An experimental study of the wetted surfaces of two- stepped planing hulls
Introduction
High lift to drag ratio and more longitudinally stability are the results of using transverse steps at the bottom of high speed planing hulls (Doctors, 1985; Savitsky and Morabito, 2010). Performance of stepped planing hulls is directly related to their bottom wetted surfaces which are dependent on the location of the steps, the height of the step, number of steps, Froude number, etc (Najafi et al., 2020). So, deep knowledge of the bottom wetted surfaces of the stepped planing hulls plays an impressive role in improving the hydrodynamical performance of these vessels.
Up to now, different towing tanks tests (Doctors, 1985; Savitsky and Morabito, 2010; Najafi et al., 2018, Najafi et al., 2019a, Najafi et al., 2019b, 2020; Clement and Pope, 1961; Gassman and Kartinen, 1994; White and Beaver, 2010; Taunton et al., 2010, 2011; Lee et al., 2014; Seo et al., 2016; De Marco et al., 2017; Cucinotta et al., 2017; Najafi et al., 2019a, Najafi et al., 2019b), numerical investigations (Najafi et al., 2019a, Najafi et al., 2019b; Lotfi et al., 2015; Kazemi et al., 2019; Najafi and Nowruzi, 2019), and mathematical studies (Svahn, 2009; Loni et al., 2013) are conducted on the hydrodynamic characteristics of the stepped planing hulls. For example, in 1961, Clement and Pope (Clement and Pope, 1961) presented some graphs of resistance and trim angle of stepless and stepped prismatic planing hulls by using empirical formulas. After that in 1994, Gassman and Kartinen (Gassman and Kartinen, 1994) experimentally investigated the effects of the step location and the longitudinal center of gravity location on the performance of stepped planing hulls. After the investigation of the hydrodynamic performance of the one-step planing hulls by scholars, in 2010, Savitsky and Morabito (Savitsky and Morabito, 2010) experimentally investigated the bottom wetted surface of simple prismatic one-step planing hull. In the same year and to produce a database for hydrodynamics of one-step and two-steps planing hulls, White and Beaver (White and Beaver, 2010) conducted a series of towing tests on the one-step and two-steps planing hulls at one hull velocity and trim angle. They indicated the lower resistance of stepped planing hulls compared to traditional hulls. Some experimental tests on two-stepped planing hull are also conducted at calm water and in waves by Taunton et al. (2010) and Taunton et al. (2011), respectively. They showed lower resistance of stepped hulls compared to stepless hull. Also, they showed insignificant effects of the steps on the dynamic trim angle. For generating more detail on the resistance of two-steps planing hulls, in 2014, Le et al. (Lee et al., 2014) performed a series of towing tests to investigate the effect of step height and its position on the total resistance of two-stepped planing hulls. They found the minimum resistance for the smallest step height forward and the largest step height aft. Hydrodynamic resistance and sea keeping ability of a planing vessel using wave-piercing and spray rails are experimentally studied by Seo et al. (2016).
During these years, in addition to experimental research in the context of the stepped planing hulls, numerical studies have been conducted. In 2017, CFD analysis and experimental investigation on the flow pattern and hydrodynamic behavior of one step planing craft are performed by De Marco et al. (De Marco et al., 2017). Cucinotta et al. (2017) performed some experimental tests to show the positive impression of artificial air cavity on resistance reduction of planing hulls. Recently, in 2019, hydrodynamic characteristics and bottom wetted area of one step planing hull is experimentally studied by Najafi et al., 2019a, Najafi et al., 2019b).
