Numerical Investigation of Cavitation Models Combined with RANS and PANS Turbulence Models for Cavitating Flow Around a Hemispherical Head-Form Body

Abstract

Accurate prediction of cavitating flows is essential for improving the performance and durability of marine and hydrodynamic systems. This study investigates the influence of different cavitation models—Kunz, Merkle, and Schnerr–Sauer—on the numerical prediction of cavitation around a hemispherical head-form body using computational fluid dynamics (CFD). Additionally, the effects of turbulence modeling approaches, including Reynolds-averaged Navier–Stokes (RANS) and partially averaged Navier–Stokes (PANS), are examined to assess their capability in capturing transient cavitation structures and turbulence interactions. The results indicate that the Schnerr–Sauer model, which incorporates bubble dynamics based on the Rayleigh–Plesset equation, provides the most accurate prediction of cavitation structures, closely aligning with experimental data. The Merkle model shows intermediate accuracy, while the Kunz model tends to overpredict cavity closure, limiting its ability to capture unsteady cavitation dynamics. Furthermore, the PANS turbulence model demonstrates superior performance over RANS by resolving more transient cavitation phenomena, such as cavity shedding and re-entrant jets, leading to improved accuracy in pressure distribution and vapor volume fraction predictions. The combination of the PANS turbulence model with the Schnerr–Sauer cavitation model yields the most consistent results with experimental observations, highlighting its effectiveness in modeling highly dynamic cavitating flows.

1. Introduction

Cavitation is a complex multiphase phenomenon that occurs when local fluid pressure drops below the vapor pressure, leading to the formation of vapor cavities. These cavities grow in low-pressure regions and collapse when they encounter higher-pressure zones, resulting in significant pressure fluctuations, turbulence, and potentially destructive effects such as erosion, noise, and vibration. Cavitation plays a crucial role in various engineering applications, including ship propellers, hydrofoils, and turbomachinery, where accurate prediction is essential for improving performance and structural reliability. Computational fluid dynamics (CFD) has been widely employed to simulate cavitating flows, yet the strong coupling between turbulence and phase change remains a major challenge in numerical modeling.

De la Cruz-Avila et al. [1] investigated cavitation within a rectangular-profile Venturi tube using numerical simulations and evaluates four turbulence models: $k-\epsilon$ realizable, $k-\epsilon$ RNG, and $k-\omega$ SST. The research highlighted the challenges in accurately predicting vapor cloud formation due to the intricate interactions between turbulence and phase change phenomena, underscoring the need for precise turbulence modeling in cavitating flows. Salvatore et al. [2] presented a benchmark study comparing seven computational models, including Reynolds-averaged Navier–Stokes (RANS), large eddy simulation (LES), and boundary element method (BEM), applied to the INSEAN E779A propeller. The findings reveal significant variations in predicting cavitation phenomena, emphasizing the challenges in modeling the strong coupling between turbulence and phase change in propeller applications. Similarly, Zhu et al. [3] evaluated the performance of various cavitation models in simulating water flow, focusing on their ability to incorporate vapor-phase transport. The study identified limitations in existing models, particularly in capturing the phase change processes accurately, highlighting the ongoing challenges in CFD simulations of cavitating flows. Pipp et al. [4] discussed the complexities involved in simulating cavitation reactors, noting that cavitation exhibits intricate flow features even in simple geometries. The authors emphasized that poor CFD approaches can lead to misinterpretations and suboptimal engineering solutions, stressing the importance of accurately modeling the interplay between turbulence and phase change.

To enhance the accuracy of cavitation simulations, various mass transfer models have been developed to describe the phase transition between liquid and vapor phases. The Kunz model is a widely used approach that introduces empirical source terms to control the vaporization and condensation processes based on local pressure conditions. This model is computationally efficient and provides stable solutions for engineering applications. Cao et al. [5] employed the Kunz cavitation model, among others, to simulate cavitating flow in a centrifugal pump. The research demonstrated that the Kunz model effectively captures cavitation characteristics while maintaining computational efficiency, making it suitable for engineering applications where stable and efficient simulations are required. Additionally, Hanimann et al. [6] investigated various cavitation models, including the Kunz model, for steady-state CFD simulations. The study found that the Kunz model exhibited favorable behavior concerning numerical stability and computational efficiency, highlighting its suitability for engineering applications requiring reliable and efficient simulations.

However, the Kunz model’s ability to resolve transient cavitation dynamics is limited, as it often predicts a more diffused cavity structure and struggles to capture small-scale turbulent features such as re-entrant jets and vortex shedding. The Merkle model adopts a similar pressure-based framework but incorporates a more refined formulation for phase change dynamics, allowing for improved predictions of steady cavitation behavior. While the Merkle model provides a balance between computational cost and accuracy, it still faces difficulties in resolving unsteady shedding behavior and turbulence–cavitation interactions in highly dynamic flow environments. Liu [7] compared the performance of the Kunz, Merkle, and Schnerr–Sauer cavitation models in simulating unsteady cavitation around a Clark-Y hydrofoil. The findings indicated that both the Merkle and Schnerr–Sauer models outperform the Kunz model in capturing unsteady cavitation phenomena, closely aligning with experimental observations. The Kunz model demonstrated limitations in resolving transient cavitation dynamics, often predicting more diffused cavity structures and inadequately capturing small-scale vortices, including re-entrant jets and vortex shedding. In contrast, the Merkle model provided more accurate simulations of unsteady cavitation flows, although it still faced challenges in fully resolving complex turbulence-cavitation interactions. Tran et al. [8] evaluated the applicability of mass transfer cavitation models, specifically the Kubota and Merkle models, for simulating cavitating flows around a NACA66 hydrofoil under both steady and unsteady conditions. The study found that the Merkle model offered improvements in simulating cavitating flows, particularly in steady-state scenarios. However, challenges persisted in accurately predicting unsteady cavitation behaviors, such as cavity shedding and turbulence–cavitation interactions, highlighting the need for further refinement in modeling approaches to capture these complex dynamics effectively.

The Schnerr–Sauer model, derived from the Rayleigh–Plesset equation, explicitly accounts for bubble dynamics in the cavitation process. This model offers a more accurate representation of cavitation growth and collapse by considering individual vapor bubbles’ expansion and contraction. Sauer and Schnerr [9] discussed the development of a cavitation model grounded in bubble dynamics, emphasizing the Schnerr–Sauer model’s foundation on the Rayleigh–Plesset equation. The research highlighted that the Schnerr–Sauer model effectively captures the growth and collapse of vapor bubbles by considering their expansion and contraction, leading to more accurate predictions of cavitation phenomena. The study also noted that the model’s ability to scale bubble growth rates allows for controlled simulation of vapor distribution within the flow. Hong et al. [10] proposed enhancements to the Schnerr–Sauer model to improve its predictive capabilities for cavitating flows. By refining the original model’s parameters, the study demonstrated improved accuracy in simulating cavitation growth and collapse dynamics. The modified model continues to rely on the Rayleigh–Plesset equation to account for individual bubble behavior, thereby offering a detailed representation of bubble dynamics within cavitating flows. Consequently, the Schnerr–Sauer model is particularly effective in capturing rapid phase transition effects and unsteady cavitation structures. However, its computational expense is significantly higher due to the increased complexity of its formulation.

