Optimal Performance of Ships Under Combined Power and Sail

1982 ◽  
Vol 26 (03) ◽  
pp. 209-218
Author(s):  
John S. Letcher
Keyword(s):  
Numerical Solution ◽  
Economic Model ◽  
Analytic Solutions ◽  
Simultaneous Equations ◽  
Simultaneous Optimization ◽  
Fixed Cost ◽  
University Of Michigan ◽  
Cost Rate ◽  
Optimal Setting ◽  
Set Up

A simplified hydrodynamic and economic model is developed to describe the operation of a ship equipped with both sails and engine. In the range of light-to-moderate winds in which use of the engine is likely to be economical, the vessel is described by a characteristic speed, a characteristic fixed-cost rate, and five dimensionless parameters (four hydrodynamic, one economic). The model includes simultaneous optimization of three control variables: sail lift, throttle setting, and course angle; optimal setting of variable draft devices can be included optionally. Although no analytic solutions are attained, the simultaneous equations expressing minimization of cost per mile made good are set up, and a general algorithm is given for numerical solution of these problems. As an illustrative example, numerical values are worked out for the 30,000-dwt square-rigged bulk cargo ship from the 1975 University of Michigan study.

A semi-infinite hydraulic fracture with leak-off driven by a power-law fluid

2017 ◽  
Vol 837 ◽  
pp. 210-229 ◽  
Author(s):  
E. V. Dontsov ◽  
O. Kresse
Keyword(s):  
Numerical Solution ◽  
Power Law ◽  
Hydraulic Fracture ◽  
Closed Form Solution ◽  
Analytic Solutions ◽  
Form Solution ◽  
Rapid Evaluation ◽  
Power Law Fluid ◽  
Parametric Space ◽  
Fluid Rheology

This study investigates the problem of a semi-infinite hydraulic fracture that propagates steadily in a permeable formation. The fracturing fluid rheology is assumed to follow a power-law behaviour, while the leak-off is modelled by Carter’s model. A non-singular formulation is employed to effectively analyse the problem and to construct a numerical solution. The problem under consideration features three limiting analytic solutions that are associated with dominance of either toughness, leak-off or viscosity. Transitions between all the limiting cases are analysed and the boundaries of applicability of all these limiting solutions are quantified. These bounds allow us to determine the regions in the parametric space, in which these limiting solutions can be used. The problem of a semi-infinite fracture, which is considered in this study, provides the solution for the tip region of a hydraulic fracture and can be used in hydraulic fracturing simulators to facilitate solving the moving fracture boundary problem. To cater for such applications, for which rapid evaluation of the solution is necessary, the last part of this paper constructs an approximate closed form solution for the problem and evaluates its accuracy against the numerical solution inside the parametric space.

scholarly journals Simulating the Effects of Noncrossing Block Sections Setting Rules on Capacity Loss of Double-Track Railway Line due to the Operation of out-of-Gauge Trains

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Yinggui Zhang ◽  
Qiong-fang Zeng ◽  
Dingyou Lei ◽  
Xinyu Wang
Keyword(s):  
Assessment Model ◽  
Simulation Experiments ◽  
Railway Line ◽  
Capacity Loss ◽  
Operation Rules ◽  
Upstream Direction ◽  
Optimal Setting ◽  
Railway Capacity ◽  
Set Up ◽  
Double Track

Dispatchers often set noncrossing block sections (NCBSs) for railway out-of-gauge train (OGT) running on double-track railway line for safety reasons. In this paper, we will investigate the best location, length, and number of noncrossing block sections to reduce railway capacity loss due to the operation of OGTs. Firstly, yielding, overtaking, stopping, starting, and other operation rules for OGTs running on double-track railway line were designed, and a simulation model based on cellular automata was further put forward. Then, an assessment model for double-track railway line capacity loss due to the operation of OGTs was set up. Some simulation experiments and the comparisons of these results were further given to achieve the optimal setting of NCBS for OGTs running on double-track railway line. In the case of NCBSs number minus one, capacity loss caused by the operation of OGTs can be reduced up to 15.2% in the upstream direction and 6.3% in the downstream direction. Also, the NCBSs should lie at the nearest block sections (BSs) to depot stations and the NCBSs lengths should be as less as possible.

