Tuesday, January 24, 2012

MrsDrPoe: Lift

It's once again Thesis Tuesday here on the blog!  Today we'll be discussing another external flow property, lift.

For asymmetrical objects moving through a fluid, there exists a resultant force from pressure and shear stress normal to the upstream velocity, termed lift.  It can be calculated as:

L = -int(p*sin(theta))dA + int(tauw*cos(theta))dA

however, as previously mentioned, these distributions are difficult to determine.  Thus, the lift coefficient is often used:

CL = L/(0.5*rho*U*U*A)

As with the drag coefficient, CL = f(shape, Re, Ma, Fr, epsilon/l).  The Froude number is only important if there is a free surface present.  Surface roughness is often unimportant in therms of lift as well.  The importance of Ma is low except for high-speed subsonic and supersonic flows.  Reynolds number also yields no great impact; however, for high-Re flows, shear stress has little effect on the shape of an object is the key factor in the lift force placed on it.

Bodies designed to generate lift, like airfoils, typically do so by generating a pressure distribution that is different on the top (low) and bottom (high) surface of the body.  For symmetric airfoils to generate lift, they must be moving through the fluid at some angle of attack.  For asymmetric airfoils, there is some non-zero angle of attack for which no lift is generated.  If the angle of attack is too large, however, the boundary layer along the airfoil separates and is unable to reattach to the body.  This event is known as stall, and it is especially dangerous if it occurs for low-flying aircraft.  For calculation of CL, the planform area (A = b*c) is used, where b is the length of the airfoil (into the page), and c is the chord length.  Thus, the lift is the dynamic pressure times the planform area of the wing.  The wing loading or average lift per unit area of the wing (L/A) is also useful for design, as is the aspect ratio (b*b)/A.  From these characteristics, it can be determined that longer wings are more efficient, but more difficult to maneuver in flight.

Since, for most cases, the shear stress is not important for calculating lift, the potential flow solution can be employed to determine this force.  For airfoils at angles of attack not equal to zero, the potential solution alone causes incorrect streamlines at the trailing edge of the airfoil.  This can be corrected with the addition of circulation or clockwise swirl to the solution.  While this may seem random, arbitrary, or inappropriate, this addition has well founded physical and mathematical grounds.

Next week, we'll look at calculating lift and drag.  Happy studying!


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