Cavitating flows exhibit inherently turbulent characteristics, making turbulence modeling a critical aspect of CFD simulations. The RANS model is one of the most commonly employed turbulence modeling approaches due to its relatively low computational cost. By averaging the effects of turbulence over time, RANS reduces the complexity of solving the full Navier–Stokes equations. However, this time-averaging process leads to the suppression of transient flow structures, making it less suitable for accurately predicting cavitation-induced turbulence, vortex interactions, and unsteady shedding behavior. To overcome these limitations, the partially averaged Navier–Stokes (PANS) model has been introduced as a hybrid approach between RANS and LES. Geng and Escaler [11] evaluated the effectiveness of various RANS turbulence models in predicting unsteady cavitation phenomena. The findings indicated that while RANS models are computationally efficient, they often struggle to capture transient flow structures such as vortex shedding and cavitation-induced turbulence. This limitation arises from the inherent time-averaging approach of RANS, which suppresses the unsteady characteristics essential for accurate cavitation prediction. Similarly, Naseri et al. [12] assessed the predictive capabilities of different turbulence models, including RANS and LES, in simulating incipient cavitation within a step nozzle. The study revealed that RANS models, such as the realizable $k-\epsilon ,k-\omega$ SST, and Reynolds Stress model, failed to predict cavitation due to their limitations in capturing low-pressure vortex cores. In contrast, the LES WALE model successfully predicted cavitation by capturing shear layer instability and vortex shedding, highlighting the necessity for models that can resolve transient flow features. Hu et al. [13] introduced a modification to the PANS model aimed at improving simulations of unsteady cavitating flows. The modified PANS model demonstrates enhanced capability in capturing transient cavitation dynamics, including vortex interactions and unsteady shedding behavior, offering a balance between computational cost and accuracy. Additionally, Huang et al. [14] applied a modified PANS model to simulate transient cavitating turbulent flows. The results showed that the modified PANS model effectively captures unsteady cavitation phenomena, such as cavity shedding and turbulence-cavitation interactions, addressing the limitations observed in traditional RANS models.

Unlike RANS, which models all turbulence scales, or LES, which resolves large-scale turbulence while modeling only small-scale effects, PANS dynamically adjusts the turbulence resolution based on local flow conditions. By selectively resolving a portion of the turbulence spectrum, PANS provides an improved representation of unsteady flow structures while maintaining a manageable computational cost. This makes it particularly useful for cavitating flow simulations, where capturing transient phenomena such as cavity shedding and re-entrant jet formation is crucial. This study aimed to investigate the influence of different cavitation models, specifically the Kunz, Merkle, and Schnerr–Sauer models, on the numerical prediction of cavitating flows around a hemispherical head-form body. Additionally, the impact of turbulence modeling approaches, including RANS and PANS, on cavitation dynamics would be examined.

The hemispherical head-form body has been widely used as a benchmark geometry for cavitation studies due to its well-documented experimental data and its ability to produce strong cavitation effects. By systematically analyzing the cavity formation process, shedding behavior, and turbulence interactions, this study sought to evaluate the predictive capabilities of different modeling approaches. The findings of this research will provide valuable insights into the selection of appropriate cavitation and turbulence models for engineering applications, thereby contributing to the advancement of high-fidelity CFD simulations of cavitating flows. Recent studies, such as Ge et al. [15], have begun to address the coupling between thermal and hydrodynamic effects in cavitating flows, proposing new modeling strategies to capture this interaction. Although the present study focused on isothermal conditions, these developments offer valuable directions for future research.

This paper is organized as follows: Section 2 outlines the numerical methods and computational setup, detailing the governing equations, cavitation models, turbulence modeling approaches, and computational framework. Section 3 presents the results and discussion, highlighting the comparative analysis of pressure distribution, cavitation structures, turbulence characteristics, and unsteady shedding behavior across different models. Finally, Section 4 provides a summary of the key findings and discusses potential directions for future research.

2. Numerical Methods and Computational Setup

2.1. Governing Equations

In this study, numerical simulations were performed using the Reynolds-averaged Navier–Stokes (RANS) and partially averaged Navier–Stokes (PANS) models to analyze turbulent flow characteristics. The governing equations for each approach are presented below.

2.1.1. Reynolds-Averaged Navier–Stokes (RANS)

The RANS formulation approximates turbulence by decomposing the flow variables into mean and fluctuating components, applying time-averaging to remove small-scale turbulent fluctuations. This approach is computationally efficient and widely used in engineering applications due to its ability to capture dominant flow structures. The governing equations for mass and momentum conservation in the RANS framework are expressed as follows:

$${\displaystyle \frac{\partial {\rho }_m}{\partial t}}+{\displaystyle \frac{\partial \left({\rho }_m{\overline{u}}_j\right)}{\partial x_j}}=0$$

(1)

$${\displaystyle \frac{\partial \left({\rho }_m{\overline{u}}_i\right)}{\partial x_i}}+{\displaystyle \frac{\partial \left({\rho }_m{\overline{u}}_i{\overline{u}}_j\right)}{\partial x_j}}=-{\displaystyle \frac{\partial \overline{p}}{\partial x_i}}+{\displaystyle \frac{\partial }{\partial x_i}}\left[{\mu }_m\left({\displaystyle \frac{\partial {\overline{u}}_i}{\partial x_j}}+{\displaystyle \frac{\partial {\overline{u}}_j}{\partial x_i}}\right)-{\tau }_{ij}\right]$$

(2)

where ${\overline{u}}_i$ and $\overline{p}$ represent the time-averaged velocity and pressure, respectively. The subscript $m$ indicates the mixture phase, for which the density and viscosity are calculated using volume–fraction-weighted averages based on the Volume of Fluid (VOF) method [16].

