Surface-piercing Hydrofoil Research Articles

Numerical investigation of the tip-vortex-induced ventilation formation mechanism for a surface-piercing hydrofoil

Recent experiments have demonstrated that tip vortices can trigger the ventilation formation around a surface-piercing hydrofoil. However, the influence of this ventilation on transient flow structures and vortex evolution remains unresolved. This paper numerically investigates the tip-vortex-induced ventilation formation for a surface-piercing hydrofoil at a stalled yaw angle. The predicted unsteady ventilated cavities with tip vortices and pressure-side spray are in reasonable agreement with experimental observations. The ventilation formation process can be divided into three stages: base ventilation, tip-vortex ventilation, and suction-side ventilation. It is indicated that ventilation has a greater impact on the lift coefficient than the drag coefficient. The lift coefficient increases during the base ventilation and tip-vortex ventilation stages due to the expansion of the low-pressure stalled flow, but decreases in the suction-side ventilation stage because of the gradual replacement of this low-pressure region by an aerated cavity. Tip-leakage and tip-separation vortices initially exist independently at the hydrofoil tip, then expand and merge through air ventilation, ultimately forming a strongly stable tip vortex. Furthermore, ventilation promotes vortex generation, with the major contributors being the vortex stretching and baroclinic torque terms.

Experimental study on the mechanism of cavitation-induced ventilation

In this study, the cavitating flow and cavitation-induced ventilation flow around a surface-piercing hydrofoil were investigated to gain in-depth understanding of the interaction mechanism between the vaporous cavity and free surface at low cavitation numbers. Experiments were conducted in a constrained-launching water tank to visualize the cavity using a high-speed camera. Unsteady cloud cavitation and cavitation-induced ventilation at atmospheric pressure were observed and analyzed while piercing the free surface. The flow regime map was summarized at a fixed aspect ratio of ARh = 1.5. Subsequently, a physical model was proposed to predict the maximum depression depth of the water surface (H) at the trailing edge of the hydrofoil. Both the physical model and experimental results reveal that the non-dimensional depth H/c has a linear relation to Fn2 c × Rec × sin2α. Finally, a criterion for cavitation-induced ventilation based on the improved lifting-line theory and a physical model were proposed. A new relation H/Lc ∼ α0.5 was obtained, where Lc is the maximum cavity length. The results of this study can guide the design and application of hydrofoils for ventilation and cavitation processes.

Wave effects on the hydroelastic response of a surface-piercing hydrofoil. Part 2. Cavitating and ventilating flows

The objective of this paper is to understand the effects of waves and vaporous cavitation upon the hydrodynamic and hydroelastic responses of a flexible surface-piercing hydrofoil, adding to the subcavitating results presented in Part 1. In general, the presence of a sufficiently large vaporous cavitation bubble facilitated the formation of a ventilated cavity, substantially reducing the angle of attack or speed required to induce fully ventilated flow, relative to subcavitating conditions. A new co-analysis procedure was used to isolate synchronous hydrodynamic modes and structural operating deflection shapes. Significant dynamic load amplification occurred when the resonant frequencies of the first twisting and second bending modes coalesced in both fully wetted and partially cavitating flows. The presence of waves did not diminish the effect of frequency coalescence, but did encourage intermittent lock-in with both leading edge cavity shedding and trailing edge vortex shedding at certain speeds. Partial cavity shedding typically had a negligible impact on the power spectral densities of structural motions because of incoherent cavity shedding. However, lock-in between the cavity shedding frequency and modal coalescence frequency led to shifting of the primary frequency peak, as well as amplified harmonics and interactions between the cavity shedding frequency and vortex shedding frequency. The transition from partially cavitating to fully ventilated flow caused sudden and large drops in the mean hydrodynamic loads and deformations, as well as substantial reductions in the intensity of the fluctuations.

