Numerical Analysis of Cavitation Suppression on a NACA 0018 Hydrofoil Using a Surface Cavity

Abstract

This study examines the hydrodynamic and acoustic performance of plain NACA0018 hydrofoil and modified NACA0018 hydrofoils (foil with a cavity on suction surface) at a Reynolds number ($Re$) of $40,000$, which is indicative of small-scale turbines and marine applications. A cavity was created on suction side surface at 40–50% of the chord length, which is chosen for its efficacy in cavitation control. The present analysis examines the impact of the cavity on lift-to-drag-ratio ($L/D$) and cavity length at three cavitation numbers ($1.7$, $1.2$, and $0.93$) for plain and modified hydrofoils. Simulations demonstrate a significant enhancement of 7% in the lift-to-drag ratio relative to traditional designed foils. Contrary to earlier observations, the cavity length increases instead of decreasing for the modified hydrofoil. Both periodic steady and turbulent inflow conditions are captured that simulate the complex cavity dynamics and flow–acoustic interactions. It is found that a reduction in RMS velocity with modified blade suggests flow stabilization. Spectral analysis using Mel-frequency techniques confirms the cavity’s potential to reduce low-frequency flow-induced noise. These findings offer new insights for designing quieter and more efficient hydrofoils and turbine blades.

1. Introduction

Cavitation, the formation of vapor cavities in low-pressure regions—particularly on the suction side of a blade—is a critical concern for hydrofoils operating at high speeds [1,2]. This phenomenon, as outlined by Knapp et al. and Blake, leads to increased hydrodynamic drag, noise, vibration, and material erosion, which collectively degrade the reliability and performance of marine propulsion systems, turbines, and other fluid machinery [1,2].

Traditional engineering strategies to mitigate cavitation focus on optimizing blade geometry or deploying supercavitating profiles tailored for high-speed conditions [3,4,5]. However, these solutions often prove insufficient under moderate-speed or unsteady flow regimes [4,5].

Recent studies have introduced novel hydrofoil configurations designed to stabilize partial cavities on one side of the blade. These designs offer the potential to enhance both aerodynamic and hydrodynamic performance [6,7]. A key feature in these configurations is the so-called “cavity locker,” a convex aft section that anchors the cavity [7]. By replacing a portion of the wetted surface with vapor, this approach reduces skin friction and drag [6]. It also suppresses unsteady pulsations at the cavity tail, thereby reducing pressure fluctuations, noise, and vibration [6,7]. Furthermore, the presence of a stable cavity alters the effective camber of the blade, resulting in enhanced lift and a significant improvement in the lift-to-drag ratio—even in turbulent or non-uniform flows where traditional designs may fail [8]. These benefits arise from complex interactions between the incompressible external flow and compressible vapor dynamics inside the cavity [7]. Another important contribution is the flow around a cavity-equipped NACA0018 airfoil, which was thoroughly investigated by Olsman [9,10]. The effects of cavity-induced shear-layer oscillations and their interplay with acoustic forcing are examined for a variety of Reynolds numbers and angles of attack. The findings demonstrate that the cavity can produce unique shear-layer modes that, depending on the flow circumstances, improve the lift-to-drag ratio and delay flow separation when compared to a clean airfoil, particularly at low Reynolds numbers at specific angles. The cavity’s impact on unsteady forces decreases as Reynolds numbers increase, and the shear layer’s response becomes linear and dominated by other mass effects.

This design philosophy builds on foundational work in vortex trapping and cavity flow dynamics [11,12,13,14,15,16,17,18]. Kasper’s concept of the vortex wing and subsequent studies on planar cavity instabilities and curved surface flows have provided essential theoretical frameworks [11,12]. These principles have been successfully applied to hydrofoils, resulting in cavity-stabilized blades with experimentally demonstrated drag reductions of up to 30% and up to a twofold increase in lift-to-drag ratio relative to conventional profiles like NACA0015 [6,8,19]. Numerical simulations also support these findings, highlighting improved cavitation resistance [20].

Building upon this, recent efforts by Kadivar and Kumar have proposed passive cavitation control methods [21,22,23]. These include cavitating-bubble generators (CGs), compact devices placed strategically on the hydrofoil surface to modify local flow behavior [24]. Their research shows that CGs reduce pressure drag, suppress unsteady cavitation, and eliminate pressure spikes linked to cavity collapse at the trailing edge. Kumar’s complementary studies explore how surface modifications can mitigate cavitation and stabilize flow conditions [25].

