Читать книгу Wind Energy Handbook - Michael Barton Graham - Страница 126

The lift and drag of a body immersed in an oncoming flow are defined as the components of force on the body in the directions normal and parallel, respectively, to the incident flow direction.

Dimensional analysis shows that in low‐speed, steady flow (that is, flow at low Mach number, so that the relative speed of the flow is much less than the speed of sound), the lift L and drag D may be expressed in the form of non‐dimensional parameters, the lift and drag coefficients:

which are both functions of the Reynolds number,

of the flow.

Here ρ is the density and ν the kinematic viscosity of the fluid, in this case air, U is the flow speed, l is a characteristic length scale (often the mean chord c), and A is an appropriate area of the body. In the case of aerofoils, wings, or turbine blades, A is usually taken to be the plan‐form area s.c, where s is the span of the whole body or of a section of the body on which the force is evaluated. Most ‘lifting surfaces’ that are designed to provide lift with minimum accompanying drag, such as the wings of subsonic aircraft and the blades of high tip speed ratio HAWTs, are of high aspect ratio with relatively gradual changes of section (chord c, thickness, camber, and twist) with respect to the spanwise direction. For these bodies the aspect ratio is defined as the span of the blade or wings divided by the mean chord. For aircraft the span is defined as the distance between the two wing tips of the wing pair, but in the case of a wind turbine, the span is the distance from the axis of rotation to the tip of a single blade. Because of the gradual variation of properties along a wing or blade, it is very convenient and in practice sufficiently accurate usually to analyse whole wing or blade forces in terms of the sum of sectional forces and sectional force coefficients. This is taken up in Section A3.8.

This form of non‐dimensionalisation is used because it is found that for similar configurations over most regimes involving air (or water), flows of typical speeds and length scales of most practical flows, force coefficients expressed in this way vary relatively slowly with respect to the other main non‐dimensional parameter of the flow, the Reynolds number. Expressing flow‐induced forces in term of these coefficients is particularly convenient when testing flows at model scale or comparing forces induced on similar shaped bodies in different fluids or flow speeds. Typical Reynolds numbers relevant to flow around wind turbine blades are of order 10⁶ to 10⁷ (order 10⁵ for small rotors of diameter ∼1 m). In this context the term ‘low Reynolds number’ is often used to describe flows where the Reynolds number is less than about 10⁵. This regime can occur in wind‐tunnel testing of small model turbines. Strictly in fluid dynamics, the term ‘low Reynolds number’ refers to the Stokes flow regime for which the Reynolds number is of order 1 and the flow approximately satisfies the Stokes Equations. It is not relevant here. It should be noted that the factor ½ was not originally in the denominator in the definition of these coefficients but was introduced later in further development of the subjects of fluid dynamics during the twentieth century because of its occurrence in related terms in Bernoulli's equation for pressure. It is now established in use for all force, pressure, and power coefficient definitions but is not completely universal, being, for example, omitted in US definitions of rotor power and thrust coefficients for helicopters.