Search

Speed and stability are two essential criteria for assessment of planing hull performance. Accordingly, the effects of step shape on these vessels’ hydrodynamic performance and stability are experimentally investigated. Five different models are studied which are based on a high-speed recreational craft and are primarily the same in form and dimensions. One of these models does not have a step, two of them have transverse steps, and two other models have Vee-shaped steps. These five models all have a length of 2.64 m, a beam of 0.55 m, a deadrise angle of 24°, and weigh 86 kg. As the parent model, that is, the non-stepped model is unstable at high speeds, this study is aimed to figure out how different types of steps could prevent this kind of instability. The trim angle, resistance, and lengths of the wetted keel and wetted chine of all these models are reported at beam Froude numbers ranging from 0.43 to 3.44. First, the non-step model is investigated in towing tank tests. The optimum position for the center of gravity of this model is determined to be at a distance of 30% of the model’s length to the transom, which leads to the lowest resistance while the model still remains stable. The models with the aft-wise Vee type and fore-wise Vee type experience the lowest and highest resistance among all studied models, respectively. The steps’ performance appears to be directly related to the ventilation condition at the bottom of stepped models. It is also observed that aft-wise Vee-shaped step leads to the most severe flow separation, and the model with this type of step has the least wetted surface area compared to other studied models.

Marine industrial engineering face crucial challenges because of environmental footprint of vehicles, global recession, construction, and operation cost. Meanwhile, Shape optimization is the key feature to improve ship efficiency and ascertain better design. Accordingly, the present paper proposes an automated optimization framework for ship hullform modification to reduce total resistance at two cruise and sprint speeds. The case study is a bow shape of a wave-piercing bow trimaran hull. To this end, a multi-objective hydrodynamic problem needs to be solved. A combined optimization strategy using CFD hullform optimization is presented using the software tools STAR-CCM+ and SHERPA algorithm as optimizer. Furthermore, a comparison is made between CAD-based and Mesh-based parametrization techniques. Comparison between geometry regeneration methods is performed to present a practical and efficient parametrization tool. Design variables are control points of FreeForm Deformation (FFD) for CAD-based method and Radial Basis Function (RBF) for Mesh-based method. The optimization results show a 4.77% and 2.47% reduction in the total resistance at cruise and sprint speed, respectively.

Providing steps at the bottom of a high-speed craft could decrease the resistance and enhance the longitudinal stability by dividing a single pressure hump into several ones and extending the hydrodynamic pressure towards aft of the vessel. In the present paper, the effects of the fore and aft steps’ locations and angles on double-stepped hulls are investigated systematically via a numerical approach. The parent model investigated in this study is a model of a high-speed recreational craft called Cougar, with a 1 : 5 scale. The three-dimensional analysis of the model is conducted via the finite volume method, and the free surface is tracked using the volume of the fluid technique. The computational domain is discretized by the overset technique, and the calculations are validated via experimental data. Overall, 27 numerical tests designed by the Taguchi experiment design method are simulated, and the resistance, trim, and rise-up values are calculated at 8 to 10 m/s speeds. The findings support the notion that the resistance increases by increasing the distance between the fore step and vessel stern. In addition, increasing the distance between the aft step and vessel stern and the increase of the angle of the fore step leads to reducing the vessel resistance. However, the results showed that finding a sensible relationship between the angle of the aft step and resistance requires more investigation. The findings revealed that the interactional effects between the angles of the aft and fore steps are the most considerable among all studied interactional effects. Among the all studied configurations, the lowest resistance was experienced by the model with an aft step at 25% of the vessel’s length to the stern, having an angle of 150°, and a fore step at 40% of the vessel’s length to the stern, having an angle of 180°.

Numerical optimization of an inverted-bow trimaran is carried out through three simulation-based design (SBD) frameworks. Different positions of the trimaran’s side hull are investigated based on a computational fluid dynamics solver using the non-dominated sorting genetic algorithm-III (NSGA-III), simultaneous hybrid exploration that is robust, progressive and adaptive (SHERPA) and response surface (RS) multi-objective optimization for resistance at cruise and sprint speeds. The aims are to create and develop a convenient tool for optimization and investigate the appropriate position of the side hull. An automated, low-cost optimization platform is achieved that can be implemented in other maritime projects. A 10.5% drag reduction for cruise speed and 6.6% reduction for sprint are obtained, corresponding to lower longitudinal and large transversal distances of the side hull. SHERPA and NSGA-III produce the same results, but SHERPA is 2.5 times faster than NSGA-III. RS obtains less desirable results, but in the lowest central processing unit time.

