MP-5350 and HR-6800, Ono Sokki, Yokohama, Japan). A 1/4-inch microphone (UC29, Rion, Kokubunji, Japan) with a preamplifier (NH05B, Rion), part of the sound level meter (UN04, Rion), was positioned at a distance of 10 cm in front of the drill head. Data (for rotation speeds up to 320,000 rpm) were collected using a sound and vibration analysis system with a measurement frequency range of up to 40 kHz (O-Solution and DS-5000, Ono Sokki). The recorded data were analyzed using fast Fourier transform (FFT) with dedicated software (Artemis SUITE, Head-acoustics GmbH, Herzogenrath, Germany).

3. Results

In this section, we present ATH simulations performed using the developed framework. The simulations include both the internal and external flow fields to provide a comprehensive understanding of the acoustic field and noise propagation mechanisms. Our numerical framework proved suitable for running CFD on supercomputers.

3.1. Flow Field

The velocity magnitude (Vmag (m/s)) distribution at different cross-sections inside the ATH is shown in Figure 4, illustrating energy transfer through the turbine before the air exits the system. The ATH comprises two stages of turbine blades (Figure 4a). Figure 4b shows a cross-sectional view at the inlet, where high-velocity airflow enters the first stage of the turbine blades. As high-pressure air enters the ATH through the inlet, it accelerates the turbine blades in the first stage, initiating high-speed rotational motion (Figure 4b). Figure 4c depicts the outlet cross-section, displaying airflow deceleration after interacting with the second stage of turbine blades. The airflow gradually decelerates before the air exits through the outlet. However, not all air exits the ATH through the outlet; a portion flows into the gap between the impeller and capsule, eventually escaping from the front (Figure 4a). This escaping high-pressure air contributes to noise generation, as revealed by the simulation.

3.2. Pressure Fluctuation

We achieved a transient simulation that captures the pressure fluctuation in the ATH. Figure 5 presents the instantaneous pressure fluctuation, $P-\overline{P}$, surrounding the ATH head, which represents the acoustic field. It should be noted that the head body of the ATH was fully included in the computational domain, and its shielding effect was accounted for in the simulation. The contours reveal that the primary noise source is located at the front of the ATH, where concentrated pressure fluctuations occur. The pressure fluctuation magnitude is within 100 Pa (ranging from −40 to 40 Pa), approximately 100 times smaller than the dominant pressure generated by the rotational speed at the airfoil tip of the impeller.

3.3. CFD Model Validation by Experimental Comparisons and Time Domain Analysis

We validated the simulation results by comparing them with experimental measurements. To investigate the acoustic characteristics, an FFT was applied. Figure 6a presents the FFT analysis of the simulated noise, recorded by a virtual microphone placed 10 cm in front of the ATH head at a rotational speed of 320,000 rpm. Figure 6b illustrates the FFT analysis result (sampling points n = 2048, Hanning window) from the actual experiment at 320,000 rpm.

Several prominent frequency components appear in both results. The significant peaks in the simulation (5555, 10,555, 16,111, and 21,111 Hz) closely match the experimental results (5200, 10,350, 16,500, and 20,750 Hz). Despite some differences in sound pressure, the predicted characteristic frequencies closely approximate those obtained from actual measurements.

The frequency deviation between the simulated and experimental results was within 7%, with the largest deviation being 6.8% at the first harmonic. These discrepancies are considered reasonable given the high-speed rotational conditions and the complexity of the airflow field. Minor differences may stem from discrepancies between simulation and experimental conditions, such as fluctuations in the experimental rotational speed, as well as geometric simplifications and mesh resolution limitations near the impeller. Despite these factors, the simulation results successfully captured the major spectral features observed in the experiment. Overall, these results indicate that the current framework accurately captures peak frequencies.

In addition to spectral validation, the transient behavior of the pressure field was analyzed to further verify the consistency of the simulated aeroacoustic response. Figure 7 shows the time-resolved contours of the pressure fluctuation field from 5 μs to 60 μs. These snapshots clearly illustrate the outward propagation of concentric acoustic wavefronts originating from the front of the ATH region. The propagation distance of approximately 20 mm over 60 μs corresponds to a frequency of ~17 kHz, which closely matches the third harmonic (16,111 Hz) observed in the simulated FFT spectrum. This time domain validation strongly supports the physical accuracy of the aeroacoustic source modeling and confirms that the dominant noise arises primarily from rotor–stator interaction.

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 (Figure 1 and Figure 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.

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. Second, a diamond bar for drilling was not inserted into the ATH, and the water spray used to cool the bar tip was omitted in both the simulation and the actual experimental measurements.

The simulation results also provide a basis for exploring noise reduction strategies, including design modifications to the impeller blades or casing geometry aimed at disrupting coherent tonal sources. By enabling rapid assessment of design modifications, this CFD framework can guide the development of quieter dental tools, fostering a more patient-friendly acoustic environment and improving the overall experience of dental procedures. Future research will focus on using the transient CFD framework to explore the relationship between geometric shapes and noise to further enhance patient comfort.

5. Conclusions

In conclusion, leveraging supercomputing resources, we developed a robust numerical framework capable of simulating the transient flow dynamics and noise generation of ATHs operating at clinical speeds of up to 320,000 rpm. The simulated results closely corresponded with the experimental measurements, effectively representing the frequency components of noise linked to patient discomfort. Our framework provides a foundation for aeroacoustic optimization for ATHs, thereby supporting the development of quieter dental devices that can enhance patient comfort and reduce anxiety in clinical settings.