Wave effects on the hydroelastic response of a surface-piercing hydrofoil. Part 1. Fully wetted and ventilated flows

This work describes the effects of waves on the hydroelastic response of a hydrofoil in fully wetted and ventilated flows. In the absence of vaporous cavitation (described in Part 2 of this paper series), shallow long-period non-breaking waves delayed ventilation inception because velocity fluctuations prevent the formation of a stably separated region of flow at the foil's leading edge. Aerated von Kármán vortex shedding occurred from the blunt trailing edge, producing vortex-induced vibration of the hydrofoil at a near-constant Strouhal number. Regular waves led to near sinusoidal oscillations of the load and deformations at the wave encounter frequency, while the mean response and the dynamic response at other frequency peaks corresponding to hydrodynamic and structural modes remained mostly unaffected. Significant dynamic load amplification was observed at a submerged aspect ratio of 2 for cases with low angles of attack because of coalescence between the second and third wetted structural modes; at high angles of attack, the amplitude of the load fluctuations and flow-induced vibrations reduced because energy was diverted away from the coalescence frequencies to the nearby vortex shedding frequency. In both calm water and wave conditions, transition from fully wetted to fully ventilated flow resulted in sudden and significant reduction in the load coefficients, as well as foil deflections. An impulse-like signature was observed in the time-frequency spectra during these transitions. In many of the cases, transition to fully ventilated flow also led to substantially reduced amplitudes in the load and deformation fluctuations.

Numerical Modeling of Surface-Piercing Flexible Hydrofoils in Waves

_ Hydrofoils made of metal alloys were broadly used on high-speed boats in the past. Nowadays, much lighter hydrofoils made of composite materials are finding increasingly more applications on sailing yachts and powerboats. However, these hydrofoils are usually rather flexible, and their design requires computationally demanding analysis, involving hydroelastic calculations. In this study, exploratory high-fidelity simulations have been carried out for surface-piercing hydrofoils in unsteady conditions with help of a computational fluid dynamics solver for fluid flow coupled with a finite element solver for the foil structure. To model unsteady foil deformations, the morphing mesh approach was utilized, and the volume-of-fluid method was applied for multiphase flow simulations. The computational setup, as well as verification and validation study, is described in this paper. Three hydrofoils of different stiffness, including a perfectly rigid foil, were simulated in both calm water conditions and regular head waves. Representative examples of foil deflections and wave patterns, as well as time-dependent structural and hydrodynamic characteristics, are presented. Introduction Hydrofoils are efficient lift-generating devices intended for application in water flows. Hydrofoils have streamlined shapes, and when operating at small incidence angles, they can produce high lift forces at relatively low drag, when moving in a certain speed range. Due to this ability, hydrofoils and their derivatives are commonly used as control and propulsive devices, e.g., as rudders, fins, and propeller sections. In the second half of the last century, hydrofoils found broad applications on fast boats, such as passenger ferries and military ships (McLeavy 1976; Matveev & Duncan 2005). These craft were able to achieve high speeds at lift–drag ratios (LDR) around 12–15, significantly higher than LDR of other hulls, such as planing boats. However, due to rather limited favorable operational conditions with regard to speed and payload, popularity of hydrofoils somewhat receded. One of drawbacks was that hydrofoils were usually made of metal alloys, thus being relatively heavy and difficult to service.

LES investigation into the cavity shedding dynamics and cavitation–vortex interaction around a surface-piercing hydrofoil

Recent experiments have found that there is unstable vaporous cavitation around a surface-piercing hydrofoil at high Froude numbers and small yaw angles, and it would promote ventilation formation [R. Huang et al., “Investigations into the ventilated cavities around a surface-piercing hydrofoil at high Froude numbers,” Phys. Fluids 34, 043304 (2022)], but the cavity shedding dynamics and the mechanism of cavitation–vortex interaction are still open problems. In this paper, the unstable vaporous cavities around a surface-piercing hydrofoil are numerically investigated using the large-eddy simulation coupled with the Schnerr–Sauer cavitation model. Numerical simulations can predict the cavity features, including an aerated base cavity aft of the hydrofoil trailing edge, vaporous cavitation at the hydrofoil suction surface, and tip–vortex cavitation. A U-shaped vapor cloud shedding together with a horseshoe vortex is observed during the unsteady cavitation evolution, that is, the cavity development, cutoff, and collapse. This irregular shedding is related to the three-dimensional reentrant jet induced by the velocity reflection at the vaporous cavity closure line. Furthermore, the effects of the vaporous cavitation on the vorticity generation are attributed to vortex stretching, baroclinic torque, and vortex dilatation by using the vorticity transport equation. This study could contribute to the novel hydrofoil designs and their flow control.