Hydrodynamic coefficients including thrust, torque and efficiency at different advance ratios are investigated for all components of a Linear-Jet propulsion system. Ansys-CFX software is utilised a...

Trimaran hull forms have been very attractive in the past decade. Hydrodynamic performance of trimaran ships is influenced by sidehull arrangement. The present study was intended to construct a surrogate model for better understanding of the hydrodynamic performance of a trimaran ship. Accordingly, seakeeping and resistance of an inverted-bow trimaran were considered as objectives of a simulation-based design (SBD) optimization framework. Different longitudinal, transversal, and vertical position of trimaran’s sidehull were investigated based on an advanced free-surface steady Reynolds-averaged Navier–Stokes (URANS) solver within StarCCM+ for resistance calculation and 3D panel method in Ansys-AQWA for seakeeping analyses. Quality and applicability of metamodeling optimization and its computational time were examined for future trimaran hull design projects. Total resistance for drag reduction, pitch and heave motion, and vertical acceleration at fore perpendicular for seakeeping performance were objectives of the study. The optimization results indicated a 6.9% drag reduction and 4.7% improvement in seakeeping performance, which yield lower longitudinal and large transversal distances of the sidehull. Furthermore, the conducted investigations demonstrated the effectiveness and capability of the proposed optimization platform for other marine industrial projects.

High-speed vessels exhibit various motions and accelerations in calm water and sea waves. For examining the behavior of high-speed vessels, it is possible to examine these movements in laboratory models. In this paper, a single-step model in calm water is experimentally tested and compared with a model of no step. The speed range of these vessels is 1 m/s to 9 m/s equivalent to Beam Froude numbers of 0.43 to 3.87. During these experiments, the resistance parameters, trim, bow, and stern rise-up as well as the center of the gravity are measured. The non-step model has longitudinal instability at a speed of 8 m/s. This instability is avoided when the vessel is equipped by a transversal step. The vessel's trim and resistance are also reduced in the planing mode in calm water. Subsequently, hydrodynamic performance and its seakeeping condition in the planing regime are investigated for both vessels in regular waves. The single-step and non-step vessels are tested in the wavelength range of [Formula: see text], and the wave height range of 6 to 18 centimeters. It is observed that stepped vessel experiences lower motions and bow accelerations and less added resistance in comparison to the non-stepped vessel.

A CFD-based adjoint solver tool is presented to modify the hullform of a trimaran ship. Cost function of optimization process is considered total for resistance of trimaran at cruise speed. Mesh se...

Linear Jet system which has a stator in addition to a rotor combines the best elements of two existing technologies of conventional screw propellers and water jets. In designing this propulsion system, tip clearance plays an essential role, since it causes the appearance of tip vortex that leads to a further loss in efficiency and a probability of cavitation phenomenon. Due to lack of any study in this regard, it is thus necessary to study tip clearance to find the appropriate geometry for linear jet propulsion system. In the current paper, hydrodynamic performance of linear jet propulsion system is numerically investigated. Accordingly, Ansys-CFX software is utilized and RANS unsteady equations are solved using SST turbulent model. Results of the proposed numerical model, in the form of thrust and torque coefficient as well as efficiency, are compared with available experimental data for a ducted propeller. It is concluded that most of the errors at various advance ratios for thrust and torque coefficients are less than 3% and relatively good agreement is observed. Hydrodynamic investigation involves five different sizes of tip clearance (2.5 to 10% of the rotor diameter). Simulation results indicate that thrust and torque coefficients decreases about 10% and 8% respectively, at the same advance coefficient (J) with an increase in tip clearance. Effects of tip clearance on tip-separation vortex and tip leakage vortex are also examined. At about 20% of chord length from the leading edge, separation occurs. As tip clearance size increases, the tip-leakage vortex also increases. At different advance ratios and higher tip clearance, an increase in vortex and a sudden decrease in thrust is generated by the propeller. By changing the time about 0.8 of the rotor periods, the evolution of the vortex generation behind the rotor at the tip of the blade is clearly observed.

