The Effects of Energy Dissipation on the Transition to Planing of a Boat

1989 ◽  
Vol 33 (01) ◽  
pp. 35-46
Author(s):  
P. M. Naghdi ◽  
M. B. Rubin
Keyword(s):  
Steady State ◽  
Energy Dissipation ◽  
Detailed Analysis ◽  
Leading Edge ◽  
Steady State Solution ◽  
State Solution ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Spray Formation ◽  
Propulsion Force

The problem of the transition to planing of a boat, in the presence of the effect of spray formation at the boat's leading edge, is investigated using a nonlinear steady-state solution of the equations of the theory of a directed fluid sheet for two-dimensional motion of an incompressible inviscid fluid. The motion of the fluid is coupled with the motion of the free-floating boat and detailed analysis is undertaken pertaining to such features as trim angle, sinkage, and propulsion force. The effects of the rate of energy dissipation arising from spray formation at the boat's leading edge, and changes in equilibrium depth, propulsion angle, and the boat's weight, are studied and shown to significantly influence the boat's planing characteristics.

On the Squat of a Ship

1984 ◽  
Vol 28 (02) ◽  
pp. 107-117 ◽  
Author(s):  
P. M. Naghdi ◽  
M. B. Rubin
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Differential Equations ◽  
Froude Number ◽  
Steady State Solution ◽  
State Solution ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Sinkage And Trim

The problem of the squat of a "two-dimensional" ship is solved using a nonlinear steady-state solution of the differential equations of the theory of a directed fluid sheet. Particular attention is focused on the prediction of the sinkage and trim of the ship, and the results for a model ship qualitatively agree with available experimental data. Specifically, the solution presented here predicts the experimentally observed dependence of the sinkage and trim on the equilibrium depth of the water (regarded here as an incompressible, inviscid fluid), and predicts a nonzero drag for subcritical ship speeds (corresponding to the values of depth Froude number F < 1). The solution also exhibits certain detailed features of the sinkage curves which apparently were not observed in the experiments mentioned above. In this connection, additional relevant experiments are suggested.

Effects of Thermal Contact Resistance on Transient Thermoelastic Contacts for an Elastic Foundation

2005 ◽  
Vol 72 (6) ◽  
pp. 972-977 ◽  
Author(s):  
Yong Hoon Jang
Keyword(s):  
Steady State ◽  
Contact Resistance ◽  
Thermal Contact Resistance ◽  
Normal Load ◽  
Thermal Contact ◽  
Leading Edge ◽  
Transient Behavior ◽  
Steady State Solution ◽  
State Solution ◽  
Winkler Foundation

The paper presents a numerical solution to the problem of a hot rigid indenter sliding over a thermoelastic Winkler foundation with a thermal contact resistance at constant speed. It is shown analytically that no steady-state solution can exist for sufficiently high temperature or sufficiently small normal load or speed, regardless of the thermal contact resistance. However, the steady-state solution may exist in the same situation if the thermal contact resistance is considered. This means that the effect of the large values of temperature difference and small value of force or velocity which occur at no steady state can be lessened due to the thermal contact resistance. When there is no steady state, the predicted transient behavior involves regions of transient stationary contact interspersed with regions of separation regardless of the thermal contact resistance. Initially, the system typically exhibits a small number of relatively large contact and separation regions, but after the initial transient, the trailing edge of the contact area is only established and the leading edge loses contact, reducing the total extent of contact considerably. As time progresses, larger and larger numbers of small contact areas are established, until eventually the accuracy of the algorithm is limited by the discretization used.

