A numerical study on noise prediction and CIS determination using CFD

1 A numerical study on noise prediction and CIS determination using CFD Byeong-U You1, Kwang-Jun Paik1, * Ho-Won Lee1, Jun-Hwan Kim1 1 Department of Naval Architecture and Ocean Engineering, Inha University, Incheon, South Korea Abstract. Recently, the issue of underwater radiated noise (URN) has been actively discussed by international organizations such as the International Maritime Organization (IMO) due to its potential impact on marine ecosystems. Among the various sources of underwater noise, external thrusters have been identified as significant contributors. The noise generated by thrusters is particularly strong when cavitation occurs, as cavitation complicates the noise characteristics and becomes a primary source of underwater noise. For submarines, stealth is directly related to survival, making noise reduction a critical concern.This study focuses on predicting propeller noise under cavitating conditions. Computational Fluid Dynamics (CFD) analysis was conducted to predict the occurrence of Tip Vortex Cavitation (TVC) in the propeller and determine the Cavitation Inception Speed (CIS). Numerical simulations were performed for the first time using the NACA 16-020 wing section in STAR-CCM+ version 18.06, applying Reynolds-Averaged Navier-Stokes (RANS), Large Eddy Simulation (LES), and Detached Eddy Simulation (DES) turbulence models. Additionally, noise predictions were carried out using the Ffowcs Williams-Hawkings (FW-H) equation and compared with experimental results from a cavitation tunnel. Based on the simulation results, the cavitation shape and associated noise characteristics were numerically analyzed, and the reliability of the CFD predictions was improved. Furthermore, a procedural approach for determining CIS was established. This study is expected to provide fundamental insights for improving the accuracy of underwater noise prediction using CFD and to serve as a basis for future research on the analysis and optimal design of cavitation-induced noise characteristics of marine propulsors. Keywords: Computational fluid dynamics, Cavitation, TVC, CIS, Hydroacoustic, NACA 16-020. 1 Introduction Cavitation is a phenomenon in which local pressure in a liquid rapidly drops below the vapor pressure, leading to the formation of microscopic vapor cavities. This phenomenon typically occurs around high-speed rotating equipment such as propellers, pumps, and turbines, and the collapse of these cavities generates strong shock waves and high-frequency noise. Cavitation induced by propeller rotation leads to erosion, vibration, and noise, resulting not only in performance degradation of propulsion and turbine systems but also in significant threats to marine ecosystems. In recent years, growing global interest in marine life protection and ocean environment conservation has led to active research and regulatory efforts aimed at mitigating Underwater Radiated Noise (URN) from ships. Major international organizations, including the International Maritime Organization (IMO), the Marine Environment Protection Committee (MEPC), the Marine Strategy Framework Directive (MSFD), and NORSOK (Norwegian Industry Standards), have proposed guidelines and recommendations for reducing underwater noise from ships. In particular, the MEPC has identified cavitation as a major source of URN and issued recommendations for noise reduction under MEPC.1/Circ.906 [1] Against this backdrop, extensive research has been conducted to understand cavitation and URN characteristics. Maines and Arndt [2] systematically investigated the formation and development mechanisms of cavitating tip vortices. While Arndt et al. [3] quantitatively investigated the occurrence conditions and vortex core characteristics of Tip Vortex Cavitation (TVC) through classical studies. Shin et al. [4] conducted model tests on NACA 16-020 and NACA 66(2)-415 hydrofoils to examine the noise characteristics associated with TVC, and Peng et al. [5] investigated the flow characteristics of tip vortex cavitation and bubble cloud formation mechanisms with and without cavitation using experiments on elliptic hydrofoils. In numerical studies, Park et al. [6] analyzed the formation mechanisms and flow characteristics of TVC on NACA sections using CFD, while Ku et al. [7] numerically predicted TVC and URN characteristics on NACA * Correspondence to: [email protected] 16th International Symposium on Practical Design of Ships and Other Floating Structures PRADS 2025 Ann Arbor, MI, USA, October 19th – 23rd 2025 2 sections by combining CFD with a Bubble Dynamics model. Jeong et al. [8] proposed a method for predicting cavitation and Cavitation Inception Speed (CIS) of submarine propellers using a bubble dynamics-based model. Furthermore, Ku et al. [9] demonstrated the capability