Cavitation control using passive flow control techniques

Cavitation is defined as the appearance of vapor cavities due to the phase change in a liquid medium.¹ Hydraulic machinery in industries has been experiencing many challenges that are associated with the cavitation phenomenon, including noise,² vibration,³ material damage,⁴ and reduced efficiency/performance.⁵ 

Since the initial investigation of Reynolds,⁶ there have been many studies that have attempted to improve our understanding of the nature of the phenomenon; focusing, among others, on processes involved in the formation of cavitation vapor, the dynamics of bubble detachment, the behavior of boundary layers, and, more recently, on how the strength, extent, dynamics, and impact of cavitation may be controlled or mitigated. The two essential prerequisite conditions needed for cavitation to develop are the presence of favorable bubble inception sites and the opportunity for the liquid pressure to fall below the saturation pressure. Dissolved gas in the liquid medium can also play a role in the activation of nucleation sites. These prerequisites commonly occur in hydraulic machinery. Sudden pressure drops over impellers and blades occur as the energy in the flow is transferred to kinetic energy in the volute and around the impeller blades.⁷ 

Initially, the bubbles in the oncoming stream on a hydrofoil or generally a surface were assumed to be micrometer-sized nuclei in the liquid and they would move along the streamline close to the solid surface. Observable bubbles of 1 mm or larger were deemed to initiate cavitation. Nuclei present in incident-free streams are a primary source of these bubbles. Nuclei passing close to the front stagnation point will experience large fluid accelerations and pressure gradients since the streamlines encountering the low-pressure region are close to the surface. The initial growth phase in all cases was characterized by a spherical cap. Bubbles are separated from walls by thin layers of liquid of a thickness equal to the boundary layer. Once the bubble enters an area of adverse pressure gradient, it begins to be pushed inward, resulting in a wedge-shaped profile. Thus, the bubble collapse begins on the exterior frontal surface, often resulting in the bubble breaking into forward and aft bubbles. This phase is called bubble traveling cavitation.^8–10 

As the bubble grows, it develops substantial spanwise vorticity as it interacts with the boundary layer. As a result, the cavitating vorticity within a bubble is concentrated as the collapse proceeds, transforming it into one (or several, or even more) cavitating vortex with a spanwise axis. When the vortex bubbles collapse, they reappear as a cloud of small bubbles. There is an occasional occurrence where bubbles pass the point where the laminar separation occurs and subsequently develop locally attached cavitation streaks at the lateral or spanwise extremities of the bubble.

This trailing edge of attached cavitation, which is attached to the solid surface, eventually extends out behind the main bubble. Consequently, the main bubble collapses first, leaving the tails to persist for a fraction longer. At this point, an attached cavity is generated, which can evolve to other type of cavitation such as cloud cavitation or supercavitation (Table II).^9,11

Once formed, cavities will eventually collapse or release clouds that will collapse resulting in a shock wave¹² and focus of energy toward walls, which typically lead to cavitation erosion and noise. Over the past four decades, significant research effort has been dedicated to investigate how cavitation may be controlled. This work has tended to focus on extruded profiles from hydrofoils, propellers, pumps, and turbine blades.

Stabilizing cavity resonance or reducing volume of wall and near wall cavities are two solutions to control, reduce, or eliminate cavitation. The presence of nuclei and micro-bubbles within liquids and at solid surfaces, surface characteristics, and Reynolds number are some factors that affect cavitation.^13–17 Adjustment or modification of one or all of these parameters can allow for effective cavitation control. However, the most important parameters which impact cavitation have been linked to the control of boundary layer separation.^1,18,19

The laminar separation can be generated downstream of an adverse pressure gradient and make a low pressure region. The separated layer can then shelter the oncoming flow and generate an attached separation cavity with low pressure at the core. It was found that suppressing or eliminating this separation can effectively delay or suppress the formation of an attached cavity.²⁰ The higher momentum of the turbulent flow improves its ability to resist adverse pressure gradient over convex surfaces and, hence, limit the incidence of separation.^1,21 Compared to turbulent boundary conditions, a laminar boundary flow is more likely to separate, resulting in a higher drag penalty. The control of boundary layer separation achieved by triggering an early transition to a turbulent boundary layer is, therefore, beneficial both in terms of its effect on drag and on cavitation. Other solutions have been considered and have shown varying degree of effectiveness.

Flow control techniques can be defined as tools to change the natural state of fluid flows and their transition into more controlled and desired flow conditions.²² Flow control strategies are divided into two types: passive and active. Passive solutions include devices that do not rely on the controller or energy sources needed for active control.²³ Passive and active can be effective techniques to manipulate and change wall-bounded or free-shear flows. This change can be made by delaying or inducing advanced transition, suppressing or boosting turbulence, and provoking or suppressing separation. These changes can increase lift, decrease drag, suppress flow-induced noise, and induce vortex mixing. Devices and structures that can manipulate the fluid dynamics of a system without an external power source include vortex generators (VGs), tailored surface roughness, injection and discharge channels, and surface obstacles as well as grooves to redirect flow and change vortices regime.

Active controls include wall temperature increase, dynamic surface modification by deformation or movable parts, and injection or flow oscillation using blowing, suction, and synthetic jets.²⁴ 

This article aims to review studies focused on passive flow controls applied to cavitation. Among these, VGs are regarded as the most effective and simplest technique and have been used in many applications such as airfoils, wind turbine blades, swept wing, and heat exchangers.²⁵ Apart from their effectiveness on boundary layer separation, their simple design, low cost, and lower drag make them an effective tool in a broad range of applications.²⁶ Because of this, while other passive flow control technologies are also reviewed, a particular emphasis has been placed on VGs.

The application of passive flow control in compressible external aerodynamics has a significant history. Although there is a noticeable difference between compressible and incompressible flows in the behavior boundary layer separation,²⁷ passive flow control studies in the compressible flow can be a good guide and pattern for incompressible flow cavitation. It is possible to correlate the compressible flow boundary layer behavior to the incompressible flows using three assumptions: (1) the boundary layer is regarded as thermally insulating, (2) the viscosity changes with absolute temperature, and (3) the flow Prandtl number is unity.²⁸ Section II of the article reviews the literature on compressible single-phase flow studies. In Sec. III, different passive flow controls are reviewed in the context of cavitation. Section IV concludes on key results and promising open research topics.

In most aerodynamic applications, such as external flow over aircraft and ground vehicles, and internal flows such as diffusers, boundary layer separation is typically an undesirable phenomenon. Depending on the nature of the wake, separation induces periodic or random pressure variations. Boundary layer separation also leads to weaker lift, increased drag, and energy losses. Finding ways to control separation and, if possible, prevent it²⁹ is clearly desirable assuming that the applied control method has no impact on efficiency or energy consumption.

