High-speed Water Tunnel Research Articles

Numerical simulation of dynamic characteristics of hydrofoil structure under cavitation conditions

In this paper, the effects of different cavitation bubble on the natural frequency, mode shape and hydrodynamic damping of the NACA0009 hydrofoil are investigated by numerical simulation method. The cantilever truncated hydrofoil model is set in a high-speed water tunnel. The dynamic characteristics of the hydrofoil structure is affected by the fluid-structure coupling. Compared to the properties of water, the density of cavitation bubbles decreases, causing an increase in the natural frequency of the structure, and the decrease in the speed of sound also causes a change in the mode shape. The growth rate of frequency under unit chord length cavitation is nonlinear as the cavitation bubble length increases. By defining a modal displacement function to compare the structural mode shapes, cavitation intensifies the bending and torsional deformation of the hydrofoil. Even if the volume of cavitation bubbles is small, the inhomogeneous distribution of acoustic pressure and changes in cavitation bubble properties can cause changes in the structural mode shapes. The one-way FSI numerical method for hydrodynamic damping in cavitating flow is established and the applicability of this method is verified by the calculation of damping in water. For the first bending mode fc1, the hydrodynamic damping with 50% chord length (0.5lc) stably attaching cavitation is simulated. As the length of the cavitation bubble increases to 0.8lc, the damping value becomes smaller. The research in this paper lays the foundation for analysing the dynamic characteristics of hydraulic machinery with cavitation using numerical simulation method.

Experimental investigation of wall-pressure fluctuations in compressible turbulent cavitating flows with emphasis on non-Gaussian features

An accurate probabilistic representation of pressure fluctuations in attached turbulent cavitating flows, especially under strong unsteady cavity regimes, i.e., cloud cavitation, is essential for the reliable prediction of cavitation loads and thus preventing potential cavitation damage. The objective of this work is to examine the wall pressure fluctuations in compressible turbulent cavitating flows, especially the non-Gaussian behaviors and their physical mechanisms. Experiments were conducted in the backward-facing wedge model installed in a high-speed water tunnel. Four high-frequency PCB pressure transducers were installed on the divergent section to capture the cavitation-induced pressure fluctuation signals. The results showed that wall-pressure fluctuations in cavitating flows present non-Gaussian features with positive skewness, and this positive skewness is independent of the cavity regime, which is an intrinsic nature of cavitating flows. However, the fluctuating pressure signals under different cavity regimes show differences. At inception and in the sheet cavity, high-frequency and low-magnitude fluctuating pressure signals are responsible for the positive skewness. At the cloud cavitation cavity, both high-frequency and low magnitude and low-frequency and high-magnitude fluctuating pressure signals are responsible for the positive skewness. In particular, when shockwave dynamics are dominant, a unique kind of fluctuating pressure signal with high frequency and large magnitude is found to be the cause. Finally, the Hilbert-Huang transform (HHT) is employed to analyze the fluctuating pressure signals in cloud cavitation, and a physical model based on cavitation bubble dynamics is proposed. The current study can help to improve the understanding of the dynamics and pressure loads of cavitation.

Hydroelastic damping of low aspect ratio cantilevered plates

This study considers the hydroelastic damping of cantilevered flat plates undergoing free vibration in flowing water. Of particular interest are plates with aspect ratios (defined as span length divided by chord length) less than one. Experimental trials involving plates of aspect ratios from 0.3 to 0.7 are conducted in a high-speed water tunnel. The tests involve flow velocities well below those corresponding to hydroelastic instability. Additionally, an unsteady, linear vortex lattice model is coupled to a structural dynamic plate model to predict flow-induced damping as a function of flow speed. The numerical model has been previously used with air, but never with water as the fluid medium. The model is able to predict the hydroelastic damping associated with the first several plate modes with less than 30% error in most cases. While the hydroelastic damping remains linear in the experimental flow regime, at higher flow speeds more complicated hydroelastic damping behavior is predicted. Numerical studies involving mass ratio, aspect ratio, and reduced velocity are conducted to predict hydroelastic damping across a wide parameter space. All else being equal, chordwise bending modes are found to exhibit two to three times greater hydroelastic damping than spanwise bending modes. There is also an inverse relationship between mass ratio and hydroelastic damping. Further, for plates with low aspect ratios and at fixed reduced velocities, hydroelastic damping increases with increasing aspect ratio.