The linear jet propulsion system, unlike pump-jets which are widely used in underwater bodies, is installed inside a tunnel under the vessel and can be used for high-speed crafts, tugs, and service boats. However, this system has not received adequate attention by researchers, which is the subject of the current study. In the present paper, hydrodynamic performance of the linear jet propulsion system is numerically investigated. Accordingly, the Ansys-CFX software is utilized and RANS equations are solved using the SST turbulent model. The results of the proposed numerical model, in the form of thrust and torque coefficient as well as efficiency, are compared with available experimental data for a ducted propeller, and good compliance is achieved. Considering the importance of stator cross section on the performance of the linear jet propulsion system, the influence of thickness and camber size of the stator on linear jet propulsion systems are examined. Based on the numerical findings, it is determined that at constant advance ratio, with increasing thickness of stator, the efficiency increases. It is also observed that as the span length increases, the maximum and minimum of the pressure coefficient increase for different thicknesses. Furthermore, it is seen that positive and negative pressure coefficients decrease with an increase in foil thickness.

Achieving noble and more practical propulsion systems is still a major concern for engineers and researchers. Accordingly, many researchers have strived to opt for better and suitable system for the targeted vessels. One of the marine propulsion systems is linear-jet propulsion which includes rotor and stator. In this paper, the effects of geometrical shape of the duct in the form of different length and angle of attack for two types of the accelerating and decelerating ducts are comprehensively explored. Furthermore, section of rotor from Kaplan series are selected and the geometrical shape effects of the rotor on hydrodynamic performance of linear-jet propulsion system are also investigated. Therefore, to obtain the effects of the expressed parameters on the hydrodynamic characteristics of this propulsion system, Ansys-CFX software has been used. The governing equations of the studied problem are RANS equations and SST k-omega turbulent model is utilized. The obtained results are presented in the form of dimensionless coefficients of the forces applied on the propulsion system. The existing data for a ducted propeller are used to validate the numerical solution. Based on the results of the numerical solution, it is concluded that use of a decelerating duct increases the efficiency of the linear-jet system. On the other hand, the use of accelerating ducts reduces the hydrodynamic efficiency of the linear jet, so the performance is not desirable at high advance ratio. Therefore, the use of decelerating ducts in the linear-jet system is found to be the appropriate choice. Results further illustrate that, if the duct length increases, the generated thrust by the rotor increases. It is also concluded that, by increasing the angle of attack of the decelerating duct, the overall efficiency of the linear-jet propulsion system decreases.

This paper presents experimental and numerical investigation of stability and rooster tail of a mono-hull high-speed planing craft with a constant deadrise angle. Initially, a one-fifth scale model was tested in a towing tank, which showed porpoising phenomenon at 8 m/s (equal to the speed of sailing). Subsequently, two wedges of 5 and 10 mm heights, based on the boundary layer calculations, were mounted on the aft section of the planing hull. These wedges were shown to increase the lift at the aft section. These experiments were carried out at different speeds up to 10 m/s in calm water. The experimental results indicated that the installed wedges reduced the trim, drag, and the elapsed time for reaching the hump peak, and also eliminated the porpoising condition. All these test cases were also numerically simulated using Star CCM+ software. The free surface was modeled using the volume of fluid scheme in three-dimensional space. The examined planing craft had two degrees of freedom, and overset mesh technique was used for space discretization. The obtained numerical results were compared with experimental data and good agreement was displayed in the presented comparisons. Ultimately, the effect of the wedge on the rooster tail behind the planing craft was studied. The results of this investigation showed that by decreasing the trim at a constant speed, the height of the generated wake profile (rooster tail) behind the craft decreases, albeit its length increases.

Trimaran vessels have been of great interest to naval architects, due to their large deck space, low resistance at high speeds and stability. Meanwhile, determination of their slamming forces in the presence of highly nonlinear waves has always been a challenge for the structural designers. However, because of novelty and complexity of their hulls, there is insufficient information in this regard, which necessitates suitable effort in filling this gap. Accordingly, in this article, using Flow-3D, a commercial computational fluid dynamics code, seakeeping of a wave-piercing trimaran is simulated in the presence of irregular waves via standard Bretschneider spectrum in sea state 5 in various seagoing modes. These modes include two speeds and two waves with encountering angles of head sea and bow quartering sea. For validation purposes, seakeeping of a trimaran vessel and water entry of a wedge-shaped section are investigated and numerical results are compared against experimental and analytical data. Good compliance of the results confirms the accuracy of the proposed numerical model. In the slamming analysis of the considered trimaran, using the relative vertical velocity of the bow section from the seakeeping analysis, the water entry problem is investigated for the most severe slamming mode. Pressure distribution caused by water entry and instantaneous impact pressure, known as structural design pressure, is computed. The exerted slamming pressure on the bottom and bow flare region is determined to be 4300 and 2100 Pa, respectively. Results indicate that during slamming phenomenon, the maximum pressure exerted on the vessel’s floor occurs at the time of impact at which the pressure coefficient is 4.4. Accurate assessment of the vessel’s vertical velocity from the start of water entry until the water surface rise-up, and the utilized technique considered for slamming phenomenon in more realistic sea condition, can be considered as important features of this study.