of CFD-based analysis to effectively predict TVC and URN for submarines. Recently, Asnaghi et al. [10] conducted high-resolution simulations of cavitating tip vortex flows and bubble dynamics using CFD with Large Eddy Simulation (LES). While Park et al. [11] numerically predicted hydrofoil TVC noise by coupling the Dissipation Vortex Model with bubble theory. However, most existing studies have been conducted under limited turbulence models and grid resolutions, which has hindered the accurate reproduction of detailed cavitation structures and their time-periodic characteristics. Differences in core vortex structure formation and boundary layer development depending on turbulence models have been reported to significantly affect the accuracy of cavitation shape and underwater noise predictions. Therefore, this study aims to overcome the limitations of previous research by comprehensively comparing and analyzing cavitation shapes and generation characteristics of the NACA 16-020 hydrofoil under various turbulence models and grid densities. In this study, the Ffowcs Williams–Hawkings (FW-H) equation was applied to predict the sound pressure level (SPL) generated by cavitation. By systematically analyzing SPL variations with changes in the cavitation number, a quantitative correlation between cavitation phenomena and URN was established. The performance of various turbulence models—including LES, Reynolds Stress Model (RSM), and Detached Eddy Simulation (DES)—was compared to evaluating their predictive capability. The influence of turbulence models and grid resolution on the accuracy of cavitation-induced URN prediction was assessed. Notably, high-resolution LES calculations exhibited trends more consistent with experimental results than conventional URANS and DES approaches under both cavitating and non-cavitating conditions. These findings provide a foundation for future studies on the acoustic characteristics of ship propellers under cavitation and for the development of optimal design strategies. Furthermore, they offer potential as a baseline dataset for evaluating cavitation inception speed (CIS). 2 Numerical set-up 2.1 Governing Equations In this study, numerical analysis was performed based on the incompressible Navier-Stokes (NS) equations. The governing equation for incompressible flow can be expressed as: 𝜕𝑢𝑖 𝜕𝑡+𝑢𝑗𝜕𝑢𝑖 𝜕𝑥𝑗=−1 𝜌𝜕𝑝 𝜕𝑥𝑖+𝜐 𝜕𝑢𝑖 𝜕𝑥𝑗𝜕𝑥𝑗 (1) where 𝑢𝑖is the averaged velocity, 𝑝 is the averaged pressure, 𝜌 is the fluid density, 𝝊 is the kinematic viscosity. The equation consists of unsteady acceleration, convective terms, pressure gradient, and viscous diffusion terms. To reproduce various turbulent flow characteristics, the following representative turbulence models were applied: 2.1.1 RSM The Reynolds Stress Model directly solves Reynolds stress terms to provide high accuracy in predicting turbulence anisotropy and second-moment effects, offering improved prediction performance over standard twoequation RANS models, especially in flows with strong curvature or rotation. 2.1.2 DES The Detached Eddy Simulation model combines the advantages of RANS and LES by applying RANS in the boundary layer region to reduce computational cost and LES in the free-stream region to resolve large-scale eddies and turbulent structures. 2.1.3 LES The Large Eddy Simulation model resolves large-scale turbulent structures directly, while smaller eddies are modeled using a Sub-Grid Scale (SGS) model. LES provides high-resolution turbulence prediction in both space and time. 3 2.2 FW-H Equation The Ffowcs Williams-Hawkings (FW-H) equation, developed by Ffowcs Williams and Hawkings, extends Lighthill's acoustic analogy by including boundary and surface effects, making it applicable to complex unsteady flow fields. The equation accounts for monopole, dipole, and quadrupole acoustic source terms to predict the sound emitted into the far-field. The general form of the FW-H equation is as follows. 1 𝑐02𝜕2𝑝′ 𝜕𝑡2−𝛻2𝑝′=𝑢𝑗𝜕 𝜕𝑡[𝜌0𝑈𝑛𝑖𝛿(𝑓)]−𝜕 𝜕𝑥𝑖[𝑃𝑖𝑗𝑛𝑗𝛿(𝑓)] +𝜕 𝜕𝑥𝑖𝑥𝑗[𝑇𝑖𝑗𝐻(𝑓) (2) 2.3 Flow Conditions and Mesh Generation The NACA 16-020 hydrofoil model was used with a chord length C=80 mm and span length S=60 mm, corresponding to an aspect ratio of 1.5. The angle of attack was set to 15°. The distance from the inlet to the hydrofoil was 375 mm, and the gap to the tank side walls was set at 100 mm. The total tank length was 1400 mm. Slip conditions were applied to the top, bottom, and side boundaries, and velocity inlet and outlet conditions were applied at the inlet and outlet. Figure 1. NACA 16-020 Figure 2. Domain and boundary conditions 2.4 Numerical Method Unsteady simulations were conducted to analyze the transient flow field using STAR-CCM+ ver. 18.06R8. A second-order temporal discretization scheme was used to improve time accuracy. The Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm was applied to couple velocity and pressure fields, providing robust numerical stability. 