The nonlinear problem of a gliding body with gravity

2013 ◽  
Vol 727 ◽  
pp. 132-160 ◽  
Author(s):  
Y. A. Semenov ◽  
G. X. Wu
Keyword(s):  
Free Surface ◽  
Body Surface ◽  
Breaking Waves ◽  
The Body ◽  
Surface Shape ◽  
Parameter Plane ◽  
Hodograph Method ◽  
Wide Range ◽  
Free Surface Shape ◽  
Analytical Expressions

AbstractAnalysis based on the velocity potential free flow theory with the fully nonlinear boundary condition is made for the steady flow generated by a body gliding along a free surface. Employing the integral hodograph method, we derive analytical expressions for the complex velocity and for the derivative of the complex potential with the coordinate of a parameter plane. The boundary value problem is transformed into a system of two integro-differential equations for the velocity modulus on the free surface and for the slope of the wetted body surface in the parameter plane. The same slope and curvature of the free surface and the body surface at the intersection are adopted to determine the separation points of the flow and from the body. Numerical results are provided for a gliding flat plate and a circular cylinder. The pressure distribution along the body and the free surface shape are presented for a wide range of Froude numbers, within the limit for which the solution corresponding to non-breaking waves downstream can be obtained.

scholarly journals Water entry of an expanding body with and without splash

2019 ◽  
Vol 862 ◽  
pp. 924-950 ◽  
Author(s):  
Y. A. Semenov ◽  
G. X. Wu
Keyword(s):  
Free Surface ◽  
Body Surface ◽  
Water Entry ◽  
The Body ◽  
Surface Shape ◽  
Cylinder Surface ◽  
Hodograph Method ◽  
Expansion Speed ◽  
Attached Flow ◽  
Self Similar

A self-similar flow generated by water entry of an expanding two-dimensional smooth and curved body is studied based on the incompressible velocity potential theory, with gravity and surface tension effects being ignored. At each expansion speed, mathematical solutions for detached flow with a splash jet and attached flow with jet leaning on the body surface are obtained, both of which have been found possible in experiment, corresponding to hydrophobic and hydrophilic bodies, respectively. The problem is solved using the integral hodograph method, which converts the governing Laplace equations into two integral equations along the half real and imaginary axes of a parameter plane. For the detached flow, the conditions for continuity and finite spatial derivative of the velocity at the point of flow departing form the body surface are imposed. It is found that the Brillouin–Villat criterion for flow detachment of steady flow is also met in this self-similar flow, which requires the curvatures of the free surface and the body surface to be the same at the detachment point. Solutions for the detached flow have been obtained in the whole range of the expansion speeds, from zero to infinity, relative to the water entry speed. For the attached flow there is a minimal expansion speed below which no solution cannot be obtained. Detailed results in terms of pressure distribution, free surface shape and streamlines and tip angle of the jet are presented. It is revealed that when solutions for both detached and attached flows exist, the pressure distributions on the cylinder surface are almost the same up to the point near the jet root. Beyond that point, the pressure relative to the ambient one drops to zero at the detachment point in the former, while it drops below zero in the jet attached on the body and then returns to zero at the contact point in the latter.

scholarly journals Splash jet generated by collision of two liquid wedges

2013 ◽  
Vol 737 ◽  
pp. 132-145 ◽  
Author(s):  
Y. A. Semenov ◽  
G. X. Wu ◽  
J. M. Oliver
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Hodograph Method ◽  
Pressure Distributions ◽  
Wide Range ◽  
Self Similar Solution ◽  
Gravity Effects ◽  
Self Similar ◽  
The Impact ◽  
Analytical Expressions

AbstractA complete nonlinear self-similar solution that characterizes the impact of two liquid wedges symmetric about the velocity direction is obtained assuming the liquid to be ideal and incompressible, with negligible surface tension and gravity effects. Employing the integral hodograph method, analytical expressions for the complex potential and for its derivatives are derived. The boundary value problem is reduced to two integro-differential equations in terms of the velocity modulus and angle to the free surface. Numerical results are presented in a wide range of wedge angles for the free surface shapes, streamline patterns, and pressure distributions. It is found that the splash jet may cause secondary impacts. The regions with and without secondary impacts in the plane of the wedge angles are determined.

