The next time you hear an airplane flying overhead, look up, and pause for a moment. What you see is a machine that is heavier than air, but which is somehow being sustained in the air. This is due to the airflow over the airplane. This airflow exerts a lift force which counteracts the weight of the airplane and sustains it in the air—a good thing. The airflow also exerts a drag force on the airplane which retards its motion—a bad thing. The drag must be counteracted by the thrust of the engine in order to keep the airplane going. The production of thrust by the engine consumes energy. Hence, the energy efficiency of the airplane is intimately related to aerodynamic drag. This is just one of many examples where the disciplines of aerodynamics and energy interact.
Aerodynamics deals with the flow of gases, particularly air, and the interaction with objects immersed in the flow. The interaction takes the form of an aerodynamic force and moment exerted on the object by the flow, as well as heat transfer to the object (aero-dynamic heating) when the flow velocities exceed several times the speed of sound.
SOURCES OF AERODYNAMIC FORCE
Stop for a moment, and lift this book with your hands. You are exerting a force on the book; the book is feeling this force by virtue of your hands being in contact with it. Similarly, a body immersed in a liquid or a gas (a fluid) feels a force by virtue of the body surface being in contact with the fluid. The forces exerted by the fluid on the body surface derive from two sources. One is the pressure exerted by the fluid on every exposed point of the body surface. The net force on the object due to pressure is the integrated effect of the pressure summed over the complete body surface. In the aerodynamic flow over a body, the pressure exerted by the fluid is different at different points on the body surface (i.e., there is a distribution of variable values of pressure over the surface). At each point, the pressure acts locally perpendicular to the surface. The integrated effect of this pressure distribution over the surface is a net force—the net aerodynamic force on the body due to pressure. The second source is that due to friction between the body surface and the layer of fluid just adjacent to the surface. In an aerodynamic flow over a body, the air literally rubs over the surface, creating a frictional shear force acting on every point of the exposed surface. The shear stress is tangential to the surface at each point, in contrast to the pressure, which acts locally perpendicular to the surface. The value of the shear stress is different at different points on the body surface. The integrated effect of this shear stress distribution is a net integrated force on the body due to friction.
The pressure (p) and shear stress (τω) distributions over an airfoil-shaped body are shown schematically in Figure 1. The pressure and shear stress distributions exerted on the body surface by the moving fluids are the two hands of nature that reach out and grab the body, exerting a net force on the body—the aerodynamic force.
RESOLUTION OF THE AERODYNAMIC FORCE
The net aerodynamic force exerted on a body is illustrated in Figure 2 by the arrow labeled R. The direction and speed of the airflow ahead of the body is denoted by V ∞, called the relative wind. The body is inclined to V ∞. by the angle of attack, α. The resultant aerodynamic force R can be resolved into two components; lift, L, perpendicular to V ∞; and drag, D, parallel to V ∞. In Figure 2, R is shown acting through a point one-quarter of the body length from the nose, the quarter-chord point. Beacuse the aerodynamic force derives from a distributed load due to the pressure and shear stress distributions acting on the surface, its mechanical effect can be represented by a combination of the net force vector drawn through any point and the resulting moment about that point. Shown in Figure 2 is R located (arbitrarily) at the quarter-chord point and the moment about the quarter-chord point, Mc/4.
The aerodynamic force varies approximately as the square of the flow velocity. This fact was established in the seventeenth century—experimentally by Edme Marione in France and Christiaan Huygens in Holland, and theoretically by Issac Newton. Taking advantage of this fact, dimensionless lift and drag coefficients, C L and C D respectively, are defined as where ρ ∞, is the ambient density in the freestream, and S is a reference area, which for airplanes is usually chosen to be the planform area of the wings (the projected wing area you see by looking at the wing directly from the top or bottom), and for projectile-like bodies is usually chosen as the maximum cross-sectional area perpendicular to the axis ofthe body (frontal area).
At flow speeds well below the speed of sound, the lift coefficient depends only on the shape and orientation (angle of attack) of the body: The drag coefficient also depends on shape and α, but in addition, because drag is partially due to friction, and frictional effects in a flow are governed by a powerful dimensionless quantity called Reynolds number, then C D is also a function of the Reynolds number, Re: where Re ≅ ρ∞V∞, c/μ∞. Here, c is the reference length of the body and μ∞ is the viscosity coefficient of the fluid. At speeds near and above the speed of sound, these coefficients also become functions of Mach number, M∞ ≅ V∞/a∞, where a∞, is the speed of sound in the freestream: Page 9 | Top of Article The lift and drag characteristics of a body in a flow are almost always given in terms of C L and C D rather than the forces themselves, because the force coefficients are a more fundamental index of the aerodynamic properties.
