diameter of a duct), the fluid begins to slow. If the slope of the divergent section is high, the flow consequently forms an unfavorable pressure gradient (i.e., hinders the boundary layer flow) as seen by the velocity profiles in Figure 3.18.
Small characteristic lengths and low speeds result in low Reynolds numbers and consequently laminar flow, which is normally a favorable condition. A point is reached in this situation where the unfavorable pressure gradient actually stops the flow within the boundary layer and eventually reverses it. The flow stoppage and reversal results in the formation of turbulence, vortices, and in general a random mixing of the fluid particles.
At this point, the boundary layer detaches or separates from the surface and creates a turbulent wake. This phenomenon is called separation, and the drag associated with it is called vortex drag. Whether the boundary layer is turbulent or laminar depends on the Reynolds number, as does the friction coefficient, as shown in Figure 3.19.
It would seem that laminar flow is always desired (for less pressure drag), and usually it is, but it can become a problem when dealing with very small UAVs that fly at low speeds. The favorable and unfavorable pressure gradients previously described also exist at very low speeds, making it possible for the laminar boundary layer to separate and reattach itself. This keeps the surface essentially in the laminar flow region, but creates a bubble of fluid within the boundary layer. This is called laminar separation and is a characteristic of the wings of very small, low‐speed airplanes (e.g., small model airplanes and very small UAVs).
The bubble can move about on the surface of the wing, depending on the angle of attack, speed, and surface roughness. It can grow in size and then can burst in an unexpected manner. The movement and bursting of the bubble disrupts the pressure distribution on the surface of the wing and can cause serious and sometimes uncontrollable air‐vehicle motion. This has not been a problem with larger, higher speed airplanes because most of the wings of these airplanes are in turbulent flow boundary layers due to the high Reynolds number at which they operate.
Figure 3.18 Boundary layer velocity profile inside a convergent–divergent duct
Figure 3.19 Skin friction versus Reynolds number
Specially designed airfoils are required for small lifting surfaces to maintain laminar flow, or the use of “trip” devices (known as turbulators) to create turbulent flow. In either case, the laminar separation bubble is either eliminated or stabilized by these airfoils. Laminar separation occurs with Reynolds numbers of about 75,000. Control surfaces, such as the elevator and aileron, are particularly susceptible to laminar separation.
3.10 Friction Drag
The friction drag mainly includes all types of drag that do not depend on production of the lift. Every aerodynamic component of aircraft (i.e., the components that are in direct contact with flow) generates friction drag. Typical components are the wing, horizontal tail, vertical tail, fuselage, landing gear, antenna, engine nacelle, camera, and strut. The zero‐lift drag is primarily a function of the external shape of the components.
Since the performance analysis is based on aircraft drag, the accuracy of aircraft performance analysis relies heavily on the calculation accuracy of friction drag (i.e., CDo). The CDo of an aircraft is simply the summation of CDo of all contributing components:
where CDof, CDow, CDoht, CDovt, CDoLG, CDoN, CDoS, and CDoP are respectively representing fuselage, wing, horizontal tail, vertical tail, landing gear, nacelle, strut, and external payload contributions in aircraft CDo. The three dots at the end of Equation (3.13) illustrate that there are other components that are not shown here. They include non‐significant components such as the antenna and pitot tube. In the majority of fixed‐wing conventional air vehicles, wing and fuselage each contribute about 30%‐40% (a total of about 60%–80%) to aircraft CDo.
Reference [12] provides a build‐up technique to calculate the contribution of each component to CDo of an aircraft. The majority of the equations are based on flight test data and wind tunnel test experiments, so the technique is mainly relying on empirical formulas.
3.11 Total Air‐Vehicle Drag
The total resistance to the motion of a subsonic air‐vehicle wing is made up of two components: the drag due to lift (induced drag) and the profile drag, which in turn is composed of the friction drag and the pressure drag (due to flow separation). For the overall air vehicle, the drag of all the non‐lift parts (e.g., fuselage, landing gear, and payload) are lumped together and called parasite (or parasitic) drag. If the various drag components are expressed in terms of drag coefficients, then simply multiplying their sum by the dynamic pressure (q) and a characteristic area (usually the wing area, S) results in the total drag:
(3.14)
where CDo is the sum of all the profile drag coefficients (it is also referred to as the zero‐lift drag coefficient) and CDi is the induced drag coefficient, whose quadratic form results in the parabolic shape of the polar curve (see Figure 3.13).
The ScanEagle UAV – developed by Boing Insitu – is composed of four field‐replaceable major modules/components: (1) nose (including payload sensors), (2) fuselage, (3) Wing, and (4) prop‐driven engine. The UAV has a cylindrical fuselage of 2 m long with a mid‐mounted swept‐back wing with winglets, endplate vertical tail and movable rudders. The nose carries a pitot tube, which is fitted with an anti‐precipitation system for cold weather operation. The air vehicle is fitted with a pusher piston engine (0.97 kW) with a two‐blade propeller. All of these external components contribute to the total vehicle drag.
Moreover,