The Reynolds stress tensor ${\tau }_{ij}$ accounts for the effect of turbulent fluctuations on the mean flow and is modeled using the Boussinesq approximation:

$${\tau }_{ij}=-{\rho }_m\overline{u_i^{\prime }{u}_j^{\prime }}=2{\left({\mu }_t\right)}_m{\overline{S}}_{ij}-{\displaystyle \frac{2}{3}}{\rho }_{m}k{\delta }_{ij}$$

(3)

where ${\overline{S}}_{ij}$ denotes the strain rate tensor derived from the time-averaged velocity field, and $k$ represents the turbulent kinetic energy. The eddy viscosity ${\left({\mu }_t\right)}_m$ is defined as:

$${\left({\mu }_t\right)}_m={\rho }_m{\displaystyle \frac{k}{\omega }}$$

(4)

where $\omega$ is the specific dissipation rate.

The turbulence closure in this study is achieved using the $k-\omega$ shear stress transport (SST) model, which effectively combines the near-wall accuracy of the $k-\omega$ model with the free-stream robustness of the $k-\epsilon$ model. This hybrid approach improves prediction accuracy in complex flow scenarios, including flow separation and adverse pressure gradients. Further details on the derivation of these equations can be found in the literature [16,17,18].

2.1.2. Partially Averaged Navier–Stokes (PANS)

The PANS model bridges the gap between RANS and DNS by resolving a portion of the turbulence spectrum while modeling the unresolved scales. This approach enhances the representation of turbulent structures without the computational cost of fully resolving all scales. The governing equations for the PANS method consist of the filtered continuity and momentum equations:

$${\displaystyle \frac{\partial {\rho }_m}{\partial t}}+{\displaystyle \frac{\partial \left({\rho }_m{\overline{u}}_j\right)}{\partial x_j}}=0$$

(5)

$${\displaystyle \frac{\partial \left({\rho }_m{\overline{u}}_i\right)}{\partial x_i}}+{\displaystyle \frac{\partial \left({\rho }_m{\overline{u}}_i{\overline{u}}_j\right)}{\partial x_j}}=-{\displaystyle \frac{\partial \overline{p}}{\partial x_i}}+{\displaystyle \frac{\partial }{\partial x_i}}\left[{\mu }_m\left({\displaystyle \frac{\partial {\overline{u}}_i}{\partial x_j}}+{\displaystyle \frac{\partial {\overline{u}}_j}{\partial x_i}}\right)-{\tau }_{ij}\right]$$

(6)

where ${\overline{u}}_i$ and $\overline{p}$ denote the partially averaged velocity and pressure, respectively. The sub-filter scale (SFS) stress tensor ${\tau }_{ij}$ accounts for the influence of unresolved turbulence on the resolved field and is modeled using the Boussinesq approximation:

$${\tau }_{ij}=-{\rho }_m\overline{u_i^{\prime }{u}_j^{\prime }}=2{\left({\mu }_u\right)}_m{\overline{S}}_{ij}-{\displaystyle \frac{2}{3}}{\rho }_m{k}_u{\delta }_{ij}$$

(7)

where ${\left({\mu }_u\right)}_m$ represents the eddy viscosity of the unresolved turbulence, expressed in terms of the unresolved turbulent kinetic energy $k_u$ and the corresponding unresolved turbulence frequency ${\omega }_u$:

$${\left({\mu }_u\right)}_m={\rho }_m{\displaystyle \frac{k_u}{{\omega }_u}}$$

(8)

For turbulence closure, the PANS approach employs the $k-\omega$ SST model, as proposed by Lakshmipathy and Girimaji [19]. This model maintains high accuracy near walls while effectively capturing free-stream turbulence, making it suitable for resolving complex flow phenomena such as separation and pressure-induced vortex structures.

To enable adaptive turbulence resolution, the PANS model introduces filter control parameters $f_k$ and $f_{\omega }$, which define the ratios of unresolved to total turbulent kinetic energy and turbulence frequency, respectively:

$$f_k={\displaystyle \frac{k_u}{k}},f_{\omega }={\displaystyle \frac{{\omega }_u}{\omega }}={\displaystyle \frac{f_{\epsilon }}{f_k}}$$

(9)

These parameters allow the PANS model to transition smoothly between RANS$\left(f_k=1\right)$ and DNS $\left(f_k=0\right)$, depending on the required level of turbulence resolution. However, determining an optimal $f_k$ value a priori is challenging due to spatial and temporal variations in turbulence characteristics. To address this issue, Luo et al. [20] proposed a dynamic formulation of $f_k$, which is determined based on the local grid spacing and the turbulence length scale. This adaptive approach ensures that turbulence resolution dynamically adjusts to the local flow conditions, enhancing accuracy while maintaining computational efficiency in high-fidelity simulations.

2.2. Cavitation Model

Cavitation is a complex phase-change phenomenon that occurs when the local pressure drops below the saturated vapor pressure, leading to the formation of vapor bubbles within a liquid. Accurate numerical modeling of cavitation relies on mass transfer models that govern the rate of phase transition between liquid and vapor phases. In this study, three different cavitation models—Kunz [21], Merkle [22], and Schnerr–Sauer [23]—are implemented to assess their capability in predicting cavitating flow structures and capturing transient characteristics of vapor formation and collapse.

The evolution of the vapor phase within a multiphase mixture is described by the transport equation for the vapor volume fraction ${\alpha }_v$, expressed as:

$${\displaystyle \frac{\partial {\alpha }_v}{\partial t}}+\nabla ·\left({\alpha }_{v}u\right)=\dot{m}$$

(10)

where $\dot{m}$ represents the mass transfer rate due to cavitation. Each cavitation model employs a different approach to determine this mass transfer rate, affecting the accuracy and stability of numerical simulations. The governing equations for the vapor volume fraction in each cavitation model are presented in a consistent format to facilitate comparison and maintain clarity in mathematical expression.

2.2.1. Kunz Model

The Kunz cavitation model is a semi-empirical approach that governs vaporization and condensation through pressure-dependent source terms. The mass transfer rate is formulated as:

$${\displaystyle \frac{\partial {\alpha }_v}{\partial t}}+\nabla ·\left({\alpha }_{v}u\right)={\displaystyle \frac{C_{prod}{\rho }_{v}min\left(p-p_v,0\right){\alpha }_v}{{\rho }_l\left(0.5{\rho }_l{U}^2\right)t_{\infty }}}-{\displaystyle \frac{C_{dest}\left(1-{\alpha }_v\right){\alpha }_v^{2}max\left(p-p_v,0\right)}{{\rho }_l{t}_{\infty }}}$$

(11)

where $C_{prod}=0.02$ and $C_{dest}=0.01$ are empirical coefficients controlling the vapor generation and condensation rates, respectively. The characteristic time scale is defined as:

$$t_{\mathrm{\infty }}={\displaystyle \frac{D_{cavitator}}{U}}$$

(12)

The Kunz model introduces diffused mass transfer rates, smoothing phase transitions and enhancing numerical stability. While this results in computational efficiency and robustness across a wide range of flow conditions, it may lead to reduced sensitivity in capturing highly dynamic cavitation structures.