One of the most important aerodynamic effects on the consumption of energy required to keep a body moving through a fluid is the aerodynamic drag. The drag must be overcome by the thrust of a propulsion mechanism, which in turn is consuming energy. Everything else being equal, the higher the drag, the more energy is consumed. Therefore, for energy efficiency, bodies moving through a fluid should be low-drag bodies. To understand how to obtain low drag, we have to first understand the nature of drag, and what really causes it.
The influence of friction on the generation of drag is paramount. In most flows over bodies, only a thin region of the flow adjacent to the surface is affected by friction. This region is called the boundary layer (Figure 3). Here, the thickness of the boundary layer is shown greatly exaggerated; in reality, for ordinary flow conditions, the boundary layer thickness, δ, on the scale of Figure 3 would be about the thickness of a sheet of paper. However, the secrets of drag production are contained in this very thin region. For example, the local shear stress at the wall, labeled in Figure 3 as τω, when integrated over the entire surface creates the skin friction drag Df on the body. The magnitude of τω, hence, Df, is determined by the nature of the velocity profile through the boundary layer, (i.e., the variation of the flow velocity as a function of distance y normal to the surface at a given station, x, along the surface). This velocity variation is quite severe, ranging from zero velocity at the surface (due to friction, the molecular layer right at the wall is at zero velocity relative to the wall) to a high velocity at the outer edge of the boundary layer. For most fluids encountered in aerodynamics, the shear stress at the surface is given by the Newtonian shear stress law:
where μ is the viscosity coefficient, a property of the fluid itself, and (dV/dy) y=0 is the velocity gradient at the wall. The more severe is the velocity variation in the boundary layer, the larger is the velocity gradient
at the wall, and the greater is the shear stress at the wall.
The above discussion has particular relevance to drag when we note that the flow in the boundary layer can be of two general types: laminar flow, in which the streamlines are smooth and regular, and an element of the fluid moves smoothly along a streamline; and turbulent flow, in which the streamlines break up and a fluid element moves in a random, irregular, and tortuous fashion. The differences between laminar and turbulent flow are dramatic, and they have a major impact on aerodynamics. For example, consider the velocity profiles through a boundary layer, as sketched in Figure 4. The profiles are different, depending on whether the flow is laminar or turbulent. The turbulent profile is "fatter," or fuller, than the laminar profile. For the turbulent profile, from the outer edge to a point near the surface, the velocity remains reasonably close to the freestrearn velocity; it then rapidly decreases to zero at the surface. In contrast, the laminar velocity profile gradually decreases to zero from the outer edge to the surface. Now consider the velocity gradient at the wall, (dV/dy) y=0, which is the reciprocal of the slope of the curves shown in Figure 4 evaluated at y = 0. It is clear that (dV/dy) y=0 for laminar flow is less than (dV/dy) y=0 for turbulent flow. Recalling the Newtonian shear stress law for τω leads us to the fundamental and highly important fact that laminar stress is less than turbulent shear stress:
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This obviously implies that the skin friction exerted on an airplane wing or body will depend on whether the boundary layer on the surface is laminar or turbulent, with laminar flow yielding the smaller skin friction drag.
It appears to be almost universal in nature that systems with the maximum amount of disorder are favored. For aerodynamics, this means that the vast majority of practical viscous flows are turbulent. The boundary layers on most practical airplanes, missiles, and ship hulls, are turbulent, with the exception of small regions near the leading edge. Consequently, the skin friction on these surfaces is the higher, turbulent value. For the aerodynamicist, who is usually striving to reduce drag, this is unfortunate. Today, aerodynamicists are still struggling to find ways to preserve laminar flow over a body—the reduction in skin friction drag and the resulting savings in energy are well worth such efforts. These efforts can take the form of shaping the body in such a way to encourage laminar flow; such "laminar flow bodies" are designed to produce long distances of decreasing pressure in the flow direction on the surface (favorable pressure gradients) because an initially laminar flow tends to remain laminar in such regions. Figure 5 indicates how this can be achieved. It shows two airfoils, the standard airfoil has a maximum thickness near the leading edge, whereas the laminar flow airfoil has its maximum thickness near the middle of the airfoil. The pressure distributions on the top surface on the airfoils are sketched above the airfoils in Figure 5. Note that for the standard airfoil, the minimum pressure occurs near the leading edge, and there is a long stretch of increasing pressure from this point to the trailing edge. Turbulent boundary layers are encouraged by such increasing pressure distributions. The standard airfoil is generally bathed in long regions of turbulent flow, with the attendant high skin friction drag. Note that for the laminar flow airfoil, the minimum pressure occurs near the trailing edge, and there is a long stretch of decreasing pressure from the leading edge to the point of minimum pressure. Laminar boundary layers are encouraged by such decreasing pressure distributions. The laminar flow airfoil can be bathed in long regions of laminar flow, thus benefiting from the reduced skin friction drag.