Investigations into the ventilated cavities around a surface-piercing hydrofoil at high Froude numbers

This study investigates the ventilated cavities around a surface-piercing hydrofoil, aiming to extend previous studies by an in-depth understanding of the vaporous cavity behaviors and the flow-regime transition at high Froude numbers. An experiment is carried out in a constrained-launching water tank with a vertically cantilevered hydrofoil piercing a still water surface. The cavity is recorded using high-speed photography, and flow-regime maps are summarized over a broad range of Froude number and yaw angle at different immersed aspect ratios. In addition to the well-known steady flow regimes (i.e., fully wetted flow and fully ventilated flow), an unsteady vaporous cavitating flow is revealed at a very high Froude number with a small yaw angle, which exhibits cavitation shedding dynamics behaviors, including the cavity growth, destabilization, and collapse. The transition from the fully wetted flow to the fully ventilated flow is attributed to the vapor-cavitation-induced ventilation besides the tip-vortex-induced ventilation. Vaporous cavitation promotes ventilation formation, but it has to meet the criterion that air should enter the sub-atmospheric cavity through the tip-vortex path before the cavity length reaches the maximum. Moreover, an improved lifting-line model is developed with considering the effects of free surface and finite aspect ratio. Both analytical modeling and experimental measurements reveal that the vaporous cavity length follows a power relation against the cavitation parameter. Such knowledge lays a foundation for the design optimization and control strategy of high-speed hydrofoils.

Research on ventilation and supercavitation mechanism of high-speed surface-piercing hydrofoil

Flow structures and hydrodynamic performance of high-speed surface-piercing hydrofoils were studied by numerical simulation, with an emphasis on the interaction mechanism between supercavitation and natural ventilation. Compared with the available experimental data, the numerical method could predict the cavitation and ventilation well. The numerical simulation results show that the flow over hydrofoil with blunt trailing edge is more conducive to separating. The semi-ogive hydrofoil was used to explore the influence of angles of attack on ventilation and cavitation. The ventilation rate increases with the increase in the angles of attack. At small attack angles (α = 0° and 2°), the regional ventilated flow is found in supercavitation. The vortex street structures and twin vortices closure mode are formed in the closure region of the supercavity. At moderate attack angles (α = 6° and 10°), the thickness of the undisturbed liquid sheet (δ) becomes thinner and the natural supercavitation transits to fully ventilated supercavitation through the cavitation-induced ventilation, but the ventilation position is different because of Taylor instability. The hydrodynamic coefficients remain relatively stable in natural supercavitation and the lift coefficient reduce to half of the original value when the supercavitation is fully ventilated, which are caused by the pressure changes on the suction and pressure surfaces.

Numerical investigations of the free surface flow around a surface piercing hydrofoil

Starting with January 2013, naval architects faces new challenges, as all ships greater than 400 tons must comply with energy efficiency index (MPEC 62, 2011). From ship hydrodynamics point of view one handy solution is using Energy Saving Devices (ESD), with the main purpose to improve the flow parameters entering the propeller. For ballast loading condition the ESD may intersect the free surface disturbing and complicating the flow due to free surface /boundary layer interaction, turbulence and breaking wave effects that coexist and which are not completely clarified so far. Therefore, a free surface flow around a NACA 0012 surface piercing hydrofoil is numerically investigated and the results are compared to experimental results obtained in the Towing Tank of the Naval Architecture Faculty, “Dunarea de Jos” University of Galati. The comparison includes drag and free surface elevation on hydrofoil surface together with numerical uncertainty.

High-fidelity simulation of a hydraulic jump around a surface-piercing hydrofoil

For a surface-piercing hydrofoil traveling at high speed, a turbulent hydraulic jump may arise at the intersection of the body with the free surface. This hydrodynamic phenomenon involves violent wave breaking, bringing great challenges for experimental analysis. In this work, a high-fidelity large eddy simulation is performed to study the turbulent air-entraining flow near foil. One advantage of the present simulation is that a quantitative analysis can be implemented even in the turbulent two-phase mixing region containing a large amount of entrained air, which is difficult for traditional experimental and theoretical approaches. We employ a conservative coupled level set/volume-of-fluid scheme to capture the free surface. A highly robust scheme is introduced to guarantee stability in simulating large density ratio two-phase flows. The present method is implemented based on a block-structured adaptive mesh, by which the efficiency of the high-fidelity simulation can be improved. The main flow features of the wedge-shaped hydraulic jump, including the wave patterns, free surface elevation, and frequency spectra, are compared with experimental data. We find that the flow structures show clear differences from those found in the canonical hydraulic jump, owing to the presence of the foil surface. Shoulder wave breaking starts at the trough of the mid-body, develops in a wedge shape, depends strongly on Froude number, and is responsible for most of the large-scale air entrainment. The properties of the turbulent hydraulic jump and some of the key quantities characterizing the air-entraining flow, including the spatial distribution of the bubble cloud, the void fraction, and the bubble/droplet size spectrum, are fully investigated for typical Froude numbers.