Based on the literature review, the focus of experimental and numerical studies has been on the hydrodynamic characteristics of the stepped planing hulls such as their resistance, sinkage, and trim angles. Moreover, only a little research can be found on the bottom wetted areas of the stepped planing hulls, which are also for one-stepped planing hulls (Savitsky and Morabito, 2010; Najafi et al., 2019a, Najafi et al., 2019b). Therefore, the lack of investigation on the detail of bottom wetted areas of the two-stepped planing hulls at various geometric characteristics of the step is evident. So, in the present study and continues of our previous experimental work in Ref (Najafi et al., 2019a, Najafi et al., 2019b). (i.e., on one-step planing hull), the major objective is to investigate the hydrodynamic parameters and bottom wetted areas of two-stepped planing hulls at different geometrical characteristics of the steps. Firstly, the results of total resistance of two-stepped Fridsma planning hulls are given. Then, reattachment lengths of separated flow, and wetted areas are presented under different deadrise angles, aft step heights, longitudinal position of the aft step from transoms, and Froude numbers. The remainder of the current paper is structured as follows: Experimental setup of two-stepped planing hulls is given in Section 2. Results of hydrodynamic parameters and bottom wetted areas are presented and discussed in Section 3. Section 4 is also given for conclusions.
Section snippets
Experimental setup
In the present work, the same as our previous study in Ref (Najafi et al., 2019a, Najafi et al., 2019b), all towing tests are conducted based on the ITTC guidelines (25th ITTC, 2008) (ITTC – Recommended Procedures and Guidelines, Testing and Extrapolation Methods High Speed Marine Vehicles, 2008) in the towing tank of National Iranian Marine Laboratory (NIMALA), Tehran, Iran. Length, width, water depth, maximum carriage speed, and maximum capacity of the force gauge of NIMALA towing tank are
Resistance
Measured experimental results of the non-dimensional form of total resistance (RT/Δ) are presented in Table 2. Fig. 3 shows the diagram of total resistance under different deadrise angles, aft step heights, and longitudinal positions of the aft step from transom. Based on Table 2 and Fig. 3, the total resistance is increased by enhancing the hull velocity. Displacement phase, transition phase (semi-planing) and planing phase are three conventional phases in motion of the planing hulls. During
conclusion
Appropriate knowledge of hydrodynamic characteristics of two-stepped planing hull is necessary to improve the design of these vessels. For this purpose, in the current paper, total resistance, trim angle, reattachment length of the separated flow, and wetted surfaces of two-stepped planing crafts are investigated at three different aft step heights, two positions of the aft step from transom, three deadrise angles and various hull velocities. Among the most important experimental findings in
Credit authorship contribution statement
Amin Najafi and Hashem Nowruzi conceived and planned the experiments. Mohammad Karami carried out the experiments. M. Javad Ameri contributed to sample preparation. Amin Najafi, Hashem Nowruzi, Mohammad Karami and M. Javad Ameri contributed to the interpretation of the results. Hashem Nowruzi took the lead in writing the manuscript. All authors provided critical feedback and helped shape the research, analysis and manuscript.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
References (23)
- et al.
An experimental comparison between different artificial air cavity designs for a planing hull
Ocean Eng.
(2017) - et al.
Experimental and numerical hydrodynamic analysis of a stepped planing hull
Appl. Ocean Res.
(2017) - et al.
Numerical investigation of a stepped planing hull in calm water
Ocean Eng.
(2015) - et al.
On hydrodynamic analysis of stepped planing crafts
Journal of Ocean Engineering and Science
(2019) - et al.
Performance prediction of hydrofoil-supported catamarans using experiment and ANNs
Appl. Ocean Res.
(2018) - et al.
Experimental investigation of the wetted surfaces of stepped planing hulls
Ocean Eng.
(2019) - et al.
Hydrodynamic assessment of stepped planing hulls using experiments
Ocean Eng.
(2020) - et al.
Model tests on resistance and seakeeping performance of wave-piercing high-speed vessel with spray rails
International Journal of Naval Architecture and Ocean Engineering
(2016) - et al.
Stepless and stepped planing hulls-graphs for performance prediction and design
Int. Shipbuild. Prog.
(1961) - et al.
Experimental and Uncertainty Analysis for Engineers
(1999)
Hydrodynamics of High-Speed Small craft(No. 292)
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