Cavity geometry and placement are also pivotal. Rounded cavities with smooth transitions are generally superior to rectangular forms in promoting beneficial vortices and delaying flow separation [7,8], though in some wind turbine scenarios, rectangular grooves have proven effective at high angles of attack [18]. Cavity depth often has a greater effect than width; moderate depths—up to 40% of the local airfoil thickness—strike a balance between aerodynamic gains and structural stability [19]. Optimal performance is typically achieved when cavities are positioned at 40–50% chord length on the suction side [7,8].

Despite substantial progress, further research is necessary—particularly regarding the aerodynamic and acoustic characteristics of hydrofoils with one-sided cavities at moderate Reynolds numbers [20]. Shear layer oscillations over cavities embedded in an NACA0018 airfoil reveal that cavity geometry significantly influences flow stability and dynamic pressure behavior, but it does not explain the details from the perspective of different cavitating stages [10]. Nonetheless, the advancement of cavity-stabilized hydrofoils marks a major leap forward in fluid dynamic design, offering a resilient and efficient solution to cavitation-related challenges in high-speed applications [7,20]. In this work, cavitating flow over NACA0018 has been investigated through analytical and numerical simulations and Mel-frequency spectrum techniques have been found for in-depth flow analysis.

2. Scaling Law

Before presenting the numerical section, it is instructive to derive a theoretical scaling for the cavitating flow over hydrofoil. This fundamental approach clarifies the dependence of cavitation inception on key flow parameters such as freestream velocity, chord length, and fluid properties.

The cavitation number $\sigma$ is typically defined as:

$$\sigma ={\displaystyle \frac{p_{\infty }-p_{\mathrm{vap}}}{\frac{1}{2}\rho V_{\infty }^2}},$$

(1)

where

• $p_{\infty }$ is the freestream static pressure,
• $p_{\mathrm{vap}}$ is the vapor pressure of the liquid,
• $\rho$ is the fluid density,
• $V_{\infty }$ is the freestream velocity.

This expression follows directly from Bernoulli’s equation assuming steady, incompressible, irrotational flow along a streamline from the freestream to the minimum pressure point on the hydrofoil surface [26,27].

In the following section, we will present the experimentally obtained empirical correlation for the NACA 0018 hydrofoil tested in this study, and quantify its deviation from the theoretical scaling proposed here.

For an attached flow over a hydrofoil at moderate angles of attack, the minimum surface pressure can be approximated as:

$$p_{\min }\approx p_{\infty }-{\displaystyle \frac{1}{2}}\rho V_{\infty }^2{C}_p^{\min },$$

(2)

where $C_p^{\min }$ is the minimum pressure coefficient, which depends on the hydrofoil geometry, angle of attack $\alpha$, and Reynolds number.

Cavitation inception is typically modeled to occur when $p_{\min }\approx p_{\mathrm{vap}}$, leading to:

$$\sigma \approx -C_p^{\min }.$$

(3)

Hence, the scaling law predicts that $\sigma$ is approximately proportional to the magnitude of the minimum pressure coefficient, which for slender airfoils often scales with:

$$C_p^{\min }\sim f(\alpha ,Re,\mathrm{geometry}).$$

(4)

2.1. Simplified Scaling Relation

The scaling laws are valid under assumptions of attached, steady flow and small angles of attack, as consistent with thin-airfoil theory [28,29,30]. If we assume geometric similarity and small variations in Reynolds number, a first-order scaling can be proposed:

$$\sigma \sim {\displaystyle \frac{p_{\infty }-p_{\mathrm{vap}}}{\frac{1}{2}\rho V_{\infty }^2}}.$$

(5)

Under constant $p_{\infty }$ and $\rho$, $\sigma$ varies primarily to $V_{\infty }^2$. This suggests that cavitation number can be collapsed across different velocities by using the $V_{\infty }^2$ scaling.

A first-order scaling of cavity length along the chord can be derived by balancing pressure recovery with vapor pressure. Assuming steady sheet cavitation and potential-flow-like pressure recovery, the cavity length $L_c$ is often scaled as:

$${\displaystyle \frac{L_c}{c}}\sim {\displaystyle \frac{1}{\sigma }}.$$

(6)

This inverse relation arises because lower cavitation numbers imply that the pressure remains below $p_{\mathrm{vap}}$ over a larger fraction of the chord. Experimental and numerical studies consistently report this approximate $1/\sigma$ scaling, though the slope and offset depend on geometry, Reynolds number, and incidence angle [28,31].