Numerical investigations into the ventilation elimination mechanism of a surface-piercing hydrofoil

This paper investigates the ventilation elimination mechanisms during the deceleration process of a surface-piercing hydrofoil using the unsteady Reynolds-averaged Navier-Stokes (RANS) method together with a Volume of Fluid (VOF) model. The numerical results are in good agreement with the experimental data. The ventilation elimination mechanism of the surface-piercing hydrofoil is analyzed from the perspectives of the hydrofoil hydrodynamic performance, the ventilated cavity evolution, vortex structures, and re-entrant jets. The results indicate that the ventilation elimination includes three stages, i.e. a decrease in the ventilated cavity, washout, and reattachment. The decrease in the ventilated cavity is due to the hydrofoil speed decrease in the FV flow. Washout is the transition from fully ventilated to partially ventilated flow, and reattachment is the transition from partially ventilated to fully wetted flow. The underwater vortex structures around the surface-piercing hydrofoil are composed of a tip vortex, an unstable vortex induced by the shear layer, and a Karman vortex caused by the vortex shedding from the trailing edge of the hydrofoil. Ventilation stability strongly depends on the re-entrant jet. When Φ (the angle between the flow direction and the closure line of the ventilated cavity) is greater than 45°, the re-entrant jet impinges on the ventilated cavity's leading edge and destabilizes the ventilated cavity.

Impact of CFD simulation parameters in prediction of ventilated flow on a surface-piercing hydrofoil

ABSTRACT This article discusses numerical prediction of ventilated flows around the surface-piercing hydrofoil. A ventilated cavity is developed on the hydrofoil surface and the growth of the cavity is uncontrolled, which can have harmful effects as it leads to changes in the lift and unexpected loads. The occurrence of ventilation is computed by a Reynolds-Averaged Navier–Stokes solver based on the Finite Volume Method and the Volume of Fluid free surface capturing. The impact of numerical parameters on the ventilation is investigated by testing various momentum, gradient, and interface-capturing schemes, turbulence intesities, acceleration and time stepping scenarios, for 10 Froude numbers and 2 angles of attack. The analysis shows that simulations are consistent and comparable with the experimental data, if proper free surface capturing scheme and very low Courant numbers are used.

Stiffness Adjustment of Surface-Piercing Hydrofoils Within Fluid-Structure Interaction

This paper presents results from numerical analysis of the fluid and structure interaction of two different hydrofoil models, Model 1 and Model 2. Analyzes were performed with stainless steel, aluminium and composite materials for Model 1, and Model 2 was created from composite with aluminium reinforcement. Models were analyzed for three different angles of attack (10, 20, 30 degrees) and for each angle three different speeds were tested (2, 4, 6 m/s). At first, the whole set of analysis was run for entirely submerged hydrofoils and later on for immersed hydrofoils to the draft h. Described numerical analysis was performed in order to adjust stiffens of hydrofoils based on different operational loads. Two-way fluid-structure interaction analysis was used which combines FEM and CFD solvers. Presented results are based on 44 analysis with which all planned conditions of hydrofoil operation were tested. Numerical analysis showed a correlation between stiffens of material i.e. structural response and hydrodynamic loading. Besides mentioned, based on analysis of Model 2 future prediction are given in a way of hydrofoil design or particularly placement for hydrofoils reinforcement.

