scholarly journals Vapour - Liquid Equilibrium Properties for Two- and Three-dimensional Lennard-Jones Fluids from Equations of State

1999 ◽  
Vol 52 (1) ◽  
pp. 101 ◽  
Author(s):  
A. Mulero ◽  
F. Cuadros ◽  
C. A. Faúndez
Keyword(s):  
Equations Of State ◽  
Three Dimensional ◽  
Numerical Data ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Liquid Equilibrium ◽  
Lennard Jones ◽  
Semi Empirical ◽  
Coexistence Densities ◽  
Good Agreement

Vapour–liquid equilibrium properties for both three- and two-dimensional Lennard-Jones fluids were obtained using simple cubic-in-density equations of state proposed by the authors. Results were compared with those obtained by other workers from computer simulations and also with results given by other more complex semi-theoretical or semi-empirical equations of state. In the three-dimensional case good agreement is found for all properties and all temperatures. In the two-dimensional case only the coexistence densities were compared, producing good agreement for low temperatures only. The present work is the first to give numerical data for the vapour–liquid equilibrium properties of Lennard-Jones fluids calculated from equations of state.

Torque and Cavitation Characteristics of Butterfly Valves

1961 ◽  
Vol 28 (4) ◽  
pp. 511-518 ◽  
Author(s):  
Turgut Sarpkaya
Keyword(s):  
Approximate Solution ◽  
Three Dimensional ◽  
Relaxation Technique ◽  
Dimensional Case ◽  
Practical Case ◽  
Two Dimensional ◽  
Actual Flow ◽  
Theoretical Results ◽  
Good Agreement

The present study deals with torque and cavitation characteristics of idealized two-dimensional and axially symmetrical butterfly valves. Theoretical results obtained for the two-dimensional case are compared with the ones obtained experimentally and by a relaxation technique. Based on the results of the two-dimensional case, an approximate solution is presented for the more general and practical case of three-dimensional butterfly valves. The results are in good agreement with the actual flow tests.

scholarly journals Anharmonic Self-Consistent Theory of Crystals. II. The 2d and 3d Quartic Crystal Models

1994 ◽  
Vol 49 (6) ◽  
pp. 663-670
Author(s):  
S. Sh. Soulayman ◽  
C. Ch. Marti ◽  
Ch. Ch. Guilpin
Keyword(s):  
Helmholtz Free Energy ◽  
Equations Of State ◽  
Three Dimensional ◽  
Inert Gases ◽  
Thermoelastic Properties ◽  
Consistent Theory ◽  
Jones Potential ◽  
Lennard Jones ◽  
2D And 3D ◽  
Strong Anharmonicity

Abstract In this paper we apply the method developed in part I for describing the crystalline state of two and three dimensional inert gases. For strong anharmonicity of fourth order, the equations of state of these gases are obtained. This way we calculate the thermoelastic properties of two and three dimensional argon, krypton and xenon using the Lennard-Jones potential. The corrections to the Helmholtz free energy and thermodynamic properties due to quantum effects are considered. The results are compared with the available experimental data.

Three-dimensional disturbances to a mixing layer in the nonlinear critical-layer regime

1995 ◽  
Vol 291 ◽  
pp. 57-81 ◽  
Author(s):  
S. M. Churilov ◽  
I. G. Shukhman
Keyword(s):  
Travelling Waves ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Critical Layer ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
New Type ◽  
Two Stages

We consider the nonlinear spatial evolution in the streamwise direction of slightly three-dimensional disturbances in the form of oblique travelling waves (with spanwise wavenumber kz much less than the streamwise one kx) in a mixing layer vx = u(y) at large Reynolds numbers. A study is made of the transition (with the growth of amplitude) to the regime of a nonlinear critical layer (CL) from regimes of a viscous CL and an unsteady CL, which we have investigated earlier (Churilov & Shukhman 1994). We have found a new type of transition to the nonlinear CL regime that has no analogy in the two-dimensional case, namely the transition from a stage of ‘explosive’ development. A nonlinear evolution equation is obtained which describes the development of disturbances in a regime of a quasi-steady nonlinear CL. We show that unlike the two-dimensional case there are two stages of disturbance growth after transition. In the first stage (immediately after transition) the amplitude A increases as x. Later, at the second stage, the ‘classical’ law A ∼ x2/3 is reached, which is usual for two-dimensional disturbances. It is demonstrated that with the growth of kz the region of three-dimensional behaviour is expanded, in particular the amplitude threshold of transition to the nonlinear CL regime from a stage of ‘explosive’ development rises and therefore in the ‘strongly three-dimensional’ limit kz = O(kx) such a transition cannot be realized in the framework of weakly nonlinear theory.

