First Paper: A General Approach to Hydraulic Lock

1967 ◽  
Vol 182 (1) ◽  
pp. 595-602 ◽  
Author(s):  
P. Dransfield ◽  
D. M. Bruce ◽  
M. Wadsworth
Keyword(s):  
Reynolds Equation ◽  
Lateral Force ◽  
Hydraulic Control ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Particular Solutions ◽  
Piston Cylinder ◽  
The One ◽  
Hydraulic Control System ◽  
General Method

The present state of knowledge on the hydraulic lock phenomena of oil hydraulic control system components is reviewed briefly. A general one-dimensional solution of the Reynolds equation which governs hydraulic lock is presented. The solution embraces the particular solutions of past workers, and allows ready solution for piston-cylinder configurations for which a one-dimensional solution is adequate. A general method for making full solutions of the Reynolds equation is presented, requiring the use of a digital computer for particular solutions. Pressure distribution, the lateral force on the piston which produces hydraulic lock, and the location of the lateral force can be obtained. The commonly occurring case of a single-land piston lying tilted in its bore is examined in detail. The limit of accuracy of a one-dimensional solution is clearly shown by illustrating the discrepancies between the one-dimensional and two-dimensional solutions for several configurations.

Comparison Between Exact and One-Dimensional Theories for Incipient Melting in Reentry Simulation

1966 ◽  
Vol 88 (4) ◽  
pp. 428-434 ◽  
Author(s):  
Richard A. Matula
Keyword(s):  
Temperature Distribution ◽  
Transient Temperature ◽  
Stagnation Temperature ◽  
Free Flight ◽  
Dimensional Solution ◽  
Radial Temperature ◽  
One Dimensional ◽  
Flight Range ◽  
Wide Range ◽  
The One

The exact transient temperature distribution in a spherical region subjected to an axisymmetric reentry heat flux has been evaluated. The results are presented in terms of nondimensional parameters, therefore they are valid for a wide range of materials, flight conditions, and nose radii. The angular dependence of the surface temperature is given as a function of time. It is also shown that the true radial temperature distribution can be represented by an exponential function. Finally, the solution is applied to reentry ablation onset studies that are being conducted in the free-flight range of the GM Defense Research Laboratories. The exact solution and the one-dimensional theory for the stagnation temperature rise of a model simulating reentry conditions in the free-flight range are compared. It is shown that the validity of the one-dimensional solution is dependent on the flight time, material properties, and nose radius of the model. Assuming that a temperature can be assigned which corresponds to incipient ablation, the present analysis is particularly useful in the prediction of ablation onset.

Two-Dimensional Analysis of Conduction-Controlled Rewetting With Precursory Cooling

1976 ◽  
Vol 98 (3) ◽  
pp. 407-413 ◽  
Author(s):  
S. S. Dua ◽  
C. L. Tien
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Dimensional Analysis ◽  
Vertical Surface ◽  
Dimensionless Temperature ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
One Dimensional ◽  
The One

This paper presents a two-dimensional analysis of the effect of precursory cooling on conduction-controlled rewetting of a vertical surface, whose initial temperature is higher than the sputtering temperature. Precursory cooling refers to the cooling caused by the droplet-vapor mixture in the region immediately ahead of the wet front, and is described mathematically by two dimensionless constants which characterize its magnitude and the region of influence. The physical model developed to account for precursory cooling consists of an infinitely extended vertical surface with the dry region ahead of the wet front characterized by an exponentially decaying heat flux and the wet region behind the moving film-front associated with a constant heat transfer coefficient. Apart from the two dimensionless constants describing the extent of precursory cooling, the physical problem is characterized by three dimensionless groups: the Peclet number or the dimensionless wetting velocity, the Biot number and a dimensionless temperature. Limiting solutions for large and small Peclet numbers have been obtained utilizing the Wiener-Hopf technique coupled with appropriate kernel substitutions. A semiempirical matching relation is then devised for the entire range of Peclet numbers. Existing experimental data with variable flow rates at atmospheric pressure are very closely correlated by the present model. Finally a comparison is drawn between the one-dimensional limit of the present analysis and the corresponding one-dimensional solution obtained by treating the dry region ahead of the wet front characterized by an exponentially decaying heat transfer coefficient.