The hydroelastic response of a surface-piercing hydrofoil in multiphase flows. Part 2. Modal parameters and generalized fluid forces

The fluid–structure interactions (FSI) of compliant lifting surfaces is complicated by free-surface and multiphase flows such as cavitation and ventilation. This paper describes the dynamic FSI response of a flexible surface-piercing hydrofoil in dry, wetted, ventilating and cavitating conditions. Experimental modal analysis is used to quantify the resonant frequencies and damping ratios of the fluid–structure system in each flow regime. The generalized hydrodynamic stiffness, fluid damping and fluid added mass are also determined as ratios to the corresponding structural modal forces. Added mass increases with increasing partial immersion of the hydrofoil and decreases in the presence of gaseous cavities. In particular, modal frequencies were observed to increase significantly in fully ventilated flow compared to fully wetted flow. The modal frequencies varied non-monotonically with speed in fully wetted flow. Gaseous cavities reduced the modal added mass and reduced the fluid disturbing force. Modal damping increases non-monotonically with increasing immersion depth. Forward speed causes the fluid damping force to increase with an approximately quadratic functional behaviour, consistent with a series expansion of the Morison equation, although damping identification became increasingly difficult at high flow speeds. The results indicate that fluid damping is greater than the associated structural damping in a quiescent liquid, and increasingly so with increasing immersion, suggesting viscous dissipation as a dominant mechanism. A preliminary investigation of modal vibration as a means of controlling the size and stability of ventilated cavities indicates that low-order modes encourage the formation of ventilation, while higher-order modes encourage the washout and elimination of ventilation.

The hydroelastic response of a surface-piercing hydrofoil in multi-phase flows. Part 1. Passive hydroelasticity

Compliant lift-generating surfaces have widespread applications as marine propellers, hydrofoils and control surfaces, and the fluid–structure interactions (FSI) of such systems have important effects upon their performance and stability. Multi-phase flows like cavitation and ventilation alter the hydrodynamic and hydroelastic behaviours of lifting surfaces in ways that are not yet completely understood. This paper describes experiments on one rigid and two flexible variants of a vertical surface-piercing hydrofoil in wetted, ventilating and cavitating conditions. Tests were conducted in a towing tank and a free-surface cavitation channel. This work, which is Part 1 of a two-part series, examines the passive, or flow-induced, fluid–structure interactions of the hydrofoils. Four characteristic flow regimes are described: fully wetted, partially ventilated, partially cavitating and fully ventilated. Hydroelastic coupling is shown to increase the hydrodynamic lift and yawing moments across all four flow regimes by augmenting the effective angle of attack. The effective angle of attack, which was derived using a beam model to account for the effect of spanwise twisting deflections, effectively collapses the hydrodynamic load coefficients for the three hydrofoils. A generalized cavitation parameter, using the effective angle of attack, is used to collapse the lift and moment coefficients for all trials at a single immersed aspect ratio, smoothly bridging the four distinct flow regimes. None of the hydrofoils approached the static divergence condition, which occurs when the hydrodynamic stiffness negates the structural stiffness, but theory and experiments both show that ventilation increases the divergence speed by reducing the hydrodynamic twisting moment about the elastic axis. Coherent vortex shedding from the blunt trailing edge of the hydrofoil causes vortex-induced vibration at an approximately constant Strouhal number of 0.275 (based on the trailing edge thickness), and leads to amplified response at lock-in, when the vortex-shedding frequency approaches one of the resonant modal frequencies of the coupled fluid–structure system.

Development of a multiphase solver for cavitation flow near free surface

A multiphase cavitation solver which is capable of dealing with multiple phase change processes is developed based on OpenFOAM platform. The solver is first applied to a high-speed projectile near the free surface. Good agreement is observed for the free surface elevation and the cavitation development process with the experimental data. Then simulations are carried out for a newly designed surface-piercing body which is composed of a cavitating hydrofoil and an underwater axisymmetric body. The flow field and hydrodynamics is investigated for the vertical surface-piercing hydrofoil with different wet depth and inflow vapor cavitation number. The wave patterns downstream of the hydrofoil and the splash jet shape on the hydrofoil surface are obtained. Furthermore, the interaction between phases and the hydrodynamic curves are analyzed in detail. Finally, the combined body effect on the free surface elevation and the hydrofoil dynamics is investigated. The obtained result gives valuable insight into the optimum design for the surface-piercing body.

