Figure 3 - uploaded by Simone Mancini
Content may be subject to copyright.
2D+T Steady stepped hull at constant trim angle as it passes through a fixed two-dimensional observation plane for each planing surface. Pressure distributions given at two different time solution.
Source publication
Stepped planing hulls enable the feasibility of running at a relatively low drag-lift ratio by means of achieving more optimal trim angle at high speeds than a similar non-stepped hull. Furthermore, stepped planing hulls ensure good dynamic stability and seakeeping qualities at high speeds. However, there is no precise method to analyze these hulls...
Contexts in source publication
Context 1
... compute the forces acting on non-step or two stepped planing hull, the 2D+T theory is utilized. Figure 3 shows a representation of the typical 2D+T theory of stepped and non-stepped hulls. for non-step planing hull, it is assumed that the boat passes through a fixed observation plane. ...
Context 2
... compute the forces acting on non-step or two stepped planing hull, the 2D+T theory is utilized. Figure 3 shows a representation of the typical 2D+T theory of stepped and non-stepped hulls. for non-step planing hull, it is assumed that the boat passes through a fixed observation plane. Within that plane, the motion of the hull appears to be similar to the constant velocity water entry of a wedge. for stepped planing hulls, the observation plane depends on a number of steps. For each section, two forces containing hydrodynamic and hydrostatic forces act on the wedge. To determine the forces, the pressure acting on the wedge should be determined. This pressure can be calculated using the following equation, which depends on the solving time. In this equation, w, c, y, c , and i are respectively: the impact velocity, the half beam of spray root, horizontal distance from the keel, derivative c with respect to time, and the number of planing ...
Citations
... Although analytical methods can be used to calculate performance predictions and motion in waves in the early-stage design, the use of CFD simulation can offer a higher level of accuracy, and would be favored in last stages of design, where more accurate predictions are required. Di Caterino et al. (2018) studied the performance and stability of a stepless hull at high speeds by employing an analytical/CFD-based method. Their results were promising and were validated it against the Savitsky method and CFD full-scale analysis. ...
... Also, numerical methods are very useful in the final stages of design due to their high reliability. Investigating the pressure distribution over planning crafts during water entry is one of the challenges that has been repeatedly carried out through numerical methods [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. Of course, all these numerical studies are supported with reliable experimental background [35][36][37]. ...
Speed and stability play crucial roles in the performance of high-speed crafts. In the present paper, a two-stepped model is tested in towing tank and compared with stepless and wedge-mounted models, which have previously been tested by the authors. This study is conducted to compare the stability and performance of the mentioned models in the displacement, semi-planing, and planing regimes. The length and width of these models are 2.64 meters and 0.55 meters, respectively. The measured parameters include trim, rise-up, and resistance. The whisker sprays of the models are also depicted at different speeds. the performance of stepped boats is not suitable prior to the planing regime. But wedged model can perform well in this area. One of the features of this type of model is having a chine. So far, no comparison has been made between the chined models. Further, the whisker spray edge approaches to the keel line by increasing speed in all considered models. These tests are conducted in three series at speeds of 2,4,6 and 8 m/s within the mentioned motion regimes. Based on the experimental findings, it is observed that tested models are stable in displacement and semi-displacement regimes. The bare hull which has no transverse step or wedge, is longitudinally unstable in planning regime. However, the vessels with two transverse steps exhibit longitudinal stability and have less drag than the bare-hull model in all motion regimes. On the other hand, the trim and rise-up in stepped as well as wedged vessel are less than those in the bare-hull model in all motion regimes. Meanwhile, the drag of the two-step model at high speeds is determined to be less than the other two models. Ultimately, using the Taguchi design method, different wedge-mounted and two-stepped vessels are selected to conduct numerical studies. These simulations are done via STAR-CCM + commercial code. The calculated results show that at speeds higher than 8 m/s, the resistance could be reduced by optimizing the step location. As the first step gets farther from the stern, the resistance of the vessel reduces. However, increasing the distance between the second step and the stern leads to a drag penalty for the vessel.