scholarly journals Asymmetric impact between liquid and solid wedges

2013 ◽  
Vol 469 (2150) ◽  
pp. 20120203 ◽  
Author(s):  
Y. A. Semenov ◽  
G. X. Wu
Keyword(s):  
Free Surface ◽  
Velocity Potential ◽  
Mapping Function ◽  
Solution Procedure ◽  
Contact Angles ◽  
The Body ◽  
Surface Shape ◽  
Parameter Plane ◽  
Complex Velocity Potential ◽  
The Impact

The hydrodynamic problem of impact between a solid wedge and a liquid wedge is analysed. The liquid is assumed to be ideal and incompressible; gravity and surface tension effects are ignored. The flow generated by the impact is assumed to be irrotational and therefore can be described by the velocity potential theory. The solution procedure is based on the analytical derivation of the complex-velocity potential in a parameter plane and the function mapping conformally the parameter plane onto the similarity plane. The mapping function is found as a combination of the derivatives of the complex potential in the similarity and parameter planes, through the integral equations for mixed and homogeneous boundary-value problems in terms of the velocity modulus and the velocity angle with the fluid boundary, together with the dynamic and kinematic boundary conditions. These equations are solved through a numerical method. The procedure is first verified through comparisons with some known results. Simulations are then made for a variety of cases, and detailed results are presented in terms of the free surface shape, streamlines, pressure distribution on the wetted solid surface, and contact angles between the free surface and the body surface.

scholarly journals Water entry of a wedge with rolled-up vortex sheet

2017 ◽  
Vol 835 ◽  
pp. 512-539 ◽  
Author(s):  
Yuriy A. Semenov ◽  
G. X. Wu
Keyword(s):  
Free Surface ◽  
Pressure Distribution ◽  
Body Surface ◽  
Vortex Shedding ◽  
Vortex Sheet ◽  
Water Entry ◽  
The Body ◽  
Surface Shape ◽  
Force Coefficients ◽  
Local Singularity

The problem of asymmetric water entry of a wedge with the vortex sheet shed from its apex is considered within the framework of the ideal and incompressible fluid. The effects due to gravity and surface tension are ignored and the flow therefore can be treated as self-similar, as there is no length scale. The solution for the problem is sought through two mutually dependent parts using two different analytic approaches. The first one is due to water entry, which is obtained through the integral hodograph method for the complex velocity potential, in which the streamline on the body surface remains on the body surface after passing the apex, leading to a non-physical local singularity. The second one is due to a vortex sheet shed from the apex, and the shape of the sheet and the strength distribution of the vortex are obtained through the solution of the Birkhoff–Rott equation. The total circulation of the vortex sheet is obtained by imposing the Kutta condition at the apex, which removes the local singularity. These two solutions are nonlinearly coupled on the unknown free surface and the unknown vortex sheet. This poses a major challenge, which distinguishes the present formulation of the problem from the previous ones on water entry without a vortex sheet and ones on vortex shedding from a wedge apex without a moving free surface. Detailed results in terms of pressure distribution, vortex sheet, velocity and force coefficients are presented for wedges of different inner angles and heel angles, as well as the water-entry direction. It is shown that the vortex shedding from the tip of the wedge has a profound local effect, but only weakly affects the free-surface shape, overall pressure distribution and force coefficients.

Inviscid free-surface flow over a periodic wall

1991 ◽  
Vol 226 ◽  
pp. 189-203 ◽  
Author(s):  
V. Bontozoglou ◽  
S. Kalliadasis ◽  
A. J. Karabelas
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Surface Shape ◽  
Flow Parameters ◽  
Material Deposition ◽  
Straightforward Method ◽  
Wide Range ◽  
Free Surface Shape

A numerical method is described, based on the hodograph formulation, for analysing in viscid, free-surface flows over a periodic wall. An efficient implementation of the wall boundary condition results in a straightforward method, accurate for a wide range of bottom undulation heights and flow parameters. It is demonstrated that a series of resonances is possible between the bottom undulations and the free surface. The steady, free-surface profiles are accurately calculated for a wide range of current velocities and are shown to be significantly dimpled by higher harmonics. A study of the flow field indicates that the free-surface shape strongly affects the velocities close to the wall, leading to distributions which change dramatically with current velocity. Some implications of the new results on the phenomena of wall dissolution or material deposition, Bragg scattering of surface waves and sediment transport in rivers, are discussed.