4 To simulate cavitation phenomena, a Volume of Fluid (VOF) model was used to capture the free surface, and the Schnerr-Sauer cavitation model [12] was adopted. Acoustic pressure data were extracted and input to the FWH model to predict time-varying SPL at monitoring points. Fast Fourier Transform (FFT) was applied to analyze the SPL frequency spectra. Three turbulence models were applied: RSM, DES, and LES. For DES, a hybrid approach combining SST k−ω for RANS regions and LES in separated regions was used. For LES, the Wall-Adapting Local Eddy-viscosity (WALE) model was applied to improve the subgrid-scale resolution. 3 Numerical Validation 3.1 Grid Sensitivity and Convergence Test 3.1.1 Convergence test To verify the reliability of the numerical simulation, a grid convergence analysis was performed using different mesh densities. The LES model was selected for the grid sensitivity study. The simulation conditions were set to match those of the experiments conducted at Chungnam National University: cavitation number σ = 2.29, inflow velocity of 10.12 m/s, inlet pressure of 120.04 kPa, and water temperature of 25.9°C (corresponding to a vapor pressure of 3336 Pa). The Grid Convergence Index (GCI) method was employed to quantitatively assess mesh sensitivity and solution stability. The time step was set to 1.0 × 10⁻⁵ s, based on the maximum frequency observed in the experiments. Mesh generation was carried out in STAR-CCM+ using an unstructured orthogonal mesh approach. Near-wall mesh refinement was applied to ensure a non-dimensional wall distance of y⁺ ≤ 1. Four mesh levels were defined: coarse (9.1 million cells), medium (20.0 million cells), fine (3 million cells), and very fine (71.2 million cells). GCI analysis showed that the uncertainty in the lift coefficient (𝐶𝐿) was 0.689%, confirming good convergence behavior. The grid refinement ratio was set to r = 1.414, and the GCI was calculated using the following equation: This is based on Celik's method.[13] 𝐺𝐶𝐼𝑓𝑖𝑛𝑒 21 =1.25|𝑄1−𝑄2 𝑄1| 𝑟21 𝑝−1 𝑤ℎ𝑒𝑟𝑒,𝑝= 1 𝑙𝑛 (𝑟21)|𝑙𝑛|∈32 ∈21||,∈𝑖𝑗=𝑄𝑖−𝑄𝑗 (3) An R value of 0.112 was obtained for the lift coefficient, which indicates monotonic convergence. This was recommended by ITTC [14]. The convergence behavior was classified as follows: 𝑅=∈32 ∈21{0<𝑅<1∶𝑚𝑜𝑛𝑜𝑡𝑜𝑛𝑖𝑐 𝑐𝑜𝑛𝑣𝑒𝑟𝑔𝑒𝑛𝑐𝑒 −1<𝑅<0∶𝑜𝑠𝑐𝑖𝑙𝑙𝑎𝑡𝑜𝑟𝑦 𝑐𝑜𝑛𝑣𝑒𝑟𝑔𝑒𝑛𝑐𝑒 |𝑅|≥1∶𝑑𝑖𝑣𝑒𝑟𝑔𝑒𝑛𝑐𝑒 (4) Table 1. Calculations of discretization error 3.1.2 Comparison with Experimental Results Fig. 3 compares the cavitation patterns obtained from numerical simulations with those observed in experiments conducted at Chungnam National University under a cavitation number of σ = 2.29 and at a VOF value of 0.5, for various mesh densities. The numerical results showed good agreement with the experimentally 𝝈 CASE Base size Num Of Grid[M] 𝑪𝑳 𝑹𝑮 GCI (%) 2.29 Coarse 0.11 9.1 0.591 0.112 0.689 Medium 0.078 20.0 0.614 Fine 0.055 33.0 0.642 Very Fine 0.039 71.2 0.645 5 observed cavitation patterns, and a clear trend of improved prediction accuracy was observed as the mesh density increased. Fig. 3 also presents a detailed analysis of the changes in cavitation patterns with increasing mesh resolution. In particular, the development of TVC was captured based on the criterion of VOF = 0.5. The LES model successfully reproduced the generation and dissipation of large-scale eddies, closely replicating the cavitation structures observed in the experiments. Furthermore, as the mesh resolution increased, the TVC structures gradually converged toward the experimental results. This demonstrates that the combination of the LES model and high-resolution mesh is highly effective for the accurate numerical prediction of cavitation and TVC phenomena. (a) Experimental Results from Chungnam National University (σ = 2.29) (b) Coarse (c) Medium (d) Fine (e) Very Fine Figure 3. Cavitation Patterns at Different Mesh Densities (VOF = 0.5) Additionally, the analysis of Fig. 4 revealed that z-direction vorticity tends to intensify with increasing mesh resolution, depending on the cavitation structure. As the surface mesh density increased, the vortex strength near the surface became more pronounced. Strong vortex structures and separation flow were observed near the trailing edge of the NACA profile. In Fig. 5, the streamline distribution was further analyzed to investigate the flow characteristics. It was confirmed that regions of high-velocity flow developed along the cavitation structures. A relatively high flow velocity was observed near the leading edge, while a low-velocity region, caused by flow separation, was identified near the trailing edge. These flow characteristics significantly influence the location of cavitation inception and the formation of vortex structures. 