... Hull optimization of these vessels is crucial for achieving safety and efficiency at high speed operations. Simple methods are mostly embarked for hull optimization at pre-stage design (Di Caterino et al. [1]), yet further attempts are needed to be made to 1) understand the impact of design parameters on the boat performance and 2) develop advanced optimization techniques, which may be used in the later stages of design process. ...
This paper uses the 2D+T method for hull optimization of double-stepped planing hulls at the early-stage design. The method is applied to investigate the impact of various step configurations on the performance of stepped planing hulls in calm water and waves. The 2D+T method utilizes pressure distributions along the hull length to calculate forces in calm water and incorporates momentum variation theory to mathematically simulate rigid body motions in waves. Previous studies have validated the accuracy of this method. The paper conducts a parametric study on a double-stepped hull, analyzing the effects of different step configurations on hydrodynamic performance in calm and rough water conditions. The results suggest that optimal location of front step is somewhere near the mid-section, and that of rear step is in the vicinity of the center of gravity for steps with identical heights. It is demonstrated that this configuration minimizes the added resistance and wave-induced motions. It is concluded that the 2D+T method can effectively assist designers in hull optimization of stepped planing hulls in the early-stage design. Further research is recommended to consider the effects of step shape in the hull optimization.
... The stepped hull is a modification of the shape of the hull, in which transverse steps are placed at the bottom, giving the hull the appearance of having two bodies: the forebody and afterbody [69]. Studies using towing tank experiments to analyze the effects of both single step [67,[70][71][72][73][74][75][76][77] and double steps [67,69,[78][79][80][81] have been widely carried out. Taunton et al. [67] conducted experimental tests to study the effect of using a step hull on the performance of highspeed planing-type vessels. ...
... Savitsky and Morabito [69] conducted an experimental analysis of the longitudinal surface shape profile behind prismatic hulls, including stepped hulls. To provide a better understanding of the effect of implementing the double step in a planing hull, other methods are also being carried out, such as a simplified method [79], the 2D+T method [78], the morphing mesh method [80], the potential flow method [76], the open and pressurized air cavities method [76], CFD with fixed mesh method [74], and CFD with dynamic mesh method [73,75]. Based on the results of previous research, flow separation occurs in the step area which then allows air to enter and makes the area not wet, where this phenomenon can reduce the wetted area and can result in a decrease in the frictional resistance [47,67,69,74,76]. ...
... Moreover, the Overset mesh method can provide higher accuracy in simulations since the moving mesh can adjust to the motion of the planing craft [87], minimizing numerical errors. Some examples of works that use the overset mesh method in planing craft simulation as done by De Marco et al. [73], Di Caterino et al. [75], Hosseini et al. [87], Samuel et al. [51] and more. The simulation results using the dynamic mesh method are closer to the results from the experiment than the static mesh method [88]. ...
Along with developing high-speed craft technology, the planing hull is growing with modifications for better performance. One such technology is stepped hull, both single and double. Planing hull with steps allows the boat to run at a relatively low drag-lift ratio with lower frictional resistance due to reduced wetted area. In this study, the hull was modified with variations in the position of the double steps, which aimed to determine the effect of the first and second step positions on the total resistance, dynamic trim, and dynamic sinkage generated by computational fluid dynamics (CFD). Based on the analysis results, variations in the position of the stepped can change the hull performance. Shortening the distance between the two steps and moving both rearwards toward the transom can lower the total resistance. The dynamic trim and dynamic sinkage decreased as the position of the two steps was shifted further forward. An equation created in a non-dimensional form relates the positions of two steps to the desired results of total resistance, dynamic trim, and dynamic sinkage, namely: {(x1-x2)/L + (x1x2)/(LB)} × Fr∇, where x1 is distance the first step from transom, x2 is the distance of the second step, L is the length of the boat, B is the beam of the boat, and Fr∇ is the volume Froude number.