Prediction of Blade Flutter in a Tuned Rotor

1985 ◽  
Author(s):  
Jianmin Xu ◽  
Zhaohong Song
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Rotating Blades ◽  
Multiple Degrees Of Freedom ◽  
Strip Theory ◽  
Blade Flutter ◽  
Good Agreement

This paper is about blade flutter in a tuned rotor. With the aid of the combination of three dimensional structural finite element method, two dimensional aerodynamical finite difference method and strip theory, the quasi-steady models in which two degrees of freedom for a single wing were considered have been extended to multiple degrees of freedom for the whole blade in a tuned rotor. The eigenvalues solved from the blade motion equation have been used to judge whether the system is stable or not. The calculating procedure has been formed and using it the first stage rotating blades of a compressor where flutter had occurred, have been predicted. The numerical flutter boundaries have good agreement with the experimental ones.

On the Hydrodynamic Interaction Between Ship and Free-Surface Motions on Vessels With Moonpools

2019 ◽  
Author(s):  
Senthuran Ravinthrakumar ◽  
Trygve Kristiansen ◽  
Babak Ommani
Keyword(s):  
Free Surface ◽  
Flow Separation ◽  
Coupling Effect ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Navier Stokes ◽  
Linear Potential ◽  
Two Dimensional ◽  
Sloshing Mode ◽  
Vessel Motion

Abstract Coupling between moonpool resonance and vessel motion is investigated in two-dimensional and quasi three-dimensional settings, where the models are studied in forced heave and in freely floating conditions. The two-dimensional setups are with a recess, while the quasi three-dimensional setups are without recess. One configuration with recess is presented for the two-dimensional case, while three different moonpool sizes (without recess) are tested for the quasi three-dimensional setup. A large number of forcing periods, and three wave steepnesses are tested. Boundary Element Method (BEM) and Viscous BEM (VBEM) time-domain codes based on linear potential flow theory, and a Navier–Stokes solver with linear free-surface and body-boundary conditions, are implemented to investigate resonant motion of the free-surface and the model. Damping due to flow separation from the sharp corners of the moonpool inlets is shown to matter for both vessel motions and moonpool response around the piston mode. In general, the CFD simulations compare well with the experimental results. BEM over-predicts the response significantly at resonance. VBEM provides improved results compared to the BEM, but still over-predicts the response. In the two-dimensional study there are significant coupling effects between heave, pitch and moonpool responses. In the quasi three-dimensional tests, the coupling effect is reduced significantly as the moonpool dimensions relative to the displaced volume of the ship is reduced. The first sloshing mode is investigated in the two-dimensional case. The studies show that damping due to flow separation is dominant. The vessel motions are unaffected by the moonpool response around the first sloshing mode.

Numerical Model of Three-Dimensional Motion of Plate-Type Wind-Borne Debris Based on Quaternions and its Improvement in Unsteady Flow

2013 ◽  
Vol 405-408 ◽  
pp. 2399-2408 ◽  
Author(s):  
An Min Fu ◽  
Peng Huang ◽  
Ming Gu
Keyword(s):  
Numerical Model ◽  
Unsteady Flow ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Moment Coefficient ◽  
Flight Mode ◽  
Gimbal Lock ◽  
Improved Model ◽  
Plate Type ◽  
Good Agreement

A numerical model of three-dimensional motion of plate-type wind-borne debris in uniform wind field based on quaternions is proposed in this paper. This model can simulate the complex 3D spinning flight robustly and efficiently with rotational quaternions, which are also free from the gimbal lock that is associated with Euler rotational matrix. The predictions from the model were then compared with the results of another quasi-steady model, and good agreement is found. For the unsteady flow involved in autorotational flight mode, the present model was improved by revising the damping moment in order to simulate the two-dimensional motion of plates with higher accuracy. Calibration of the damping moment coefficient was performed through a direct comparison of the predicted non-dimensional angular velocity with the results of CFD-RBD model. The predictions of the improved model agree reasonably well with the CFD-RBD results, which verifies the accuracy of the improved model in predicting the two-dimensional trajectories of plates.