2.2. Lift Coefficient Scaling

In classical potential flow over a hydrofoil, the lift coefficient scales with angle of attack:

$$C_L\sim 2\pi \alpha ,$$

(7)

As suggested for small angles (thin-airfoil theory) under cavitating conditions, the effective camber line changes as the cavity acts like a partial solid extension of the foil. This often reduces effective circulation and alters lift scaling:

$$C_L\approx f(\alpha ,\sigma ),$$

(8)

where f is a decreasing function of the cavitation number at low $\sigma$ (longer cavities shield more of the suction side). Empirical data often show roughly quadratic corrections in $\sigma$ near inception, motivating empirical fits of the form:

$$C_L\approx C_{L0}-k{(1-\sigma )}^2.$$

(9)

2.3. Drag Coefficient Scaling

In non-cavitating flow, hydrofoil drag is primarily due to skin friction and pressure drag, scaling approximately as:

$$C_D\sim {\displaystyle \frac{1}{Re}}+C_{D,p},$$

(10)

where $C_{D,p}$ depends on separation and pressure recovery. Under cavitating conditions, a vapor cavity substantially modifies pressure distribution and increases form drag. A first-order model assumes that the cavity reduces adverse pressure gradients but adds a low-density wake:

$$C_D\sim C_{D0}+\Delta C_D\left(\sigma \right),$$

(11)

with $\Delta C_D$ often empirically observed to decay exponentially with increasing $\sigma$, since shorter cavities reduce form drag:

$$\Delta C_D\left(\sigma \right)\sim exp(-a\sigma ).$$

(12)

2.4. Need for Empirical Correlations

These scaling laws provide a theoretical baseline, suggesting:

• $\sigma \propto 1/V_{\infty }^2$ under constant $p_{\infty }$ and $p_{\mathrm{vap}}$,
• $L_c/c\propto 1/\sigma$,
• $C_L$ decreasing quadratically in $(1-\sigma )$,
• $C_D$ showing exponential dependence on $\sigma$.

Empirical studies, however, are derived from this simplified scaling and verified by experimental and numerical data. These empirical relations hold good, except for higher angles of attack, low cavitation numbers, or when boundary layer separation affects $C_p^{\min }$.

2.5. Plain Hydrofoil Performance

The empirical correlations for cavitation characteristics of the smooth NACA0018 hydrofoil are derived from experimental data [32,33]. The cavity length ($L_c$), lift coefficient ($C_L$), and drag coefficient ($C_D$) are expressed as functions of the cavitation number ($\sigma$):

$$\begin{array}{cc}\hfill L_c^{\mathrm{smooth}}& =0.15c{\displaystyle \frac{1.1-\sigma }{0.2+\sigma }}\hfill \end{array}$$

(13)

$$\begin{array}{cc}\hfill C_L^{\mathrm{smooth}}& =0.85-0.25{(1-\sigma )}^2\hfill \end{array}$$

(14)

$$\begin{array}{cc}\hfill C_D^{\mathrm{smooth}}& =0.018+0.12e^{-3.5\sigma }\hfill \end{array}$$

(15)

where $c=0.165$ m is the chord length. These correlations are valid for $\sigma \in [0.4,1.2]$ at $\alpha =8^{\circ }$ and $\mathrm{Re}\approx 1.6\times {10}^5$.

2.6. Modified Hydrofoil Performance

The modified hydrofoil features a rectangular groove/cavity on the suction surface at $x/c=0.4$ with dimensions $d_g=0.02c$, $w_g=0.03c$ [34,35], where $d_g$, $w_g$ are cavity depth (vertical dimension) and cavity width (streamwise length along the chord), respectively. The cavity characteristics are modified as:

$$\begin{array}{cc}\hfill L_c^{\mathrm{grooved}}& =0.72\times L_c^{\mathrm{smooth}}\hfill \end{array}$$

(16)

$$\begin{array}{cc}\hfill C_L^{\mathrm{grooved}}& =C_L^{\mathrm{smooth}}+0.08(1-\sigma )\hfill \end{array}$$

(17)

$$\begin{array}{cc}\hfill C_D^{\mathrm{grooved}}& =0.018+0.09e^{-4.0\sigma }\hfill \end{array}$$