The idea of using passive flow control and vortex generation in hydro- or aerodynamic applications is well established and has led to a broad range of studies. Since the late 1990s, several investigations have been focused on the effectiveness of using different passive flow control methods on boundary layer separation and aerodynamic performance.²⁵ According to the analysis of drag coefficients for various Reynolds numbers on a smooth sphere compared to a rough sphere or one with an obstacle, a drag crisis occurs at lower Reynolds numbers, also affecting boundary layer separation (Fig. 1).^30,31

The results of these studies guide the implementation of passive control methods in cavitation studies. Vortex generators, distributed roughness, leading-edge slats,^32,33 flow vanes,³⁴ leading-edge serrations,³⁵ slotted airfoils,³⁶ and suction and blowing techniques^24,37,38 have all been considered for the application in external aerodynamics.

There is ample evidence that increased surface roughness can be harnessed to induce vortex shedding, insert energy into the boundary layer, and trigger an early transition to turbulence. This has been shown to delay boundary layer separation and increase the extent of the attached flow region.^39,40 Effects reported include lift recovery and noise reduction.^41,42 Surface roughness is also effective in postponing stall phenomena and improving an airfoil's aerodynamic performance.⁴⁰ 

VGs were initially introduced as small aerodynamic devices attached to a part of an aerodynamic vehicle. They are able to generate a small vortex downstream. VGs can have a similar effect transferring momentum from the free stream to the near wall region. They can provide one of the most practical means to control flow separation over airfoils because of their small size.⁴³ Benefits include increased lift, delayed stall, and drag reduction. Most of the published research in this field concentrates on finding a design that optimizes the vortex generators' height, geometry, and location upstream of the separation line. The most important parameters are the geometry, the height $, h$⁠, the height to pitch ratio, $h/δ$⁠, the array layout, $ΔXVG$⁠, $l/h$⁠, and $β$⁠. Different VG designs and their important parameters are shown in Fig. 2.

Inducing streamwise instabilities and vortices is one of primary ideas for suppressing the boundary layer separation. In the 1970s, Kuethe⁴⁴ observed a type of centrifugal instability called Taylor–Goertler that can lead to the formation of arrays of streamwise vortices over a concave surface. They tested wave-type VGs and with $h/δ$ in the range 0.27 to 0.42. They observed that VGs caused streamwise vortices in the boundary layer because of a Taylor–Goertler instability. VGs were used to suppress the Kármán vortex stream and to reduce acoustic disturbances in the wake area. They could also confine the velocity deficit region in the wake resulting in improved performance.

Rao and Kariya⁴⁵ investigated so-called submerged VG where the VG height was kept smaller than the boundary layer (⁠$h/δ≤0.625$⁠). A comparison with conventional VGs (⁠$h/δ ∼1$⁠) showed that a much lower parasitic drag and better performance in boundary layer separation could be achieved by confining the VG in the boundary layer. Since this seminal work, research has focused on these so-called submerged VGs,^45–49 which have also been called micro-VGs,^50–53 sub-boundary-layer VGs,^54,55 and micro-vanes.⁵⁶ It has been shown, in particular, that VGs with $0.1≤h/δ≤0.5$ could provide sufficient momentum transfer toward the wall and over extended downstream region. With a smaller footprint, submerged VGs have also proven to be more versatile for a wider range of applications.

Research on micro-vortex generators (mVGs) has targeted two main research questions; how effective are mVGs at delaying boundary layer separation and what type of vortical flow is generated downstream. A summary is presented in Table I, where studies are classified based on the VGs characteristic parameters such as geometry and location for effective flow control.²⁶ 

Lin et al. conducted important experimental studies on the mVGs effectiveness on boundary layer using a 2D backward-facing curved ramp at low speed at NASA Langley Research Center.^46,47,49,50 They tested numerous mVGs and other passive flow control methods. Their performance measured in terms of the relative reduction in the extent of the separation region is shown in Fig. 3, with the VG geometries defined in (a), (d), (f), and (g). The most effective methods, such as mVGs and large longitudinal surface grooves, were shown to generate streamwise vortices. mVGs (counter-rotating and co-rotating vane-type VGs with h/δ ∼ 0.2 and h/δ ∼ 0.8) and Wheeler VGs (wishbone and doublet) were found to have almost the same effects on separation delay. Other methods, such as spanwise cylinders and transverse grooves, generated higher forms of drag and proved less effective.^47,49,50

In Fig. 4, visualization of oil flow separation downstream of the baseline surface (without VGs) [Fig. 4(a)] were compared with conventional counter-rotating VGs with flow at $6$ and $10 h$ upstream of baseline separation [Figs. 4(b) and 4(c)]. The results of the study found that vortices generated by conventional VGs are stronger than needed and yet are not suppressing separation, while the mVGs achieved close to a 90% reduction in separation and did not generate pockets of recirculating flow. Measurements of surface pressure along the streamwise direction and at three spanwise locations shown in Fig. 5, clarified the role of mVGs in eliminating separation. Most notable is the lower three-dimensional variability in pressure distribution along the spanwise direction on the shoulder region of the ramp.

Lin et al.⁴⁹ examined the impact of further reduction in $h/δ$ from $0.2$ to $0.1$ and observed a deterioration in the mVG effect on separation. These results confirmed that mVGs can be more effective in controlling flow separation than larger VG but care must be taken in determining an effective height to boundary layer thickness ratio to avoid.

Ashill et al.⁵⁵ performed a comparative study on wedge type and counter-rotating mVGs located $52h$ upstream of the baseline separation line. The counter-rotating mVGs [Fig. 2(e)] with a $1h$ spanwise gap proved most effective at suppressing boundary layer separation.

Gorton et al.⁵¹ studied the effects of mVG profile changes (Fig. 6) in suppressing separation from a backward-facing ramp with co-rotating Gothing VGs [Fig. 2(c)]. The study relied on oil-flow visualization illustrated in Fig. 7. Figure 7(a) shows two large spiral nodes and a central reverse flow at the ramp in the baseline case. The mVGs proposed by Gorton et al.⁵¹ with $h/δ ∼0.2$ is shown in Fig. 7(b) to alter the direction of near-wall flow sufficiently to suppress separation.