An Experimental and Numerical Study of the Isothermal Flowfield Behind a Bluff Body Flameholder

1997 ◽  
Vol 119 (2) ◽  
pp. 328-339 ◽  
Author(s):  
C. N. Raffoul ◽  
A. S. Nejad ◽  
R. D. Gould ◽  
S. A. Spring
Keyword(s):  
Steady State ◽  
Bluff Body ◽  
Recirculation Zone ◽  
Numerical Study ◽  
Steady State Solution ◽  
Accurate Solution ◽  
State Solution ◽  
Laser Doppler Velocimeter ◽  
Two Dimensional ◽  
Reynolds Stresses

An experimental and numerical investigation was conducted to study the turbulent velocities and stresses behind a two-dimensional bluff body. Simultaneous three-component laser-Doppler velocimeter (LDV) measurements were made in the isothermal incompressible turbulent flowfield downstream of a bluff body placed at midstream in a rectangular test section. Mean velocities and Reynolds stresses were measured at various axial positions. Spanwise velocity measurements indicated that the flow is three dimensional in the recirculation zone of the bluff body. Confidence in the accuracy of the data was gained by calculating the mass fluxes at each axial station. These were found to agree with each other to within ±3 percent. A parallel Computational Fluid Dynamics (CFD) study was initiated to gage the predictive accuracy of currently available CFD techniques. Three solutions were computed: a two-dimensional steady-state solution using the standard k-ε model, a two-dimensional time-accurate solution using the standard k-ε model, and a two-dimensional time-accurate solution using a Renormalized-Group (RNG) k-ε turbulence model. The steady-state solution matched poorly with the data, severely underpredicting the Reynolds stresses in the recirculation zone. The time-accurate solutions captured the unsteady vortex shedding from the base of the bluff body, providing a source for the higher Reynolds stresses. The RNG k-ε solution provided the best match to the data.

A Nonlinear Theory of Sloshing in Rectangular Tanks

1974 ◽  
Vol 18 (04) ◽  
pp. 224-241 ◽  
Author(s):  
Odd M. Faltinsen
Keyword(s):  
Steady State ◽  
Power Series ◽  
Boundary Value Problem ◽  
Nonlinear Theory ◽  
Reasonable Agreement ◽  
Steady State Solution ◽  
State Solution ◽  
Two Dimensional ◽  
The Stability ◽  
Theory And Experiment

A two-dimensional, rigid, rectangular, open tank without baffles is forced to oscillate harmonically with small amplitudes of sway or roll oscillation in the vicinity of the lowest natural frequency for the fluid inside the tank. The breadth of the tank is 0(1) and the depth of the fluid is either 0(1) or in-finite. The excitation is 0(ε) and the response is 0(ε1/3). A nonlinear, inviscid boundary-value problem of potential flow is formulated and the steady-state solution is found as a power series in ε1/3 correctly to 0(ε). Comparison between theory and experiment shows reasonable agreement. The stability of the steady-state solution has been studied.

Response of a Submerged Cylindrical Shell to an Axially Propagating Step Wave

1965 ◽  
Vol 32 (4) ◽  
pp. 788-792 ◽  
Author(s):  
M. J. Forrestal ◽  
G. Herrmann
Keyword(s):  
Cylindrical Shell ◽  
Steady State ◽  
Wave Front ◽  
Transverse Shear ◽  
Shell Theory ◽  
Steady State Solution ◽  
State Solution ◽  
Rotatory Inertia ◽  
Shear Deformations ◽  
Axial Coordinate

An infinitely long, circular, cylindrical shell is submerged in an acoustic medium and subjected to a plane, axially propagating step wave. The fluid-shell interaction is approximated by neglecting fluid motions in the axial direction, thereby assuming that cylindrical waves radiate away from the shell independently of the axial coordinate. Rotatory inertia and transverse shear deformations are included in the shell equations of motion, and a steady-state solution is obtained by combining the independent variables, time and the axial coordinate, through a transformation that measures the shell response from the advancing wave front. Results from the steady-state solution for the case of steel shells submerged in water are presented using both the Timoshenko-type shell theory and the bending shell theory. It is shown that previous solutions, which assumed plane waves radiated away from the vibrating shell, overestimated the dumping effect of the fluid, and that the inclusion of transverse shear deformations and rotatory inertia have an effect on the response ahead of the wave front.

Sign in / Sign up

Export Citation Format

Share Document