The One-Dimensional Analysis of Oscillatory Heat Transfer in a Fin Assembly

1992 ◽  
Vol 114 (3) ◽  
pp. 548-552 ◽  
Author(s):  
J. M. Houghton ◽  
D. B. Ingham ◽  
P. J. Heggs
Keyword(s):  
Heat Transfer ◽  
Thermal Effects ◽  
Transient Heat Transfer ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Extended Surface ◽  
Extended Surfaces ◽  
The One ◽  
Physical Boundary ◽  
Surface Heat Exchanger

Studies of the transient heat transfer within extended surfaces have so far considered the fins in isolation. The isolated fin model is not representative of the physical boundary conditions within an extended surface heat exchanger since it does not account for the thermal effects of the supporting interface. The aim of this study is to extend the work on transient heat transfer within finned surfaces by incorporating the supporting wall in the problem. A mathematical one-dimensional solution for harmonic oscillatory heat transfer in a fin assembly is derived. It is concluded that, unlike steady-state situations, the transient heat transfer in a fin assembly can only be found by considering both the wall and the fins simultaneously.

Air Temperature Distribution Inside of a Longitudinal Highway Tunnel: A Case Study

2012 ◽  
Vol 433-440 ◽  
pp. 6384-6389 ◽  
Author(s):  
Xing Han ◽  
Xu Zhang
Keyword(s):  
Steady State ◽  
Temperature Distribution ◽  
Air Temperature ◽  
State Theory ◽  
One Dimensional ◽  
Highway Tunnel ◽  
Temperature Enhancement ◽  
The One ◽  
General Method

With the development of tunneling technology and the increase of transportation, the mobiles are discharging more and more heat into the tunnel nowadays, which will cause the temperature enhancement. In this paper, general method of calculating the heat discharge is studied, and temperature distribution in the tunnels, which use different ventilation systems, is studied according to the one-dimensional steady state theory. One tunnel is taken for example to calculate the temperature distribution. The result can b e used in the relevant design and research.

A Simplified One-Dimensional Thermal Model for Journal Bearings

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Daquan Liu ◽  
Wen Zhang ◽  
Tiesheng Zheng
Keyword(s):  
Thermal Effects ◽  
Thermal Model ◽  
Reynolds Equation ◽  
Computing Time ◽  
One Dimensional ◽  
Lubricating Film ◽  
Direct Solution Method ◽  
The One ◽  
Generalized Reynolds Equation ◽  
Good Agreement

The variational approach, which is used to solve the Reynolds equation based on the assumption of constant temperature, is extended to the generalized Reynolds equation calculation. The direct solution method of the generalized Reynolds equation is presented, where the pressure of the nodal points and the cavitation zone boundary of the film can be determined without iterating. A simplified one-dimensional thermal model is built on the basis of the original two-dimensional thermal model. The model not only concerns the thermal effects of the lubricating film, but also offers a direct and rapid numerical algorithm for solving lubricating film temperature field. The numerical results of the temperature distributions for the one model are in good agreement with experiment, and less computing time is needed.

scholarly journals Currents induced by long waves propagating towards a beach over a wavy bed

2000 ◽  
Vol 413 ◽  
pp. 317-343 ◽  
Author(s):  
H. KYOTOH ◽  
S. FUJII ◽  
D. V. TO
Keyword(s):  
Mass Flux ◽  
Wave Motion ◽  
Shallow Water Equation ◽  
Swash Zone ◽  
Two Dimensional ◽  
Maclaurin Series ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Bed Slope ◽  
The One

