Planing Surface Research Articles

Dynamic motion analysis of stepless and stepped planing hulls in random waves: A CFD model perspective

Predicting the dynamic responses of planing hulls in real sea conditions is important for identifying how basic design factors influence their seakeeping performance. Hence, there is a pressing need to provide high-fidelity models for predicting the motions of these hulls in random waves, representing actual seas. In this article, a computational-based model for solving viscous fluid flow around the vessel is built to address this problem. Three different planing hulls, denoted as C, C1, and C2, each distinguished by the number of steps incorporated on their bottom surfaces (1 and 2 indicating the respective step count, with case C being the stepless hull), are modeled in a Computational Fluid Dynamics (CFD) tank, allowing for analysis of the effects of steps on dynamic responses of a planing surface operating in random waves. CFD data is compared against those collected in towing tank tests, revealing a satisfactory level of accuracy. Extreme value and gamma distributions are shown to give probabilities of maxima/minima of displacements and vertical acceleration at the center of gravity (CG) for all three hulls. It is shown that the stepless boat may be exposed to lower vertical acceleration at an early planing speed, but at higher planing speeds, a double-stepped design mitigates the vertical acceleration. Nevertheless, the double-stepped hull would experience more significant extreme heave responses across all speeds and may be exposed to less significant extreme pitch responses during the ride at the highest speed compared to the stepless and one-stepped hulls. The skewness of heave and pitch is evaluated, and it is found that the heave response tends to skew toward positive values (upward). This skewness becomes more noticeable with increasing speed but remains insensitive to wave steepness. Additionally, the pitch response at lower planing speeds shows a partial skew towards negative values (bow-down), but eventually, they may also be partially skewed towards positive values at higher speeds. Moreover, a correlation is observed between the kurtosis of responses of different hulls and the occurrence of the 1/100 highest responses, indicating that a kurtosis greater than 3.0 would result in more extreme responses. Overall, this analysis offers practical insights into planing hull behavior in actual sea conditions from a CFD model perspective, highlighting the potential of CFD in simulating this complex problem.

Curiosities of two-dimensional planing

The traditional deep-water analysis of two-dimensional planing is studied in detail and applied to efficient splash-free and optimal profiles, as well as to flat plates. The methodology is used to analyze both free-to-rise and free-to-rise-plus-trim profiles. In some cases, the predictions exhibit unexpected discontinuous behavior for the lift, wetted length and other results, with respect to the parameters describing the curvature of the planing surface. These discontinuities are due to the nonlinearities inherent in the practical planing problem, as opposed to previous simplified analyses in which the wetted length was specified.

Analysis of Surface Profile Error of Ultra-Precision Diamond Planing Based on Power Spectral Density

Vibration in ultra-precision machining is an inherent physical phenomenon and a key factor affecting surface generation. However, the influence of the vibration characteristics of aerostatic guideways on the machining morphology has not been fully studied. In this article, a diamond micro-planing experiment was carried out on an oxygen-free copper workpiece using a homemade three-axis machine tool, and a white-light interferometer was used to measure the surface topography of the planing surface. The power spectral density of the surface topography was analyzed, and the spatial wavelength components of the surface topography were extracted. Then, the vibration characteristics of the aerostatic guideway were measured in both the space domain and the time domain. A comprehensive analysis of the main components of the workpiece surface error morphology and the vibration characteristics of the guideway shows that the time-domain vibration of the aerostatic guideway is the main factor causing the surface topography error of the workpiece.

Study on Scale Effects of Hydrodynamics around Prismatic Planing Surface by using CFD

Study on Scale Effects of Hydrodynamics around Prismatic Planing Surface by using CFD

Os solos e a evolução de paisagens na Serra do Espinhaço Meridional, Brasil

The Serra do Espinhaco Meridional (SdEM) is a mountain range in the orogenic belt range of the Proterozoic Eon, whose lithology is formed mainly by quartzites and phyllites, which originate shallow and acidic soils. Its relief comprises a succession of planing surfaces, such as Chapadao do Couto, separated by dissected areas. e objective of this work was to understand the distribution and characterize the soils of a toposequence, to contribute to the understanding of the evolution of the landscape of Chapadao do Couto and SdEM. Evidence has been found that the Chapadao do Couto planing surface was formed in the Paleocene/ Eocene and dissected intermittently since then, with the soils of the tops and slopes of its hills being formed and eroded cyclically. e depressions were also intermittently filled by mineral and organic sediments. e installation of the drainage network and the formation of the hills began in the Tertiary, while the genesis of current soils began in the Late Pleistocene and the Holocene.

