Pressure Distribution Function Research Articles

Some thermodynamic properties of fluids SF6, SF6–Ar, and SF6–Kr using new HFD-like potentials including three-body interactions: The inversion method and molecular dynamics simulation

A new pair-potential energy function of sulfur hexafluoride has been determined via the inversion of reduced viscosity collision integrals at zero pressure and fitted to obtain a Hartree–Fock dispersion (HFD)-like potential form. The pair-potential reproduces the second virial coefficient and transport properties of sulfur hexafluoride in a good accordance with experimental data over wide ranges of temperatures. Molecular dynamics (MD) simulation has been also performed to obtain pressure, self-diffusion coefficient, and radial distribution function of fluid sulfur hexafluoride at different temperatures and densities using the calculated HFD-like pair-potential. We have also obtained pressures of SF6–Ar and SF6–Kr fluid mixtures at constant temperature at different densities using new two-body HFD-like models. To take higher-body forces into account, three-body potentials of Wang and Sadus (2006) [22,23] and Hauschild and Prausnitz (1993) [24] have been used with the two-body HFD-like potentials of SF6, SF6–Ar, and SF6–Kr systems to improve the prediction of the calculated properties without requiring an expensive three-body calculation. The MD simulation of sulfur hexafluoride has been also used to determine a new equation of state.

Consolidation Behavior of Soils Subjected to Asymmetric Initial Excess Pore Pressure Distributions with One-Way Drainage

A consolidating clay layer can be singly or doubly drained. The degree of consolidation is a function of the initial excess pore pressure distribution and the drainage conditions. Traditional geotechnical engineering practice assumes a uniform initial excess pore pressure distribution, for which the singly drained and doubly drained solutions to Terzaghi's one-dimensional consolidation theory are available in most textbooks. In this paper, several symmetric and asymmetric initial excess pore pressure distributions are studied using a series solution method. Excess pore pressure isochrones and average degree of consolidation plots are generated for all cases, assuming an impervious boundary at the base of the clay stratum. These plots enable users to determine the average degree of consolidation and pore pressure at a specific depth for a variety of loading scenarios. Pore pressure redistribution is also clearly more prevalent in singly drained clays, where pore-water pressures at certain depths increase at certain times, a phenomenon not generally expected during consolidation.

Additional interfacial force in lattice Boltzmann models for incompressible multiphase flows

The existing lattice Boltzmann models for incompressible multiphase flows are mostly constructed with two distribution functions: one is the order parameter distribution function, which is used to track the interface between different phases, and the other is the pressure distribution function for solving the velocity field. In this paper, it is shown that in these models the recovered momentum equation is inconsistent with the target one: an additional force is included in the recovered momentum equation. The additional force has the following features. First, it is proportional to the macroscopic velocity. Second, it is zero in every single-phase region but is nonzero in the interface. Therefore it can be interpreted as an interfacial force. To investigate the effects of the additional interfacial force, numerical simulations are carried out for the problem of Rayleigh-Taylor instability, droplet splashing on a thin liquid film, and the evolution of a falling droplet under gravity. Numerical results demonstrate that, with the increase of the velocity or the Reynolds number, the additional interfacial force will gradually have an important influence on the interface and affect the numerical accuracy.

Research on Roll Force for Variable Gauge Rolling

The production of materials saving products such as Longitude Profile plates (LP plate) and Tailor Rolled Blanks (TRB) needs to solve the problem of the calculation of variable gauge rolling (VGR) parameters. It has been proved that Karman differential equation of force equilibrium for simple rolling is a special case of VGR equations when vy＝0. Differential equations of force equilibrium for both upwards rolling and downwards rolling were solved and the rolling pressure distribution function for VGR was got in this paper. Finally, details of a set of experiments were presented and the theoretical model of rolling force was proved to be reasonable.

Transport, thermodynamic, and structural properties of fluid ammonia using a new intermolecular potential: The inversion method and molecular dynamics simulation

A new pair-potential energy function of ammonia has been determined via the inversion of reduced viscosity collision integrals and fitted to obtain a Hartree–Fock dispersion (HFD)-like potential form. The pair-potential reproduces the second virial coefficient, viscosity, thermal conductivity, and self-diffusion coefficient of ammonia in a good accordance with experimental data over wide ranges of temperatures. Molecular dynamics (MD) simulation has been also performed to obtain pressure, self-diffusion coefficient, and radial distribution function of fluid ammonia at different temperatures and densities using the calculated HFD-like pair-potential. To take higher-body forces into account, three-body potential of Hauschild and Prausnitz (1993) [19] extended as a function of density and temperature and used with the HFD-like potential to improve the prediction of the pressures of fluid ammonia without requiring an expensive three-body calculation. The results are in a good agreement with experiment and literature values.

