Analyzing a Solution Method of Navier-Stokes Equations of Nanofluids in Isothermal Laminar Flow in the Hydrodynamic Entry Region of a Tube

2013 ◽  
Vol 2 (3) ◽  
pp. 231-236
Author(s):  
Seyyed Shahabeddin Azimi ◽  
Mansour Kalbasi
Keyword(s):  
Laminar Flow ◽  
Solution Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

Some numerical experiments on developing laminar flow in circular-sectioned bends

1985 ◽  
Vol 154 ◽  
pp. 357-375 ◽  
Author(s):  
J. A. C. Humphrey ◽  
H. Iacovides ◽  
B. E. Launder
Keyword(s):  
Shear Stress ◽  
Laminar Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Streamwise Velocity ◽  
Navier Stokes ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Numerical Predictions

The paper reports numerical solutions to a semi-elliptic truncation of the Navier–Stokes equations for the case of developing laminar flow in circular-sectioned bends over a range of Dean numbers. The ratios of bend radius to pipe radius are 7:1 and 20:1, corresponding with the configurations examined experimentally by Talbot and his co-workers in recent years. The semi-elliptic treatment facilitates a much finer grid than has been possible in earlier studies. Numerical accuracy has been further improved by assuming radial equilibrium over a thin sublayer immediately adjacent to the wall and by re-formulating the boundary conditions at the pipe centre.Streamwise velocity profiles at Dean numbers of 183 and 565 are in excellent agreement with laser-Doppler measurements by Agrawal, Talbot & Gong (1978). Good, albeit less complete, accord is found with the secondary velocities, though the differences that exist may be mainly due to the difficulty of making these measurements. The paper provides new information on the behaviour of the streamwise shear stress around the inner line of symmetry. Upstream of the point of minimum shear stress, our numerical predictions display a progressive shift towards the result of Stewartson, Cebici & Chang (1980) as the Dean number is successively raised. Downstream of the minimum, however, in contrast with the monotonic approach to an asymptotic level reported by Stewartson, the numerical solutions display a damped oscillatory behaviour reminiscent of those from Hawthorne's (1951) inviscid-flow calculations. The amplitude of the oscillation grows as the Dean number is raised.

On a theory of laminar flow in channels of a certain class. II

1975 ◽  
Vol 77 (1) ◽  
pp. 199-224 ◽  
Author(s):  
L. E. Fraenkel ◽  
P. M. Eagles
Keyword(s):  
Differential Operator ◽  
Laminar Flow ◽  
Mathematical Analysis ◽  
Stokes Equations ◽  
Partial Differential Operator ◽  
Formal Theory ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Curvature Parameter

This paper continues (and concludes) the mathematical analysis begun in (8) of a formal theory of viscous flow in channels with slowly curving walls. In that paper, the theory was shown to yield strict asymptotic expansions, in powers of the small curvature parameter, of exact solutions of the Navier-Stokes equations, but the proofs were restricted to a set of Reynolds numbers and wall divergence angles that is distinctly smaller than the set on which the formal approximation is defined. In the present paper, we study in more detail a certain linear, partial differential operator TN, the invertibility of which is essential to the proofs. This operator is shown to be invertible (and the formal theory is thereby justified) on a parameter domain that is much larger than and may well be the whole of . A key step is to associate with TN a family of operators that approximate TN locally and have much simpler coefficients.

Inward Flow Between Stationary and Rotating Disks

2014 ◽  
Vol 136 (10) ◽  
Author(s):  
Achhaibar Singh
Keyword(s):  
Laminar Flow ◽  
Flow Field ◽  
Velocity Distribution ◽  
Stokes Equations ◽  
Tangential Velocity ◽  
Rotating Disk ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Rotating Disks ◽  
Navier Stokes Equations

The present study predicts the flow field and the pressure distribution for a laminar flow in the gap between a stationary and a rotating disk. The fluid enters through the peripheral gap between two concentric disks and converges to the center where it discharges axially through a hole in one of the disks. Closed form expressions have been derived by simplifying the Navier– Stokes equations. The expressions predict the backflow near the rotating disk due to the effect of centrifugal force. A convection effect has been observed in the tangential velocity distribution at high throughflow Reynolds numbers.