ANÁLISE DOS DEPÓSITOS DE LATERITAS NIQUELÍFERAS DO BRASIL A PARTIR DO CONCEITO DE SISTEMAS MINERAIS HOLÍSTICOS

O conceito de sistema mineral, o qual interpreta os depósitos minerais relacionando-os à dinâmica terrestre, atualmente é utilizado para interpretação da gênese dos depósitos de maneira holística, sendo importante ferramenta para a pesquisa mineral. Nesse sentido, o presente trabalho faz uma interpretação do níquel laterítico segundo preceitos dos sistemas minerais, e aponta áreas potenciais para novas pesquisas no Brasil. Uma das principais fontes de níquel provém de minerais formados por alterações superficiais de rochas ultramáficas submetidas à climas tropicais e à relativa estabilidade tectônica, existindo, no território brasileiro, diversas regiões potenciais. Os melhores protólitos que se tem registro no Brasil são complexos ultramáficos-máficos estratiformes. Entretanto, os complexos ofiolíticos associados às faixas móveis pré-cambrianas, correspondem a um importante ambiente geotectônico que pode hospedar depósitos. Praticamente todos os protólitos brasileiros estão serpentinizados, processo que de certa forma auxiliou na precipicitação e acumulação de níquel dissolvido em ambiente supergênico. Quanto à geomorfologia, o processo está intimamente relacionado com as superfícies de aplainamento. Na maioria das lateritas niquelíferas brasileiras, as condições paleobioclimáticas submeteram os silicatos primários portadores de níquel das rochas ultramáficas, exumadas pelas superfícies de aplainamento, ao intemperismo químico, ou seja, à hidrólise, forçando a precipitação da Ni-goethita (nível oxidado) e posteriormente à dissolução, reprecipitação e formação das ‘garnieritas’ (nível silicatado).

Hydrodynamics of planing surfaces with negative deadrise angles

Existing physical model test data indicate that negative-deadrise planing surfaces may be capable of producing greater lift and lift-to-drag ratios than positive-deadrise planing surfaces. However, there is a lack of systematic experiments in which deadrise is varied with all other parameters are fixed. In this study, computational fluid dynamics software STAR-CCM+ is applied to simulate fixed-attitude prismatic planing hulls with variable deadrise, including positive and negative angles. Mesh dependency study and comparison with experimental data have been performed. The main reported hydrodynamic characteristics include the lift and drag coefficients, wetted area, and center of pressure. The negative-deadrise hulls are found to possess higher lift capabilities, while the highest lift-drag ratio is achieved by the zero-deadrise hull. With elimination of side wetting on negative-deadrise hulls, their efficiencies can be significantly increased.

Experimental Study on Planing Motion of a Cylinder at Angle of Attack in the Cavity Formed behind an Axisymmetric Cavitator

This article presents experimental studies of the planing motion of an axisymmetric cylindrical body along the surface of a cavity formed behind an axisymmetric cavitator at some angle of attack. The main focus is on the analysis of processes of interaction between the planing body and cavity surfaces. It also develops methods for determining the forces and cavity shape in the interaction zone and behind the planing surface. A number of issues related to supercavitating motion at shallow depth are investigated for moderate Froude numbers under conditions of non-negligible gravity effect.

Experimental and Numerical Research on the Influence of Stern Flap Mounting Angle on Double-Stepped Planing Hull Hydrodynamic Performance

In the current hydrodynamic research relating to planing hulls, the stern flap and steps are generally considered to be two independent resistance reduction measures. Limited research has focused on the coupled effects of flaps and steps. Therefore, experimental and numerical simulation methods are carried out in this paper to explore the influence of the flap mounting angle coupled with the steps. A series of model towing tests were implemented for a double-stepped planing hull with 2°, 3° and 4.5° flap angles. The test results show that, as the mounting angle increased, the low speed resistance performance was improved and the porpoising critical speed was delayed, with a slight resistance cost. Based on the tests, a numerical simulation method was established with volume Froude numbers ranging from 0.88 to 5.20. The simulated hull flow field showed good agreement with the testing data. The simulation results suggest a cavity induces the negative pressure after the steps; the cavity core region is the air phase, and this expands with the air–water mixture flow. The cavity also causes wetted surface reduction and pressure distribution changes. Finally, comparisons of cavities after-steps and load coefficients of different planing surfaces among models were considered. Numerical results analysis gave distinct interpretations for the experimental phenomenon of porpoising critical speed increasing with a slight resistance increment.