For the understanding of longshore currents along a natural beach, the effects of bottom unevenness are considered to be important, especially for the flow in the swash zone. Currents in the swash zone are strongly influenced by the bed slope because the effect of gravity overwhelms the effect of the depth change. In the present paper, we investigate these effects and focus on waves propagating from offshore over a flat ocean basin of constant depth to a beach with a sloping wavy bottom. The waves are incident at a small angle to the beach normal, and the bed slope in the alongshore direction is varied slowly. To simplify the problem, only cnoidal waves and solitary waves are considered and the bed level is varied sinusoidally in the longshore direction.A perturbation method is applied to the two-dimensional nonlinear shallow water equation (two-dimensional NLSWE) for the wave motion in order to generate a more simplified model of wave dynamics consisting of a one-dimensional NLSWE for the direction normal to the beach and an equation for the alongshore direction. The first equation, the one-dimensional NLSWE, is solved by Carrier & Greenspan's transformation. The solution of the second one is found by extending Brocchini & Peregrine's solution for a flat beach. Two methods for the solution of the one- dimensional NLSWE are introduced in order to get a solution applicable to large-amplitude swash motions, where the amplitude is comparable to the beach length. One is the Maclaurin expansion of the solution around the moving shoreline, and the other is Riemann's representation of the solution, which exactly satisfies the one-dimensional NLSWE and the boundary conditions. After doing a consistency check by confirming that Riemann's method, a numerical solution, agrees with the exact solution for an infinitely long, sloping beach, we assumed that the Maclaurin series solution can also describe wave motion in the swash zone properly not only for this model but also for our ‘wavy’, finite beach model.The solution obtained from the Maclaurin series is then plugged into the equation for the alongshore direction to calculate the shore currents induced by wave run-up and back-wash motions, where a ‘weakly two-dimensional solution’ is derived from geometrical considerations. The results show that since the water depth near the shoreline is comparable to the bed level fluctuations, the flow is strongly affected by the bed unevenness, leading to recognizable changes in shoreline movement and the time-averaged velocity and the mass flux of the flow in the swash zone. More specifically, the inhomogeneity of the alongshore mass flux generates offshore currents because of the continuity condition for the fluid mass.

Elastic Deformation of Surface Roughness in Thin Film Hydrodynamic Lubrication

2011 ◽  
Author(s):  
Kazuyuki Yagi ◽  
Joichi Sugimura
Keyword(s):  
Thin Film ◽  
Elastic Deformation ◽  
Small Amplitude ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Rigid Surface ◽  
Local Pressure ◽  
One Dimensional ◽  
Compliant Surface ◽  
The One

In the current study, the influence of elastic deformation in thin film hydrodynamic lubrication was numerically investigated. The one dimensional Reynolds equation was solved with considering the piezoviscosity effect of the lubricant and elastic deformation of the sliding surface in flat-flat contacts. The contact area comprised of a stationary rigid surface with sine waves with amplitude of several nano meters and a moving flat compliant surface. The obtained numerical results show that small amplitude of roughness compared with the averaged film thickness influences the pressure distribution of the hydrodynamic film. Reduction of the roughness and decay in wave of the roughness occurred because of the elastic deformation induced by local pressure generation.

Nonlinear Ion Acoustic Waves in a Magnetized Dusty Plasma in the Presence of Nonthermal Electrons

2009 ◽  
Vol 64 (5-6) ◽  
pp. 370-376 ◽  
Author(s):  
Taraknath Saha ◽  
Prasanta Chatterjee ◽  
Mohamed Ruhul Amin
Keyword(s):  
Dusty Plasma ◽  
Acoustic Waves ◽  
Two Dimensional ◽  
Ion Acoustic Waves ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Nonthermal Electrons ◽  
Magnetized Dusty Plasma ◽  
Ion Acoustic ◽  
The One

The Kadomtsev-Petviashili (KP) equation is derived for weakly nonlinear ion acoustic waves in a magnetized dusty plasma in the presence of nonthermal electrons. Soliton solutions are obtained in both the one-dimensional and two-dimensional framework. For the one-dimensional soliton solution the ‘tanh’ method is considered while the two-dimensional solution is obtained by a method introduced by S.V. Manacov et al., Phys. Lett. A 63, 205 (1977). It is found that in case of the onedimensional solution, both compressive and rarefactive solitary waves exist which could be obtained depending on the ratio of the electron and ion density. It is also seen that the nonthermal distribution of electrons has some significant effect in the shape of both the one-dimensional and two-dimensional solitary wave.

Sign in / Sign up

Export Citation Format

Share Document