Implicit solution method for incompressible Navier-Stokes equations including two-layer k-tau turbulence model

AIAA Journal ◽  
1996 ◽  
Vol 34 (12) ◽  
pp. 2501-2508 ◽  
Author(s):  
Jurg Kuffer ◽  
Bernhard Muller ◽  
Torstein K. Fannelop
Keyword(s):  
Turbulence Model ◽  
Solution Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

Boundary layer problems for the two-dimensional compressible Navier–Stokes equations

2016 ◽  
Vol 14 (01) ◽  
pp. 1-37 ◽  
Author(s):  
Shengbo Gong ◽  
Yan Guo ◽  
Ya-Guang Wang
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Stokes Equations ◽  
Degenerate Parabolic Equations ◽  
Navier Stokes ◽  
Large Space ◽  
Comparison Theory ◽  
Navier Stokes Equations ◽  
Boundary Layer Problems ◽  
Space Interval

We study the well-posedness of the boundary layer problems for compressible Navier–Stokes equations. Under the non-negative assumption on the laminar flow, we investigate the local spatial existence of solution for the steady equations. Meanwhile, we also obtain the solution for the unsteady case with monotonic laminar flow, which exists for either long time small space interval or short time large space interval. Moreover, the limit of these solutions with vanishing Mach number is considered. Our proof is based on the comparison theory for the degenerate parabolic equations obtained by the Crocco transformation or von Mises transformation.

Wave patterns in plane Poiseuille flow created by concentrated disturbances

1989 ◽  
Vol 208 ◽  
pp. 639-656 ◽  
Author(s):  
Fei Li ◽  
Sheila E. Widnall
Keyword(s):  
Laminar Flow ◽  
Reynolds Stress ◽  
Poiseuille Flow ◽  
Fourier Transforms ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Plane Poiseuille Flow ◽  
Turbulent Spot ◽  
Navier Stokes Equations ◽  
Wave Patterns

A model is constructed for perturbations created in the surrounding laminar flow by a turbulent spot in plane Poiseuille flow. The turbulent spot is represented as a distribution of increased Reynolds stress, which travels steadily through the surrounding laminar flow. The Navier-Stokes equations are linearized and are solved by using Fourier transforms in the plane parallel to the channel walls and a finite-difference method in the direction perpendicular to the walls. The travelling Reynolds stress distribution acts as a forcing term in the equations.Numerical results show that a packet of oblique waves are generated around the disturbance when the force is antisymmetric with respect to the channel centreline, whereas no identifiable wave crests are found when the forcing is symmetric. Furthermore, wavelengths of the typical waves composing the packet are insensitive to the size of the region of Reynolds stress. The dependencies of the flow field on Reynolds number and spot speed are investigated. In the case of symmetric forcing, the flow is forced around the disturbance, causing distortions to the basic velocity profiles. These results are in qualitative agreement with experimental observations.

MODELLING THE HEAVE OSCILLATIONS OF VERTICAL CYLINDERS WITH DAMPING PLATES

2021 ◽  
Vol 158 (A3) ◽  
Author(s):  
A Lavrov ◽  
C Guedes Soares
Keyword(s):  
Experimental Data ◽  
Laminar Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Moving Mesh ◽  
Navier Stokes ◽  
Morison Equation ◽  
Navier Stokes Equations ◽  
Vertical Cylinders ◽  
Semi Empirical

The laminar flow around heaving axisymmetric and three-dimensional cylinders with damping plates is numerically studied for various Keulegan-Carpenter numbers. The Navier-Stokes equations are solved using OpenFOAM, which is applied to the flow on a moving mesh. For processing of results the semi-empirical Morison equation is used. Calculations are conducted for one cylinder, one cylinder with one disk, one cylinder with two disks, and one cylinder with one pentagonal plate. The calculated values are compared against experimental data.

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