Experimental studies of the unsteady hydrodynamic loads on a tension-leg platform at high Reynolds numbers

This paper presents experimental studies on the unsteady hydrodynamic loads (forces and moments) on a Tension-Leg Platform (TLP) due to the action of a steady current at high Reynolds numbers (Re) in a high-speed cavitation water tunnel. Five current incidence angles (θ) ranging from 0° to 45° are selected for the present tests. The achieved Reynolds numbers of 9.5×104≤Re≤5.7×105 span from the subcritical to supercritical flow regimes. The experimental results show that at Re<2.2×105, the mean streamwise force coefficient C¯x increases as Re grows for 0° current incidence, while it reduces slightly for 15°, 22.5∘, 30° and 45° current incidences. At Re≥2.2×105, C¯x remains roughly unvaried with Re for each current incidence angle. The fluctuating streamwise force coefficient Cx′ drops gradually as Re increases from 9.5×104 to 2.2×105, and then they rise slightly for all the current incidences. The fluctuating transverse force coefficients (Cy′) in the supercritical regime (2.2×105<Re<5.7×105) are less than those in the subcritical regime (9×104<Re<1.5×105), which is independent of θ. The fluctuating yaw moment coefficients (CMz′) show a declining trend with the increase of Re for 0°, 15°, 22.5∘ and 30° current incidences. In the supercritical regime, the measured Cy′ and CMz′ for 22.5∘ current incidence are larger, comparing with those for the other current incidence angles. In addition, the correlations between forces and yaw moment indicate that the fluctuating transverse force is the main contribution to the fluctuating yaw moment. Furthermore, the effect of the immersed column height (H) on the forces and yaw moment is examined. It is found that, in the supercritical regime, generally Cy′ and CMz′ grow as H∕D (where D is the column diameter) increases from 1.0 to 1.57.

Experimental Study on Morphological Characteristics of Ventilated Supercavity of Double Disc Cavitator Projectile

Based on the principle of independence of cavity sections expansion, a double disc cavitator for underwater projectiles is proposed in this paper.The high-speed water tunnel experiment is carried out to study the generation and morphological characteristics of the ventilated supercavity which generated by this series of double disc cavitator.The experiment observed the ventilated supercavity morphology under the different cone angles by changing the ventilation flow coefficient.The experimental results show that there are two kinds of cavitation states:the front disc preferential cavitation and the rear disc preferential cavitation. The transition between these two states occur at a cone angle about 55°.The value of the critical ventilation flow coefficient when generating stable ventilation supercavity has a positive correlation with the cone angle.The front disc and the rear disc of the cavitator have mutual inhibitory effect on the production of ventilated supercavities.And the morphological characteristics of ventilated supercavity do not increase with the increasing of ventilation flow coefficient, but there is an upper limit value of ventilation flow coefficient.

Experimental investigation of ventilated partial cavitation

This study presents the experimental investigation on the cavity regime and the corresponding geometric characteristic of ventilated partial cavitation (VPC). Experiments are conducted in the high-speed water tunnel at Saint Anthony Falls Laboratory. A backward-facing cavitator mounted on the ceiling of test section is used to generate the VPC. The flow filed and the dynamic motion of VPC are captured by the imaging system under varying water speeds and ventilation rates. Four distinct cavity regimes are classified, referred to as foamy cavity (FC), transition cavity (TC), open cavity (OC) and two-branch cavity (TBC). The distribution of these cavity regimes over Froude number (Fr) and ventilation coefficient (CQs) is summarized in a regime map with FC and TBC occupying the majority portion of the map. More importantly, the CQs−Fr curves demarcating neighboring cavity regimes are revealed satisfying a clear linear relation for FC–TC and a quadratic relation for TC–OC and OC–TBC when Fr is subtracted with a constant corresponding to the inception condition of the cavity regime. Such trends are attributed to the two gas entrainment mechanisms present in VPC, referred to as recirculating vortex entrainment and cavity closure entrainment. Moreover, the geometric characteristic of VPC characterized by the cavity length is examined. With increasing ventilation at fixed Fr, the cavity length grows linearly in OC regime and remains unchanged in TBC regime. The maximum cavity length of OC is found to be within around 7 times of cavitator height. With increasing Fr at fixed ventilation, the cavity length first grows proportional to Fr2 in TBC regime but drops sharply with a small increase of Fr when the cavity transitions from TBC to OC. At fixed Fr, the cavity underpressure rises to maximum (minimum σC) and stays unchanged in TBC upon increasing ventilation. As a result, in TBC, the cavity length is shown to satisfy a power law relation with respect to Fr or σC, while in OC, the cavity length is influenced by the interplay among CQs, σC and Fr with no clear trend observed.