Contact of an asymmetrical rounded apex wedge with a half plane

Two-dimensional elastic contact problem of an asymmetrical rounded apex wedge with a half plane is considered and an analytical solution is presented for vertical and horizontal external loading in the presence of coulomb friction. The pressure and shear distribution functions are found in closed form under partial slip condition. Further by utilizing a new relation Muskhelishvili’s potential function is obtained and results are analyzed. Designing better cutting tools, selecting fretting fatigue test pads and deeper lap joint analyzing are several practical applications of the outcomes.

Development of the theory of a self-consistent field for polyelectrolyte solutions

A new theoretical approach to calculating the thermodynamic and structure functions of polyelectrolyte solutions is proposed, based on the method of Gaussian equivalent representation for calculating the functional integrals. Formulas for the mean-force potential, osmotic pressure, and complete monomer-monomer pair distribution functions are presented. A sodium polystyrene sulfonate solution with NaCl additives is considered as an example.

A direct‐forcing pressure‐based lattice Boltzmann method for solving fluid–particle interaction problems

AbstractA direct‐forcing immersed boundary‐lattice Boltzmann method (IB–LBM) is developed to simulate fluid–particle interaction problems. This method uses the pressure‐based LBM to solve the incompressible flow field and the immersed boundary method to handle the fluid–particle interactions. The pressure‐based LBM uses the pressure distribution functions instead of the density distribution functions as the independent dynamic variables. The main idea is to explicitly eliminate the compressible effect due to the density fluctuation. In the IB method, a direct‐forcing method is introduced to capture the particle motion. It directly computes an IB force density at each lattice grid from the differences between the pressure distribution functions obtained by the LBM and the equilibrium pressure distribution functions computed from the particle velocity. By applying this direct‐forcing method, the IB–LBM becomes a purely LBM version. Also, by applying the Gauss theorem, the formulas for computing the force and the torque acting on the particle from the flows are derived from the volume integrals over the particle volume instead of from the surface integrals over the particle surface. The order of accuracy of the IB–LBM is demonstrated on the errors of velocity field, wall stress, and gradients of velocity and pressure. As a demonstration of the efficiency and capabilities of the new method, sedimentation of a large number of spherical particles in an enclosure is simulated. Copyright © 2010 John Wiley & Sons, Ltd.

Simulation of flow and heat transfer with evaporation in a porous wick of a CPL evaporator on pore scale by lattice Boltzmann method

A three-dimensional transient double-population thermal lattice Boltzmann BGK scheme for the global evaporator of a CPL is proposed to describe the heat and mass transfer in the porous wick, the cover plate and the vapor groove. The lattice BGK D3Q6 model, developed on passive-scalar approach, is proposed to represent the energy distribution function. The D3G15 incompressible lattice BGK model is chosen to represent the pressure distribution function to calculate the pressure and velocity fields. The random porous structure is reconstructed by the quartet structure generation set (QSGS) and is coupled to the lattice Boltzmann method (LBM) by some special boundary schemes for pore scale simulation. The numerical results of different working conditions and different working fluids are presented, which can improve the understandings of heat and mass transport mechanisms in a CPL evaporator and provide guidance for the evaporator design in a CPL system.

Theoretical Study of Static and Dynamic Characteristics for Eccentric Cylinders Lubricated With Ferrofluid

The aim of this study is to explore the static and dynamic performance characteristics of finite journal bearings lubricated with a non-Newtonian ferrofluid in the presence of an external magnetic field using the spectral method technique. The modified Reynolds equation governing the film pressure, coming out from the combination of the momentum and continuity equations, is derived. We use the pressure distribution function to study the static and dynamic characteristics and the stability of the given system. Numerical applications are achieved in order to investigate the influence of the various parameters on the stability behavior of the system. For instance, it is observed that the journal loci get stable as the magnetic force increases. The non-Newtonian, the distance ratio, and the magnetic parameters play an important role in administrating the stability behavior. The non-Newtonian parameter is found to stabilize the system, while the magnetic force coefficient destabilizes it. Furthermore, for law eccentricity ratios, the stability of this system is significant.