(18)

Figure 1 shows the variation of cavity length, drag, and lift with the cavitation number. The empirical relations capture the trend well, with deviations within 10% of the experimental data. Figure 2 compares the cavitation behavior of a plain NACA0018 hydrofoil and an NACA0018 hydrofoil with a surface cavity modification across a range of cavitation numbers $\sigma$, the drag coefficient, and the lift coefficient variation with the cavitation number based on the empirical relation. This figure compares the cavitation behavior of a plain NACA0018 hydrofoil and an NACA0018 hydrofoil with a surface cavity modification across a range of cavitation numbers $\sigma$. The top plot shows that cavity length increases as $\sigma$ decreases, with the plain hydrofoil generating longer cavities than the cavity-modified one. The middle plot indicates that the lift coefficient ($C_L$) drops more sharply for the plain hydrofoil under stronger cavitation. The bottom plot shows that the drag coefficient ($C_D$) increases more rapidly for the plain hydrofoil. Overall, the cavity-modified surface helps suppress cavity growth and reduces performance losses under cavitating conditions.

2.7. Physical Interpretation of Groove Effects

The groove modifies cavitation through three primary mechanisms:

1.

A reduction in capacity length of 28% observed as grooves capture tip leakage vortices (TLV), generating secondary counter-rotating vortices that reduce TLV strength by 30% [34]:

$${\mathrm{\Gamma }}_{\mathrm{GLV}}=0.3{\mathrm{\Gamma }}_{\mathrm{TLV}}$$

(19)

2.

Grooves create local pressure rise zones that delay cavitation inception by $\Delta \sigma \approx 0.15$ [36]:

$$\Delta p_{\mathrm{groove}}=0.12\rho U_{\infty }^2$$

(20)

3.

Lift enhancement and drag reduction observed due to preservation of the leading-edge suction pressure distribution and a reduction of lift hysteresis of 40% during cavitation cycles [35]. The modified drag equation reduces the drag induced by cavitation by lowering the oscillation amplitude of the cavity.

3. Numerical Section

The numerical simulation aims to verify the empirical relation concerning drag, lift, and cavity length variation with plain NACA foil and modified NACA foil.

3.1. Governing Equations

The incompressible, unsteady Reynolds-Averaged Navier-Stokes (URANS) equations govern the flow over the NACA0018 hydrofoil. These include the continuity and momentum equations:

Continuity equation:

$${\displaystyle \frac{\partial U_i}{\partial x_i}}=0$$

(21)

Momentum equation:

$${\displaystyle \frac{\partial U_i}{\partial t}}+U_j{\displaystyle \frac{\partial U_i}{\partial x_j}}=-{\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial P}{\partial x_i}}+{\displaystyle \frac{\partial }{\partial x_j}}\left[\nu \left({\displaystyle \frac{\partial U_i}{\partial x_j}}+{\displaystyle \frac{\partial U_j}{\partial x_i}}\right)-\overline{u_i^{\prime }{u}_j^{\prime }}\right]$$

(22)

where $U_i$ is the mean velocity component, P is the pressure, $\rho$ is the density, $\nu$ is the kinematic viscosity, and $-\overline{u_i^{\prime }{u}_j^{\prime }}$ is the Reynolds stress tensor.

3.2. Computational Domain and Mesh

A structured rectangular two-dimensional computational domain is used, extending $10c$ upstream, $20c$ downstream, and $10c$ in the normal direction from the hydrofoil chord (c) with 160 mm length. The mesh is very fine near the wall to ensure $y^{+}$$\le 1$ for accurate resolution of the boundary layer near hydrofoil. Grid independence is verified by comparing lift and drag coefficients in three mesh densities: coarse (140,000 cells), medium (270,000 cells), and fine (442,000 cells). The finer mesh is selected as it provides a balance between accuracy and computational cost. Figure 3 shows the two-dimensional computational domain used for simulating flow over an NACA0018 hydrofoil. The hydrofoil is placed at an $8^{\circ }$ angle of attack (AOA) at a distance of 10 chord lengths ($10C$) from the inlet and $20C$ below the top and above the bottom walls, where C represents chord length. The cavity dimension is selected as height (h) 17.5 and width (w) 35 so that width to height ratio remain 2. The inlet is specified with a velocity boundary condition, the outlet with a pressure boundary, and both walls are treated as no-slip boundaries. This setup ensures sufficient space to capture flow development and cavitation effects around the hydrofoil.

The structured mesh was created for plain and cavity NACA0018 foil by using the advance meshing tool ICEM-CFD and is shown in the Figure 4 and Figure 5. The mesh quality is close to 1 with a lower aspect ratio. The number of the node is 442,000, finally selected after grid convergence, shown in the

Table 1. Grid independence at 8 degree AOA and Re 40,000.

Number of Nodes	${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{L}}$	Normalized Cavity Length
Coarse Mesh	0.091	0.94	0.03
Medium Mesh	0.086	0.88	0.05
Fine Mesh	0.083	0.79	0.06

. The grid independence test with $C_D$, $C_L$ and normalized cavity length (normalized with chord length) shows that the fine mesh is suitable for further simulations, as variation between medium and fine meshes is found to be very low.

3.3. Turbulence Model: k-$k_L$-$\omega$

The k-$kL$-$\omega$ three-equation model is used to capture the characteristics of turbulent and transitional flow. The k-$kL$-$\omega$ turbulence model is especially beneficial for simulating flow over an NACA0018 hydrofoil due to its precise predictions of laminar-to-turbulent transition, flow separation, and adverse pressure gradients, all of which are essential for hydrofoil performance. Research indicates that the k-$kL$-$\omega$ model produces enhanced predictions of lift and drag coefficients relative to traditional turbulence models, with errors often around 5% compared to experimental data. This model accurately preserves vortical structures and resolves separation bubbles, rendering it highly suitable for representing the intricate flow phenomena surrounding hydrofoils. The advantages have been substantiated in the research conducted by Walters and Leylek [37], who confirmed the model for transitional and separated flows over airfoils.

The governing equations are:

Turbulent kinetic energy ($\mathit{k}$):

$${\displaystyle \frac{\partial \left(\rho k\right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho U_{j}k\right)}{\partial x_j}}=P_k-{\beta }^{*}\rho k\omega +{\displaystyle \frac{\partial }{\partial x_j}}\left[(\mu +{\sigma }_k{\mu }_t){\displaystyle \frac{\partial k}{\partial x_j}}\right]$$

(23)

Specific dissipation rate ($\mathit{\omega }$):

$${\displaystyle \frac{\partial \left(\rho \omega \right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho U_j\omega \right)}{\partial x_j}}=\alpha {\displaystyle \frac{\omega }{k}}{P}_k-\beta \rho {\omega }^2+{\displaystyle \frac{\partial }{\partial x_j}}\left[(\mu +{\sigma }_{\omega }{\mu }_t){\displaystyle \frac{\partial \omega }{\partial x_j}}\right]$$

(24)

Turbulent length scale ($\mathit{kL}$):

$${\displaystyle \frac{\partial \left(\rho kL\right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho U_{j}kL\right)}{\partial x_j}}=\rho C_{kL}{P}_{k}L-\rho C_{kL2}{k}^{3/2}+{\displaystyle \frac{\partial }{\partial x_j}}\left[(\mu +{\sigma }_{kL}{\mu }_t){\displaystyle \frac{\partial kL}{\partial x_j}}\right]$$

(25)

where ${\mu }_t=\rho k/\omega$ is the eddy viscosity.

3.4. Cavitation Model: Schnerr–Sauer

The Schnerr–Sauer cavitation model [38] is used to simulate phase change between liquid and vapor. The Schnerr–Sauer cavitation model is a model widely utilized in cavitation modeling because of its efficacy in accurately representing the dynamics of vapor bubble formation and collapse, as well as the transient development of cavitation regions, all while ensuring high computational efficiency. The model is successfully used for both steady and unstable cavitating flows, establishing it as a reliable choice for predicting cavitation behavior in engineering applications. The easier formulation, based on bubble dynamics, enables a strong and physically consistent description of complex cavitation processes [39,40].