On the internal flow of a ventilated supercavity

This study presents an experimental investigation on the internal flow of a ventilated supercavity using fog flow visualization and particle image velocimetry (PIV) measurements. The ventilated supercavity is generated on a backward-facing cavitator and studied in the high-speed water tunnel at St. Anthony Falls Laboratory. Fog particles are introduced into the supercavity through the ventilation line, and then illuminated by a laser sheet for flow visualizations and PIV measurements. The experiments are performed on the supercavities with two closure types, i.e. the re-entrant jet (RJ) and the twin vortex (TV), under the same water tunnel flow condition but different ventilation rates. The flow visualization revealed three distinct regions within the supercavity, including the ventilation influence region near the cavitator, the extended internal boundary layer along the liquid–gas interface and the reverse flow region occupying a large centre portion of the supercavity. The streamwise and vertical extent of the ventilation influence region, the streamwise growth of the internal boundary layer and the reverse flow within the supercavity are then quantified through PIV flow measurements. Compared to the RJ case, the results indicate that the TV supercavity yields a longer vertical extent of the ventilation influence region, a thinner internal boundary layer and a stronger reverse flow. The internal flow results suggest that at the upstream of the location of the maximum cavity diameter, the gas enters the forward flow (including the internal boundary layer and the forward moving portion of the ventilation influence region) from the reverse flow, while at the downstream of that location, the gas is stripped from the internal boundary layer and enters the reverse flow due to the increasing adverse pressure gradient in the streamwise direction. The above results are combined with visualization results of the supercavity geometry and closure patterns to further explain the influence of gas leakage mechanisms on cavity growth and closure transition. Specifically, visualization of the cavity geometry change during the RJ to TV supercavity transition indicates external flow separation associated with a critical incline angle of the bottom liquid–gas interface at the closure contributes to the onset of RJ closure. The closure visualization shows the coexistence of the toroidal vortex and twin-vortex tubes for the RJ supercavity leads to two gas leakage mechanisms: one associated with the shedding of toroidal vortices ($Q_{RJ}$) and the other due to the gas entrained by the internal boundary layer and leaking from the twin-vortex tubes ($Q_{TV}$). For the RJ supercavity, with increasing ventilation input, due to the reduction of $Q_{RJ}$, the supercavity needs to elongate to increase the gas entrained by the internal boundary layer (i.e. $Q_{TV}$) to balance the ventilation increase. The elongation of the supercavity leads to reduced flow separation, and eventually a transition to the TV supercavity with ventilation above a critical value. For the TV supercavity, $Q_{RJ}$ is absent. An increase of ventilation input can be balanced by the increase of $Q_{TV}$ associated with the widening of the twin-vortex tubes, and therefore, no appreciable elongation of cavity length is observed.

Robust control of a small-scale supercavitating vehicle: From modeling to testing

By traveling inside a gas cavity, a supercavitating vehicle can reduce hydrodynamic drag, increase speed, and minimize power consumption. The main challenge for controlling a supercavitating vehicle is a nonlinear force that arises when the vehicle back-end pierces the cavity. This force, referred to as planing, leads to oscillatory motion and instability. In an effort to develop robust control technologies for supercavitating vehicles, we developed and tested a control methodology for a small-scale system capable of freely rotating about its pitch axis in a high-speed water tunnel. We constructed a low-order nonlinear model of the longitudinal vehicle motion that is based on experimental observations and physical principles. By using this model, we developed a controller design method that delivers a proof of performance in the face of nonlinear and uncertain planing forces. Experiments with the vehicle prototype in the water tunnel suggest that the proposed control technique ensured higher performance when the uncertain planing dynamics are considered in the control synthesis.

