To read the full version of this content please select one of the options below:

The approximation method in the problem on a flow of viscous fluid around a thin plate

Yanina Berdnik (Faculty of Mathematics, Mechanics and Computer Science, Southern Federal University, Rostov-on-Don, Russian Federation)
Alexey Beskopylny (Don State Technical University, Rostov-on-Don, Russian Federation)

Aircraft Engineering and Aerospace Technology

ISSN: 0002-2667

Article publication date: 12 March 2019

Issue publication date: 15 August 2019

Abstract

Purpose

The paper aims to obtain an effective solution to the problem on a flow of viscous fluid around a thin plate using a new approximation method based on the exact Navier–Stokes equations. Also, correction factors are proposed to improve the obtained solution at high Reynolds numbers.

Design/methodology/approach

The paper has opted for a method that is based on an approximation scheme for certain perturbations concerning the velocity of the oncoming unperturbed flow behind a leading edge of the plate as a zero approximation step. The perturbations are assumed to be small, far from the plate when compared to the basic flow to justify the linearization. Numerical methods are used for the integral equations at each approximation step.

Findings

This paper provides the friction force coefficient compared with the classical Blasius solution and the ANSYS results. Also, some diagrams of the velocity distribution in the flow are presented. The first and second approximation steps provide a sufficiently high degree of accuracy.

Research limitations/implications

Because of the chosen research approach, the results may lack accuracy for low and average Reynolds numbers. Thus, researchers are encouraged to improve the proposed method further.

Practical implications

The paper includes implications for the development of an aircraft design or a wind turbine design considering a wing as a thin plate at the first approximation.

Originality/value

This paper provides a new approximation method based on the exact Navier–Stokes equations, in contrast to the known solutions.

Keywords

Citation

Berdnik, Y. and Beskopylny, A. (2019), "The approximation method in the problem on a flow of viscous fluid around a thin plate", Aircraft Engineering and Aerospace Technology, Vol. 91 No. 6, pp. 807-813. https://doi.org/10.1108/AEAT-07-2018-0196

Publisher

:

Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited