Fully numerical solutions of the hartree-fock equation in momentum space: A numerical study of the He atom and H+2 ion

1988 ◽  
Vol 34 (S22) ◽  
pp. 445-456 ◽  
Author(s):  
Wilfredo Rodr�guez ◽  
Yasuyuki Ishikawa
Keyword(s):  
Momentum Space ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Hartree Fock ◽  
He Atom

Correlation in the Ground State of He Atom

1981 ◽  
Vol 36 (3) ◽  
pp. 272-275 ◽  
Author(s):  
Subal Chandra Saha ◽  
Sankar Sengupta
Keyword(s):  
Ground State ◽  
Zero Order ◽  
Consistent Variation ◽  
Hartree Fock ◽  
Perturbation Procedure ◽  
Self Consistent ◽  
He Atom ◽  
Atomic Parameters

It is possible to reproduce the entire results of Pekeris et al. of different atomic parameters for the He atom by introducing (ll) type correlation in a self consistent variation perturbation procedure using the Hartree-Fock (HF) wavefunction as the zero-order wavefunction

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

A Numerical and Experimental Investigation of Turbulent Heat Transport Downstream From an Abrupt Pipe Expansion

1983 ◽  
Vol 105 (4) ◽  
pp. 862-869 ◽  
Author(s):  
R. S. Amano ◽  
M. K. Jensen ◽  
P. Goel
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Separated Flow ◽  
Flow Region ◽  
Reynolds Numbers ◽  
Turbulent Heat ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Pipe Expansion

An experimental and numerical study is reported on heat transfer in the separated flow region created by an abrupt circular pipe expansion. Heat transfer coefficients were measured along the pipe wall downstream from an expansion for three different expansion ratios of d/D = 0.195, 0.391, and 0.586 for Reynolds numbers ranging from 104 to 1.5 × 105. The results are compared with the numerical solutions obtained with the k ∼ ε turbulence model. In this computation a new finite difference scheme is developed which shows several advantages over the ordinary hybrid scheme. The study also covers the derivation of a new wall function model. Generally good agreement between the measured and the computed results is shown.

Computational Fluid Dynamics Evaluation of Heat Transfer Correlations for Sodium Flows in a Heat Exchanger

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Seok-Ki Choi ◽  
Seong-O Kim ◽  
Hoon-Ki Choi
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Turbulence Model ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Cross Flow ◽  
Turbulence Models ◽  
Parallel Flow ◽  
Sst Model ◽  
Heat Transfer Correlations

A numerical study for the evaluation of heat transfer correlations for sodium flows in a heat exchanger of a fast breeder nuclear reactor is performed. Three different types of flows such as parallel flow, cross flow, and two inclined flows are considered. Calculations are performed for these three typical flows in a heat exchanger changing turbulence models. The tested turbulence models are the shear stress transport (SST) model and the SSG-Reynolds stress turbulence model by Speziale, Sarkar, and Gaski (1991, “Modelling the Pressure-Strain Correlation of Turbulence: An Invariant Dynamical System Approach,” J. Fluid Mech., 227, pp. 245–272). The computational model for parallel flow is a flow past tubes inside a circular cylinder and those for the cross flow and inclined flows are flows past the perpendicular and inclined tube banks enclosed by a rectangular duct. The computational results show that the SST model produces the most reliable results that can distinguish the best heat transfer correlation from other correlations for the three different flows. It was also shown that the SSG-RSTM high-Reynolds number turbulence model does not deal with the low-Prandtl number effect properly when the Peclet number is small. According to the present calculations for a parallel flow, all the old correlations do not match with the present numerical solutions and a new correlation is proposed. The correlations by Dwyer (1966, “Recent Developments in Liquid-Metal Heat Transfer,” At. Energy Rev., 4, pp. 3–92) for a cross flow and its modified correlation that takes into account of flow inclination for inclined flows work best and are accurate enough to be used for the design of the heat exchanger.