Development and Validation of a New Scoring Tool to Evaluate the Clinical Evolution of Adult Patients with Nonsegmental Vitiligo

Dermatology ◽  
2021 ◽  
pp. 1-9
Author(s):  
María Luisa Peralta-Pedrero ◽  
Denisse Herrera-Bringas ◽  
Karla Samantha Torres-González ◽  
Martha Alejandra Morales-Sánchez ◽  
Fermín Jurado Santa-Cruz ◽  
...  
Keyword(s):  
Body Surface ◽  
Task Force ◽  
Intraclass Correlation ◽  
The Body ◽  
Response To Treatment ◽  
Similar Response ◽  
Clinical Evolution ◽  
Wide Range ◽  
Patient Reported ◽  
Extreme Groups

<b><i>Background:</i></b> Vitiligo has an unpredictable course and a variable response to treatment. Furthermore, the improvement of some vitiligo lesions cannot be considered a guarantee of a similar response to the other lesions. Instruments for patient-reported outcome measures (PROM) can be an alternative to measure complex constructions such as clinical evolution. <b><i>Objective:</i></b> The aim of this study was to validate a PROM that allows to measure the clinical evolution of patients with nonsegmental vitiligo in a simple but standardized way that serves to gather information for a better understanding of the disease. <b><i>Methods:</i></b> The instrument was created through expert consensus and patient participation. For the validation study, a prospective cohort design was performed. The body surface area affected was measured with the Vitiligo Extension Score (VES), the extension, the stage, and the spread by the evaluation of the Vitiligo European Task Force assessment (VETFa). Reliability was determined with test-retest, construct validity through hypothesis testing, discriminative capacity with extreme groups, and response capacity by comparing initial and final measurements. <b><i>Results:</i></b> Eighteen semi-structured interviews and 7 cognitive interviews were conducted, and 4 dermatologists were consulted. The instrument Clinical Evolution-Vitiligo (CV-6) was answered by 119 patients with a minimum of primary schooling. A wide range was observed in the affected body surface; incident and prevalent cases were included. The average time to answer the CV-6 was 3.08 ± 0.58 min. In the test-retest (<i>n</i> = 53), an intraclass correlation coefficient was obtained: 0.896 (95% CI 0.82–0.94; <i>p</i> &#x3c; 0.001). In extreme groups, the mean score was 2 (2–3) and 5 (4–6); <i>p</i> &#x3c; 0.001. The initial CV-6 score was different from the final one and the change was verified with VES and VETFa (<i>p</i> &#x3c; 0.05, <i>n</i> = 92). <b><i>Conclusions:</i></b> The CV-6 instrument allows patient collaboration, it is simple and brief, and it makes it easier for the doctor to focus attention on injuries that present changes at the time of medical consultation.

Advanced CFD Simulations of free-surface flows around modern sailing yachts using a newly developed openFOAM solver

2016 ◽  
Author(s):  
Janek Meyer ◽  
Hannes Renzsch ◽  
Kai Graf ◽  
Thomas Slawig
Keyword(s):  
Free Surface ◽  
Large Scale ◽  
Breaking Waves ◽  
Free Surface Flows ◽  
Body Motion ◽  
Computational Time ◽  
Efficient Computation ◽  
Surface Flows ◽  
Scale Free ◽  
Wide Range

While plain vanilla OpenFOAM has strong capabilities with regards to quite a few typical CFD-tasks, some problems actually require additional bespoke solvers and numerics for efficient computation of high-quality results. One of the fields requiring these additions is the computation of large-scale free-surface flows as found e.g. in naval architecture. This holds especially for the flow around typical modern yacht hulls, often planing, sometimes with surface-piercing appendages. Particular challenges include, but are not limited to, breaking waves, sharpness of interface, numerical ventilation (aka streaking) and a wide range of flow phenomenon scales. A new OF-based application including newly implemented discretization schemes, gradient computation and rigid body motion computation is described. In the following the new code will be validated against published experimental data; the effect on accuracy, computational time and solver stability will be shown by comparison to standard OF-solvers (interFoam / interDyMFoam) and Star CCM+. The code’s capabilities to simulate complex “real-world” flows are shown on a well-known racing yacht design.