Ashill et al.^54,55 also studied the flow characteristics of mVGs at the UK Defense Evaluation Research Agency Boundary Layer Tunnel. They performed tests for a range of mVGs with $h/δ ∼ 0.5$⁠, including the single vane, counter-rotating vane-type, forwards, and backward wedges shown in Fig. 2. The generated vortex strength was estimated from flow field measurements using a laser doppler anemometer up to $15h$ downstream of the mVGs⁵⁵ and up to $50h$ downstream of the mVGs.⁵⁴ They proposed a correlation for the non-dimensional circulation and used the concept of a mVG sufficient height.⁵⁵ The correlation provides a prediction of the VG vortex strength downstream and is applicable for a wide range of Reynolds numbers. No relation is provided, however, between the sufficient height and a physical dimension of the mVGs. The study found that forwards-wedges and the joint-vane mVG create counter-rotating vortices sharing a mutual interface.⁵⁵ Measurements indicated that this led to reduced vortex strength. The vortices generated by backward wedge mVGs were found to be always closer to the wall impacting on wall shear.

Counter-rotating vane mVGs were shown to double the vortex strength when tested up to 50 $h$ downstream of the mVGs. The joined-vane and the forwards-wedge mVGs produced stronger vortex decay than the two 1 and 2 h spaced counter-rotating vanes mVGs at a downstream distance of up to $15 h$⁠. In terms of adverse pressure gradient, spaced vanes proved to be more efficient than joined vanes. In comparison to counter-rotating vanes, forward-wedge mVGs reduced drag by 60%. According to the analysis of counter-rotating vanes, increasing the gap ratio can help decrease the generated drag of devices.

In other studies, Yao et al.⁵⁷ and Allan et al.⁵⁸ conducted an experimental and numerical analysis of single vane-type mVGs on a flat plate. A flow field measurement system was developed to characterize embedded streamwise vortices downstream of mVGs. Their system consisted of a 3D stereo-imaging and particle image velocimetry (PIV) system covered downstream vane-type mVGs. CFD and experimental results both demonstrated that downstream of mVGs, vortices decay substantially regardless of the device incidence angle.

The effectiveness of wedge-shaped and counter-rotating vane mVGs interaction with shocks and boundary layer at Mach numbers of 1.5 and 1.3. was also investigated by Holden and Babinsky.⁵⁹ They observed that both types of mVGs affected the separation bubble under shock and the vortex intensity. Although the vane type mVGs were shown to have a stronger effect because of the higher vortex strength closer to the surface, both types of mVGs can create a wave pattern consisting of shocks, re-expansions, and shocks. Wave drag and pressure losses increase due to this pattern. It was also observed that wedge-shaped mVGs generated vortices that lifted off the surface more quickly.

Babinsky et al.⁶⁰ and Ghosh et al.⁶¹ conducted experimental and CFD analyses of forward wedge type mVG. The formation and evolution of multiple pairs of counter-rotating streamwise vortices were observed downstream of the mVGs as shown in Fig. 8. A low-momentum region forms in the wake of the wedge along the centerline between consecutive mVGs. The magnitude of momentum deficit was found to be proportional to the size of mVGs and inversely proportional to the drag induced by wedge-type while the two counter-rotating vortices act to transfer high momentum from the boundary layer peripheral region to the surface. Despite the strongest effects and greatest drag caused by the largest mVGs, the smallest mVGs (⁠$h/δ=0.3$⁠) had similar effects on separation with lower induced drag. The results also indicated that mVGs should be located closer to the adverse pressure gradients region than traditional VGs.

Dong et al.⁶² proposed a new slotted ramp-type mVGs and numerically investigated their effect on the flow separation in supersonic flow. A more complicated wake structure was observed, including two confluent counter-rotating streamwise vortices and an increase in number of streamwise vortices. The interaction of these vortices with the primary counter-rotating vortex pair could increase the lifetime of vortices and boost the vortex intensity. These slotted mVGs also decrease the generated drag compared to standard micro-ramps and improve the separation control performance.

Sun et al.⁶³ developed a conceptual description of the evolution of the vortical structures in the wake of the micro-ramps in supersonic flows as illustrated in Fig. 9. Based on Li and Liu⁶⁴ and Sun et al.,⁶⁵ velocity shear and, consequently, pressure gradients downstream of micro-ramps induce swirling vortices in an arc or ring shape. The mechanism of vortex generation can be linked to Kelvin–Helmholtz (K–H) instabilities. The model of Sun et al.⁶³ depicts the dynamics of vortices in stages of K–H evolution. Initially, the streamwise vortices generated as focused filaments which quickly lose their stability and change into arch-shape K–H vortices. The wavelength of the instability starts to increase due to shear velocity and vortex pairing increase. As the legs of the arch-shaped K–H vortices grow and merge with neighboring vortices, vortex rings are eventually formed. As a result of streamwise vortices, downward motion is induced at this stage. Turbulent distortion eventually causes the ring vortices to break down.

Sun et al.^66,67 also conducted a numerical modeling to analyze the wake of micro-ramp VGs under hypersonic conditions. They observed a type of arch-type vortices that grow moving downstream and breaking the primary vortices. They found that these mVGs can generate spanwise structures caused by the impinging of the arc-like vortices. Their result showed that drag and heat flux were reduced after applying mVGs to change the cortical structure pattern.

Other applications of passive control in compressible flows not in the scope of this article are reviewed in detail by Akhter and Omar⁶⁸ and Genç et al.²⁵ 

As a conclusion of this section, the results show that mVGs can effectively control flow separation over airfoils. The most important effects relate to boundary layer separation. The generation of streamwise vortices in the boundary layer, transfers momentum toward near the wall, delaying and suppressing boundary layer separation, increasing lift, and decreasing drag and pressure recovery downstream of VGs. The mVGs are quite efficient in suppressing shock-induced separation in supersonic flow and reducing the reverse flow region. The highest effectiveness has been observed in cases with fixed boundary layer separation by locating the VG closer than $100h$ distance upstream of baseline separation.

The geometry and arrangement of mVGs are critical parameters. The best performances have generally been reported with $0.2<h/δ<0.5$⁠, but effective flow separation is still possible with $0.1<h/δ<0.2$⁠. The counter-rotating mVGs have demonstrated better efficiency in 2D flow separation tests, whereas co-rotating mVGs have been found more effective in 3D separation tests. From the literature reviewed here, the most effective distance between the upstream mVGs and the baseline separation is in the range of $5h$ to $30h$⁠.

In this section, we focus on passive techniques to control cavitation. Several methods, including geometry modification, injection, drainage, surface conditioning, obstacles, grooves, and VGs, have been proposed to attempt to passively control the boundary layer and cavitation instability effects. Table II summarizes the different types of cavitation to understand better the analyses reviewed in this article. Sections III A–III F present a review of studies of these different methods and their effects on cavitation. The summary overview of the methods and key results are presented in Table III–Table V.

