Potential Core of a Submerged Laminar Jet

This study is intended to clarify the flow pattern in the flow developing region of an axisymmetric laminar water jet issuing into the surrounding calm water. The jet, initially having a potential core region of some extent at the nozzle exit, was studied. The numerical solution of the Navier-Stokes equations in the developing region was obtained using a finite-difference approximation. The velocity profile was measured using a miniature cone-type hot probe. Flow visualization by the hydrogen bubble method was also performed. Experiments were carried out for the jet Reynolds number ranging from 100 to 600. The flow pattern in the developing region was made clear. The experimental results were compared with the numerical solution.

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On a finite-difference approximation for the steady-state navier-stokes equations

Journal of Computational Physics ◽

10.1016/0021-9991(80)90186-2 ◽

1980 ◽

Vol 36 (2) ◽

pp. 236-248 ◽

Cited By ~ 10

Author(s):

Nobumasa Takemitsu

Keyword(s):

Steady State ◽

Finite Difference ◽

Stokes Equations ◽

Finite Difference Approximation ◽

Navier Stokes ◽

Difference Approximation ◽

Navier Stokes Equations

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SCALING OF FLUID RECOVERY FROM PERCOLATION FRACTALS

Fractals ◽

10.1142/s0218348x94000302 ◽

1994 ◽

Vol 02 (02) ◽

pp. 269-272 ◽

Cited By ~ 1

Author(s):

IAN D WEDGWOOD ◽

DONALD M MONRO

Keyword(s):

Stokes Equations ◽

Petroleum Reservoirs ◽

Finite Difference Approximation ◽

Navier Stokes ◽

Difference Approximation ◽

Viscous Effects ◽

Navier Stokes Equation ◽

Navier Stokes Equations ◽

Reservoir Models ◽

Wide Range

We report on the recovery of fluid driven through percolation lattices across a range of scales using a finite difference approximation to the Navier-Stokes equation. This is important in the study of recovery from petroleum reservoirs, in which flow occurs over a wide range of scales, from the microscopic pores right up to the full reservoir. This variation of scale presents difficulties, since flow at the pore level is subject to predominantly viscous effects, whereas at the larger scales the viscous effects may become negligible in comparison with inertial effects. The Navier-Stokes equations may differ greatly with scale. Theoretical rock structures are created using percolation lattices and the flow properties of identical rock structures are then examined as a function of scale. The resultant recovery rates exhibit similarity across scale which would simplify the study of geological reservoir models.

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Numerical Solution of the Navier–Stokes Equations Using Multigrid Methods with HSS-Based and STS-Based Smoothers

Symmetry ◽

10.3390/sym12020233 ◽

2020 ◽

Vol 12 (2) ◽

pp. 233

Author(s):

Galina Muratova ◽

Tatiana Martynova ◽

Evgeniya Andreeva ◽

Vadim Bavin ◽

Zeng-Qi Wang

Keyword(s):

Stokes Equations ◽

Hermitian Matrix ◽

Multigrid Methods ◽

Finite Difference Approximation ◽

Navier Stokes ◽

Difference Approximation ◽

Algebraic Equations ◽

Navier Stokes Equations ◽

Linear Algebraic Equations ◽

Discretized Systems

Multigrid methods (MGMs) are used for discretized systems of partial differential equations (PDEs) which arise from finite difference approximation of the incompressible Navier–Stokes equations. After discretization and linearization of the equations, systems of linear algebraic equations (SLAEs) with a strongly non-Hermitian matrix appear. Hermitian/skew-Hermitian splitting (HSS) and skew-Hermitian triangular splitting (STS) methods are considered as smoothers in the MGM for solving the SLAE. Numerical results for an algebraic multigrid (AMG) method with HSS-based smoothers are presented.

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Numerical solution of 2D Navier–Stokes equation discretized via boundary elements method and finite difference approximation

Engineering Analysis with Boundary Elements ◽

10.1016/j.enganabound.2018.08.004 ◽

2018 ◽

Vol 96 ◽

pp. 64-77 ◽

Cited By ~ 12

Author(s):

Zeynab Sedaghatjoo ◽

Mehdi Dehghan ◽

Hossein Hosseinzadeh

Keyword(s):

Finite Difference ◽

Numerical Solution ◽

Stokes Equation ◽

Boundary Elements ◽

Finite Difference Approximation ◽

Navier Stokes ◽

Difference Approximation ◽

Navier Stokes Equation ◽

Boundary Elements Method

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Numerical Simulation of Combustion and Rotor-Stator Interaction in a Turbine Combustor

International Journal of Rotating Machinery ◽

10.1155/s1023621x03000344 ◽

2003 ◽

Vol 9 (5) ◽

pp. 363-374 ◽

Cited By ~ 6

Author(s):

Dragos D. Isvoranu ◽

Paul G. A. Cizmas

Keyword(s):

Numerical Algorithm ◽

Stokes Equations ◽

Species Conservation ◽

Finite Difference Approximation ◽

Navier Stokes ◽

Difference Approximation ◽

Combustion Model ◽

Combustion Gases ◽

Fully Implicit ◽

Correction Technique

This article presents the development of a numerical algorithm for the computation of flow and combustion in a turbine combustor. The flow and combustion are modeled by the Reynolds-averaged Navier-Stokes equations coupled with the species-conservation equations. The chemistry model used herein is a two-step, global, finite-rate combustion model for methane and combustion gases. The governing equations are written in the strong conservation form and solved using a fully implicit, finite-difference approximation. The gas dynamics and chemistry equations are fully decoupled. A correction technique has been developed to enforce the conservation of mass fractions. The numerical algorithm developed herein has been used to investigate the flow and combustion in a one-stage turbine combustor.

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