2.2.2. Merkle Model

The Merkle cavitation model employs a pressure-driven mass transfer formulation to regulate phase change dynamics more directly. The governing equation for vapor volume fraction is given by:

$${\displaystyle \frac{\partial {\alpha }_v}{\partial t}}+\nabla ·\left({\alpha }_{v}u\right)={\displaystyle \frac{C_{evap}{\rho }_{v}max\left(p_v-p,0\right)}{{\rho }_l{t}_{\infty }}}-{\displaystyle \frac{C_{cond}{\rho }_{v}max\left(p-p_v,0\right)}{{\rho }_l{t}_{\infty }}}$$

(13)

where $C_{evap}$ and $C_{cond}$ are empirical coefficients that control the rates of evaporation and condensation, respectively. Unlike the Kunz model, the Merkle model establishes a stronger coupling between local pressure gradients and phase transition rates. This enables more accurate representation of cavitation inception and collapse, particularly in regions of strong pressure fluctuations. However, while the Merkle model improves vapor cloud shedding predictions in vortex-dominated flows, it may still underestimate large-scale vapor cloud breakup in highly unsteady regimes.

2.2.3. Schnerr–Sauer Model

The Schnerr–Sauer model is derived from the Rayleigh–Plesset equation and explicitly incorporates bubble dynamics into the cavitation process. It describes the vapor fraction evolution through:

$${\displaystyle \frac{\partial {\alpha }_v}{\partial t}}+\nabla ·\left({\alpha }_{v}u\right)={\displaystyle \frac{C_e{\rho }_v{\rho }_l}{\rho }}{\displaystyle \frac{\left(1-{\alpha }_v\right){\alpha }_v}{3R_b}}\sqrt{{\displaystyle \frac{2\left|p_v-p\right|}{3{\rho }_l}}}\hspace{1em}\hspace{1em}\mathrm{if}p<p_v$$

(14)

$${\displaystyle \frac{\partial {\alpha }_v}{\partial t}}+\nabla ·\left({\alpha }_{v}u\right)={\displaystyle \frac{C_c{\rho }_v{\rho }_l}{\rho }}{\displaystyle \frac{\left(1-{\alpha }_v\right){\alpha }_v}{3R_b}}\sqrt{{\displaystyle \frac{2\left|p-p_v\right|}{3{\rho }_l}}}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{if}p>p_v$$

(15)

where $C_e$ and $C_c$ are empirical coefficients, and $R_b$ represents the mean bubble radius, which is dynamically determined based on the local vapor volume fraction. The mean bubble radius $R_b$ is defined as:

$$R_b={\left({\displaystyle \frac{{\alpha }_v}{1-{\alpha }_v}}{\displaystyle \frac{3}{4\pi }}{\displaystyle \frac{1}{n_0}}\right)}^{{\displaystyle \frac{1}{3}}}$$

(16)

where $n_0=1.6\times {10}^{13}$ is the initial number of bubbles. Unlike the Kunz and Merkle models, which rely on pressure-based empirical source terms, the Schnerr–Sauer model directly accounts for cavitation physics at the microscopic scale, capturing bubble growth and collapse mechanisms more realistically. This enables more accurate simulation of vapor shedding, re-entrant jet interactions, and turbulent wake dynamics.

2.3. Computational Domain and Boundary Conditions

The computational domain for the numerical simulation of axisymmetric flow around a hemispherical head-form is schematically illustrated in Figure 1. The domain is carefully structured to ensure the accurate representation of flow characteristics while mitigating potential distortions caused by boundary interactions. To achieve a balance between computational efficiency and the physical fidelity of the simulation, the domain dimensions are selected based on established best practices in numerical studies of similar flow configurations. The inlet boundary is positioned 30 times the characteristic radius $\left(30R\right)$ upstream of the hemispherical head to allow the incoming flow to fully develop before interacting with the model. Downstream, the outlet is placed at a distance of $50R$ to provide adequate space for wake development and to minimize numerical artifacts such as pressure wave reflections. The radial extent of the domain extends $30R$ from the centerline, ensuring that the boundary does not impose artificial confinement effects that could influence turbulence structures and cavitation behavior.

To reduce computational expenses while maintaining the accuracy of the solution, an axisymmetric boundary condition is applied along the centerline of the domain. This condition enforces the assumption that the flow is symmetric about the central axis, reducing the computational complexity compared to a full three-dimensional simulation while preserving the essential physics of the problem. The simulation is conducted under a cavitation number $\left(\sigma \right)$ of 0.3, which determines the free-stream velocity as $0.7\hspace{0.17em}\mathrm{m}/\mathrm{s}$. This choice ensures that the computational setup accurately reproduces the expected cavitating flow conditions, facilitating direct comparisons with experimental data and theoretical predictions. At the inlet, a uniform velocity of $0.7\hspace{0.17em}\mathrm{m}/\mathrm{s}$ is prescribed, accompanied by appropriate turbulence properties such as turbulent kinetic energy $\left(k\right)$ and specific dissipation rate $\left(\omega \right)$. These turbulence parameters are initialized using empirical formulations derived from prior studies to ensure accurate modeling of the interplay between turbulence and cavitation. At the outlet boundary, a pressure outlet condition is imposed, where the static pressure is set equal to the ambient reference pressure $\left(p_{\infty }\right)$, maintaining consistency with the prescribed cavitation number while minimizing artificial pressure fluctuations that could arise from numerical reflections. The lateral boundaries are placed sufficiently far from the body (typically $30R$) to prevent artificial confinement effects that could influence the flow field. A no-slip boundary condition is applied to the solid surfaces of both the hemispherical head and the cylindrical section, enforcing zero velocity at the wall. Near-wall turbulence effects are modeled using wall functions in cases where resolving the boundary layer fully would be computationally prohibitive. The choice of near-wall treatment is based on grid resolution and turbulence model selection, ensuring an optimal balance between computational efficiency and accuracy. This domain configuration, including the inlet and outlet positions and radial extent, was selected based on validated practices established in previous studies on axisymmetric cavitating flows [24]. The configuration ensures sufficient development of the incoming flow and prevents numerical reflections at the outlet, which are critical for achieving stable cavitation patterns. Therefore, the selected setup is not tailored to a specific case but is applicable to a broad range of similar flow conditions involving hemispherical or bluff bodies.

