Maximization of the lift/drag ratio of airfoils with a turbulent boundary layer: Sharp estimates, approximation, and numerical solutions

2009 ◽  
Vol 49 (3) ◽  
pp. 559-572
Author(s):  
A. M. Elizarov ◽  
A. N. Kalimullina
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Numerical Solutions ◽  
Sharp Estimates ◽  
Drag Ratio

scholarly journals Application of the Method of Integral Relations to the Calculation of Two-Dimensional Incompressible Turbulent Boundary Layer

1981 ◽  
Vol 48 (4) ◽  
pp. 701-706 ◽  
Author(s):  
W.-S. Yeung ◽  
R.-J. Yang
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Numerical Solutions ◽  
Experimental Results ◽  
Two Dimensional ◽  
Incompressible Turbulent Boundary Layer ◽  
Method Of Integral Relations ◽  
Integral Relations

The orthonormal version of the Method of Integral Relations (MIR) was applied to solve for a two-dimensional incompressible turbulent boundary layer. The flow was assumed to be nonseparating. Flows with favorable, unfavorable, and zero pressure gradient were considered, and comparisons made with available experimental data. In general, the method predicted very well the experimental results for flows with favorable or zero pressure gradient; for flows with unfavorable pressure gradient, it predicted the experimental data well only up to a certain distance from the initial station. This result is due to the flow not being in equilibrium beyond that distance. Finally, the scheme was shown to be efficient in obtaining numerical solutions.

Approximate Solution—One-Dimensional Energy Equation for Transient, Compressible, Low Mach Number Turbulent Boundary Layer Flows

1989 ◽  
Vol 111 (3) ◽  
pp. 619-624 ◽  
Author(s):  
J. Yang ◽  
J. K. Martin
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Turbulent Boundary Layer ◽  
Internal Combustion Engines ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Empirical Relation ◽  
Approximate Solutions ◽  
Low Mach Number ◽  
One Dimensional

Unsteady surface heat-flux and temperature profiles in the transient, compressible, low Mach number, turbulent boundary layer typically found in internal combustion engines have been determined by numerically integrating a linearized form of the one-dimensional energy equation. An empirical relation for μt/μ has been used to consider turbulent conductivity. Approximate solutions have been acquired by multiparameter fits to the numerical solutions. Comparisons of the approximate solutions with motored engine experiments show good agreement.

The Turbulent Boundary Layer Near a Corner

1976 ◽  
Vol 43 (4) ◽  
pp. 567-570 ◽  
Author(s):  
M. Shafir ◽  
S. G. Rubin
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Secondary Flow ◽  
Numerical Solutions ◽  
Main Stream ◽  
Interference Effects ◽  
Flat Plates ◽  
Motion Models ◽  
Secondary Motion ◽  
Layer Behavior

Turbulent boundary-layer behavior in the vicinity of a right-angle corner formed by intersecting flat plates is considered. Due to interference effects a secondary flow is induced. Numerical solutions are obtained for the main stream and secondary motion. Models with and without intermittency factors are considered. It is shown that the secondary motion is significantly different for laminar and turbulent conditions. Similar behavior has previously been observed experimentally.

A One-Parameter Integral Method for Turbulent Transpired Boundary Layer Flow

1990 ◽  
Vol 112 (4) ◽  
pp. 433-436 ◽  
Author(s):  
L. C. Thomas ◽  
H. M. Kadry
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layer Flow ◽  
Integral Method ◽  
Numerical Solutions ◽  
Momentum Equation ◽  
Total Stress ◽  
Turbulent Boundary Layer Flow ◽  
Layer Flow

This paper presents the development of a practical one-parameter integral method for transpired turbulent boundary layer flow. The method involves the use of one-parameter polynomial approximations for total stress and the solution of the familiar integral momentum equation. The method is compared with experimental data and numerical solutions for a range of near equilibrium boundary layers.

scholarly journals On the question of computing convective heat transfer parameters in a laminar-to-turbulent boundary layer on an impermeable hemispherical surface

2019 ◽  
pp. 17-28
Author(s):  
V.V. Gorskiy ◽  
A.G. Leonov ◽  
A.G. Loktionova
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Numerical Solutions ◽  
Turbulent Viscosity ◽  
Effective Length ◽  
Viscosity Models ◽  
Transfer Parameters

In order to qualitatively solve the problem of computing convective heat transfer parameters in a laminar-to-turbulent boundary layer, it is necessary to numerically integrate differential equations descrybing that layer, completed by semiempirical turbulent viscosity models. These must be validated using results of experimental investigations where the gas dynamics of a gas flow around a body is correctly simulated. In terms of practical applications, developing relatively simple yet highly accurate computation methods is important. At present, the most widely used method to solve this type of problems in aviation and aerospace engineering is the effective length method developed by V.S. Avduevskiy, Academician. The paper shows that significant errors characterise computations using this method and traditional turbulent viscosity models to determine parameters of those blunted components of aircraft that are subjected to the highest temperatures. We present a solution to this problem, based on constructing systematic numerical solutions to the equations describing the laminar-to-turbulent boundary layer and subsequently approximating them. We prove that this approach ensures both acceptable computation accuracy and solution simplicity.

Turbulent boundary layer heat transfer of CuO–water nanofluids on a continuously moving plate subject to convective boundary

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jiaojiao Zhang ◽  
Shengna Liu ◽  
Liancun Zheng
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Velocity Ratio ◽  
Moving Plate ◽  
Convective Boundary ◽  
Turbulent Region ◽  
Different Shapes

Abstract The turbulent boundary layer (TBL) heat transfer of CuO–water nanofluids on a continuously moving plate subject to convective boundary are investigated. Five different shapes of nanoparticles are taken into account. Prandtl mixing length theory is adopted to divide the TBL into two parts, laminar sub-layer and turbulent region. The numerical solutions are obtained by bvp4c and accuracy is verified with previous results. It is found that the transfer of momentum and heat in the TBL is more obvious in laminar sub-layer than in turbulent region. The rise of velocity ratio parameter increases the velocity and temperature while decreases the local friction coefficient. The heat transfer increases significantly with the increase of velocity ratio parameter, Biot number, and nanoparticles volume fraction. For nanoparticles of different shapes, the heat transfer characteristics are Nu x (sphere) < Nu x (hexahedron) < Nu x (tetrahedron) < Nu x (column) < Nu x (lamina).

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