A new efficient technique using Laplace transforms and smooth expansions to construct a series solution to the time-fractional Navier-Stokes equations

Abstract In this paper, numerical solution of fractional order Navier-Stokes equations in unsteady viscous fluid flow is found using q-homotopy analysis transform scheme. Fractional derivative is considered in Caputo sense. The proposed technique is a blend of q-homotopy analysis scheme and transform of Laplace. It executes well in efficiency and provides h-curves that show convergence range of series solution.

Download Full-text

Analytical Approach to a Slowly Deforming Channel Flow with Weak Permeability

Zeitschrift für Naturforschung A ◽

10.1515/zna-2010-1202 ◽

2010 ◽

Vol 65 (12) ◽

pp. 1033-1038 ◽

Cited By ~ 6

Author(s):

Syed Tauseef Mohyud-Din ◽

Ahmet Yıldırım ◽

Sefa Anıl Sezer

Keyword(s):

Series Solution ◽

Analytical Approach ◽

Homotopy Perturbation Method ◽

Stokes Equations ◽

Rectangular Channel ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Remarkable Improvement ◽

Homotopy Perturbation ◽

Expanding Or Contracting Walls

In this paper, we develop the analytical solution of the Navier-Stokes equations for a semi-infinite rectangular channel with porous and uniformly expanding or contracting walls by employing the homotopy perturbation method (HPM). The series solution of the governing problem is obtained. Some examples have been included. The results so obtained are compared with the existing literature and a remarkable improvement leads to an excellent agreement with the numerical results.

Download Full-text

Laminar flow in symmetrical channels with slightly curved walls, I. On the Jeffery-Hamel solutions for flow between plane walls

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1962.0087 ◽

1962 ◽

Vol 267 (1328) ◽

pp. 119-138 ◽

Cited By ~ 75

Keyword(s):

Series Solution ◽

Stokes Equations ◽

Asymptotic Series ◽

Navier Stokes ◽

Physical Parameters ◽

Navier Stokes Equations ◽

Laminar Separation ◽

Single Region ◽

Leading Term ◽

Asymptotic Series Solution

The Jeffery-Hamel solutions for plane, viscous, source or sink flow between straight walls are not unique. In this paper these solutions are regarded as providing the leading term of a series solution for a class of channels with walls that are nearly straight in a certain sense, but are such that the fluid is not required to emerge from, or converge on, a point. This approach suggests a further condition which the appropriate solution must satisfy, and hence leads to uniqueness in a limited domain of the physical parameters. The resulting velocity profiles include, at one extreme, the parabolic one of Poiseuille flow, and, at the other, profiles with a single region of flow reversal at each wall. The way is thus opened to an asymptotic series solution of the Navier-Stokes equations which shows laminar separation

Download Full-text

Remarks on the asymptotic behaviour of solutions to the compressible Navier–Stokes equations in the half-line

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s030821050200032x ◽

2002 ◽

Vol 132 (03) ◽

pp. 627

Keyword(s):

Asymptotic Behaviour ◽

Stokes Equations ◽

Half Line ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Asymptotic Behaviour Of Solutions

Download Full-text

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

JOURNAL OF MECHANICAL ENGINEERING AND SCIENCES ◽

10.15282/jmes.14.4.2020.05.0579 ◽

2020 ◽

Vol 14 (4) ◽

pp. 7369-7378

Author(s):

Ky-Quang Pham ◽

Xuan-Truong Le ◽

Cong-Truong Dinh

Keyword(s):

Stokes Equations ◽

Three Dimensional ◽

Axial Compressor ◽

Aerodynamic Performance ◽

Numerical Results ◽

Single Stage ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Operating Stability ◽

Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

Download Full-text