The vapor volume fraction ${\alpha }_v$ is governed by:

$${\displaystyle \frac{\partial \left({\rho }_v{\alpha }_v\right)}{\partial t}}+\nabla ·\left({\rho }_v{\alpha }_v\mathbf{U}\right)=\dot{m}$$

(26)

Mass transfer rate:

$$\dot{m}={\displaystyle \frac{{\rho }_v{\rho }_l}{{\rho }_m}}{\alpha }_v(1-{\alpha }_v){\displaystyle \frac{3}{R}}\sqrt{{\displaystyle \frac{2}{3}}{\displaystyle \frac{|p-p_{\mathrm{sat}}|}{{\rho }_l}}}·\mathrm{sign}(p-p_{\mathrm{sat}})$$

(27)

Bubble radius:

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

(28)

where $n_0$ is the bubble nuclei number density, $p_{\mathrm{sat}}$ is the saturation pressure, and ${\rho }_m={\alpha }_v{\rho }_v+(1-{\alpha }_v){\rho }_l$.

3.5. Numerical Scheme and Convergence

A pressure-based transient solver is used with second-order upwindfor momentum, quickly for the volume fraction; second-order upwind is used for the turbulence kinetic energy, the specific dissipation rate, and laminar kinetic energy. The SIMPLE scheme is applied for pressure velocity coupling. Least square cell based gradient is applied. Lift and drag coefficients along with five monitor points are created. Convergence is achieved when residuals fall below ${10}^{-6}$ for continuity and momentum, and ${10}^{-5}$ for turbulence and cavitation equations. Time-step independence is ensured with $\Delta t={10}^{-4}$ s.

3.6. Validation

The numerical setup is validated by comparing simulated lift and drag coefficients and vortex shedding frequency with experimental data for similar hydrofoils. The present URANS approach predicts these parameters within 5–7% of experimental values, confirming the reliability of the methodology. Validation is shown in

Table 2. Validation with other experimental data at 8 degree AOA and Re (40,000) [9,10].

List	${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{L}}$
Reference	0.077	0.82
Present work	0.083	0.795

, which helps enable the numerical scheme to capture the trend.

4. Results

The section is extended with three subsections for detailed analysis.

4.1. Contours of Velocity and Vapor Fraction

Figure 6 shows velocity contour plots around an NACA0018 hydrofoil for two surface conditions: (a) plain and (b) cavity-modified. In subplot (a), strong vortex structures are visible near the trailing edge, indicating flow separation and increased unsteadiness. In contrast, subplot (b) shows a more streamlined flow with suppressed vortex formation due to the cavity-modified surface. This implies that surface modification reduces flow separation and stabilizes the flow, potentially enhancing hydrofoil performance under cavitating conditions ($\sigma =1.7$).

Figure 7 compares the cavitation behavior between a plain NACA0018 airfoil and a modified NACA0018 with a cavity. The cavitation number is reduced from (a) to (c), so the cavity size is at the maximum in the case of Figure 7a. In the plain airfoil, cavitation typically initiates at the leading edge or low-pressure regions, forming vapor bubbles that collapse downstream, leading to noise, vibrations, and potential surface erosion. In contrast, the cavity in the modified airfoil alters the pressure distribution, which can either delay cavitation onset or stabilize vapor formation, reducing the harmful effects of bubble collapse. As the cavitation number decreases, the size of the vapor cavity on the suction side of a hydrofoil or airfoil increases. In fact, the cavity can act as a low-pressure region that increases the risk or extent of cavitation, and the observed increase in cavity size with a surface cavity is consistent with established cavitation dynamics. Therfore, it can be observed that at $\sigma$ = 0.93, cavitation size is more in the presence of the cavity on the surface.

4.2. Forces and Monitor Points

Figure 8 shows the five monitor points on the suction side to investigate the cavity evalution in the shear layer and wake. Several monitor points were created on the suction surface to study cavity evolution in the shear layer and wake. For clarity, five representative points are discussed in the results.

Figure 9 compares the root mean square (RMS) speed (velocity magnitude fluctuations) at five monitor points for three cavitation numbers ($\sigma$ = 1.7, 1.23, and 0.93). For the plain NACA foil (a), the average RMS speed at all monitor points is highest at $\sigma$ = 1.7 and reduces with cavitation. For modified foil, it is found that overall RMS speed values are much lower than the plain case, and the average RMS speed remains low across all cavitation numbers, indicating the cavity effectively suppresses velocity fluctuations. This was also observed by [34], who demonstrates that the vortex cavitation was supressed.

Figure 10 shows the vapor fraction at five monitor points for three different cavitation numbers ($\sigma =1.7$, $1.23/1.29$, and $0.93$) for (a) the plain NACA0018 and (b) the modified NACA0018. For both cases, the vapor fraction increases as the cavitation number decreases, indicating more intense cavitation at lower $\sigma$. It was found here that the presence of cavity shifts the cavitation formation downstream as monitor points 1 and 2 are zero, demonstrating the cavity’s effectiveness in suppressing cavitation in these regions.

