## Lift and drag forces fluid and turbine machinery

Here we introduce the forces of lift and drag which are as fundamental to turbine motion as they are to sailing yachts and airplanes, for they apply to any solid object immersed in a fluid flow. Obtaining rotary motion on a shaft from a flow of water or air is the basis of every turbine, relating, in this book, to hydro turbines (Section 8.4 onwards for conventional hydropower, Sections 13.4 and 13.5 for tidal power), wind turbines (Section 9.2 onwards), and wave power turbines, (included in Section 12.5).

In Figure 2.7(a) a solid object is immersed asymmetrically in a fluid so there is a relative fluid velocity flowing from left to right. However, because of intricacies of the flow pattern passing the object, the resulting force on the object is unlikely to be parallel to the upstream flow. If the total (vector)

Figure 2.7 Sketches to illustrate fluid flow around moving objects. (a) Any object moving at relative velocity u will experience both lift and drag forces. (b) Smooth streamlines to reduce drag. (c) Contorted streamlines to increase drag. (d) Section of airfoil wing, shaped to increase lift and reduce drag.

Figure 2.7 Sketches to illustrate fluid flow around moving objects. (a) Any object moving at relative velocity u will experience both lift and drag forces. (b) Smooth streamlines to reduce drag. (c) Contorted streamlines to increase drag. (d) Section of airfoil wing, shaped to increase lift and reduce drag.

force exerted on the body is F; the drag force FD is the component of that force in the direction of the upstream flow and the lift force FL is the component normal to the flow. It is the lift force that twists and turns the object. To illustrate how these forces arise, consider vehicles driving down a long straight open road in otherwise still air. The drag force from air resistance is reduced if the streamlines flow smoothly around the vehicle, as in the 'streamlined' car shown in Figure 2.7(b). However, even with perfect streamlining, the drag force will not be zero because of the viscous friction between the fluid and the surface of the solid, as described in Section 2.4. Since turbulence greatly increases the effect of such friction, as explained in Section 2.5, a vehicle designer seeking minimum fuel consumption and good performance reduces drag with fluid flow around the vehicle as smooth as possible, with few sharp corners and projecting parts.

Figure 2.7(c) illustrates a vehicle being slowed down by a parachute, as in some cars seeking speed records. Increased drag, the opposite of streamlining, is now required. Some typical fluid pathlines are indicated from the relative motion of the body and the fluid that determines the flow pattern, and as measured by an observer moving beside at the velocity of the car. In the observer's frame of reference, the fluid air hits the parachute and loses most of its forward momentum. By the momentum theorem, a force has been exerted on the fluid by the body (i.e. by the car and its parachute). Consequently, the fluid has exerted an equal and opposite force on the body. This force is in the direction of the flow and is a classic example of a drag force. This set of forces is analogous to that in an impulse turbine (compare Figure 8.3 for hydro power, a cup anemometer (Figure 9.4b) and a wind 'drag machine' (Section 9.3.4)).

In Figure 2.7(d), the 'vehicle' is an airplane wing; such an aerofoil is thin, with a sharp trailing edge and more curved on the top than on the bottom. This deflects and changes the flow so a positive upward force (lift) occurs, so enabling the aircraft to take off and fly. Lift force can be experienced by holding one's arm out of a moving car rear window and shaping the hand as an aerofoil; drag, of course, will also be experienced. Aerofoils are used in many other applications besides airplanes, in particular for the blades of wind turbines, where the mechanics are dominated by lift forces (Section 9.5).

Basically, an aerofoil generates lift because the flow near the top surface follows a curved path. If the local curvature of the streamline above the top surface is R (as indicated in Figure 2.7(d)) then the fluid experiences an acceleration of u2/R inwards (i.e. in this case downward towards the aerofoil); the calculation is the same as that of the centripetal force acting on a particle pulled by a string into a circular motion, given in elementary physics texts. Thus the aerofoil creates a force pulling downward on the fluid above it. By the momentum theorem, the fluid correspondingly exerts an upward force on the wing. Since the curvature is less on the lower side, the corresponding forces (now upward on the fluid, downward on the aerofoil) are smaller than those on the upper side. The result is a net upward force, lift, on the aerofoil. This force is manifested by the fluid having a higher pressure below the aerofoil than above it - a result that can be derived from Bernoulli's equation (2.3).

The same principles apply, yet the details are more complicated, when an airplane flies upside down, when a vertical-axis wind turbine blade passes across the wind every 180° of rotation (Figure 9.4b) and when air motion reverses across a Wells turbine in an oscillating-column wave power machine (Figure 12.14).

Stall for an airplane occurs when the lift force is less than the gravitational force. This can occur because the relative speed of the air and the wings has lessened, or because the orientation of all or parts of the wing has changed. Stall is a dangerous condition for an airplane, but can be helpful in a wind turbine to prevent overspeed.

## Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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