In the current paper, different geometrical parameters of the trimaran hull ship are investigated to achieve the optimal points of geometry parameters. Considering the fixed displacement volume, the values of the longitudinal center of buoyancy, block coefficient, midsection coefficient as well as the side hull length and position are computed and using Lackenby shift transformation, the geometry is reconstructed during the optimization process. It is then necessary to compute the ship resistance of the reconstructed geometry which is hereby accomplished by slender body method. Subsequently, D-optimal method is used for finding the best parameters to achieving minimum resistance at cruise and sprint speeds. Two strategies are pursued to find optimum value of design variable: trimaran hull transformation and separated hull approach. Generally, a hull optimization process takes huge time and depending on the applied methodology, it might take somewhere between 6 months and 2 years. However, through slender body method and design of experiment study, proposed in this paper, the total time of global optimization process is only 1 week. Meanwhile, 9.1% resistance reduction at cruise speed and 2.24% resistance reduction at sprint speed is achieved. Hence, a successful ship hull optimization with suitable computational time and effort is the novelty of the current work. The conducted optimization indicates that two parameters of longitudinal center of buoyancy and block coefficient have significant effect on the total resistance. Comparison of the original and optimized hull signals the validity and superiority of the proposed optimization strategy, which can be extended to other maritime industrial projects.

In this paper, flow around a submerged controllable pitch propeller is analyzed by developing a general 3D unsteady numerical model, based on boundary element method (BEM) in an infinite extended flow. BEM is combined with time stepping method to model the freely moving/unsteady trailing vortex sheet emanating from each blade trailing edge. In this way, the vortex blade–wake interaction can correctly be taken into consideration. As boundary integral equations are inherently unstable, a smoothing mollifier is applied to damp the singularity effect. Through this effort, attempt has been made to investigate the effect of blade rotation about its spindle on hydrodynamic performance of the controllable pitch propeller. For this reason, relative motion is applied on equation for each blade. This is the main novelty of the paper since little or no effort has been devoted to this subject, thus far. On the other hand, by using an unsteady time stepping method, the rollup wake pattern can be captured throughout simulation by changing the propeller pitching angle. It is demonstrated that the time stepping scheme combined by filtering method can successfully capture the rollup wake pattern during simulation time.

This paper investigates the improvement of the bow region of the trimaran ship hull, and proposes a Computational Fluid Dynamics (CFD)-based automated method to reduce total resistance. The main objectives pursued in the present study include: 1) to create and develop a useful optimization platform to modify the ship hull and 2) to investigate the effect of different inverted bow on the hydrodynamic performance of trimaran ship. A wave-piercing bow trimaran hull was taken as the baseline design. The ship bow has been redesigned using Arbitrary Shape Deformation (ASD) technique, which defines the input variables for the optimization process. The objective function was the drag force, and this study is conducted at cruise speed. To accomplish this task, two optimization methods were sequentially applied. A Latin Hypercube Sampling tool distributes design points and an Radial Basis Function (RBF)-based surrogate model is constructed to investigate system behavior. The final optimum design of Design Of Experiment (DOE) study was introduced to the direct optimization SHERPA algorithm as a baseline design. The integration of CFD solver, geometric parameterization and optimizer tools is managed by the HEEDS MDO software package using a multi-connection method. The optimization results show that the optimization was successfully carried out and the resistance was reduced by 10.2%. The comparison between the initial hull and the optimized hull shows that the proposed optimization platform can be used for ship hull optimization in industrial application and significantly reduces the computational time and workload.

One of the most well-known strategies to eliminate or reduce the longitudinal instabilities in planing hull, is to reduce the trim of the craft. In the current study, porpoising is controlled through creating a transverse step, and the combination of adding a wedge to the stern and transverse step in the vessel. Usually, performance of stepped boats is not suitable in pre-planing regime. However, through the proposed method, stepped model performance can be improved prior to the planing regime. The investigated craft is a 2.56 m long monohull high speed model with speed range of 1,3,5,7 and 9 m/s. The obtained results indicate that best performance is acquired by the step and wedge model at the beginning of the planing regime. From 3 to 7 m/s, drag of stepped and wedged models has the lowest value and above 7 m/s and at 9 m/s, the stepped model has the lowest resistance. Among the investigated methods, using combined step and wedge indicates largest reduction in trim angle (At speeds of 3 to 9 m/s). It can therefore be concluded that model equipped by combination of wedge and step improves the poor performance of the stepped models prior to the planing regime.