2.4. Computational Grids

Figure 2 presents the structured computational grid designed for the numerical simulation of axisymmetric cavitating flow around a hemispherical head-form body. The figure provides two views of the structured mesh: (a) a perspective view, which highlights the overall distribution and topology of the grid, and (b) a side view, which illustrates the radial and axial grid resolution. The computational grid is a body-fitted structured hexahedral mesh, carefully designed to conform to the contours of the hemispherical head-form body. This structured topology ensures high numerical accuracy by minimizing interpolation errors and improving solution stability. To accurately capture boundary layer effects and cavitation dynamics, a non-uniform grid refinement strategy is implemented. Near the wall, the grid is highly refined to resolve velocity gradients and pressure fluctuations, with the first grid layer positioned to maintain a non-dimensional wall distance $\left(y^{+}<1\right)$. This allows for the precise modeling of turbulence and cavitation inception.

The computational domain is discretized with $N_x=70$ grid points along the body’s length from the inlet, while $N_R=60$ grid points are allocated in the radial direction to capture flow structures around the hemispherical head-form. To accurately capture wake structures and cavitation effects, the domain extends downstream with $N_o=80$ grid points from the body to the outlet. The circumferential direction is discretized using $N_c=16$ grid points, ensuring adequate resolution of three-dimensional flow characteristics. The total number of computational cells in the structured mesh is approximately 168,000, providing sufficient refinement for capturing cavitation dynamics. A grid independence study was conducted to confirm that further refinement does not significantly alter the results of primary flow parameters such as pressure distribution, wake structure, and cavitation formation. This ensures that the grid resolution is adequate for accurately capturing flow physics without excessive computational cost. The medium grid employed in this study was selected based on a prior grid-independence study [25] which demonstrated that key flow parameters converged with less than 2% variation between medium and fine grid resolutions.

2.5. Numerical Methods

The numerical simulations in this study were performed using OpenFOAM, employing advanced discretization techniques to enhance computational accuracy and stability. Time integration was carried out using the second-order implicit Crank–Nicolson scheme, which minimizes truncation errors and improves temporal accuracy, making it well-suited for transient flow problems. This method effectively balances numerical precision and computational cost, ensuring reliable predictions of unsteady flow characteristics.

For spatial discretization, a second-order central difference scheme was applied to compute the spatial derivatives of velocity and pressure. This scheme preserves accuracy while maintaining numerical stability, particularly in resolving complex turbulence structures. To mitigate numerical oscillations and improve solution robustness, a linear upwind divergence scheme with a limiter was implemented. This approach effectively controls numerical diffusion while maintaining the accuracy of convective transport terms, thereby ensuring stable and physically consistent results.

In the discretization of the volume fraction equation for multiphase flow, a high-resolution Total Variation Diminishing (TVD) scheme was adopted to minimize numerical dissipation. Specifically, the vanLeer scheme was applied to the convective term, which helps retain sharp fluid interfaces and prevents excessive numerical diffusion. To further enhance interface capturing accuracy, the Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM) was utilized. This method ensures sharp and well-defined phase boundaries even in highly dynamic flow conditions, reducing interface smearing and preserving phase integrity.

For pressure–velocity coupling, the PIMPLE algorithm was employed, which integrates the Pressure Implicit with Splitting of Operators (PISO) and Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithms. This hybrid approach enhances numerical stability and convergence efficiency, particularly for simulations involving strong turbulence and transient multiphase interactions. The PIMPLE algorithm dynamically adjusts the number of corrector steps, improving the robustness of the solver under rapidly varying flow conditions.

By incorporating these advanced numerical techniques within the OpenFOAM framework, the computational model effectively captures complex fluid interactions, ensuring high-fidelity simulation of turbulent multiphase flows. The combination of second-order discretization schemes, specialized interface capturing methods, and an efficient pressure–velocity coupling strategy provides a well-balanced and accurate approach for solving unsteady flow problems.

To ensure solution accuracy and numerical stability, a residual-based convergence criterion was employed throughout all simulations. The iterative process continued until the residuals of all governing equations including continuity, momentum, turbulence, and vapor volume fraction were reduced below $1\times {10}^{-8}$. Additionally, the number of outer corrector steps in the PIMPLE loop was set to 3 to ensure solver robustness, particularly in highly unsteady cavitating regions.

3. Results and Discussion

3.1. Pressure Coefficient Distribution

Figure 3 presents a comparative analysis of the pressure coefficient $\left(C_p\right)$ distribution along the normalized surface length $\left(s/D\right)$ for different turbulence and cavitation models. The experimental reference data from Rouse and McNown [26] and the numerical results of Park and Rhee [27] are included to validate the computational results. The CFD simulations were conducted under the same inflow velocity and cavitation number as those used in the experiments, specifically $U=0.7\hspace{0.17em}\mathrm{m}/\mathrm{s}$ and $\sigma =0.3$, to ensure consistency between the numerical and experimental configurations. This consistency between numerical and experimental conditions establishes a rigorous validation framework, enabling accurate evaluation of the predictive performance of the various turbulence and cavitation model combinations. The figure provides insights into the influence of the selected turbulence models (RANS and PANS) as well as the cavitation models (Kunz, Merkle, and Schnerr–Sauer) on the predicted pressure distribution. The pressure coefficient $\left(C_p\right)$ is defined as:

$$C_p={\displaystyle \frac{p-p_{\infty }}{0.5\rho U^2}}$$

(17)

where $p$ is the local pressure, $p_{\infty }$ is the reference pressure in the free stream, $\rho$ is the fluid density, and $U$ is the free-stream velocity.

At the leading edge $\left(s/D\approx 0\right)$, all computational models capture the initial pressure peak, closely matching the experimental data, which indicates a well-resolved stagnation region. As the flow progresses downstream, a rapid pressure drop is observed due to flow separation and cavitation onset. The discrepancies among the different models become more pronounced in the reattachment region $\left(1.0\le s/D\le 2.5\right)$, where pressure recovery occurs. Notably, the PANS model exhibits a smoother transition in the pressure recovery region compared to the RANS model, suggesting improved resolution of transient turbulent structures and cavitation dynamics. Among the cavitation models, the Schnerr–Sauer model predicts a pressure profile that closely aligns with experimental data, particularly around $s/D\approx 2$.

These observations served as the basis for evaluating the predictive accuracy of each turbulence and cavitation model combination. As shown in Figure 3, all computational models accurately capture the pressure drop near the leading edge $\left(s/D\approx 0\right)$, consistent with experimental data. In the reattachment region $\left(1.0\le s/D\le 2.5\right)$, where discrepancies become more pronounced, the PANS model demonstrates a notably smoother pressure recovery than the RANS models, indicating improved capability in capturing transient turbulent structures. Among the cavitation models, the Schnerr–Sauer model provides the best agreement with experimental measurements. In particular, the combination of the PANS turbulence model with the Schnerr–Sauer cavitation model yields the closest match to the measured pressure profile, especially in the reattachment zone around $s/D\approx 2$, validating its superior predictive performance in capturing cavitation-induced flow phenomena. The Merkle model shows a similar trend, but with slight deviations in the pressure recovery magnitude, likely due to differences in the phase change treatment and vapor volume fraction estimation. The Kunz model, in both PANS and RANS formulations, demonstrates a marginally lower pressure recovery, which may be attributed to differences in mass transfer rate modeling and cavitation bubble dynamics.