Frequency Spectrum

Figure 11 compares the frequency spectra of velocity fluctuations at five monitor points (MP-1 to MP-5) for both the plain and modified NACA0018 airfoils under different cavitation numbers. Figure 11a,b show the plain airfoil at higher cavitation numbers, where the amplitude of low-frequency fluctuations is much larger, indicating stronger unsteady flow and cavitation activity. Figure 11c,d display the results for the modified airfoil with a cavity, where the amplitude of fluctuations is significantly reduced across all frequencies and monitor points. This demonstrates that the surface cavity effectively suppresses unsteady flow and cavitation-induced velocity fluctuations, especially at lower cavitation numbers.

Figure 12 displays Mel-frequency spectrograms of vapor fraction value for different cavitation numbers. Figure 12a,c show low-frequency, broadband energy concentrated at lower Mel frequencies, indicating persistent low-frequency flow structures or oscillations. In contrast, Figure 12b,d reveal much broader frequency content, especially in (b), where a burst of high energy at low frequencies is followed by a rapid decay, suggesting a transient event such as cavitation inception or strong unsteady flow. The differences in spectral energy distribution across panels reflect changes in flow physics—such as the onset of cavitation or the presence of a surface cavity—affecting the unsteady flow and acoustic response. The plain hydrofoil spectrograms reveal strong low-frequency energy and pronounced broadband high-frequency components in the log scale, indicating high vapor fraction fluctuations caused by unsteady sheet cavity shedding and fluctuations. In contrast, the modified hydrofoil exhibits lower and more stable energy across both normal and log scales, with smoother low-frequency variations and minimal high-frequency content.

Table 3. Summary of lift-to-drag-ratio and cavity length for plain hydrofoil.

Cavitation Number	$\mathit{L}/\mathit{D}$ for Plain	Normalized Cavity Length for Plain
1.7	8.9	0.6
1.23	9.1	0.18
0.93	9.6	0.06

shows the lift-to-drag ratio and cavity length for plain, whereas

Table 4. Summary of lift-to-drag-ratio and cavity length for modified hydrofoil.

Cavitation Number	$\mathit{L}/\mathit{D}$ for Modified	Cavity Length for Modified
1.7	9.6	0.91
1.23	9.8	0.6
0.93	9.9	0.31

shows it for modified NACA0018.

The altered hydrofoil exhibits enhanced aerodynamic efficiency with extended cavity development. At a cavitation number ($\sigma$) of 1.7, it attains a superior L/D ratio (9.6 versus 8.9) and a significantly longer cavity (0.91 versus 0.6) in comparison to the ordinary hydrofoil. At $\sigma =0.93$, the L/D ratio exhibits a minor rise (9.9 compared to 9.6); however, the cavity length experiences a substantial growth (0.31 compared to 0.06). This signifies that the alteration improves both lift production and cavity formation under cavitating conditions. The longer cavity helps stabilize flow structures and suppress unsteady cavitation, which are the main contributors to drag and noise in cavitating conditions.

5. Conclusions

The numerical study confirms that incorporating a surface cavity on an NACA0018 hydrofoil significantly modifies flow separation, wake structure, and unsteady cavitation dynamics. Although the cavity geometry increases overall cavity length at lower cavitation numbers—consistent with fundamental cavitation physics—it nonetheless stabilizes the flow, suppresses unsteady shear-layer oscillations, and reduces velocity fluctuations at key monitoring points. The lift-to-drag (L/D) ratio increases by approximately 7% at a cavitation number ($\sigma$) of 1.7 and by 3.1% at $\sigma$ = 0.9 for the modified hydrofoil. It was found that features like riblets or surface roughness can sometimes reduce cavity size, but a large geometric cavity such as this case does not function in the same way. In fact, the cavity size becomes bigger with a cavity on the surface as the cavity can act as a low-pressure region that increases the risk or extent of cavitation. Frequency spectrum and Mel-frequency analyses further reveal reduced low-frequency acoustic energy, indicating effective mitigation of noise-generating flow instabilities. These results underscore the promise of surface-cavity modifications for enhancing the performance of hydrofoils and turbine blades in practical marine applications.