Using the controllable pitch propeller (CPP) in marine propulsion system makes it possible to have maximum ship speed and low fuel consumption at different engine rpm. Good maneuverability is another advantage of such propeller. This feature has persuaded designers to use CPP in ships with various mission profiles like tugs or ferries. The hub boss is of great importance in CP Propellers because it provides housing for blade actuation mechanism. On the other hand, hub boss geometry should be selected as small as possible since it has negative effect on hydrodynamic performance of propeller, specially its thrust and efficiency. In this article, a 3D potential flow-based solver is developed to predict the hydrodynamic characteristic of marine propellers for preliminary and basic design purposes. Through applying the time stepping scheme, it is possible to generate the rollup wake pattern at each time step. As a result, the interaction of vortex wake-lifting/non-lifting bodies are correctly taken into consideration. Validation of the proposed numerical model is carried out with two standard marine propellers (DTMB4119 and KP505) and a high skewed B-series Controllable Pitch Propeller (CPP). Subsequently, a series of parametric simulations are performed on different non-dimensional hub diameters of a CP propeller to find an appropriate hub diameter (big enough to provide CPP mechanism) with highest propeller performance. Ultimately, the suitable hub diameter is determined for an appropriate design of a CP propeller. Rollup pattern for the RV propeller with different hub diameters.

Stability of a high-speed craft is an essential matter, and porpoising is one of the most critical instabilities that could occur in some planing hulls due to inappropriate design. In this paper, the porpoising phenomenon and variation of step location yielding resistance reduction are studied through experimental and numerical methods. The investigated models include a single-step model and a nonstep model with the same general shape, but with different step location. The nonstep model is previously tested, but the single-step model is examined in the present study. The nonstep model experiences porpoising at 8 m/s speed, but the single-step model remains stable at the same speed. A three-dimensional CFD analysis is conducted using the finite volume method (FVM). On the contrary, the volume of fluid (VOF) scheme is used for free surface modeling, and the overset mesh technique is implemented within StarCCM+ software. The CFD results of total hydrodynamic resistance and dynamic trim angle are compared against the experimental data. The numerical results are in good agreement with the experimental data. Subsequently, ten different stepped models are simulated to examine their effects. The longitudinal distance between steps and aft of these models are in the range of 19 to 50 percent of the length of models. The obtained results show that as steps are located farther than aft, the models become more stable, and resistance increases due to trim reduction. Finally, the optimum location of the step is extracted with the aim of minimizing the resistance through the design of experiment (DOE) method. Based on the DOE method, it is observed that the sensitivity of the drag value to the step location is higher than the speed.

A 3D unsteady computer solver is presented to compute incompressible Navier-Stokes equations combined with the volume of fraction (VOF) method on an arbitrary unstructured domain. This is done to simulate fluid flows in various applications, especially around a marine vessel. The Navier-Stokes solver is based on the fractional steps method coupled with a finite volume scheme and collocated grids by which velocity components and pressure fields are defined at the center of the control volume. However, the fluxes are defined at the midpoint on their corresponding cell faces. On the other hand, the CICSAM (Compressive Interface Capturing Scheme for Arbitrary Meshes) scheme is applied to capture the free surface. In the presented fractional step method, the pressure Poisson equation suffers from poor convergence rate by simple iterative methods like Successive Overrelaxation (SOR), especially in simulating complex geometrics like a ship with appendages. Therefore, to accelerate the convergence rate, an agglomeration multigrid method is applied on arbitrary moving mesh for solving pressure Poisson equation with two well-known cycles, V and W. In order to maintain accuracy, the geometry details should not change in grid coarsening procedure. Therefore, the boundary faces are assumed to be fixed in all grids level. This assumption requires nonstandard cells in coarsening procedures. To investigate the performance of the applied algorithm, various flows including one and two-phase flows are studied in two and three dimensions. It is found that the multigrid method can speed up the convergence rate of fractional step twofold. In most cases (not all), W cycle displays better performance. It is also concluded that the efficiency of the cycle depends on the number of meshes and complexity of the problem and this is mainly due to the data transferring between grids. Therefore, the type of cycle should be selected judiciously and carefully, while considering the mesh size and flow properties.