Study on Process Monitoring of Elliptical Vibration Cutting by Utilizing Internal Data in Ultrasonic Elliptical Vibration Device

In the present study, monitoring of elliptical vibration cutting process by utilizing internal data in the ultrasonic elliptical vibration device without external sensors such as a dynamometer and displacement sensor is investigated. The internal data utilized here is the change of excitation frequency, i.e. resonant frequency of the device, voltages applied to the piezoelectric actuators composing the device, and electric currents flowing through the actuators. These internal data change automatically in the elliptical vibration control system in order to keep a constant elliptical vibration against the change of the cutting process. Correlativity between the process and the internal data is described by using a vibration model of ultrasonic elliptical vibration cutting and verified by several experiments, i.e. planing and mirror surface finishing of hardened die steel carried out with single crystalline diamond tools. As a result, it is proved that it is possible to estimate the elements of elliptical vibration cutting process, e.g. tool wear and machining load, which are important for stable cutting in such precision machining.

Development of a 2D+T theory for performance prediction of double-stepped planing hulls in calm water

In this article, a mathematical model based on the 2D+T theory has been developed to predict the performance of two-stepped planing hulls in calm water. It has been attempted to develop a mathematical model without using regression formulas. It leads to development of a computational model with no common limitations related to empirical models which have an individual range of applicability. For this purpose, theoretical solution of water entry of a two-dimensional wedge section has been implemented to compute the pressure distribution over wedge section entering water, and then normal forces acting on the two-dimensional sections are computed. Bottom of the boat has been divided into three different planing surfaces including fore, middle and aft bodies. Computations are performed for each of these surfaces. By integrating the two-dimensional sectional normal forces over the entire wetted length of the vessel, the trim angle, wetted surface and resistance have been obtained. To evaluate the accuracy of the presented method, the obtained results are compared against experimental data and a previous empirical-based method developed by authors. The comparison suggests that the proposed method predicted dynamic trim angle, wetted surface and resistance of double stepped boats with reasonable accuracy. The mean errors in prediction of trim angle, wetted surface and resistance are, respectively, 13%, 16% and 8%. It should also be noted that although computation of running attitudes and resistance of double-stepped planing boats are targeted in this article, the mathematical model has been developed in such a way that it has the potential to model transverse and vertical motions of two-stepped planing hulls in future studies.

On application of three-dimensional linearized potential-flow model for shallow-water planing

Hydrodynamics of planing hulls is affected by proximity to the seabed floor in shallow waters. In this study, a three-dimensional steady linearized model based on the potential theory is applied to model flat planing surfaces at finite water depth and finite Froude numbers. Modeling results for shallow waters agree with experimental data in the subcritical and supercritical regimes sufficiently far from the critical speed that corresponds to the depth Froude number of unity. At the critical speed, nonlinear and unsteady effects become important, and a different modeling approach is required.

Reativation of Taxaquara Fault and its morphotectonic influence on the evolution of Jordão River catchment, Paraná, Brasil