Investigation into the behaviors of ventilated supercavities in unsteady flow

A systematic investigation of ventilated supercavitation behaviors in an unsteady flow is conducted using a high-speed water tunnel at the Saint Anthony Falls Laboratory. The cavity is generated with a forward facing model under varying ventilation rates and cavitator sizes. The unsteady flow is produced by a gust generator consisting of two hydrofoils flapping in unison with a varying angle of attack (AoA) and frequency (fg). The current experiment reveals five distinct cavity states, namely, the stable state, wavy state, pulsating state I, pulsating state II, and collapsing state, based on the variation of cavity geometry and pressure signatures inside the cavity. The distribution of cavity states over a broad range of unsteady conditions is summarized in a cavity state map. It shows that the transition of the supercavity from the stable state to pulsating and collapsing states is primarily induced by increasing AoA while the transition to the wavy state triggers largely by increasing fg. Remarkably, the state map over the non-dimensionalized half wavelength and wave amplitude of the perturbation indicates that the supercavity loses its stability and transitions to pulsating or collapsing states when the level of its distortion induced by the flow unsteadiness exceeds the cavity dimension under a steady condition. The state maps under different ventilation rates and cavitator sizes yield similar distribution but show that the occurrence of the cavity collapse can be suppressed with increasing ventilation coefficient or cavitator size. Such knowledge can be integrated into designing control strategies for the supercavitating devices operating under different unsteady conditions.

Design of a bubble collecting section in a high speed water tunnel for ventilated supercavitation experiments

The main objective of the present study is to design a bubble collecting section for use in ventilated supercavitation experiments. The large amounts of air ventilated around a cavitator split into small bubbles that follow the water’s passage through the water tunnel. The presence of these bubbles in the test section of the water tunnel prevents effective observation of supercavitation. To enable the clear observation of cavitation shape, a bubble collecting section with large volume is necessary upstream of the test section to collect bubbles. The buoyancy of bubbles provides a simple means for their collection. However, the bubbly flows in such systems have rather high velocities and a non-uniform velocity distribution, which degrades the buoyancy effect. In the present study, a bubble collecting section with three porous plates that produce a uniformly low velocity distribution is designed and analyzed with numerical methods. The effectiveness of this approach is assessed experimentally with the 1/10 miniature model. The reduction of the void fraction downstream of the bubble collecting section was also assessed in the test section. The bubble collecting section in the full-scale water tunnel was also eventually found to be well designed through flow speed measurements and bubble visualization in the test section.

A comparative study of natural and ventilated supercavitation across two closed-wall water tunnel facilities

Despite half a century of experimental investigation into both natural and ventilated supercavitation, there are still significant discrepancies among the results, in terms of supercavity geometry and ventilation demand, etc., under approximately similar conditions from different water tunnel facilities. To understand the influences of the flow facilities on the supercavitation experiments, a systematic comparison is conducted using the results from two closed-wall water tunnels, i.e. the Saint Anthony Falls high-speed water tunnel and the Chuangnam National University Closed Tunnel. For both ventilated and natural supercavitation, the experimental conditions from the two facilities are designed to match over a wide range of Froude number and blockage ratio, etc. For the ventilated supercavitation, the cavitation number for generating a ventilated supercavity and the hysteresis process for sustaining a supercavity show a proper match across the two facilities while holding the Froude number and blockage ratio constant. However, the ventilation demand to form a supercavity shows a noteworthy difference across the facilities even under the same Froude number and blockage ratio. Such a difference in the ventilation requirement is attributed to the mismatch of Reynolds number, the detailed geometry of the cavitator models as well as the test section which influences the pressure distribution along the span of the supercavity. Similarly, for natural supercavitation, both facilities yield a similar vaporous cavitation number for the supercavity formation under the same Froude number and blockage ratio, as well as similar choking behavior, i.e. cavitation number stays constant despite the decrease of test section pressure once a natural supercavity forms. The theoretical analysis of the choking phenomenon explains the trend of cavitation number under choking and its dependence on cavitator geometry, Froude number as well as the pressure loss in the water tunnel. A geometry comparison is conducted for both natural and ventilated supercavities in the two facilities under the same Froude number, blockage ratio and cavitation number. The comparison results show differences in the normalized cavity total length across different facilities as well as supercavity types despite the similarities in the supercavity maximum diameter and half-length. These differences were attributed to the variance in the pressure and flow distributions from the different facilities and across ventilated and natural supercavitation. The natural supercavities from the two facilities are further compared with the estimated natural supercavitation in unbounded flow under the same cavitation conditions. The comparison result highlights the limitation of the conventional theory in capturing the cavity geometries in actual experiments.