The numerical results using the PANS model demonstrate a more refined capture of pressure variations compared to the RANS model. This suggests that the PANS approach provides better turbulence resolution in cavitating flows, improving predictions of flow separation and reattachment dynamics. However, the extent to which PANS enhances accuracy varies depending on the cavitation model used. Specifically, the PANS with the Schnerr–Sauer model shows the closest agreement with experimental results, indicating its robustness in capturing pressure fluctuations and cavitation dynamics. To objectively assess the performance of each model, we compared the simulation results with available experimental data, focusing on pressure behavior in the stagnation and reattachment regions. Among the combinations tested, the PANS turbulence model coupled with the Schnerr–Sauer cavitation model demonstrated the best agreement with the measurements, particularly in the pressure recovery zone $\left(1.0\le s/D\le 2.5\right)$. These comparisons support the conclusion that this combination provides the most reliable prediction under the present flow conditions.

3.2. Time-Averaged Cavitation Structures

To gain deeper insight into how these models affect the spatial pressure field and cavitation structures, Figure 4 visualizes the time-averaged pressure coefficient $\left(C_p\right)$ contours with overlaid streamlines for each model combination. This figure extends the findings from Figure 3 by offering a spatial representation of pressure variations and cavitation structures across different modeling approaches. The contours highlight how turbulence modeling influences the formation and evolution of cavitation within the separated shear layer and wake region.

A high-pressure region near the leading edge corresponds to the stagnation point, consistent with the sharp pressure peak observed in Figure 3. As the flow separates and cavitation develops along the surface, a pronounced low-pressure region emerges, where phase transition from liquid to vapor occurs. The extent and structure of this low-pressure zone vary significantly depending on the turbulence and cavitation models used. Comparing the RANS results (Figure 4a–c) with the PANS results (Figure 4d–f), a distinct difference in the predicted cavitation structures emerges. The PANS models generally exhibit a more continuous and elongated cavitation region, whereas the RANS models tend to predict a more abrupt cavitation closure. To enhance interpretability, the cavitation closure and re-entrant jet locations are annotated in Figure 4. The cavitation closure refers to the point where the vapor cavity terminates and pressure begins to recover, often followed by the formation of a re-entrant jet—a reverse flow moving upstream along the wall. These features are critical for understanding cavity shedding and collapse mechanisms, and their positions vary depending on the turbulence and cavitation models used. This behavior suggests that the PANS model better captures unsteady characteristics of cavitation shedding and re-entrant jet formation, which are crucial for accurately modeling cavitation dynamics.

Among the cavitation models, the Schnerr–Sauer model (Figure 4c,f) predicts the most extended cavitation region, aligning well with the lower pressure region observed in Figure 3. This is likely due to its formulation being based on a bubble number density approach, allowing for a more detailed representation of cavitation phase change dynamics. The Merkle model (Figure 4b,e) exhibits a similar cavity shape but with a slightly less pronounced low-pressure region, indicating differences in mass transfer modeling. The Kunz model (Figure 4a,d) predicts a more confined cavity region, corresponding to its lower pressure recovery trend in Figure 3, suggesting a relatively stronger tendency for re-entrant flow and cavitation closure.

The streamline patterns further illustrate the impact of turbulence modeling on the flow reattachment process. In the RANS results, the reattachment point appears slightly upstream compared to the PANS results, implying that the PANS models enhance the resolution of turbulent structures governing flow separation and reattachment. This effect is particularly evident in the Schnerr–Sauer model, where the PANS simulation (Figure 4f) predicts a more diffused low-pressure region with a gradual transition to the recovery zone.

By visualizing the spatial pressure field, Figure 4 reinforces the trends identified in Figure 3, demonstrating how turbulence and cavitation models collectively shape cavitation behavior. While the PANS model improves cavitation prediction by resolving transient dynamics more effectively, cavitation model selection remains a key factor in determining cavity extent and closure characteristics. To further quantify the cavitation extent and intensity, Figure 5 presents the time-averaged vapor volume fraction $\left({\alpha }_{mean}\right)$ contours.

Figure 5 builds upon the insights gained from the pressure coefficient distributions in Figure 4 by providing a direct visualization of the time-averaged vapor volume fraction $\left({\alpha }_{mean}\right)$ contours for different turbulence and cavitation models. These contours illustrate the spatial distribution of the vapor phase within the flow field (${\alpha }_{mean}=0$ indicating pure liquid, and ${\alpha }_{mean}=1$ representing full vapor), offering a deeper understanding of cavitation extent and intensity predicted by each model. By comparing the vapor volume fraction across different modeling approaches, the influence of turbulence and cavitation models on cavitation development, closure behavior, and cavity shedding characteristics can be assessed.

Across all six subfigures, a high vapor volume fraction is observed in the cavitation region, where low-pressure conditions promote the phase transition from liquid to vapor. The extent and structure of this cavitation region vary significantly among different turbulence and cavitation model combinations. The RANS models (Figure 5a–c) predict a relatively compact cavitation region, while the PANS models (Figure 5d–f) exhibit an elongated cavity, consistent with the more diffused low-pressure region observed in Figure 4. This observation aligns with the expectation that PANS provides an improved representation of unsteady cavitation structures due to its ability to resolve a wider range of turbulence scales compared to RANS.

Among the cavitation models, notable differences emerge in the predicted cavity extent and closure behavior. The annotated cavitation closure points in Figure 5 mark the downstream limit of the vapor cavity, where the transition back to the liquid phase occurs. These locations also correlate with the regions where re-entrant jets originate, playing a key role in modulating vapor collapse and downstream flow separation. The length and sharpness of the closure vary significantly across turbulence and cavitation model combinations. The Schnerr–Sauer model (Figure 5c,f) predicts the most extended cavitation region, which aligns well with its lower pressure distribution in Figure 4. This behavior can be attributed to the model’s dependence on the bubble number density approach, which allows for a more gradual cavitation closure. The Merkle model (Figure 5b,e) exhibits a similar cavity extent but with a slightly lower vapor volume fraction in the core region, indicating a more abrupt re-condensation process. The Kunz model (Figure 5a,d) predicts the most confined cavitation region, suggesting a stronger re-entrant flow mechanism leading to early cavity closure. These differences highlight the sensitivity of cavitation predictions to the mass transfer formulation in each model.