... The most accurate method can be claimed to be the CFD (Computational Fluid Dynamics) two phase VOF (Volume of Fluid) analysis. However, the long calculation time limits the use to the analysis of few operating conditions only, so that it is usually adopted to investigate the effects of particular hulls components, like spray rails (Samuel Trimulyono et al., 2021), stepped hull forms De Marco et al., 2017;Di Caterino et al., 2018;Lotfi et al., 2015), and hull tunnels (Yousefi et al., 2014). CFD can also be useful to evaluate the predictivity of simplified models, allowing one to study single components of total lift and drag forces Khazaee et al., 2019), but also to understand the behavior of the added resistance (Kim et al., 2017b;Kim and Kim, 2018). ...
The availability of accurate numerical tools for predicting the energy consumption of recreational crafts is pivotal in view of reducing the environmental impact on local waters. A computationally efficient digital twin capable of accurately predicting the boat resistance is thus required to account for the energy fluxes.
In the study, an improved 3-DOF (Degree-of-freedom) 2D + t approach, aimed at predicting the forward resistance of a planing craft in waves and wind conditions is developed and validated. With respect to the existing literature models, a simplified methodology to account for diffraction forces is proposed, together with a novel approach for the estimation of the transom effects on drag and lift forces. A throughout comparison of model results with literature data of different planing hulls is presented, showing the potential of the proposed methodology.
The developed model was applied to a 10 m flybridge test case, also including the effects of wind resistance. To this purpose, a dedicated CFD (Computational fluid dynamics) analysis of the freeboard aerodynamics has been attained and correlations for lift and drag coefficients are proposed. In addition, the potential of the proposed methodology is shown also in terms of passenger comfort by assessing the habitability under different wave conditions.
... Step can create a significant reduction of a dynamic wetted surface and of the dynamic trim angle during high-speed forward motion and thus achieve a reduction of resistance at high speed. There are four options for the hydrodynamic analysis of a stepped hull: the towing tank test [1][2][3], empirical method [4,5], analytical methods [6], and numerical simulation [7,8]. ...
... These methods-based designs were presented, starting from a non-stepped hull configuration, a multiple-step solution was developed and an optimization of the unwetted aft body area behind the steps was performed. The goal of the optimization is drag reduction and dynamic stability [9] . The validation of the 2D+t model for single stepped planing hull with the experimental data in terms of; resistance, dynamic trim, and wetted surface area was carried out by Bilandi [10] . ...
The demand for high-speed boats that operating near to shoreline is increasing nowadays. Understanding the behavior and attitude of high-speed boats when moving in different waterways are very important for boat designer. Usually, they using experimental model testing for resistance prediction and dynamic force but this method is high consuming time, and cost. When planing boats are moving at high speed, two forces participate in their support, they are the hydrodynamic lift created by the shape of the planing hull, and the lift force resulting from displacing part of the liquid (buoyancy force).This research uses a CFD (Computational Fluid Dynamics) analysis to investigate the shallow water effects on prismatic planing hull. The turbulence flow around the hull was described by Reynolds Navier Stokes equations RANSE using the k-ɛ turbulence model. The free surface was modelled by the volume of fluid (VOF) method. The analysis is steady for all the ranges of speeds except those close to the critical speed range Fh =0.84 to 1.27 due to the propagation of the planing hull solitary waves at this range. For this fluctuation in the results, the average numerical value of the results was taken to compare it with the experiment.In this study, the planing hull lift force, total resistance, and wave pattern for the range of subcritical speeds, critical speeds, and supercritical speeds have been calculated using CFD. The numerical results have been compared with experimental results. The dynamic pressure distribution on the planing hull and its wave pattern at critical speed in shallow water were compared with those in deep water.The numerical results give a good agreement with the experimental results whereas total average error equals 7% for numerical lift force, and 8% for numerical total resistance. The worst effect on the planing hull in shallow channels occurs at the critical speed range, where solitary wave formulates.