Influence of the thickness of monolithic compliant coatings on the skin friction drag

In this study, the drag reduction capabilities of compliant coatings made from viscoelastic silicon rubbers are verified experimentally. A series of single-layer compliant coatings of homogeneous materials with constant thicknesses were used. The experiments were performed at different flow velocities in a high-speed water tunnel of Pusan National University. They were accompanied by experimental determination of dynamic viscoelastic properties of the coating materials. Then, for each coating, a dynamic compliance in frequency domain was estimated. Assuming that the coatings interact effectively only with dynamic structures of turbulent boundary layer in a frequency band corresponding to the region about the maximum compliance, promising ranges of flow velocity and coating thickness are outlined. The predicted ranges are compared favourably with the experimental observations in the high-speed water tunnel.

Air entrainment characteristics of artificial supercavities for free and constrained closure models

Artificial supercavitation is a promising technology for the drag reduction of high-speed underwater vehicles, whereby a cavity is generated through air entrainment to encompass the entire vehicle. Supercavitation experiments are conventionally conducted in closed wall water tunnels. In order to properly extend these results to the operation of underwater vehicles in the ocean, it is imperative to understand the underlying physics governing these processes. The current study focuses upon the factors that govern the ventilation demand of a supercavitating vehicle operating under artificial supercavitation mode. Systematic artificial supercavitation experiments are carried out in a high-speed water tunnel with two different experimental models and high-speed visualization and measurements of air entrainment are carried out at different stages of supercavity formation, sustenance and collapse. Our measurements suggest a marked difference between the two experimental models for formation, sustenance and critical air entrainments of supercavities. Such differences are explained based on the understanding of fundamental physical factors governing the process, such as bubble breakup, coalescence and the effect of the presence of a body inside the supercavity.

A dynamic testbed for supercavitating vehicle control

Supercavitating vehicles are capable of achieving unprecedented speeds due to the presence of a large gas cavity surrounding their bodies. The control design and validation of these vehicles is challenging because planing forces, oscillations, and instability arise when the vehicle pierces the supercavity. In this paper, we propose a methodology to test control algorithms for a supercavitating vehicle subject to planing. With a free-to-rotate scale vehicle in a high-speed water tunnel, we reproduce planing and are capable of assessing active control technologies experimentally. Sponsored by the Office of Naval Research.

Modeling, Control, and Experimental Validation of a High-Speed Supercavitating Vehicle

Underwater vehicles that travel inside a bubble or supercavity offer possibilities for high-speed and energy-efficient transportation of cargo and personnel. Validation and testing of mathematical models and control systems for these vehicles is a challenge due to the cost and complexity of experimental facilities and testing procedures. A cost-efficient and low-complexity approach to the experimental validation of mathematical models and control systems for a supercavitating test vehicle is presented in this paper. The proposed method enables the testing of control algorithms subject to steady and unsteady flows in a high-speed water tunnel. The method combines a real-time simulation of the vehicle dynamics, force measurements from an experimental scale vehicle, and flight control computer to reproduce the vehicle motion subject to realistic flow conditions and hardware constraints as actuator saturation and time delay. The model of the vehicle dynamics, used for the validation infrastructure and control design, is derived using experimental data. A controller designed to track pitch angle reference commands was tested on the experimental platform. The test cases validated the operation of the vehicle and controller subject to steady and unsteady flows.

Measurements in the wake of a ventilated hydrofoil: a step towards improved turbine aeration techniques

The purpose of this study is to develop the necessary algorithms to determine the bubble size distribution and velocity in the wake of a ventilated or cavitating hydrofoil utilizing background illumination. A simplified experiment was carried out to validate the automatic bubble detection algorithm at the Saint Anthony Falls Laboratory (SAFL) of the University of Minnesota. The experiment was conducted in the SAFL high-speed water tunnel. First, particle shadow velocimetry (PSV) images of a bubbly flow were collected. Bubbles were identified in the images using an edge detection method based on the Canny algorithm. The utilized algorithm was designed to detect partly overlapping bubbles and reconstruct missing parts. After all images were analyzed, the bubble velocity was determined by applying a tracking algorithm. This study has shown that the algorithm enables reliable analysis of irregularly shaped bubbles even when bubbles are highly overlapped in the wake of the ventilated hydrofoil. It is expected that this technique can be used to determine the bubble velocity field as well as the bubble size distributions.