The properties of a solid surface, coatings, and roughness influence boundary layers, affecting heat transfer and momentum transfer through the fluid–surface interface and influencing cavitation. The boundary layer flow over smooth and rough surfaces is shown in Fig. 10.

The flow over the leading edge of a smooth surface is laminar, and at some point, it becomes turbulent as a result of a flow instability. A thin layer of laminar flow forms along the length of a smooth surface after transiting into a turbulent boundary layer [Fig. 10(a)]. Figure 10(b) illustrates how roughness on the surface of a flow can cause flow instability upstream, resulting in increased turbulence disrupting the viscous layer, causing the roughness layer to form, affecting pressure drop and heat transfer.⁷² Therefore, boundary layer separation and cavitation can be controlled by transitioning to turbulent boundary layers earlier and increasing momentum near the surface.

The first studies, which considered leading-edge roughness to investigate its effect on boundary layer separation, was conducted by Dryden⁷³ and Kerho and Bragg.⁷⁴ The authors observed that the roughness induced boundary layer transition from laminar to turbulent flow has a completely different mechanism than a natural transition in the smooth airfoil and, the roughness moved trigger of transition to, or very close, the trailing edge of the roughness. Stutz⁷⁵ investigated the influences of the roughness and divergent geometries located beneath the internal two-phase flow's cavity. The study concluded that the roughness could not significantly affect the void fraction distribution, cavity area, and time-averaged velocity. Other findings included that cavity roughness does not impact skin friction drag.

Coutier-Delgosha et al.⁷⁶ focused on the wall roughness and its effect on the unsteady behavior of the cavity flow. They observed a significant rise in the frequency of oscillations and a decline in the intensity of pressure fluctuations. A significant reduction in the cavity length was also observed. A study by Ausoni et al.^77,78 examined the effects of tripping the turbulent boundary layer on the wakes of blunt trailing edge symmetric hydrofoils under one specific condition. The leading-edge transition was shown to promote a more organized vortex shedding with decreased vortex shedding frequencies. In Fig. 9, a top view visualization and measurements of vortex-induced vibrations are shown. As well as confirming the tripped transition, the study also revealed a significant increase in vortex-induced hydrofoil vibration and wake velocity fluctuations. The spanwise organization of vortices was strengthened, as was the strength of the vortices. This reduction in spanwise non-uniformities over the boundary layer was linked to the boundary layer turbulent transition at the leading-edge of the hydrofoil. The study also showed how the roughness induced transition led to the generation of small bubble clouds with potentially detrimental erosive properties (Fig. 11).

The application of $15 μm$ sandpaper roughness on the NACA 66 hydrofoil decreased the characteristic lift and momentum coefficients and increased the drag coefficient.⁷⁹ Petkovšek et al.⁸⁰ investigated hydrodynamic cavitation behavior from laser-textured surfaces and found major effects on the characteristics of cavitation with sensitivity to type of micro-structuring. By comparison against highly polished cases, the extent of cavitation was reduced with some of the laser-textures.

Emelyanenko et al.⁸¹ implemented a superhydrophobic coating on stainless steel operating under cavitation in heavily loaded hydraulic systems. Micro- and nano-textures were developed by a nanosecond infrared laser and studied under long-term continuous contact with water. The hydrophobic properties and chemical stability were confirmed. Additional tests under prolonged exposure to abrasive wear and cavitation loads showed significant improvement to the functional durability.

Cavitation inception and development was investigated using hydrofoils with smooth and rough (0.4 μm) leading edges by Tao et al.⁸² According to their research, cavitation inception was enhanced by roughness when incidence angles are below 2°. The roughness element decreases wettability and traps more gas, which can enhance surface nucleation and increase the risk of cavitation. In their studies of hydrofoils with high incidence angles (>3°), roughness significantly delayed cavitation incipience while developed cavitation was almost the same between smooth and rough hydrofoils. Based on their argument, this unexpected incipient delay was caused by the boundary layer structure changes due to roughness.

Churkin et al.⁸³ also conducted a study to determine how wall roughness impacts the cavitation structure. Under specific conditions, it has been demonstrated that varying the surface roughness type and characteristics can control the formation of cavities. Onishi et al.⁸⁴ studied the effects of hydrophilic and hydrophobic coatings on cavitation of tidal turbines and also observed that hydrophilic coating could reduce the incipient cavitation number. A lower growth of cavitation was linked to the hydrophilic of textures, especially at small angles of attack. Issues related to the coating lifetime with loss of effectiveness after 210 s of exposure to cavitation were reported. Hao et al.⁸⁵ also used high speed PIV to analyze the cavitation mechanism after the addition of surface roughness over the hydrofoil's entire surface. The results show that the cloud cavitation mechanism changes significantly compared to smooth hydrofoil surfaces. Over a rough hydrofoil, cloud cavitation appears as attached subulate cavities while cavitation over smooth surfaces form finger-structured cavities. The roughen hydrofoil also experienced a longer cloud cavitation period and higher cavitation growth rate.

Chen et al.⁷⁰ focused on the effects of localized roughness modification concentrating on the hydrofoil leading edge. They observed that both lift and drag coefficients were increased by surface roughening. The lift-to-drag ratio was also slightly increased, and the incipient cavitation number could be reduced by generating higher turbulent kinetic energy and lowering the minimum surface pressure at the leading edge. The roughness did not affect, however, the formation and transition to cloud cavitation. The change in cavitation patterns in this study is shown in Fig. 12.

The efficacy of a range of artificial roughness types on propeller tip vortex cavitation was also investigated by Asnaghi et al.⁸⁶ Both of their numerical and experimental analysis showed that in the case of optimum roughness, tip vortex cavitation inception decreased around 33%, while drag force increased less than 2% compared to the smooth hydrofoil. It is found that compared to the smooth foil, the roughness separation line induces more distribution of vorticity over the tip, which led to the vortex strength reduction.

Svennberg et al.⁸⁷ tested two configurations of uniform and non-uniform roughness patterns of 230 μm height applied over an elliptical foil. The roughness has been shown to result in lower angular momentum one chord length downstream of the tip without notable change in the radius of the vortex core. The study found that the cavitation number for tip vortex cavitation inception can be reduced by 33% for a 2% increase in drag by optimizing the roughness pattern. No obvious differences were noted when comparing the effect of uniform and non-uniform roughness distributions on cavitation inception properties. Non-uniform roughness distributions did, however, have a detrimental effect on drag. Also, while the application of surface roughness did not increase the risk of the foil sheet cavity, it was found to impact on the small scale nuclei production. This was explained by the hydrophobic nature of the roughened surfaces, as roughness elements create nano- and micro-sized residual air pockets from which small nuclei are continuously produced as a result of local degassing.