Pipe Response Under Concentrated Lateral Loads and External Pressure

2005 ◽  
Author(s):  
Spyros A. Karamanos ◽  
Charis Eleftheriadis
Keyword(s):  
Three Dimensional ◽  
External Pressure ◽  
Absorption Capacity ◽  
Pressure Effects ◽  
Analytical Models ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Lateral Loads ◽  
Offshore Pipelines ◽  
Different Levels

The present paper examines the denting deformation of offshore pipelines and tubular members (D/t≤50) subjected to lateral (transverse) quasi-static loading in the presence of uniform external pressure. Particular emphasis is given on pressure effects on the ultimate lateral load of tubes and on their energy absorption capacity. Pipe segments are modeled with shell finite elements, accounting for geometric and material nonlinearities, and give very good predictions compared with test data from non-pressurized pipes. Lateral loading between two rigid plates, a two-dimensional case, is examined first. Three-dimensional case, are also analyzed, where the load is applied either through a pair of opposite wedge-shaped denting tools or a single spherical denting tool. Load-deflection curves for different levels of external pressure are presented, which indicate that pressure has significant influence on pipe response and strength. Finally, simplified analytical models are proposed for the two-dimensional and three-dimensional load configurations, which yield closed-form expressions, compare fairly well with the finite element results and illustrate some important features of pipeline response in a clear and elegant manner.

scholarly journals The interaction of atoms and molecules with solid surfaces XII—Critical phenomena in a two-dimensional gas

1937 ◽  
Vol 163 (912) ◽  
pp. 132-138 ◽  
Keyword(s):  
Critical Temperature ◽  
Equation Of State ◽  
Critical Phenomena ◽  
Three Dimensional ◽  
Inert Gases ◽  
Two Dimensional ◽  
Lennard Jones ◽  
Low Concentrations ◽  
High Concentrations ◽  
The Right

In a paper recently published by Professor Lennard-Jones and the author (Lennard-Jones and Devonshire 1937) the equation of state of a gas at high concentrations has been calculated in terms of the interatomic fields. The equation found had the right kind of properties and, in particular, using the interatomic fields previously determined from the observed equation of state at low concentrations (Lennard-Jones 1931), the critical temperature was given correctly to within a few degrees for the inert gases. In this paper we shall apply the same method to determine the equation of state of a two-dimensional gas. Although such a gas cannot strictly be obtained in practice, an inert gas adsorbed on a surface (or in fact any gas held by van der Waals’ forces only) would probably behave very much like one, the fluctuations of the potential field over the surface not being of much importance. In confirmation of this it may be noted that the specific heat of argon adsorbed on charcoal was found by Simon (Simon 1935) to be equal to that of a perfect two-dimensional gas down to 60° K. A gas adsorbed on a liquid would be an even better representation of a two-dimensional one. Some measurements on the adsorption of krypton and xenon on liquid mercury have been made by Cassel and Neugebauer (Cassel and Neugebauer 1936), and they found no trace of any critical phenomena though they worked at temperatures considerably below the critical temperature of xenon. Our results are in agreement with this, for they show that the critical temperature of a two-dimensional gas should be about half that of the corresponding three-dimensional one.

Numerical and experimental analysis of two-dimensional separated flows over a flexible sail

2002 ◽  
Vol 466 ◽  
pp. 319-341 ◽  
Author(s):  
O. LORILLU ◽  
R. WEBER ◽  
J. HUREAU
Keyword(s):  
Velocity Field ◽  
Numerical Data ◽  
Separated Flows ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Two Dimensional Model ◽  
Wake Model ◽  
Lift And Drag ◽  
Particle Imaging ◽  
Good Agreement

This paper is a numerical analysis of the flow over a exible sail with the usual two-dimensional model of ideal weightless incompressible fluid. The sail is assumed to be impervious, inelastic and weightless, and may or may not be mounted on a mast. Separated or attached flows are considered at any angle of attack. Our method is validated by numerical and experimental results, i.e. the sail shape and velocity field are determined by particle imaging velocimetry, and lift and drag by aerodynamic balance. Despite the simplicity of the wake model we use (the Helmholtz model), the computed free streamline geometry and especially the sail shape are in good agreement with the experimental and numerical data.

A Study of Wear Rate Estimation of Coatings by a Numerical Method

2011 ◽  
Vol 675-677 ◽  
pp. 675-680 ◽  
Author(s):  
Yu Sen Yang ◽  
Wesley Huang
Keyword(s):  
Mathematical Model ◽  
Mathematical Method ◽  
Three Dimensional ◽  
Numerical Algorithms ◽  
Numerical Data ◽  
Wear Volume ◽  
Two Dimensional ◽  
Considerable Time ◽  
Volume Measurements ◽  
Ball On Disc

The paper reported using a mathematical model that simulated the wear volume in comparison to measurement by a ball-on-disc for deposited CrN films on tool steel (JIS SKD11). Three dimensional profile instruments were used to measure the wear scar trace for variations of numerical data of two dimensional profiles. By using numerical algorithms, the wear volume measurements of wear profiles are to save considerable time and economical. A new mathematical method is issued for determining wear volumes in this study. The estimated results were precisely fitted as compared with other calculations for three dimensional estimations of wear volumes.

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