Comparing the turbulence models, the PANS simulations (Figure 5d–f) show a more continuous and elongated vapor region than the RANS results, further reinforcing the notion that PANS better captures transient cavitation dynamics. The gradual vapor concentration gradient in the PANS cases suggests enhanced resolution of unsteady shedding and vapor transport mechanisms, whereas the RANS cases exhibit a more distinct vapor-liquid interface, indicating a relatively more deterministic closure behavior. This effect is particularly pronounced in the Schnerr–Sauer model (Figure 5f), where the vapor volume fraction transitions more smoothly, consistent with the extended low-pressure region observed in Figure 4f.

These findings underscore the benefits of employing the PANS turbulence model for more accurate cavitation predictions while also emphasizing the significant role of the cavitation model in determining cavity length, closure behavior, and vapor fraction distribution. While Figure 5 provides a global perspective on cavitation extent, a more detailed view is necessary to examine closure dynamics and downstream flow characteristics. Therefore, Figure 6 presents a refined analysis focusing on the cavity closure region and the interactions between vapor and liquid phases.

3.3. Cavity Closure and Flow Reattachment

Figure 6 shows a detailed examination of time-averaged vapor volume fraction $\left({\alpha }_{mean}\right)$ distributions with overlaid streamlines, emphasizing the cavity closure region and the downstream flow field. This detailed perspective enables a more precise assessment of cavitation dynamics, including shedding behavior, re-entrant flow mechanisms, and turbulence model influences on cavity evolution and collapse. In all six subfigures, the cavitation region exhibits a high vapor volume fraction near the leading edge and gradually transitions to a lower vapor concentration as the cavity closes. The interaction between the vapor phase and the surrounding liquid is particularly evident in the downstream shear layer, where turbulence-driven mixing occurs. The overlaid streamlines further illustrate flow detachment, cavity-induced circulation, and turbulence effects on vortex formation and shedding.

A comparison of the RANS (Figure 6a–c) and PANS (Figure 6d–f) results reveals significant differences in the predicted cavity closure dynamics. The PANS simulations predict a more elongated cavity with a smoother transition to the re-entrant flow region, suggesting a more gradual vapor condensation process. In contrast, the RANS models tend to predict more abrupt cavity closure with sharper vapor–liquid interfaces, indicating a stronger tendency for rapid condensation and re-entrant jet formation. These differences suggest that the PANS turbulence model enhances the resolution of unsteady cavitation structures, leading to a more physically representative prediction of cavitation shedding and vortex interaction.

Among the cavitation models, the Schnerr–Sauer model (Figure 6c,f) predicts the most extensive vapor region, consistent with its lower pressure distribution observed in Figure 4. This extended cavitation region aligns with the more diffused and gradual closure behavior, which is particularly noticeable in the PANS with the Schnerr–Sauer model (Figure 6f). The Merkle model (Figure 6b,e) shows a relatively confined cavity with a slightly reduced vapor fraction in the shear layer, indicating a stronger vapor re-condensation process. The Kunz model (Figure 6a,d) exhibits the most compact cavity structure, with a more pronounced re-entrant jet effect leading to early cavity detachment.

The streamline patterns further illustrate the impact of turbulence and cavitation model selection on the flow reattachment process. In the RANS simulations, the recirculation zone appears more localized and abrupt, whereas in the PANS simulations, the cavity closure occurs more gradually, with a more pronounced vortex shedding effect. This behavior suggests that PANS better captures the unsteady dynamics of vapor transport and turbulence–cavity interactions, making it a more suitable approach for modeling highly transient cavitating flows.

3.4. Time-Dependent Cavitation Dynamics

Building on the findings from Figure 6, which highlight the influence of turbulence and cavitation models on steady-state vapor volume fraction distributions, Figure 7 and Figure 8 extend the investigation by exploring the time evolution of vapor volume fraction (α), offering deeper insights into the transient behavior of cavitation structures across different turbulence and cavitation models.

Figure 7 presents the time-dependent cavitation behavior obtained from RANS simulations, while Figure 8 showcases the corresponding PANS results. Each row in these figures represents a successive time step, starting from an initial reference time $T$ and progressing through incremental stages $\left(T+∆t, T+2∆t, \mathrm{a}\mathrm{n}\mathrm{d} T+3∆t\right)$. This sequential representation facilitates a direct comparison of cavitation shedding dynamics and highlights how different modeling approaches influence transient vapor transport mechanisms.

In Figure 7, the cavitation structures predicted by the RANS models (Figure 7a–c) exhibit a periodic and relatively deterministic shedding process, where the cavity initially elongates before undergoing abrupt detachment and condensation due to the influence of the re-entrant jet. Across all three cavitation models, the shedding cycle follows a well-defined pattern, characterized by a sharp vapor–liquid transition and a rapid return to a non-cavitating state in the wake region. The Kunz model (Figure 7a) predicts a compact cavitation region with rapid shedding and re-condensation, while the Merkle model (Figure 7b) exhibits a slightly smoother cavity evolution with a more gradual transition between detachment and collapse. The Schnerr–Sauer model (Figure 7c) predicts the largest and most persistent cavitation region, with a relatively continuous phase transition between vapor and liquid, suggesting that the bubble-based cavitation model promotes more gradual vapor entrainment and cavity closure.

In contrast, Figure 8, which depicts the PANS simulations (Figure 8a–c), reveals a fundamentally different cavitation shedding mechanism compared to the RANS results. The PANS turbulence model provides a more detailed resolution of unsteady turbulence structures, leading to a more continuous and less abrupt vapor transport process. The shedding cycle observed in the PANS simulations is less periodic and more irregular, with a gradual evolution of cavitation structures rather than a sharp, periodic detachment. The Kunz model (Figure 8a) still displays a well-defined shedding cycle, but the transition between vapor and liquid appears more diffused compared to its RANS counterpart. The Merkle model (Figure 8b) predicts a more continuous vapor region, with a gradual vapor shedding mechanism that aligns with the progressive re-entrant jet development observed in Figure 6. The Schnerr–Sauer model (Figure 8c) exhibits the longest and most unsteady cavitation region, characterized by a diffuse vapor phase and complex interactions with turbulent eddies, leading to a highly transient cavity evolution.