scholarly journals Assymmetric eddy populations in adjacent basins – a high resolution numerical study of the Tyrrhenian and Ligurian Seas

2012 ◽  
Vol 9 (6) ◽  
pp. 3521-3566 ◽  
Author(s):  
R. M. A. Caldeira ◽  
X. Couvelard ◽  
E. Casella ◽  
A. Vetrano
Keyword(s):  
High Resolution ◽  
Ocean Circulation ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Mesoscale Eddy ◽  
Leeward Side ◽  
Boundary Current ◽  
High Concentration ◽  
Eddy Activity ◽  
Tyrrhenian Basin

Abstract. A high-resolution ocean circulation modelling system forced with a high-resolution numerical wind product was used to study the mesoscale and sub-mesoscale eddy population of the North-Western Mediterranean Sea, contrasting eddy-activity between the Tyrrhenian and Ligurian sub-basins. Numerical solutions reproduced some of the known regional dynamics, namely the occurrence and oceanic implications of Mistral events, the convective cell leeward of the Gulf of Lion, as well as the Balearic frontal system. Calculated transport across the Corsica Channel followed a similar trend, when compared to the transport computed from a moored current meter. The analysis of the results showed that surface eddy activity is mostly confined to the boundary-currents, whereas in the deeper layers most eddies are concentrated on the central-deeper part of the basins. The Liguro-Provençal basin shows a much higher concentration of intermediate and deep-water eddies, when compared to the Tyrrhenian basin. Sub-mesoscale surface eddies tend to merge and migrate vertically onto intermediate waters. Intense eddy activity in the boundary-current surrounding the Liguro-Provençal Gyre, concentrate high-productivity, manifested by higher concentrations of mean sea surface chlorophyll, in the central part of the gyre, defined herein as the Ligurian Productive Pool (LPP). On average, the Tyrrhenian was mostly oligotrophic except for a small productive vortice in the south-eastern (leeward) side of Corsica. The transport in the Tyrrhenian Gyre, and across the basin is one order of magnitude higher than the transport calculated for the Liguro-Provençal basin. A high concentration of eddies in the passage between the Balearic Archipelago and Sardinia suggests retention and longer residence times of nutrient rich water in the "Ligurian pool", compared to a "fast draining" Tyrrhenian basin. Previous studies support the cyclonic gyre circulation generated in the Liguro-Provençal basin but more studies are needed to address the surface and deep mesoscale activity of the Tyrrhenian basin.

Numerical Solution for Boundary Layer Flow of a Dusty Micropolar Fluid Due to a Stretching Sheet with Constant Wall Temperature

2021 ◽  
Vol 87 (1) ◽  
pp. 30-40
Author(s):  
Anisah Dasman ◽  
Abdul Rahman Mohd Kasim ◽  
Iskandar Waini ◽  
Najiyah Safwa Khashi’ie
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Wall Temperature ◽  
Micropolar Fluid ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Particle Interaction ◽  
Dust Particles ◽  
Constant Wall Temperature

This paper aims to present the numerical study of a dusty micropolar fluid due to a stretching sheet with constant wall temperature. Using the suitable similarity transformation, the governing partial differential equations for two-phase flows of the fluid and the dust particles are reduced to the form of ordinary differential equations. The ordinary differential equations are then numerically analysed using the bvp4c function in the Matlab software. The validity of present numerical results was checked by comparing them with the previous study. The results graphically show the numerical solutions of velocity, temperature and microrotation distributions for several values of the material parameter K, fluid-particle interaction parameter and Prandtl number for both fluid and dust phase. The effect of microrotation is investigated and analysed as well. It is found that the distributions are significantly influenced by the investigated parameters for both phases.