A Computational framework to design optimally loaded supercavitating hydrofoils by differential evolution algorithm and a new viscous lifting line method

The engineering design of a three dimensional submerged hydrofoil operating at very high speeds is obtained leveraging a Differential Evolution (DE) approach. The final goal is to identify the optimal load distribution over the span of a super-cavitating hydrofoil by using a design by optimization approach driven by hydrodynamic analysis of complex, turbulent, multi-phase flows. We achieve this goal by modeling the load distribution over the hydrofoil by means of a B-spline curve, which provides a rigorous parametric description of the hydrofoil operating conditions through the points of the load distribution control polygon. The parametric model includes design variables representing the most relevant hydrofoil shape parameters. We predict hydrodynamic performance by means of a Viscous Lifting Line method specifically conceived for the application targeted in the present study. This computational model accounts for the strong non-linear hydrodynamic characteristics of super-cavitating hydrofoils. We demonstrate the validity of the proposed design by optimization framework for high speed super-cavitating hydrofoils showcasing two design applications, namely a fully submerged hydrofoil operating close to a rigid boundary and a surface-piercing hydrofoil with variable dihedral angle. A statistical analysis of DE algorithm is performed to assess its performance on such an engineering design problem.

Numerical simulation of air ventilation and its suppression on inclined surface-piercing hydrofoils

Hydrofoils with significant camber and thickness can be hydrodynamically advantageous over thin low-camber hydrofoils commonly used on boats with surface-piercing hydrofoil systems, especially at lower speeds when a pronounced drag hump is usually present and cavitation is not yet an issue. The main drawback of such high-lift hydrofoils is a danger of being ventilated with air that can easily propagate from the atmosphere along the foil suction side resulting in a drop of the foil lift-drag ratio. The air ventilation is a complex physical process, modeling of which remains a challenging task. In this study, a computational fluid dynamics solver STAR-CCM+ is applied for simulating air ventilation phenomena on surface-piercing hydrofoils. A good agreement is obtained with available test data for relevant configurations. It is also shown that small fences appropriately placed on the inclined surface-piercing hydrofoil can suppress both downward air ventilation and upward water spray, resulting in greater performance of high-lift hydrofoils at moderate Froude numbers.

Analysis of Ventilation Regimes of the Oblique Wedge-Shaped Surface Piercing Hydrofoil During Initial Water Entry Process

Abstract The suction side of a surface piercing hydrofoil, as a section of a Surface Piercing Propeller (SPP), is usually exposed to three phases of flow consisting air, water, and vapour. Hence, ventilation and cavitation pattern of such section during the initial phase of water entry plays an essential role for the propeller’s operational curves. Accordingly, in the current paper a numerical simulation of a simple surface piercing hydrofoil in the form of an oblique wedge is conducted in three-phase environment by using the coupled URANS and VOF equations. The obtained results are validated against water entry experiments and super-cavitation tunnel test data. The resulting pressure curves and free surface profiles of the wedge water entry are presented for different velocity ratios ranging from 0.12 to 0.64. Non-dimensional forces and efficiency relations are defined in order to present the wedge water entry characteristics. Congruent patterns are observed between the performance curves of the propeller and the wedge in different fully ventilated or partially cavitated operation modes. The transition trend from fully ventilated to partially cavitated operation of the surface piercing section of a SPP is studied and analyzed through wedge’s performance during the transitional period.

Hydroelastic analysis of surface piercing hydrofoil during initial water entry phase

In the current paper, numerical simulations of Fluid structure interaction (FSI) of a SP (Surface Piercing) hydrofoil are conducted in order to study the influence of elasticity on the initial water entry ventilation. Using ANSYS multi physics solvers, two-way FSI analyses are conducted by the implicit coupled URANS (Unsteady Reynolds averaged Navier–Stokes) equations and finite element method. Numerical result is validated by the well known rigid and elastic wedge water entry problems. Subsequently, computational results are presented for different velocity ratios range [0.38, 0.64] and elasticity factor range [0, 4]. Similar to the Surface Piercing Propeller (SPP), performance curves of a wedge water entry are defined. The obtained similar trend of propeller and wedge performance curves in fully ventilated, transition, and partially cavitated operation modes shows that the adopted approach (2D-study) can be appropriate for future related studies. FSI simulation results indicate that structural deformation can highly affect the location of transition point and shifts it toward the fully ventilated part at high Froude number and elasticity factor. The overall efficiency loss due to increase of foil elasticity is observed and overshoot time of the foil deformation related to the variation of Froude number and elasticity factor, is evaluated.