The effects of focused transducer geometry and sample size on the measurement of ultrasonic transmission properties

The response of two coaxially aligned weakly focused ultrasonic transducers, typical of those employed for measuring the attenuation of small samples using the immersion method, has been investigated. The effects of the sample size on transmission measurements have been analyzed by integrating the sound pressure distribution functions of the radiator and receiver over different limits to determine the size of the region that contributes to the system response. The results enable the errors introduced into measurements of attenuation to be estimated as a function of sample size. A theoretical expression has been used to examine how the transducer separation affects the receiver output. The calculations are compared with an experimental study of the axial response of three unpaired transducers in water. The separation of each transducer pair giving the maximum response was determined, and compared with the field characteristics of the individual transducers. The optimum transducer separation, for accurate estimation of sample properties, was found to fall between the sum of the focal distances and the sum of the geometric focal lengths as this reduced diffraction errors.

Analysis of the Stress Intensity of Rotor Blade in Hydraulic Retarder

Based on CFD numeric simulation for hydraulic retarder under full-filled condition, the pressure distribution functions of the rotor blades surfaces are approached by coordinate transformation and surface fitting. Through the APDL program, loads which involved not only centrifugal force but also flow pressure are loaded on the FEA model according to the approximating pressure functions. The FEA model is solved and the blades strength is analyzed more accurately. Noted moment and speed, that is respectively 4000 N • m and 1343rpm, is determined under the promise of blade strength, and controlling strategy is made that constant braking torque shoud be carried out when speed is higher than noted value .

Interaction of a hollow cylinder of finite length and a plate with a cylindrical cavity with a rigid insert

Two problems of the interaction of a hollow circular cylinder with load-free ends and an unbounded plate with a cylindrical cavity and a symmetrically imbedded rigid insert are considered. Homogeneous solutions are found and the generalized orthogonality of these solutions is used when the modified boundary conditions are satisfied. As a result, we have a system of two integral equations in functions of the displacements of the outer and inner surfaces of the hollow cylinder. These functions are sought in the form of sums of a trigonometric series and a power function with a root singularity. The ill-posed infinite systems of linear algebraic equations obtained are regularized by the introduction of small positive parameters. Since the elements of the matrices of the systems as well as the contact stresses are defined by poorly converging numerical and functional series, an efficient method for calculating of the remainders of the above-mentioned series is developed. Formulae are found for the contact pressure distribution function and the integral characteristic. Examples of the calculation of the interaction of the cylinder and the plate with an insert are given. The method of solving contact problems described here has been used earlier 1,2 and the generalized orthogonality of the solutions found for bodies of finite dimensions, that is, for a rectangle and cylinders of finite length, is its basis. Problems for hollow cylinders with a band 2 and an insert reduce to a system of two integral equations, and the problem for a rectangle 1 reduces to one integral equation. Solving these integral equations, ill-posed systems of linear algebraic equations are obtained which are subject to regularization 3 .

Pressure in a Deep-Water Stokes Wave

In this paper we provide a qualitative description of the pressure distribution function for a deep-water Stokes wave.

Analysis of Dynamic Stiffness and Damping of Partial Porous Aerostatic Thrust Bearings

Porous materials have been successfully used in an aerostatic bearing. In this paper, the dynamic stiffness and damping of partial porous aerostatic thrust bearings are analyzed by numerical calculation method. Firstly, the pressure distribution function of the bearing is divided into the static and dynamic pressure distribution functions through minor perturbation method. Then, the static and dynamic pressure distribution functions are calculated by FEM. Finally, the dynamic stiffness and damping coefficients of the bearing are solved. The result indicates that the dynamic stiffness increases obviously with the increment of supply pressure and first increases then decreases with the increment of frequency, and that there is negative damping in the low frequency band and the supply pressure has a great impact on the stability of the bearing.

The contact problem for a viscoelastic layer and rigid cylinder during regular sliding

The contact problem is formulated for a rigid cylinder and viscoelastic layer in sliding. The solution of the contact problem is reduced to the solution of an integral equation the core of which possesses a logarithmic feature and contains a sum of nonintrinsic integrals. The method of solution of this integral equation is disclosed. The effect of the viscoelastic properties of the layer on the contact pressure distribution is analyzed. It is shown that the function of the contact pressure distribution can have two maxima. The obtained solution of the problem is compared with the analytical solutions for two limiting cases: the solution of the contact problem for a rigid cylinder and viscoelastic semispace described in the works of L.A. Galin and I.G. Goryacheva and the approximate solution of the problem for a thin viscoelastic layer. The developed method of solving the contact problem for a viscoelastic layer can be used to calculate the contact parameters in friction units with coatings from composite materials having viscoelastic properties.