The study of cavitation extends beyond inception, and a significant research effort has been dedicated to the study following growth and collapse stages of cavitation. Published studies^88–90 have considered the effect of shock waves,^91–94 refraction wave^91,95–100 thermal growth^95,101–109 and fluids properties,^107,110,111 and, in particular, liquid compressibility and viscosity^{110,112–117} and the presence of non-condensable gas.^118–120 Not many studies, however, have focused on the effect of passive flow control on bubble growth and collapse. The most likely reason for this is the clearer role played by surface modification in controlling boundary layer separation than bubble growth and collapse. One notable exception is the work by Kadivar et al.¹²¹ who recently used a rigid aluminum plate with shark skin-inspired micro-structured riblets to investigate the effects of regular surface roughness on the bubble dynamics of a single cavitation bubble. A micro-structured V-shaped riblet was used to study the dynamics of a single laser-generated cavitation bubble. During the first collapse, microbubbles formed between the bubble and the riblet surface were shown to reduce the momentum of the micro-jet produced by the collapse. The micro-structured riblets were then linked to a reduction in extent of cavitation-induced erosion. A recent study by Gonzalez-Avila et al.¹²² also proposed a biomimetic gas entrapment by micro-textured surfaces (GEMS) derived from the mushroom-shaped features found in hairs and cuticles of sea skaters and springtails. The GEMS, produced by using SiO₂/Si substrates and micro-fabrication techniques, were shown to trap air when immersed in water. The entrapped air, in turn, was shown to repel cavitation bubbles and protect against cavitation erosion. The process of formation, growth, and collapse of cavitation bubbles is illustrated in Fig. 13 with and without surface topographies. Experimental results presented demonstrated the effectiveness of the technique for a wide range of bubbles to surface distances.

A summary of important studies for cavitation control using surface roughness is presented in Table III.

Direct optimization of the blade profiles and geometries can also contribute to cavitation mitigation. Some of the earliest studies in this respect relate to efforts dedicated to the development of a series of nonsymmetrical hydrofoils specifically designed to reduce the cavitation bucket in practical applications. Cavitation bucket is a diagram which can characterized the cavitation inception by presenting how minimum pressure coefficient (⁠$Cpmin)$ vary with angle of attack (Fig. 14). Results indicate that a significant delay in cavitation inception could be achieved.^123,124

Kyparissis and Margaris^125,126 worked on different centrifugal pump blade designs, including double-arc synthetic blades and different blade leading edge angles. The investigation considered pump hydraulic performance and cavitation in tandem. The blade leading-edge angles were experimentally tested over a range of $9°, 15°,and 21°$⁠. For low and high angle, attached cavitation was found to move from the pressure to the suction side, respectively, while cavitation could be eliminated $15°$ blade leading edge angle of attack. It is because the testing condition is close to that of the best efficiency point. Increasing the blade leading angle of attack in this study could increase the total head and efficiency. Other studies have documented the benefit of increasing the blade leading edge. Shi et al.¹²⁷ applied a biomimetic tubercle on the design of a tidal turbine leading-edge. They observed that the appendages could constrain the extent of the cavitation region but this was achieved at the cost of higher cavitation number and earlier onset of cavitation.

As the shape of the blade tips can have a significant effect on tip leakage, foils with various tip shapes, such as squealer tips,^128–130 thickened tips,¹³¹ rounded tips,^132,133 and C-grooves¹³⁴ have been studied. The casing grooves may also serve as an effective solution for suppressing the tip-leakage vortex (TLV), according to Kang et al.¹³⁵ and Hah et al.¹³⁶ It has been confirmed, however, that the effect of passive control strategies in the control of tip leakage is greatly influenced by gap size.¹³⁷ 

The study by Custodio et al.¹³⁸ focused on the characteristics of cavitation inception with wavy leading-edge patterns. The authors found that hydrofoils with medium and large protuberances can confine the cavitation region behind the protuberance troughs. By contrast, standard hydrofoils showed sheet cavitation over the entire span. Zhao and Wang¹³⁹ conducted numerical simulation to determine the effect of the bionic fin-fin structure on cavitation on a hydrofoil surface. Their results showed that these structures are able to increase the lift-to-drag ratio and decrease the turbulent kinetic energy and would be an effective passive control method for cavitation. A novel design for a hydrofoil with twin protuberances to mimic the two prominent tubercles found on the flipper of a humpback whale was proposed and studied by Kant and Bhattacharyya.¹⁴⁰ This design was characterized by its ability to limit the separation zone between the chordwise vortices shed from the two humps at high angles of attack (>20°). Although the pre-stall lift coefficient achieved by the modified profile was lower, the maximum lift was increased. The two protuberances were found to reduce the extent of stall separation by altering the interaction of the two chordwise vortices over the suction side, resulting in an enhanced lift after stall. At pre-stall and post-stall angles of attack, the amplitude and spacing of the two protuberances had an important impact on the lifting characteristics. It has been determined that such modifications can effectively control flow at high angles of attack and can be tailored for specific marine applications.

The leading-edge protuberances of humpback whale flippers were also incorporated in hydrofoil modifications by Li et al.¹⁴¹ to study the impact on cavitation. The wavy leading edge considered improved the lift–drag characteristics and reduced cavitation volume by around 30%. The shedding of cavitation bubbles was also stabilized by reducing the wavelength and increasing the amplitude of the shape modification. Increasing the amplitude significantly reduced the cavitation volume, decreased the amplitude of pressure, and overall enhanced the suppression of cavitation.

According to a recent study of a hydrofoil with flipper protuberances on the leading edge,¹⁴² the hydrodynamic performance and cavitation characteristics were significantly affected. A flow visualization illustrates how the hydrodynamics and pressure distributions of modified hydrofoils result from periodic and symmetric streamwise vortices that originate from protuberances. The location and scale of cavitation are considerably restricted by the streamwise vortices of modified hydrofoils. The relationship between pressure fluctuations and cavity evolution is also analyzed with a simplified one-dimensional model. Their results showed cavity volume acceleration is attributed to pressure fluctuations, which can be used to control cavitation oscillations in engineering designs.

