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.

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.

Frequency response analysis of periodically time varying circuits

2018 ◽  
Vol 37 (3) ◽  
pp. 1204-1213
Author(s):  
Igor Korotyeyev
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Steady State Solution ◽  
Variable Coefficients ◽  
State Solution ◽  
Response Analysis ◽  
Time Varying ◽  
Content Type ◽  
Frequency Responses ◽  
Definition Of

Purpose The purpose of this paper is to introduce a method for the analysis of steady-state processes in periodically time varying circuits. The method is based on a new definition of frequency responses for periodic time-varying circuits. Design/methodology/approach Processes in inverter circuits are often described by differential equations with periodically variable coefficients and forcing functions. To obtain a steady-state periodic solution, the expansion of differential equations into a domain of two independent variables of time is made. To obtain differential equations with constant coefficients the Lyapunov transformation is applied. The two-dimensional Laplace transform is used to find a steady-state solution. The steady-state solution is obtained in the form of the double Fourier series. The transfer function and frequency responses for the inverter circuit are introduced. Findings A set of frequency characteristics are defined. An example of a boost inverter is considered, and a set of frequency responses for voltage and current are presented. These responses show a resonance that is missed if the averaged state-space method is used. Originality/value A new definition of frequency responses is presented. On the basis of frequency responses, a modulation strategy and filters can be chosen to improve currents and voltages.

Numerical Simulation of Thermal Stratification in the Upper Plenum of Fast Reactor

2013 ◽  
Author(s):  
Seok-Ki Choi ◽  
Tae-Ho Lee
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Thermal Stratification ◽  
Numerical Solutions ◽  
Steady State Solution ◽  
Temporal Variations ◽  
State Solution ◽  
Thermal Mixing ◽  
Commercial Code ◽  
Inlet Conditions

A numerical analysis of the thermal stratification in the upper plenum of the MONJU fast breeder reactor was performed. Calculations were performed for a 1/6 simplified model of the MONJU reactor using the commercial code, CFX-13. To better resolve the geometrically complex upper core structure of the MONJU reactor, the porous media approach was adopted for the simulation. First, a steady state solution was obtained, and the transient solutions were then obtained for the turbine trip test conducted in December 1995. The time dependent inlet conditions for the mass flow rate and temperature were provided by JAEA. Good agreement with the experimental data was observed for the steady state solution. The numerical solution of the transient analysis shows the formation of thermal stratification within the upper plenum of the reactor vessel during the turbine trip test. The temporal variations of temperature were predicted accurately by the present method in the initial rapid coastdown period (∼300 seconds). However, the transient numerical solutions show a faster thermal mixing than that observed in the experiment after the initial coastdown period. A near homogenization of the temperature field in the upper plenum is predicted after about 900 seconds, which is a much shorter-term thermal stratification than the experimental data indicates.

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.

THE MARGINAL STABILITY OF AUTONOMOUS DIFFERENTIAL EQUATIONS

1993 ◽  
Vol 03 (03) ◽  
pp. 785-788
Author(s):  
N.N. GREENBAUN
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Steady State Solution ◽  
Usual Method ◽  
State Solution ◽  
Marginal Stability ◽  
State Variables ◽  
Autonomous Differential Equations

Solutions in the vicinity of a steady state solution to a system of autonomous nonlinear differential equations are of interest to modelers. The usual method for determining marginal stability of the steady state is the Routh-Hurwitz criterion. The method offered here is less complicated and more efficient when the number of state variables exceeds three.

The boundary layer on a fixed sphere on the axis of an unbounded rotating fluid

1982 ◽  
Vol 123 ◽  
pp. 219-236 ◽  
Author(s):  
S. C. R. Dennis ◽  
D. B. Ingham
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Procedure ◽  
Steady State Solution ◽  
State Solution ◽  
Partial Differential ◽  
Boundary Layer Equations ◽  
Finite Set

The problem of determining both the steady and unsteady axially symmetrical motion of a viscous incompressible fluid outside a fixed sphere when the fluid at large distances rotates as a solid body is considered. It is assumed that the Reynolds number for the motion is so large that the boundary-layer equations may be assumed to hold. The steady-state boundary-layer equations are solved using backward- forward differencing and the terminal solutions at the equator and the pole of the sphere are generatedas part ofthe numerical procedure. To check that this steady-state solution can be approached from an unsteady situation, the case of a sphere that is initially rotating with the same constant angular velocity as the fluid and is then impulsively brought to rest is investigated. I n this case the motion is governed by a coupled set of three nonlinear time-dependent partial differential equations, which are solved by employing the semi-analytical method of series truncation to reduce the number of independent variables by one and then solving by numerical methods a finite set of partial differential equations in one space variable and time. The physical properties of the flow are calculated as functions of the time and compared with the known solution at small times and the steady-state solution.

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