... Generally, the computational tools are less expensive than experimental tests and more reliable than analytical/empirical methods. Hence, CFD tools are now widely used and are considered useful especially in the early-stage design phases, when understanding the behavior of the flow near and behind the hull can help designers improve the performance of high-speed planing hulls, as pointed out, for instance, by Di Caterino et al. (2018) [4]. ...
Computational Fluid Dynamics simulations of planing hulls are generally considered
less reliable than simulations of displacement hulls. This is due to the flow complexity around planing hulls, especially in the bow region, where the sprays are formed. The recent and constant increasing of computational capabilities allows simulating planing hull features, with more accurate turbulence models and advanced meshing procedures. However, mesh-based approaches based on the finite volume methods have shown to be limited in capturing all the phenomena around a planing hull. As such, the focus of this study is on evaluating the ability of the Smoothed Particle Hydrodynamics mesh-less method to numerically solve the 3-D flow around a planing hull and simulate more accurately the spray structures, which is a rather challenging task to be performed with mesh-based tools. A novel application of the DualSPHysics code for simulating a planing hull resistance test has been proposed and applied to the parent hull of the Naples warped planing hull Systematic Series. The drag and the running attitudes (heave and dynamic trim angle) are computed for a wide range of Froude’s numbers and discussed concerning experimental values.
... It was considered that the unsteady turbulent phenomena cause this difference. Di Caterino et al. 26 showed that the 2D + t methods could be used in the design and optimization processes. They used the 2D + t approach by producing different stepped hull configurations. ...
The hydrodynamic characteristics of the planing hulls in particular at the planing regime are completely different from the conventional hull forms and the determination of these characteristics is more complicated. In the present study, calm water hydrodynamic characteristics of planing hulls are investigated using a hybrid method. The hybrid method combines the dynamic trim and sinkage from the Zarnick approach with the Savitsky method in order to calculate the total resistance of the planing hull. Since the obtained dynamic trim and sinkage values by using the original Zarnick approach are not in good agreement with experimental data, an improvement is applied to the hybrid method using a reduction function proposed by Garme. The numerical results obtained by the hybrid and improved hybrid method are compared with each other and available experimental data. The results indicate that the improved hybrid method gives better results compared to the hybrid method, especially for the dynamic trim and resistance. Although the results have some discrepancies with experimental data in terms of resistance, trim and sinkage, the improved hybrid method becomes appealing particularly for the preliminary design stage of the planing hulls.
... For example, Niazmand Bilandi et al. (2018) analytically studied the resistance, wetted surface and dynamic trim angle of a single-step planing hull by using 2D+T method. Di Caterino et al. (2018) proposed CFD-based design approach to optimize the un-wetted aft body surface behind the steps. Their results indicated good accordance compared with the 2D + T analytical method. ...
In the present paper, the hydrodynamic performance of stepped planing craft is investigated by computational fluid dynamics (CFD) analysis. For this purpose, the hydrodynamic resistances of without step, one-step, and two-step hulls of Cougar planing craft are evaluated under different distances of the second step and LCG from aft, weight loadings, and Froude numbers (Fr). Our CFD results are appropriately validated against our conducted experimental test in National Iranians Marine Laboratory (NIMALA), Tehran, Iran. Then, the hydrodynamic resistance of intended planing crafts under various geometrical and physical conditions is predicted using artificial neural networks (ANNs). CFD analysis shows two different trends in the growth rate of resistance to weight ratio. So that, using steps for planing craft increases the resistance to weight ratio at lower Fr and decreases it at higher Fr. Additionally, by the increase of the distance between two steps, the resistance to weight ratio is decreased and the porpoising phenomenon is delayed. Furthermore, we obtained the maximum mean square error of ANNs output in the prediction of resistance to weight ratio equal to 0.0027. Finally, the predictive equation is suggested for the resistance to weight ratio of stepped planing craft according to weights and bias of designed ANNs.