Lattice Boltzmann simulations of two-phase flow with high density ratio in axially symmetric geometry

In this paper, a two-phase lattice Boltzmann (LB) model, developed for simulating fluid flows on a Cartesian grid at high liquid-to-gas density ratios, is adapted to an axisymmetric coordinate system. This is achieved by incorporating additional source terms in the planar evolution equations for the density and pressure distribution functions such that the axisymmetric mass and momentum conservation equations are recovered in the macroscopic limit. Appropriate numerical treatment of the terms is performed to obtain stable computations at high density ratio for this axisymmetric model. The particle collision is modeled by employing multiple relaxation times to attain stability at low viscosity. The model is evaluated by verifying the Laplace-Young relation for a liquid drop, comparing computed frequency of oscillations of an initially ellipsoidal drop with analytical values and comparing the behavior of a spherical drop impinging on a wet wall with prior results. The time evolution of the radial distance of the tip of the corona, formed when the drop impinges, agrees well with prior data.

On the refracted patterns produced by liquid vortices

A theoretical analysis of the refracted shadows produced by steady and time-decaying liquid vortices under uniform illumination from above is given in this article. An expression for the induced shadow intensity is derived and found to be a function of the vortex’s free surface profile, i.e., function of the static pressure distribution. The patterns for different focusing depth are given and compared with previous visualization results from the literature. The phenomenon is examined and illustrated as a bench mark case by using both steady and time-decaying algebraic vortex models. However, this study can be extended to check the feasibility of recovering the main flow properties by analyzing the luminous image intensity of the refracted patterns. The present analysis is valid only when the swirl velocity is order of magnitude higher than the meridional flow components and the vorticity is concentrated within the core region and of intense conditions.

The contact problem for a rectangle with stress-free side faces

The plane contact problem for an elastic rectangle into which two symmetrically positioned punches are impressed is considered. Homogeneous solutions are constructed that leave the side faces of the rectangle stress-free. When the modified boundary conditions using generalized orthogonality of the homogeneous solutions are satisfied, the problem reduces to a Friedholm integral equation of the first kind in the function describing the displacement of the surface of the rectangle outside the contact area. This function is sought in the form of the sum of a trigonometric series and a power function with a root singularity. The ill-posed infinite system of algebraic equations thereby obtained is regularized by introducing a small positive parameter (Ref. Kalitkin NN. Numerical Methods. Moscow: Nauka; 1978), and, after reduction, has a stable regularized solution. Since the matrix elements of the system are determined by a poorly converging number series, an effective method was developed for calculating the residues of the series. Formulae are found for the contact pressure distribution function and dimensionless indentation force. Since the first formula contains a third-order derivative of the functional series, when it is used, a numerical differentiation procedure is employed (Refs. Kalitkin NN. Numerical Methods. Moscow: Nauka; 1978; Danilina NI, Dubrovskaya NS, Kvasha OP et al. Numerical Methods. Textbook for Special Colleges. Moscow: Vysshaya Shkola; 1976). Examples of a calculation for a plane punch are given.

Development of Automatic Immediate Fitting Socket (AIFS) System for Artificial Leg Socket Modeling using Fuzzy Set Control

The Automatic Immediate Fitting Socket (AIFS) system was developed to reduce the time consumption for making an artificial leg. The AIFS is composed of an outer shell, a particle containing bag and three air bags. The rigidity of the AIFS can be controlled by the application of negative pressure between the outer shell and the particle bag. The three air bags are used for adjusting the shape of the socket. A fuzzy set theory was utilized for the real-time automatic control of the socket shape based on the subjective evaluation by amputee. Two experiments were conducted for evaluation of this system. One was for measurement of contact pressures between the surface of the stump and the socket during walking. This result revealed that the pressure distribution function of the AFIS was more uniform than conventional artificial legs. Another experiment was conducted for evaluation of a shape-modelling function. The shape-modelling performance was evaluated by measuring the cross-section area ratio of the stump calf to the stump end. This ratio with AIFS was about 1.5 times as large as the conventional artificial leg. This result showed that AIFS system provides a suitable shape for walking. The entire AIFS modeling process including test walking was completed in 40 minutes, which is significantly shorter than the time for the conventional modeling process.