A direct comparison between Figure 7 and Figure 8 highlights the fundamental differences between RANS- and PANS-based cavitation predictions. The RANS models produce a periodic and deterministic shedding behavior, where the cavity undergoes a sharp phase transition, resulting in a rapid condensation and re-entrant jet formation process. In contrast, the PANS simulations capture a more continuous and gradually evolving cavitation structure, with a less deterministic shedding process and enhanced turbulence–cavity interaction effects. This behavior suggests that the PANS model provides a more accurate representation of unsteady cavitation dynamics, as it resolves a wider range of turbulence scales, allowing for a more physically realistic vapor transport mechanism. This enhanced unsteady behavior can be attributed to the ability of the PANS model to resolve a broader spectrum of turbulent eddies, which play a key role in modulating cavity shedding and local condensation processes. In contrast, the RANS model filters out small-scale turbulent fluctuations, resulting in a more periodic and simplified representation of cavitation dynamics. This ability to capture small-scale eddies enables more accurate simulation of transient phenomena such as re-entrant jet formation and cavity breakup, which are highly sensitive to turbulence fluctuations.

The choice of cavitation model further influences the time-dependent vapor distribution. The Schnerr–Sauer model consistently predicts the most extensive cavitation region, while the Kunz model generates the most compact cavity, characterized by early detachment due to pronounced re-entrant jet effects. The Merkle model lies between these two extremes, striking a balance between abrupt shedding and gradual detachment. These variations emphasize the importance of cavitation model selection in accurately capturing unsteady cavitating flow behavior.

3.5. Turbulence Kinetic Energy Distribution

Having established the differences in cavitation shedding dynamics between RANS and PANS models, Figure 9 shifts the focus to the distribution of turbulence kinetic energy (TKE), normalized as $\left(k/U^2\right)$. This analysis provides further insight into turbulence–cavitation interactions, particularly in terms of flow separation, vortex formation, and energy cascade effects within the cavity region.

The contours in Figure 9 illustrate the spatial distribution of turbulence kinetic energy across the flow domain, revealing how the choice of turbulence and cavitation model affects turbulence generation, dissipation, and interaction with cavitation structures. Across all subfigures, the region of highest turbulence intensity is concentrated in the shear layer near the cavity closure, where instabilities and re-entrant jet interactions contribute to enhanced turbulence production. TKE values decrease gradually downstream, indicating the progressive dissipation of turbulence energy as the flow reattaches.

A comparison between the RANS results (Figure 9a–c) and the PANS results (Figure 9d–f) reveals distinct differences in the predicted turbulence intensity. The RANS simulations produce relatively localized regions of elevated turbulence kinetic energy, particularly near the cavity closure region. This localized turbulence is attributed to the periodic nature of cavity shedding, where large-scale structures dominate the turbulence production. The PANS simulations, in contrast, predict a more extended and diffused turbulence intensity distribution, indicating the presence of finer turbulent structures and a more gradual turbulence cascade. This suggests that PANS captures a wider range of turbulent eddies, leading to a more physically representative turbulence distribution compared to RANS.

Among the cavitation models, the Schnerr–Sauer model (Figure 9c,f) predicts the most widespread turbulence intensity region, consistent with its larger predicted cavitation extent in Figure 5 and Figure 6. This extended turbulence region is likely due to the more gradual cavitation closure process and the increased interaction between the vapor and liquid phases. The Merkle model (Figure 9b,e) exhibits an intermediate turbulence distribution, with a slightly more confined turbulence intensity region compared to the Schnerr–Sauer model but more extensive than the Kunz model. The Kunz model (Figure 9a,d) predicts the most localized turbulence distribution, suggesting that its more confined cavitation region leads to a more abrupt turbulence transition.

A key observation from Figure 9 is that the PANS turbulence models predict lower peak turbulence kinetic energy values compared to RANS models. This trend is consistent with previous studies, which have shown that PANS turbulence modeling reduces excessive turbulence production, leading to a more accurate representation of energy dissipation and turbulence–cavitation interactions. The gradual decay of turbulence intensity in PANS simulations indicates that finer turbulence structures play a greater role in the energy cascade process, allowing for a more detailed representation of turbulence-induced cavitation dynamics. The improved spatial distribution of turbulence intensity in the PANS model also enhances the energy cascade process, allowing finer turbulent structures to contribute to vapor transport and cavity deformation. These findings highlight the critical importance of turbulence resolution in accurately modeling the interaction between turbulence and cavitation.

4. Summary and Conclusions

This study investigated the impact of different cavitation models (Kunz, Merkle, and Schnerr–Sauer) and turbulence modeling approaches (RANS and PANS) on the numerical prediction of cavitating flows around a hemispherical head-form body. The results demonstrated that the Schnerr–Sauer model, which incorporates bubble dynamics based on the Rayleigh–Plesset equation, provided the most accurate prediction of cavitation structures, capturing extended vapor regions and pressure fluctuations more effectively than the Merkle and Kunz models. This work contributes to the field by establishing a unified simulation framework, allowing a fair and consistent comparison across multiple cavitation and turbulence models. The identical boundary conditions and numerical setups eliminate biases, ensuring the reliability of the comparative evaluation. The Merkle model exhibited intermediate accuracy, while the Kunz model predicted a more diffused and prematurely closed cavitation region, limiting its ability to resolve transient cavitation phenomena. Turbulence modeling significantly influenced cavitation dynamics. The PANS approach consistently outperformed RANS, improving the resolution of transient cavitation structures, such as cavity shedding, re-entrant jets, and turbulence–cavitation interactions. This finding highlights the enhanced predictive accuracy of the PANS–Schnerr–Sauer model combination for transient cavitating flows, closely matching the experimental results. The PANS with Schnerr–Sauer combination provided the best agreement with experimental data, highlighting its capability in capturing unsteady cavitation behavior and turbulence interactions. An analysis of turbulence kinetic energy (TKE) confirmed that PANS reduces excessive turbulence production, resulting in a more physically accurate representation of cavitation-induced turbulence. Furthermore, by incorporating turbulence kinetic energy (TKE) analysis, the study delivers physical insights into the role of turbulence–cavitation interactions, including energy dissipation, re-entrant jet formation, and cavity deformation. This serves as a major contribution, enhancing the mechanistic understanding of unsteady cavitation dynamics.

Time-dependent analysis further revealed that RANS predicted periodic and deterministic cavitation shedding, whereas PANS captured a more continuous and irregular shedding process, leading to more accurate modeling of unsteady cavitating flows. Overall, these findings suggest that the Schnerr–Sauer model, coupled with the PANS turbulence approach, offers the highest accuracy for numerical simulations of cavitating flows. Future work should focus on extending this analysis to three-dimensional cavitating flows and higher-fidelity turbulence models such as DES and LES, as well as experimental validation using time-resolved flow measurements to further enhance model accuracy and reliability in engineering applications. Although the present study considers isothermal conditions, recent investigations such as that of Ge et al. [15] have emphasized the importance of incorporating thermodynamic effects in cavitation modeling. Including such effects in future simulations could improve physical realism and expand the applicability of the current framework, particularly for thermally sensitive cavitating flows.