Implementation of DTM as a numerical study for the Casson fluid flow past an exponentially variable stretching sheet with thermal radiation

2021 ◽  
pp. 2150111
Author(s):  
Khadijah M. Abualnaja
Keyword(s):  
Fluid Flow ◽  
Thermal Radiation ◽  
Numerical Method ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Transformation Method ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Special Cases

This paper introduces a theoretical and numerical study for the problem of Casson fluid flow and heat transfer over an exponentially variable stretching sheet. Our contribution in this work can be observed in the presence of thermal radiation and the assumption of dependence of the fluid thermal conductivity on the heat. This physical problem is governed by a system of ordinary differential equations (ODEs), which is solved numerically by using the differential transformation method (DTM). This numerical method enables us to plot figures of the velocity and temperature distribution through the boundary layer region for different physical parameters. Apart from numerical solutions with the DTM, solutions to our proposed problem are also connected with studying the skin-friction coefficient. Estimates for the local Nusselt number are studied as well. The comparison of our numerical method with previously published results on similar special cases shows excellent agreement.

scholarly journals Numerical Study of Branched Turboprop Inlet Ducts Using a Multiple Block Grid Procedure

1991 ◽  
Author(s):  
Anil K. Tolpadi ◽  
Mark E. Braaten
Keyword(s):  
Numerical Solutions ◽  
Numerical Study ◽  
Three Dimensional ◽  
Separated Flow ◽  
Experimental Tests ◽  
Spherical Particles ◽  
Branch Duct ◽  
Pressure Losses ◽  
Overlapping Grids ◽  
Inlet Duct

An important requirement in the design of an inlet duct of a turboprop engine is the ability to provide foreign object damage protection. A possible method for providing this protection is to include a bypass branch duct as an integral part of the main inlet duct. This arrangement would divert ingested debris away from the engine through the bypass. However, such an arrangement could raise the possibility of separated flow in the inlet, which in turn can increase pressure losses if not properly accounted for during the design. A fully elliptic three-dimensional body-fitted computational fluid dynamics (CFD) code based on pressure correction techniques has been developed that has the capability of performing multiple block grid calculations compatible with present day turboshaft and turboprop branched inlet ducts. Calculations are iteratively performed between sets of overlapping grids with one grid representing the main duct and a second grid representing the branch duct. Both the grid generator and the flow solver have been suitably developed to achieve this capability. The code can handle multiple branches in the flow. Using the converged flow field from this code, another program was written to perform a particle trajectory analysis. Numerical solutions were obtained on a supercomputer for a typical branched duct for which experimental flow and pressure measurements were also made. The flow separation zones predicted by the calculations were found to be in good agreement with those observed in the experimental tests. The total pressure recovery factors measured in the experiments were also compared with those obtained numerically. Within the limits of the grid resolution and the turbulence model, the agreement was found to be fairly good. In order to simulate the path of debris entering the duct, the trajectories of spherical particles of different sizes introduced at the inlet were determined.

Numerical Study of Droplet Evaporation in a High-Temperature Stream

1983 ◽  
Vol 105 (2) ◽  
pp. 389-397 ◽  
Author(s):  
M. Renksizbulut ◽  
M. C. Yuen
Keyword(s):  
Heat Transfer ◽  
High Temperature ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Number Range ◽  
Transfer Rates ◽  
Pressure Drag ◽  
Continuity Equations ◽  
Stream Density ◽  
Solid Spheres

Numerical solutions for high-temperature air flowing past water and methanol droplets and solid spheres, and superheated steam flowing past water droplets were obtained in the Reynolds number range of 10 to 100. The coupled momentum, energy, and specie continuity equations of variable thermophysical properties were solved using finite difference techniques. The numerical results of heat transfer and total drag agree well with existing experimental data. Mass transfer decreases friction drag significantly but at the same time increases pressure drag by almost an equal amount. The net effect is that the standard drag curve for solid spheres can be used for evaporating droplets provided the density is the free stream density and the viscosity of the vapor mixture is evaluated at an appropriate reference temperature and concentration. Both the mass efflux and variable properties decrease heat transfer rates to the droplets.

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