The numerical solution of certain integral equations with non-integrable kernels arising in the theory of crack propagation and elastic wave diffraction

1969 ◽  
Vol 265 (1163) ◽  
pp. 353-381 ◽  
Keyword(s):  
Integral Equation ◽  
Elastic Wave ◽  
Numerical Solution ◽  
Wave Diffraction ◽  
Crack Surface ◽  
Relative Displacement ◽  
Method Of Solution ◽  
Set Up ◽  
Prestressed State ◽  
Numerical Method Of Solution

An infinite elastic medium is initially at rest in a prestressed state of plane- or anti-plane strain. At time t = 0 a plane crack comes into existence which occupies a strip parallel to the y axis and whose width varies in time. Assuming that the components of the traction are known on the crack surface it is possible to set up an integral equation on the area of the crack for the relative displacement across the crack. Although the kernel of this integral equation is non-integrable a method is found for discretizing it and a numerical method of solution is carried out. The results, which in some cases are the solutions of diffraction problems, are presented graphically.

Evaluating relief center designs for disaster relief distribution

2018 ◽  
Vol 8 (1) ◽  
pp. 22-48 ◽  
Author(s):  
Merve Ozen ◽  
Ananth Krishnamurthy
Keyword(s):  
Disaster Response ◽  
Analytic Solutions ◽  
Design Decisions ◽  
Content Type ◽  
Effective Strategies ◽  
Humanitarian Organizations ◽  
State Dependent ◽  
Relief Distribution ◽  
Set Up ◽  
The Impact

Purpose Relief item distribution to victims is a key activity during disaster response. Currently many humanitarian organizations follow simple guidelines based on experience to assess need and distribute relief supplies. However, the interviews with practitioners suggest a problem in efficiency in relief distribution efforts. The purpose of this paper is to develop a model and solution methodology that can estimate relief center (RC) performance, measured by waiting time for victims and throughput, for any RC design and analyze the impact of key design decisions on these performance measures. Design/methodology/approach Interviews with practitioners and current practice guidelines are used to understand relief distribution and a queuing network model is used to represent the relief distribution. Finally, the model is applied to data from the 2015 Nepal earthquake. Findings The findings identify that dissipating congestion created by crowds, varying item assignment decisions to points of distribution, limiting the physical RC capacity to control congestion and using triage queue to balance distribution times, are effective strategies that can improve RC performance. Research limitations/implications This research bases the RC designs on Federal Emergency Management Agency guidelines and assumes a certain area and volunteer availability. Originality/value This paper contributes to humanitarian logistics by discussing useful insights that can impact how relief agencies set up and operate RCs. It also contributes to the queuing literature by deriving analytic solutions for the steady state probabilities of finite capacity, state dependent queues with blocking.

scholarly journals Discussion on Reservoir dispatch during a sudden accident of water pollution in a long distance river

2018 ◽  
Vol 246 ◽  
pp. 01004
Author(s):  
Shen-guang Fang ◽  
Li-qin Cui ◽  
He Yong
Keyword(s):  
Water Pollution ◽  
Storage Capacity ◽  
Analytic Solutions ◽  
Time Duration ◽  
Long Distance ◽  
Long Time ◽  
Set Up ◽  
Sudden Water Pollution ◽  
Short Time ◽  
And Diffusion

A mathematical model of river hydrodynamics with cascade reservoirs and pollutant has been established and verified by using analytic solutions of partial differential equation for transportation and diffusion. Ten dispatch schedules of single or multi- reservoirs have been set up and executed according to that a pollution accident occurred upstream or downstream to a reservoir. It shows that which dispatch schedule should be selected was decided by sensitive factors of a target river segment downstream. A dispatch model of large flux with short time duration by utilizing a reservoir nearest to the segment was more appropriate for which was more sensitive to concentration than other factors, while a model of appropriate flux discharge with long time duration was more suitable for those being more sensitive to extra concentration retention of pollutants. Compared with a single reservoir dispatch, multi-reservoirs have larger effective storage capacity to reduce the loss by a sudden water pollution accident better by supplement water step by step from upstream to downstream.

A Fluid Film Squeezed Between Two Rotating Parallel Plane Surfaces

1985 ◽  
Vol 107 (1) ◽  
pp. 110-115 ◽  
Author(s):  
E. A. Hamza
Keyword(s):  
Numerical Solution ◽  
Nonlinear Equations ◽  
Load Capacity ◽  
Equations Of Motion ◽  
Analytic Solutions ◽  
Parallel Plane ◽  
Fluid Film ◽  
Inertial Forces ◽  
Nonlinear Equations Of Motion ◽  
Radial Outflow

This paper is concerned with the motion of a fluid film squeezed between two rotating parallel plane surfaces. Attention is given to the case of impulsive squeezing and impulsive rotation. Approximate analytic solutions are obtained and a numerical solution to the full nonlinear equations of motion is presented. The results show that the centrifugal inertial forces increase the radial outflow and reduce considerably the load capacity while the noncentrifugal inertial forces increase the torque.

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