Semi-submerged operation of surface-piercing propellers can cause severe structural stress and deflection due to the high-rate variation of the hydrodynamic loads on each blade in one cycle of revolution. Therefore, a proper hydroelastic analysis regarding these propellers seems imperative. Accordingly, in this article, hydrodynamic performance of a surface-piercing propeller is studied by considering the structural flexibility. The one-way and two-way coupled unsteady Reynolds-averaged Navier–Stokes equations (finite volume method used for the fluid analysis) and direct finite element method (used for the structural analysis) are utilized to analyze an 821-b surface-piercing propeller model. The obtained ventilation patterns and hydrodynamic loads on a single blade of this propeller are compared with the published experimental data. ANSYS multiphysics solvers are used to conduct the targeted simulations. The results are presented for different velocity ratios in the range of [0.8, 1.2] and Froude number Fr = 6.0. The blade maximum deformation and von Mises stress are presented in one cycle of revolution. Based on the obtained results, one may conclude that both the adopted approaches predict the propeller transient hydrodynamic characteristics with good accuracy, compared with the experimental data. However, the two-way approach displays lower maximum structural displacement and stress than one-way simulation. This is attributed to the fact that the two-way approach takes into consideration the added mass and damping effects of the surrounding fluid around the blade.

In the current paper, different experiments are conducted on a high speed planing craft in irregular waves, with and without a wedge. Performance and seakeeping aspects of these planing hulls in the form of trim, rise-up, and resistance in regular waves and heave, pitch, bow, and center of gravity (CG) acceleration in irregular waves are extracted in time series. Irregular waves represent sea state 3 with 12cm height and peak period of 1.66. A model length of 2.63m and 1:5 scale is considered and all data for irregular waves are scaled, as well. The deadrise angle is constant and is taken to be 24 degrees. The targeted experimental tests are conducted for four longitudinal Froude numbers of 1.0, 1.18, 1.37, and 1.57, which are all in the planing regime. The results are analyzed for the mean height of wave, significant wave height, RMS, and spectrum. The comprehensive study of wedges' effects is also presented which indicates that a wedge can decrease the motions and accelerations, exceedingly. Ultimately, the obtained results are compared against those by Fridsma (1971) and Soletic (2010) and it is demonstrated that motions and accelerations are indeed reduced.

Current paper deals with hydroelastic impact of asymmetric and symmetric wedge sections with oblique speed into calm water. It is aimed to provide a better insight regarding fluid–structure interaction of the wedge sections of a high-speed craft into water in more realistic condition, in the presence of heel angle and oblique speeds. The defined problem is numerically investigated by coupled Finite Volume Method and Finite Element Method under two-way approach consideration. Accuracy of the proposed model is assessed in different steps. The results of current method are compared against previous experimental, numerical and theoretical methods and good agreement is displayed in these comparisons. Subsequently, the method is used in order to examine the fluid and structure behavior during the elastic impact of the wedge into water. Accordingly, four different physical situations are simulated. In the first part, symmetric impact with no oblique speed is simulated. The results of this part show fluctuations in vertical force and pressure of the midpoint during the impact time. Also, the relation of deadrise with deflection and pressure is observed in this part. In the second part, heel angle is also taken into consideration. It is concluded that the pressure and deflections at the right side of the wedge reduce, but these parameters increase at the left side. Moreover, it is observed that, the pressure at the midpoint of the left side of the wedge with deadrise angle of 10°, becomes negative, when the wall of the flexible wedge reaches its largest deflection. It is also observed that, the pressure at left side of the wedge with deadrise angle of 20°, reaches zero. Such behavior does not occur for the wedges of 30° and 45° deadrise angles. In the third part of simulations, oblique water entry of a flexible wedge of 20° deadrise angle is simulated, and no heel angle is considered. Harmonic behavior is observed for the vertical force, horizontal force, pressure of the midpoint and its deflection. First peaks of all of these variables are larger than the second peak. The obtained results lead us to conclude that an increase in oblique speed yields larger deflection and pressure at the right side. Meanwhile, no significant effect is observed for the left side of the wedge. Also, larger oblique speed is found to yield larger forces and angular moment. Final part of simulations involves the oblique water entry of a flexible wedge of 5° heel angle. Comparison of the results in the final part with that of third part, show that heel angle affects the pressure and deflection at both sides of the wedge. It is also observed that pressure and deflections of the left side increase, while those of right side increase. It is also seen that, similar as in the case of no heel angle, an increase in oblique speed leads to an increase of pressure and deflection at the starboard. It also leads to an increase in frequency of the vibration at right side.

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.