Drag Reduction by Microvortexes in Transverse Microgrooves

A transverse microgrooved surface was employed here to reduce the surface drag force by creating a slippage in bottom layer in turbulent boundary layer. A detailed simulation and experimental investigation on drag reduction by transverse microgrooves were given. The computational fluid dynamics simulation, using RNG k- ε turbulent model, showed that the vortexes were formed in the grooves and they were a main reason for the drag reduction. On the upside of the vortex, the revolving direction was consistent with the main flow, which decreased the flow shear stress by declining the velocity gradient. The experiments were carried out in a high-speed water tunnel with flow velocity varying from 17 to 19 m/s. The experimental results showed that the drag reduction was about 13%. Therefore, the computational and experimental results were cross-checked and consistent with each other to prove that the presented approach achieved effective drag reduction underwater.

A prediction of drag reduction by entrapped gases in hydrophobic transverse grooves

The drag reduction effect of super-hydrophobic surface induced by the entrapped gas is unstable due to the gradual disappearance of the trapped gas. In this paper, a hydrophobic transverse grooved surface was designed to sustain gas in valleys. A detail numerical simulation was presented to investigate the flow field near the proposed surface. When water flowed over this surface, the entrapped gas was blocked by the ridges and the solid-liquid interface was replaced by the liquid-gas interface due to the entrapped gas, furthermore the micro-vortex formed in the groove. Because there was an effective slippage between water and solid induced by the entrapped gas, the velocity gradient of boundary layer decreased, which contributed to a remarkable drag reduction effect. Additionally, considering the extra undesired pressure drag reduction which negatively impacted the drag reduction effect of this method, the total drag coefficient including the viscous drag coefficient and the pressure coefficient was analyzed. An effective drag reduction rate of about 15% was achieved and the effect of this method was confirmed by experiments conducted in a high-speed water tunnel when grooves were optimized.

Investigation of the Behavior of Ventilated Supercavities in a Periodic Gust Flow

A ventilated supercavity consists of a large, gas-filled bubble enveloped around an underwater vehicle that allows for significant drag reduction and increases in vehicle speed. Previous studies at the Saint Anthony Falls Laboratory (SAFL) focused on the behavior of ventilated supercavities in steady horizontal flows. In open waters, vehicles can encounter unsteady flows, especially when traveling near the surface, under waves. In supercavitation technology, it is critical that the vehicle remains within the cavity while traveling through water to avoid unwanted planing forces. A study has been carried out in the high-speed water tunnel to investigate the effects of unsteady flow on axisymmetric supercavities. An attempt is made to duplicate sea states seen in open waters. In an effort to track cavity dimensions throughout a wave cycle, an automated cavity-tracking script has been developed. Using a high-speed camera and the proper software, it is possible to synchronize cavity dimensions with pressure measurements taken inside the cavity. Results regarding supercavity appearance, cavitation parameters, and their relation to sea state conditions are presented. It was found that flow unsteadiness caused a decrease in the overall length of the supercavity while having only a minimal effect on the maximum diameter. The supercavity volume varied with cavitation number, and a possible relationship between the two was explored.

Measurements in High Void-Fraction Bubbly Wakes Created by Ventilated Supercavitation

A study of ventilated supercavitation in the reentrant jet regime has been carried out in the high-speed water tunnel at St. Anthony Falls Laboratory as the hydrodynamics part of an interdisciplinary study on stability and control of high-speed cavity-running bodies. The work is aimed at understanding the interaction between a ventilated supercavity and its turbulent bubbly wake, with the goal to provide the information needed for the development of control algorithms. Particle image velocimetry (PIV) measurements in high-void fraction bubbly wakes created by the collapse of ventilated supercavities are reported. Bubble velocity fields are obtained and are shown to submit to the same high Reynolds number similarity scaling as the single-phase turbulent axisymmetric wake. A grayscale technique to measure local average void fraction is outlined. Results of a time-resolved PIV experiment at 2000 Hz, using an adaptive masking scheme based on a sliding intensity threshold filter, are also presented.