Grooves and riblets are defined as streamwise channels on the surfaces and have been extensively studied for their drag reduction properties.^143–145 They have also shown potential benefits for cavitation control. A numerical and experimental study was undertaken by Li et al.¹⁴⁶ to examine how distributed grooves affected cavitation around the body of revolution. Numerical simulations showed that the grooves accentuated the pressure variations along the tunnel. Grooves also resulted in significant fluctuations of pressure on the surface. According to both experimental and numerical results, groove width was shown to affect the amplitude and interval of fluctuation and, therefore, the cavitation distribution.

Following a study on the benefit of surface roughness on unsteady shedding of cloud cavitation, Danlos et al.¹⁴⁷ investigated longitudinal grooves and their effect on sheet cavitation. Grooves were found to suppress cloud cavitation instabilities.¹⁴⁸ Liu and Tan^134,149 studied grooves' effects on suppressing tip vortices, which are precursor to cavitation inception. The analysis confirmed the ability of grooves to suppress the leakage vortices near the leading-edge of the hydrofoil subject to careful positioning.

To control TLV cavitation, overhanging grooves (OHG) were fitted to hydrofoils by Cheng et al.¹⁵⁰ A significant improvement in cavitation suppression was observed with the OHG compared to the baseline, conventional grooves and anti-cavitation lip (ACL) with a minimal effect on hydrofoil performance. Effective reduction in the intensity of TLVs and tip-separation vortices was achieved with small gap sizes. The OHGs were shown to increase the TLV core size when the gap size was in the medium to large range, increasing, in turn, the minimum local pressure. OHGs were also examined for their effect on hydrofoils, indicating that they can effectively suppress the fluctuation of TLV cavitation without significantly altering the time-averaged drag or lift.

Another important family of passive flow control methods relies on drainage and injection. Kato et al.¹⁵¹ developed a method based on the water discharge from a slit from the hemispherical shaped leading edge. The momentum injection created a wavy motion in the boundary layer with a wavelength higher than the boundary layer thickness. This transitional flow motion could generate an inflection in the velocity profile and disturb the separation zone. It was shown that sheet cavitation on the hydrofoil could be suppressed completely. Arndt et al.¹⁵² also found that the injection of air on the leading edge of a NACA 0015 hydrofoil minimized cavitation erosion.

The application of bleed and jet reinjection flow control on turbopumps were investigated by Japikse.¹⁵³ The auto-oscillation region on the pump impeller suction surface was eliminated, and cavitation happened at a lower cavitation number, while also improving the pump's total head and efficiency, and increasing the suction's specific speed.

Zhu et al. and Bing and Hongxun^154,155 studied gap drainage in the centrifugal pump impeller as illustrated in Figs. 15(a) and 15(b). The approach was shown to act on cavitation while improving the pump hydraulic performance. A new type of cavitation was observed due to a change in the discharge flow due to drainage and the cavitation volume in the impeller channel.

The effect of water injection on cavitation suppression over NACA0066 hydrofoil was also investigated by Wang et al..¹⁵⁷ An optimization of the position and angle of the jet were shown to have a significant effect on cavitation suppression. According to this study, this type of water injection can increase the boundary layer's velocity gradient and decrease the extent of flow separation. A decrease in the thickness of the recirculation zone and, consequently, of the re-entrant jets' velocity were also observed.

Kamikura et al.¹⁵⁶ implemented an asymmetric slit on the axial inducer's blades to observe specifically to study the effect on cavitation, as shown in Fig. 14(c). Results showed that this technique is effective on cavitation instabilities suppression while they were installed in the proper arrangement. It was observed that by viewing the flow field in a circumferential direction around the slit near the blade tip, the wave from the jet divided the cavity, which then decreased the cavity volume. Furthermore, the asymmetric arrangement of the slit in the inducer can disturb the regularity of rotating cavitation because the slit flow rates differ differently in each blade. The summary of important studies in the blade profile and geometry modification, drainage and injection, and grooves and slits is presented in Table IV.

Early investigations of the effect of flow obstacles were precursors to VG studies. Kawanami et al.¹⁵⁸ studied the structure of cloud cavitation in the wake of obstacles on hydrofoils. As re-entrant jets were shown to affect the periodic shedding and generation of cloud cavitation, the obstacle on the foil was able to block the re-entrant jet off, consequently preventing the generation of cloud cavitation. In comparison with hydrofoil without obstacle, the noise intensity and hydrofoil drag were remarkably reduced. After this seminal work, several studies have continued to explore the interaction between obstacles and cavitation instabilities.^159–162 Enomoto et al.¹⁶³ presented a study in which obstacle plates were attached upstream of helical inducers in order to suppress cavitation surges observed under partial flow conditions. Installing axi-symmetric and axi-asymmetric obstacle plates of ring type could narrow the range of the onset regions of oscillating cavitation surge. Obstacle plates with a blockage factor of 30% reduced cavitation surge oscillations to a negligible level. The suppression effects became greater with the increased blockage factor. In a follow up study on inducer performance and cavitation surge suppression, Kim et al.¹⁶⁴ considered two kinds of inducers with blade tips of 8° and 14°. The experimental study considered various axial positions of the obstacle to inducer inlet and various blockage ratios against the flow passage area. A blockage of about 50% between the flow passage and the obstruction was recommended as the optimal ratio. The most appropriate axial position of the obstacle upstream of the inducer inlet must take account of the inducer blade angle with a smaller blade angle requiring a shorter distance. Axis-asymmetrical obstacles were also shown to cause vibrations even under normal operating conditions at high Net Positive Suction Head (NPSH).

Huang et al.¹⁶⁵ used a trip bar on an axisymmetric projectile to weaken the re-entrant jets and pressure wave propagating from the collapse of cavities. An investigation of supercavitating flow was conducted around three different conical cavitators with wedge angles of 30°, 45°, and 60 ° by Kadivar et al.¹⁶⁶ The wedge angle of the cavitator was found to be the most effective design criteria to increase the cavity length. The results have shown that as cavitation number decreases, drag coefficient decreases, and the drag coefficient of a cavitator increases with the increasing wedge angle when inlet velocity is constant. The cavity length was increased both for the lower and higher supercavitation conditions studied numerically. Che et al.¹⁶⁷ focused on a spanwise obstacle located on the suction side of the hydrofoil shown in Fig. 16. The near-wall pressure increased in the wake of obstacles and led to suppression of sheet cavitation. The hydrofoil modification, however, had little impact under transitional cavity oscillation most likely because of the inherently unstable flow as shown in Fig. 17.

Positioning the obstacle downstream of a flat hydrofoil was investigated by Zhang et al.¹⁶⁸ While no significant change in the average cavity length was observed at equivalent cavitation number, the obstacle did affect the dynamics, strength and direction of re-entrant jets.

