Airfoil: Difference between revisions
No edit summary |
Rescuing 1 sources and tagging 0 as dead. #IABot (v1.6.2) (Balon Greyjoy) |
||
Line 209: | Line 209: | ||
| publisher = McGraw-Hill |
| publisher = McGraw-Hill |
||
}} |
}} |
||
*[http://www.desktopaero.com/appliedaero/airfoils1/tatderivation.html Desktopaero] |
*[https://web.archive.org/web/20070222145228/http://www.desktopaero.com/appliedaero/airfoils1/tatderivation.html Desktopaero] |
||
*[http://s6.aeromech.usyd.edu.au/aero/thinaero/thinaero.pdf University of Sydney, Aerodynamics for Students] |
*[http://s6.aeromech.usyd.edu.au/aero/thinaero/thinaero.pdf University of Sydney, Aerodynamics for Students] |
||
*{{cite book |
*{{cite book |
Revision as of 04:00, 22 January 2018
An airfoil (American English) or aerofoil (British English) is the shape of a wing, blade (of a propeller, rotor, or turbine), or sail (as seen in cross-section).
An airfoil-shaped body moved through a
The lift on an airfoil is primarily the result of its
Overview
A
Any object with an angle of attack in a moving fluid, such as a flat plate, a building, or the deck of a bridge, will generate an aerodynamic force (called lift) perpendicular to the flow. Airfoils are more efficient lifting shapes, able to generate more lift (up to a point), and to generate lift with less drag.
A lift and drag curve obtained in
Airfoil design is a major facet of
Movable high-lift devices,
A laminar flow wing has a maximum thickness in the middle camber line. Analyzing the Navier–Stokes equations in the linear regime shows that a negative pressure gradient along the flow has the same effect as reducing the speed. So with the maximum camber in the middle, maintaining a laminar flow over a larger percentage of the wing at a higher cruising speed is possible. However, some surface contamination will disrupt the laminar flow, making it turbulent. For example, with rain on the wing, the flow will be turbulent. Under certain conditions, insect debris on the wing will cause the loss of small regions of laminar flow as well.[5] Before NASA's research in the 1970s and 1980s the aircraft design community understood from application attempts in the WW II era that laminar flow wing designs were not practical using common manufacturing tolerances and surface imperfections. That belief changed after new manufacturing methods were developed with composite materials (e.g., graphite fiber) and machined metal methods were introduced. NASA's research in the 1980s revealed the practicality and usefulness of laminar flow wing designs and opened the way for laminar flow applications on modern practical aircraft surfaces, from subsonic general aviation aircraft to transonic large transport aircraft, to supersonic designs.[6]
Schemes have been devised to define airfoils – an example is the
Airfoil terminology
The various terms related to airfoils are defined below:[8]
- The suction surface (a.k.a. upper surface) is generally associated with higher velocity and lower static pressure.
- The pressure surface (a.k.a. lower surface) has a comparatively higher static pressure than the suction surface. The pressure gradient between these two surfaces contributes to the lift force generated for a given airfoil.
The geometry of the airfoil is described with a variety of terms :
- The leading edge is the point at the front of the airfoil that has maximum curvature (minimum radius).[9]
- The trailing edge is defined similarly as the point of maximum curvature at the rear of the airfoil.
- The chord lineis the straight line connecting leading and trailing edges. The chord length, or simply chord, , is the length of the chord line. That is the reference dimension of the airfoil section.
The shape of the airfoil is defined using the following geometrical parameters:
- The mean camber line or mean line is the locus of points midway between the upper and lower surfaces. Its shape depends on the thickness distribution along the chord;
- The thickness of an airfoil varies along the chord. It may be measured in either of two ways:
Some important parameters to describe an airfoil's shape are its camber and its thickness. For example, an airfoil of the NACA 4-digit series such as the NACA 2415 (to be read as 2 – 4 – 15) describes an airfoil with a camber of 0.02 chord located at 0.40 chord, with 0.15 chord of maximum thickness.
Finally, important concepts used to describe the airfoil's behaviour when moving through a fluid are:
- The aerodynamic center, which is the chord-wise length about which the pitching moment is independent of the lift coefficient and the angle of attack.
- The center of pressure, which is the chord-wise location about which the pitching moment is zero.
Thin airfoil theory
Thin airfoil theory is a simple theory of airfoils that relates angle of attack to lift for incompressible, inviscid flows. It was devised by German-American mathematician Max Munk and further refined by British aerodynamicist Hermann Glauert and others[13] in the 1920s. The theory idealizes the flow around an airfoil as two-dimensional flow around a thin airfoil. It can be imagined as addressing an airfoil of zero thickness and infinite wingspan.
Thin airfoil theory was particularly notable in its day because it provided a sound theoretical basis for the following important properties of airfoils in two-dimensional flow:[14][15]
- on a symmetric airfoil, the chordbehind the leading edge.
- on a cambered airfoil, the aerodynamic center lies exactly one quarter of the chord behind the leading edge.
- the slope of the lift coefficient versus angle of attack line is units per radian.
As a consequence of (3), the section lift coefficient of a symmetric airfoil of infinite wingspan is:
- where is the section lift coefficient,
- is the chordline.