6 (a) Coarse (b) Medium (c) Fine (d) Very Fine Figure 4. Z-Direction Vorticity and Cavitation at Different Mesh Densities at LES (a) Coarse (b) Medium (c) Fine (d) Very Fine Figure 5. Streamline and Cavitation at Different Mesh Densities at LES Fig. 6 presents the velocity distribution in the z-direction at the position of x/c = 0.5. This represents the radial velocity component relative to the NACA profile. It was observed that, with increasing mesh density, the boundary between highand low-velocity regions became more sharply defined. In the high-resolution mesh, the velocity gradient was distinctly captured, allowing for a more precise reproduction of the detailed flow structures. Additionally, Fig. 7 shows the vorticity distribution at the same position as x/c = 0.5. In all mesh conditions, repeated generation and dissipation of vorticity were observed. As the mesh resolution increased, the size and intensity of the vorticity structures became more pronounced. These results further demonstrate that the 7 combination of high-resolution mesh and the LES model is particularly effective for the accurate prediction of vortex structures and turbulent motions. (a) Coarse (b) Medium (c) Fine (d) Very Fine Figure 6. Z-Direction Velocity at x/c = 0.5 for Different Mesh Densities at LES (a) Coarse (b) Medium (c) Fine (d) Very Fine Figure 7. Vorticity Distribution at x/c = 0.5 for Different Mesh Densities at LES Fig. 8 presents the predicted SPL results under various mesh conditions and compares them with experimental data (EFD, Experimental Fluid Dynamics). The analysis showed that, as the mesh density increased, the predicted trends of maximum sound pressure (dB) and frequency variation gradually approached the experimental results. Notably, in the high-resolution mesh, the primary peak values and frequency ranges of the SPL spectrum exhibited good agreement with the experimental data. 8 In this study, considering the SPL prediction results in conjunction with the GCI analysis and flow pattern comparisons, the fine grid condition was ultimately selected as the final computational mesh for the analysis. (a) Experimental Results from Chungnam National University (σ = 2.29) (b) Coarse (c) Medium (d) Fine (e) Very Fine Figure 8. Validation of Sound Pressure Level (SPL) at Different Mesh Densities Using LES Figure 9 shows the computation time for each mesh resolution. Because computation time varies depending on the number of cores and the computer specifications, all values were normalized with respect to the computation time of the Very Fine mesh. Consequently, the computation times for the Coarse, Medium, Fine, and Very Fine meshes corresponded to approximately 14%, 28%, 42%, and 100% of the Very Fine mesh time, respectively. 9 Figure 9. Relative Computation Time for Different Mesh Densities 3.2 Validation According to Turbulence Models The predictive performance of cavitation patterns was evaluated for different turbulence models. Numerical simulations were conducted under identical flow conditions using three turbulence models: LES, DES, and RSM. The analysis conditions were set to match the experimental conditions of Chungnam National University: cavitation number σ = 2.29, flow velocity of 10.12 m/s, inlet pressure of 120.04 kPa, and fluid temperature of 25.9°C (corresponding to a saturated vapor pressure of 3336 Pa). Fig. 9 presents a comparison of the cavitation structures predicted by each turbulence model. The LES model most closely reproduced the cavitation patterns observed in the experiments, indicating its superior capability to accurately capture turbulent structures and the generation and dissipation of eddies. In contrast, the RSM and DES models exhibited relatively stable and smoother cavitation structures, but with less detailed variability compared to the LES results. (a) Experimental Results from Chungnam National University (σ = 2.29) (b) RSM (c) DES (d) LES Figure 10. Cavitation Patterns by Turbulence Model (VOF = 0.1) The z-direction vorticity distributions for each turbulence model, together with the corresponding cavitation patterns, are compared in Fig. 10. In the RANS-based RSM model, vorticity near the surface was relatively low, and no distinct eddy structures indicative of vortex formation were observed. In the DES model, the SST k–ω model was applied in the boundary layer region, while the flow transitioned to an LES model in the free-stream region. As a result, partial eddy structures were observed near the interface between the two models. In contrast, the LES model continuously captured strong eddy generation and dissipation in both the separation-induced vortices from the NACA surface and the cavitation regions. Fig. 11 presents the comparison of streamline distributions among the turbulence models. The RSM model exhibited an overall uniform velocity distribution, whereas the DES model showed a tendency for low-velocity