Using obstacles for control of baled cavitation in water jet pumps is investigated by Zhao et al.¹⁶⁹ They implemented a pair of tandem obstacles on the suction side of the pump. It is observed that there is more resistance against the incipient and the development of leading-edge cavities after using obstacles. Although sheer energetic cavitation appears after obstacles with foamy wakes, pressure gradients analysis shows that these obstacles were effective in blade cavitation. However, the hydraulic performance loss, including 6% head drop and 5.6% efficiency drop, was observed because of violent pressure fluctuations after using obstacles on the blade.

A recent study by Lin et al.¹⁷⁰ has analyzed the influence of arc obstacles on the evolution of cavitation over flat hydrofoils. Experimental evidence has shown that the shedding of cavitation and the distribution of air over the flat hydrofoils are influenced by the obstacles. The arc obstacles were shown to stabilize the leading edge of the shedding cavity and restrict its size, which inhibits cavitation.

The ability of VGs to control boundary layer separation has been exploited on hydrofoils to destabilize attached cavities. The schematic of Fig. 18 (Ref. 171) illustrates how counter-rotating vortices generated upstream of the cavity by the VG delays separation and promotes the formation of a smaller cavity with a growth and shedding behavior similar to the attached cavity generated by laminar boundary layer separation but with some important distinction. Its leading edge is observed to move dynamically, likely due to a thin liquid layer separating the cavity from the wall as conjectured by the authors, and the cavity edge shows oscillations indicative of a turbulent flow.

The low-pressure core of the streamwise vortices induces stable vortex cavitation, which breaks down into bubble clouds upstream of the attached cavity. Similar observations were made in a study of VGs by An.¹⁷² The application of VGs in control of cavitation in multi-propulsion vessels was studied by Liang-mei.¹⁷³ They found a significant improvement in cavitation instability and declining pressure fluctuation.

The application of bubble generators on cavitation control was studied by Javadi et al.¹⁷⁴ through a two-dimensional cavitation calculation. This bubble generator was actually a wedge type VG. Their numerical analysis showed that this VG can make a low pressure recirculation region (below saturation pressure) behind the VG. Bubbles then start to generate and grow in this region. By controlling this condition, the bubbly flow becomes stable and will not vanish, or in other words, interfere and stop the cavitation process. They observed that the whole cavitation process, including vaporization, bubble generation, and bubble implosion, could be affected, and lift and drag fluctuations could be reduced.

Vortex generators that have been optimized can also be used for TLV cavitation suppression. The experimental results of Amini et al.¹⁷⁵ have shown that the winglets could effectively increase the radius of the tip vortex and delay the initial inception of the TLV cavitation process. The ACL, however, is the only proposed method that has actually been applied. Results showed that it is difficult for the ACL to have a satisfactory inhibitory effect on TLV cavitation, and once the vortex generators are not operating under design conditions, a more intense level of cavitation will be induced.^137,176

A recent numerical study by Kadivar et al.¹⁷⁷ proposed a new type of VG called cavitating bubble generators (CGs) (Fig. 19). The CGs were adopted from wedge-type VGs were used before for aerodynamics application with the aim of generating cavitating bubbles at the suction side of hydrofoil. They observed that the high momentum fluid from the free stream flow moved to the hydrofoil's near-wall low energy region. These CGs could generate vortices downstream and move higher kinetic energy flow to the vicinity of the hydrofoil surface. Consequently, quick high-pressure pulsations near the hydrofoil surface were reduced, and the resistance against pressure rise before boundary layer separation was increased. They found that the vortex structures were significantly modified on the suction side and the hydrofoil wake region. This phenomenon suppresses the cyclic behavior of unsteady cloud cavitation and declining turbulent velocity fluctuation in that area. The experimental investigation of CGs proved an essential role of re-entrant jets on cloud cavity shedding structure.¹⁷⁸ Their experiment proved the reduction of pressure pulsation's amplitude in instabilities of cavitation dynamic. As a result, they can be used as a useful tool for delaying cloud cavitation formation. A comparison between hydrofoil with and without CGs is presented in Fig. 20. In another study, a CG was installed adjacent to the cavitation inception on a semi-circular leading-edge flat plate to control and manipulate unsteady dynamics of cavitation surge. The CG was shown to mitigate large-scale cavities, suppress the spanwise instability of adjacent cavities, and suppress large-scale cavities over the flat plate. Passive control was observed to reduce the dominant frequency of pressure pulsations.¹⁷⁹ 

Xu et al.¹⁸⁰ used cavitators placed at various locations on a hydrofoil's bottom surface to study the supercavitation flow around it. As their observations showed, a localized high-pressure region appears between the leading edge of the hydrofoil and the cavitator, and downstream of the cavitator, the pressure is equal to the saturated vapor pressure of water. Based on the magnitude and distribution of pressure on the hydrofoil surfaces, the lift coefficient increased as the cavitator was positioned farther away from the leading edge and toward the trailing edge. Alternatively, there was a strong correlation between drag coefficients and the maximum thickness of cavitating wakes, which was used as a proxy for the drag coefficient.

Kadivar et al.¹⁸¹ also examined a single spanwise row of cylindrical obstacles named cylindrical cavitating bubble generators (CCGs), shown in Fig. 21. Similar effects were observed such as a reduction in the adverse pressure gradient at the end of cavity, weakening of re-entrant jets and turning unsteady cavity structure to a quasi-stable cavity structure. As a result, the instability of cloud cavitation was mitigated and the near-wall high-pressure pulsation dampened. One key difference to previously studied CCGs is that only small-scale cavity structures are shed while large-scale cavitation clouds are effectively suppressed. It was also observed that vibration-induced cavitation as well as wall-pressure peaks on materials with solid surfaces were significantly reduced.^181,182 In another study, high-speed visualization, PIV, and a hydroacoustic pressure transducer were used to experimentally analyze the effects of CCGs on turbulence behavior and the amplitude-frequency spectra of pressure pulsations associated with oscillations in the attached cavity length and cloud cavitation instabilities. This study confirmed that CCGs is quite effective at hindering the development of cloud cavitation and at decreasing the strength of middle- and side-entrant jets, which are the primary mechanism that cause unstable cloud cavitation.¹⁸³ 