(The above expression is also applicable to a cambered airfoil where is the angle of attack measured relative to the
Also as a consequence of (3), the section lift coefficient of a cambered airfoil of infinite wingspan is:
- where is the section lift coefficient when the angle of attack is zero.
Thin airfoil theory does not account for the
Derivation of thin airfoil theory
The airfoil is modeled as a thin lifting mean-line (camber line). The mean-line, y(x), is considered to produce a distribution of vorticity along the line, s. By the Kutta condition, the vorticity is zero at the trailing edge. Since the airfoil is thin, x (chord position) can be used instead of s, and all angles can be approximated as small.
From the Biot–Savart law, this vorticity produces a flow field where
is the location where induced velocity is produced, is the location of the vortex element producing the velocity and is the chord length of the airfoil.
Since there is no flow normal to the curved surface of the airfoil, balances that from the component of main flow , which is locally normal to the plate – the main flow is locally inclined to the plate by an angle . That is:
This integral equation can by solved for , after replacing x by
- ,
as a Fourier series in with a modified lead term
That is
(These terms are known as the Glauert integral).
The coefficients are given by
and
By the Kutta–Joukowski theorem, the total lift force F is proportional to
and its moment M about the leading edge to
The calculated Lift coefficient depends only on the first two terms of the Fourier series, as
The moment M about the leading edge depends only on and , as
The moment about the 1/4 chord point will thus be,
- .
From this it follows that the center of pressure is aft of the 'quarter-chord' point 0.25 c, by
The aerodynamic center, AC, is at the quarter-chord point. The AC is where the pitching moment M' does not vary with angle of attack, i.e.,
See also
Notes
- ^ "...the effect of the wing is to give the air stream a downward velocity component. The reaction force of the deflected air mass must then act on the wing to give it an equal and opposite upward component." In: Halliday, David; Resnick, Robert, Fundamentals of Physics 3rd Edition, John Wiley & Sons, p. 378
- ^ "If the body is shaped, moved, or inclined in such a way as to produce a net deflection or turning of the flow, the local velocity is changed in magnitude, direction, or both. Changing the velocity creates a net force on the body" "Lift from Flow Turning". NASA Glenn Research Center. Archived from the original on 5 July 2011. Retrieved 2011-06-29.
{{cite web}}
: Unknown parameter|deadurl=
ignored (|url-status=
suggested) (help) - ^ "The cause of the aerodynamic lifting force is the downward acceleration of air by the airfoil..." Weltner, Klaus; Ingelman-Sundberg, Martin, Physics of Flight – reviewed, archived from the original on 2011-07-19
{{citation}}
: Unknown parameter|deadurl=
ignored (|url-status=
suggested) (help) - ^ "...if a streamline is curved, there must be a pressure gradient across the streamline..."Babinsky, Holger (November 2003), "How do wings work?" (PDF), Physics Education
- ^ Croom, C. C.; Holmes, B. J. (1985-04-01). Flight evaluation of an insect contamination protection system for laminar flow wings.
- ^ Holmes, B. J.; Obara, C. J.; Yip, L. P. (1984-06-01). "Natural laminar flow experiments on modern airplane surfaces".
{{cite journal}}
: Cite journal requires|journal=
(help) - ^ XFOIL
- ^ Hurt, H. H., Jr. (January 1965) [1960]. Aerodynamics for Naval Aviators. U.S. Government Printing Office, Washington, D.C.: U.S. Navy, Aviation Training Division. pp. 21–22. NAVWEPS 00-80T-80.
{{cite book}}
: CS1 maint: multiple names: authors list (link) - ISBN 0-7506-5111-3.
- ^ ISBN 0-7506-5111-3.
- ISBN 978-0-470-53975-0.
- ISBN 978-0-13-227268-1.
- Abbott, Ira H., and Von Doenhoff, Albert E. (1959), Theory of Wing Sections, Section 4.2, Dover Publications Inc., New York, Standard Book Number 486-60586-8
- ^ Abbott, Ira H., and Von Doenhoff, Albert E. (1959), Theory of Wing Sections, Section 4.3
- ISBN 0-273-01120-0
- ^ Aerospaceweb's information on Thin Airfoil Theory
- ^ Morris, Wallace J., II (2009). "A universal prediction of stall onset for airfoils at a wide range of Reynolds number flows". Ph.D. Thesis.
{{cite journal}}
: CS1 maint: multiple names: authors list (link) - ISSN 0022-1120.
- doi:10.3390/aerospace3020009.)
{{cite journal}}
: CS1 maint: unflagged free DOI (link - ISSN 0022-1120.
References
- Anderson, John, D (2007). Fundamentals of Aerodynamics. McGraw-Hill.
{{cite book}}
: CS1 maint: multiple names: authors list (link) - Desktopaero
- University of Sydney, Aerodynamics for Students
- Batchelor, George. K (1967). An Introduction to Fluid Dynamics. Cambridge UP. pp. 467–471.
External links
- UIUC Airfoil Coordinates Database
- Airfoil & Hydrofoil Reference Application
- FoilSim An airfoil simulator from NASA