Distribution of Wave Impact Forces From Breaking and Non-Breaking Waves

2009 ◽  
Author(s):  
Anne M. Fullerton ◽  
Thomas C. Fu ◽  
Edward S. Ammeen
Keyword(s):  
Free Surface ◽  
Wave Height ◽  
Breaking Waves ◽  
Qualitative Assessment ◽  
Total Force ◽  
Impact Loads ◽  
Wave Impact ◽  
Data Set ◽  
Wave Characteristics ◽  
Wide Range

Impact loads from waves on vessels and coastal structures are highly complex and may involve wave breaking, making these changes difficult to estimate numerically or empirically. Results from previous experiments have shown a wide range of forces and pressures measured from breaking and non-breaking waves, with no clear trend between wave characteristics and the localized forces and pressures that they generate. In 2008, a canonical breaking wave impact data set was obtained at the Naval Surface Warfare Center, Carderock Division, by measuring the distribution of impact pressures of incident non-breaking and breaking waves on one face of a cube. The effects of wave height, wavelength, face orientation, face angle, and submergence depth were investigated. A limited number of runs were made at low forward speeds, ranging from about 0.5 to 2 knots (0.26 to 1.03 m/s). The measurement cube was outfitted with a removable instrumented plate measuring 1 ft2 (0.09 m2), and the wave heights tested ranged from 8–14 inches (20.3 to 35.6 cm). The instrumented plate had 9 slam panels of varying sizes made from polyvinyl chloride (PVC) and 11 pressure gages; this data was collected at 5 kHz to capture the dynamic response of the gages and panels and fully resolve the shapes of the impacts. A Kistler gage was used to measure the total force averaged over the cube face. A bottom mounted acoustic Doppler current profiler (ADCP) was used to obtain measurements of velocity through the water column to provide incoming velocity boundary conditions. A Light Detecting and Ranging (LiDAR) system was also used above the basin to obtain a surface mapping of the free surface over a distance of approximately 15 feet (4.6 m). Additional point measurements of the free surface were made using acoustic distance sensors. Standard and high-speed video cameras were used to capture a qualitative assessment of the impacts. Impact loads on the plate tend to increase with wave height, as well as with plate inclination toward incoming waves. Further trends of the pressures and forces with wave characteristics, cube orientation, draft and face angle are investigated and presented in this paper, and are also compared with previous test results.

Transient Temperature Involving Oscillatory Heat Source With Application in Fretting Contact

2007 ◽  
Vol 129 (3) ◽  
pp. 517-527 ◽  
Author(s):  
Jun Wen ◽  
M. M. Khonsari
Keyword(s):  
Heat Source ◽  
Oscillation Amplitude ◽  
The Body ◽  
Transient Temperature ◽  
Dimensionless Frequency ◽  
Heat Sources ◽  
Infinite Body ◽  
Fitting Method ◽  
Wide Range ◽  
Analytical Expressions

An analytical approach for treating problems involving oscillatory heat source is presented. The transient temperature profile involving circular, rectangular, and parabolic heat sources undergoing oscillatory motion on a semi-infinite body is determined by integrating the instantaneous solution for a point heat source throughout the area where the heat source acts with an assumption that the body takes all the heat. An efficient algorithm for solving the governing equations is developed. The results of a series simulations are presented, covering a wide range of operating parameters including a new dimensionless frequency ω¯=ωl2∕4α and the dimensionless oscillation amplitude A¯=A∕l, whose product can be interpreted as the Peclet number involving oscillatory heat source, Pe=ω¯A¯. Application of the present method to fretting contact is presented. The predicted temperature is in good agreement with published literature. Furthermore, analytical expressions for predicting the maximum surface temperature for different heat sources are provided by a surface-fitting method based on an extensive number of simulations.

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