Che et al.¹⁷¹ considered counter-rotating delta-shaped mVGs built into a quasi-two-dimensional NACA0015 hydrofoil (Fig. 22). The type and geometry of mVG was based on designs from Lin²⁶ and Godard and Stanislas³⁷ reviews to control boundary layer separation using VGs.¹⁸⁴ They designed five counter-rotating delta-shaped mVGs with different $h/δ$ in the range of 0.5–2.5. The $ΔXVG$ were set at 2.5 mm from the hydrofoil leading edge based on the position of boundary layer separation at the leading edge obtained from their 2D numerical modeling results. The study demonstrated that the mVG can suppress the laminar separation under non-cavitating conditions. MVGs located within the viscous sub-layer close to the cavitation detachment point failed to suppress the attached cavitation. Results did show, however, that the transition region and attached cavitation were affected. The authors found that at lower heights relative to the viscous sub-layer, mVGs can generate longer counter-rotating and cavitating vortices within the boundary layer. These mVGs could also fix cavitation inception causing more stable sheet cavitation and cloud cavity shedding. The attached cavitation over the smooth hydrofoil showed a formation of “divot” or “finger” structure as well as two-dimensional Tollmien–Schlichting waves which are shown in Fig. 23. Divots are three-dimensional flow structures which appear near the cavity interface. They occur at moderately high Reynolds numbers because of local disturbances near cavity interfaces. Upstream of the detachment point, local disturbances were caused by a breakdown of the laminar boundary separation, resulting in a divot when a jet of fluid penetrated the cavity.¹⁹ Tollmien–Schlichting waves are known as streamwise instabilities that occur prior to the transition to turbulence in boundary layers. This instability initiates because of the interaction of disturbances with leading edge roughness and can be slowly intensified while moving downstream and can help with the process of turbulence transition.¹⁸⁵ In comparison with a smooth hydrofoil surface, cavitation started closer to the leading edge, eliminating classic “fingering structures” and Tollmien-Schlichting waves.¹⁸⁴ 

They observed a new structure for cavitation onset while the cavitation onset disappears close to the laminar separation. In the new structure, stable vortex cavitation and subsequent vortex breakdown resulted in bubbly structures, which was finally expressed as an attached cavity region. This vortex break-down was delayed when they reduced the height of mVGs. This delay resulted in a rise in cavitation vortex pattern length. This result showed the potential of mVGs in control of cavity dynamics considering the re-entrant jet penetration depth. The flow visualization of attached cavitation during cloud cavitation without and with VGs in this study is presented in Figs. 23 and Fig. 24.

In another study, Che and coauthors analyzed the instability of the attached cavitation produced with mVGs.¹⁸⁶ This study confirmed that these mVGs are an effective passive control for attached cavitation dynamics and changed the surface wall's vicinity's flow dynamics. The results also emphasized again that the mVGs could increase the cavity length and induce counter-rotating streamwise vortices. The mVGs could change the sheet cavity structure to a uniform cavity in a spanwise direction by inducing consistent separate vortex cavitation streaks. The mVGs showed their ability to fix the attached cavitation inception line location, thereby limiting instabilities caused by spanwise disturbances.

In this study, Che et al.¹⁸⁶ interpret two types of Rayleigh–Taylor (R–T) and K–H instabilities, while cavity shedding and re-entrant jet interactions happened over a smooth hydrofoil and hydrofoil with mVGs. Re-entrant jets are generated by exposing cavity closure to an adverse pressure gradient. After propagating upstream, these re-entrant jets impact the cavity interface, causing the cavity to shed. It is possible to interpret the interaction of re-entrant jets and cavities as an R–T. A re-entrant jet and cavity interface at the leading edge interact, generating several cavitating vortices that are indicative of the K–H instability. The K-H instability interpretation has been explained by different shearing velocities causing cavity shedding.

Che et al.¹⁸⁶ presented evidence that reverse flow beneath the attached cavities, which were linked to R–T and K–H instabilities, were suppressed. The mVGs were shown to influence partial cavity oscillations, transitional cavity oscillations, and transition between these two instabilities. Experimentation was extended to measure cavitation erosion and analyze impulsive loading from cavity collapse as a measure of the intensity and aggressiveness of cavitation structure with mVGs.¹⁸⁷ The study also included an analysis of the dynamic behavior of the re-entrant jet, shown in Fig. 25. The effect of the mVGs included suppression under certain condition of periodic shedding and reduction of the maximum pressure fluctuations and associated acoustic power. The arrangement and geometry were shown to be an important factor in determining leading-edge erosion, which was shown to increase at lower angles of attack.

The application of mVGs has started to be investigated in applications other than 2D hydrofoil. Examples include the study by Huang et al.¹⁸⁸ They investigated the effects of VGs on cavitation in marine shipping. The VGs studied could lead to more uniform wake and milder propeller cavitation. These VGs could decrease pressure fluctuations and cause a more uniform distribution of energy. Li et al.¹⁸⁹ designed a delta-shaped VG to solve the vibration problem in the hull propeller and improve the ship wake quality and uniformity. The VG design was based on the ship body lines. It improved the wake uniformity in certain positions as it could generate a more moderate circumference transition and effectively increase the velocity in high wake areas. Additionally, the VGs were able to smoothly transition the unsteady cavitation of the blade in circumference direction and decrease the amplitude of pressure fluctuations. The distance between the positions of blade cavitation collapses, and ship bottom shell was increased after using VGs.

Teplov and Lomakin¹⁹⁰ used computation simulation to examine mVGs located at the front edge on the suction side of impeller blades in a centrifugal pump and analyzed their effect on the cavitation characteristics, efficiency, and pump head. The NPSH was significantly decreased, and the pump efficiency above the best efficiency point was increased.

A study published recently by Chen et al.¹⁹¹ investigated the effects on cavitation of two schematic designs of mVGs around a NACA66 hydrofoil. Two different sets of mVG were installed and positioned upstream of (mVG-1) and within (mVG-2) the laminar separation zone of the baseline hydrofoil. The experimental results indicated that the mVG-1 could promote inception of cavitation earlier than the baseline hydrofoil, while mVG-2 delayed cavitation inception especially at small angle of attack cases. Two reasons were suggested for the effect of the mVG-1. The mVG-1 modification was shown to generate fingerlike vortex at its rear, which was observed before in previous studies^85,171,184 and is shown in Fig. 23. These vortexes were responsible to induce fingerlike vortex cavitation. In addition, the mVG-1 increases the length of the laminar separation bubble (LSB), resulting in laminar boundary layer separation with a lower pressure minimum. Since mVG-2 was located in a high pressure zone from the leading-edge, there are insufficient downstream fingerlike vortices to induce cavitation, which can reduce LSB length. Smaller LSB was able to suppress cavitation at α = 6°–8°. A summary of studies in the field of obstacles and VGs in cavitation control studies is presented in Table V.