Author: John E. Yates Publisher: ISBN: Category : Languages : en Pages : 65
Book Description
The theory of oscillating thin airfoils in incompressible viscous flow is formulated and applied to the calculation of steady and unsteady loads on the family of symmetric Joukowski airfoils. The theory is reduced to the form of an integral equation with kernel function whose solution is obtained with a modal expansion technique familiar from flat plate thin airfoil theory. The effect of viscosity is to change the order of the singularity in the kernel function such that a unique solution is obtained for any cross sectional geometry without using an auxiliary uniqueness criteria like the Kutta condition or principle of minimum singularity. Viscous thin airfoil calculations for an airfoil with sharp trailing edge are in agreement with the results of potential theory with Kutta condition. Viscous thin airfoil steady and unsteady calculations for an airfoil with elliptic cross section are in much better agreement with experimental results. It is concluded that viscous thin airfoil theory is a practical tool for introducing simultaneously the effects of viscosity and geometric thickness in two-dimensional unsteady aerodynamic theory.
Author: John E. Yates Publisher: ISBN: Category : Languages : en Pages : 53
Book Description
The general problem of a lifting incompressible viscous thin airfoil is formulated and the viscous counterpart of the classical thin airfoil equation is derived. For any Reynolds number, however large, it is shown that the Cauchy singularity in the kernel is replaced by a logarithmic singularity and the resulting kernel does not have upstream/downstream symmetry. The downstream influence decays algebraically, while upstream influence decays exponentially with distance away from the singularity. A moment solution of the viscous airfoil equation is developed in the limit of high Reynolds number. The classical steady state 'Kutta Condition' is derived in the limit and the Reynolds number correction is found to be of order (1/1n Re), much greater than inviscid boundary layer thickness effects. For Reynolds numbers between one and ten million there is a 20% reduction in the lift curve slope that offsets the increase due to geometric thickness. The correction correlates reasonably well with experiment for a large variety of thin airfoils. The unsteady viscous thin airfoil equation is derived and the singularities of the kernel are discussed in the light of recent experimental work on oscillating airfoils.
Author: National Aeronautics and Space Administration (NASA) Publisher: Createspace Independent Publishing Platform ISBN: 9781722914233 Category : Languages : en Pages : 102
Book Description
A unified viscous theory of 2-D thin airfoils and 3-D thin wings is developed with numerical examples. The viscous theory of the load distribution is unique and tends to the classical inviscid result with Kutta condition in the high Reynolds number limit. A new theory of 2-D section induced drag is introduced with specific applications to three cases of interest: (1) constant angle of attack; (2) parabolic camber; and (3) a flapped airfoil. The first case is also extended to a profiled leading edge foil. The well-known drag due to absence of leading edge suction is derived from the viscous theory. It is independent of Reynolds number for zero thickness and varies inversely with the square root of the Reynolds number based on the leading edge radius for profiled sections. The role of turbulence in the section induced drag problem is discussed. A theory of minimum section induced drag is derived and applied. For low Reynolds number the minimum drag load tends to the constant angle of attack solution and for high Reynolds number to an approximation of the parabolic camber solution. The parabolic camber section induced drag is about 4 percent greater than the ideal minimum at high Reynolds number. Two new concepts, the viscous induced drag angle and the viscous induced separation potential are introduced. The separation potential is calculated for three 2-D cases and for a 3-D rectangular wing. The potential is calculated with input from a standard doublet lattice wing code without recourse to any boundary layer calculations. Separation is indicated in regions where it is observed experimentally. The classical induced drag is recovered in the 3-D high Reynolds number limit with an additional contribution that is Reynold number dependent. The 3-D viscous theory of minimum induced drag yields an equation for the optimal spanwise and chordwise load distribution. The design of optimal wing tip planforms and camber distributions is possible with the viscous 3-D wing theory. ...
Author: Mrinal Kaushik Publisher: Springer ISBN: 9811316783 Category : Technology & Engineering Languages : en Pages : 512
Book Description
This book is intended as a text for undergraduate and graduate courses in aerodynamics, typically offered to students of aerospace and mechanical engineering programs. It covers all aspects of aerodynamics. The book begins with a description of the standard atmosphere and basic concepts, then moves on to cover the equations and mathematical models used to describe and characterize flow fields, as well as their thermodynamic aspects and applications. Specific emphasis is placed on the relation between concepts and their use in aircraft design. Additional topics of interest to the reader are presented in the Appendix, which draws on the teachings provided in the text. The book is written in an easy to understand manner, with pedagogical aids such as chapter overviews, summaries, and descriptive and objective questions to help students evaluate their progress. Atmospheric and gas tables are provided to facilitate problem solving. Lastly, a detailed bibliography is included at the end of each chapter to provide students with further resources. The book can also be used as a text for professional development courses in aerodynamics.
Author: John E. Yates
Author: J. E. Yates
Author: John E. Yates
Author: John E. Yates
Author: National Aeronautics and Space Administration (NASA)
Author: John E. Yates
Author: Edmund Charles Lary
Author: Mrinal Kaushik
Author: John E. Yates
Author: James Liburdy