The Parana basin is one of the major morphotectures of the South American continent. Although its tectono-sedimentary evolution has been widely studied and fairly well understood, this paper aims to fill a gap in knowledge comprising the tectonic evolution after the end of its last sedimentary cycle, in the Upper Cretaceous. In this context, the Jordan River watershed, situated in the surroundings of Guarapuava municipality, south central region of Parana State, was selected for structural and morphometric analysis where the Cretaceous volcanic rocks of Serra Geral Formation are exposed. The Jordan River watershed was studied for the influence exerted by Taxaquara Fault Zone on its morphologic evolution, since Taxaquara Fault Zone is associated to the Brazilian cycle and extends eastwards to the Ribeira belt in the state of Sao Paulo. The morphometric analysis consisted in the interpretation of the Jordan River watershed drainage network and relief elements, considering the distribution of existing knickpoints in the water courses. Structural analysis was based on the calculation of the stress fields responsible for the activation of local fault zones, which were determined by their spatial arrangement and the statistical and mechanical treatments of structural data. During the Oligocene and Miocene, erosional processes developed a planing surface which marks the relief in the central region of the Jordan River watershed and serves as a stratigraphic marker for the associated deformational events. Three events that contributed to the morphological framework of the Jordan River watershed were defined: an oldest one, probably active before the development of the Jordan pediplane in the Paleogene, by a NE-SW maximum horizontal stress (SHmax); and two more recent ones, being one of Plio-Pleistocene age, with a N05W SHmax, and a still active event of transtensive nature showing a N75W SHmax. The paleostress analysis points to a similarity between the Cenozoic evolution of Parana Basin and the tafrogenic basins of southeast Brazil, revealing the amplitude of the deformation events associated to the studied period and ensuring the importance of further studies on the morphotectonic evolutions of intracratonic regions of the South American plate and their correlation to the Andean tectonic cycle.

On hydrodynamics of a planing plate in a laterally restricted channel

A problem of a planing surface moving steadily at finite Froude numbers in a laterally restricted seaway is considered in this note. A linearized potential flow method based on point sources is applied to model hydrodynamics of a planing plate. Numerical results are obtained and presented for the lift coefficient and the center of pressure. The variable parameters include the ratio of the channel width to the plate beam, beam-based Froude number, and nominal aspect ratio of the plate. A comparison is shown with empirical correlations for unrestricted seaway and with theoretical results for the limiting two-dimensional case.

Assessment of URANS surface effect ship models for calm water and head waves

Surface effect ship (SES) air cushion and seal models are implemented in an URANS hydrodynamics solver. The air cushion is modeled either as a prescribed pressure patch, or as a compressible isothermal/adiabatic ideal stagnant air with fan and leakage flows. The seals are either discretized as hinged bodies or modeled as 2D planing surfaces with hydrodynamic interaction. Verification and validation studies are performed using T-Craft experimental data for calm water resistance, sinkage and trim at Froude number (Fr)=0.1–0.6; impulsive heave and pitch decay at Fr=0; and wave-induced resistance and motion predictions in head waves at Fr=0 and 0.6. The compressible air cushion model with fan and leakage flows perform better than those without the fan and leakage flows and the prescribed pressure patch model. The hinged seal model performs better than the 2D planing surface model, but is computationally expensive for time accurate simulations. Therefore, the 2D planing surface model is used for the validation studies. SES simulations on grids with 5.3M cells show grid verification intervals of 6%, which are comparable to those reported for displacement and semi-planing hull studies on similar grid sizes. On an average calm water and impulsive motion predictions compare within 8.5% of the experimental data, and wave-induced motion predictions show somewhat larger error of 13.5%. The errors levels are mostly comparable to those for displacement and semi-planing and planing hulls. The study identifies that most critical advancement needed for SES simulations is the seal modeling including fluid structure interaction.

From red cells to soft lubrication, an experimental study of lift generation inside a compressible porous layer

It is a new concept for porous media flow that a hydrodynamic lifting force is generated inside a highly compressible porous layer as a planing surface glides over it. The concept originated from the observation of the pop-out phenomena of red blood cells over the endothelial glycocalyx layer (EGL) lining the inner surface of our blood vessels (Feng & Weinbaum, J. Fluid Mech., vol. 422, 2000, pp. 282–317). In the current paper, we report an experimental study to examine this concept. A novel testing set-up was developed that consists of a running conveyer belt covered with a soft porous sheet, and a fully instrumented upper planar board, i.e. planing surface. The generation of pore pressure was observed and captured by pressure transducers when the planing surface glides over the porous sheet. Its distribution strongly depends on the relative velocity between the planing surface and the running belt, the mechanical and transport properties of the porous sheet as well as the compression ratios at the leading and trailing edges. The relative contribution of the transiently trapped air to the total lift was evaluated by comparing the pore pressure to the total lifting pressure measured by a load cell mounted between two adjacent pressure transducers. For a typical running condition with a polyester porous material ($k=h_{2}/h_{1}=5$, $\unicode[STIX]{x1D706}=h_{2}/h_{0}=1$, $U=3.8~\text{m}~\text{s}^{-1}$, where $h_{2}$, $h_{1}$, are the porous layer thickness at the leading and trailing edges, respectively; $h_{0}$ is the un-deformed porous layer thickness; and $U$ is the velocity of the running belt), over 68 % of the local lift is generated by the pore pressure. The results conclusively verified the validity of lift generation in a highly compressible porous layer as a planing surface glides over it. This study provides the foundation for the application of highly compressible porous media for soft lubrication with minimal frictional losses. It also sheds some light on the biophysics study of the EGL.

A three-dimensional vortex method for the hydrodynamic solution of planing cambered dihedral surfaces

A new numerical approach based on the Vortex Lattice Method (VLM) for the solution of the hydrodynamic performances of cambered hulls in steady planing is formulated and validated. Due to its fully 3D formulation, the method can be applied to both cambered and un-cambered dihedral planing surfaces of any shape without any further approximation. The exact three-dimensional wetted surface of the hull is where the body boundary condition is fulfilled. The sprays region detaching both in front of the stagnation root line and from the wet portion of the chine are modeled in the numerical scheme by means of additional vortex lattice regions. The dynamic boundary condition at the stern of the hull is non-linear with respect to the perturbation potential. Results show the dynamic pressure consistently accounts for the 3D features of the flow especially in the case of cambered planing surfaces. The numerical method is verified by a systematic analysis against semi-empirical methods and it is finally validated with experimental results on prismatic as well as cambered dihedral planing surfaces. Excellent correlations are found for both types of planing surfaces that range in the same confidence interval of higher fidelity numerical models, such as RANSE solvers.

A study on the effect of the cushion pressure on a planing surface

The study of a planing flat plate may be considered as a topic of wide interest for academic and industrial applications. From experimental and numerical studies, flow separation occurs near the stagnation point and a thin jet sprays forward along the plate, while a clear wave pattern develops downstream. In the present study, the effect on the jet-root position caused by a cushion pressure applied on the downstream free surface is considered and the consequent variation in lift and drag coefficients is studied. This canonical problem is important in the design of Surface Effects Ships (SES), the bow seal of which may be assumed as a planing deformable surface with a cushion pressure behind it. This study focuses on the hydrodynamic interaction between the plate and the cushion pressure; as such, the plate geometry is prescribed. A two-dimensional numerical study of this problem has been performed in the present work using a finite-volume Chimera-overlapping-grids approach to numerically solve the Navier–Stokes equations; the free surface is handled by means of two-phase level-set method. Validity of the results is assessed by the comparison with theoretical and numerical results available in the literature.

Dynamic Performance of the National Technical University of Athens Double-chine Series Hull Forms in Random Waves

A systematic series of double-chine, wide-transom hull forms with warped planing surface has been developed at the Laboratory for Ship & Marine Hydrodynamics (LSMH) of the National Technical University of Athens during the last two decades. The series are suitable for medium and large ships operating at high but preplaning speeds and consist of five hull forms. Two scaled models for each hull form have been constructed and tested in calm water and in waves. In this article, systematic experimental results in random waves are presented. More specifically, the parent hull form with L/B = 5.50 was tested in three-level keel displacements, whereas the two corner hull forms with L/B = 4.0 and 7.0 were tested at the central displacement. Thus, the effects of both the displacement and the L/B ratio on the seakeeping responses are investigated. All tests were performed at two speeds corresponding to Fn = 0.34 and 0.68 using the Bretschneider spectral model with nondimensional modal periods TP' = TP/v(L/g) = 2.0-5.0 at steps of 0.5 and model significant wave heights H1/3 in the 8- to 16-cm range to represent moderate waves. Assuming linearity, the results for heave, pitch, acceleration, and added resistance are divided by H1/3 (i.e., they refer to H1/3 equal to unity).

Dynamic Performance of the National Technical University of Athens Double-chine Series Hull Forms in Random Waves

A systematic series of double-chine, wide-transom hull forms with warped planing surface has been developed at the Laboratory for Ship & Marine Hydrodynamics (LSMH) of the National Technical University of Athens during the last two decades. The series are suitable for medium and large ships operating at high but preplaning speeds and consist of five hull forms. Two scaled models for each hull form have been constructed and tested in calm water and in waves. In this article, systematic experimental results in random waves are presented.