The North American P-51 Mustang, designed at the outset of World War II, was the first production aircraft to employ a laminar flow airfoil. However, laminar flow is a sensitive phenomenon; it readily gets unstable and tries to change to turbulent flow. For example, the slightest roughness of the airfoil surface caused by such real-life effects as protruding rivets, imperfections in machining, and bug spots can cause a premature transition to turbulent flow in advance of the design condition. Therefore, most laminar flow airfoils used on production aircraft do not yield the extensive regions of laminar flow that are obtained in controlled laboratory tests using airfoil models with highly polished, smooth surfaces. From this point of view, the early laminar flow airfoils were not successful. However, they were successful from an entirely different point of view; namely, they were found to have excellent high-speed properties, postponing to a higher flight Mach number the large drag rise due to shock waves and flow separation encountered near Mach 1. As a result, the early laminar flow airfoils were extensively used on jet-propelled airplanes during the 1950s and 1960s and are still employed today on some modem high-speed aircraft.
In reality, the boundary layer on a body always starts out from the leading edge as laminar. Then at some point downstream of the leading edge, the laminar boundary layer become unstable and small "bursts" of turbulent flow begin to grow in the flow. Finally, over a certain region called the transition region, the boundary layer becomes completely turbulent. For purposes of analysis, it is convenient to draw a picture, where transition is assumed to occur at a point located a distance x cr, from the leading edge. The accurate knowledge of where transition occurs is vital to an accurate prediction of skin friction drag. Amazingly, after almost a century of research on turbulence and transition, these matters are still a source of great uncertainty in drag predictions today. Nature is still keeping some of her secrets from us.
Skin friction drag is by no means the whole story of aerodynamic drag. The pressure distribution integrated over the surface of a body has a component parallel to the flow velocity V ∞, called form drag, or more precisely pressure drag due to flow separation. In this type of drag, such as the flow over a sphere, the boundary layer does not totally close over the back surface, but rather separates from the surface at some point and then flows downstream. This creates a wake of low-energy separated flow at the back surface. The pressure on the back surface of the sphere in the separated wake is smaller than it would be if the flow were attached. This exacerbates the pressure difference between the higher pressure on the front surface and the lower pressure on the back surface, increasing the pressure drag. The bigger (fatter) the wake, the higher the form drag. Once again we see the different effects of laminar and turbulent flow. In the case where the boundary layer is laminar, Page 12 | Top of Article the boundary layer separates near the top and bottom of the body, creating a large, fat wake, hence high pressure drag. In contrast, where the boundary layer is turbulent, it separates further around the back of the sphere, creating a thinner wake, thus lowering the pressure drag. Form drag, therefore, is larger for laminar flow than for turbulent flow. This is the exact opposite of the case for skin friction drag. To reduce form drag, you want a turbulent boundary layer.
For a blunt body, such as a sphere, almost all the drag is form drag. Skin friction drag is only a small percentage of the total drag. For blunt bodies a turbulent boundary layer is desirable. Indeed, this is the purpose of the dimples on the surface of a golf ball—to promote turbulent flow and reduce the aerodynamic drag on the ball in flight. The nose of an airplane is large compared to a golf ball. Hence, on the airplane nose, the boundary layer has already become a turbulent boundary layer, transitioning from laminar to turbulent in the first inch or two from the front of the nose. Therefore, dimples are not necessary on the nose of an airplane. In contract, the golf ball is small—the first inch or two is already too much, so dimples are placed on the golf ball to obtain turbulent flow right from the beginning.
For a body that is producing lift, there is yet another type of drag—induced drag due to lift. For example, consider an airplane wing, that produces lift by creating a higher pressure on the bottom surface and a lower pressure on the top surface. At the wing tips, this pressure difference causes the flow to try to curl around the tips from the bottom of the tip to the top of the tip. This curling motion, superimposed on the main freestream velocity, produces a vortex at each wing tip, that trails downstream of the wing. These wing tip vortices are like minitornadoes that reach out and alter the pressure distribution over the wing surface so as to increase its component in the drag direction. This increase in drag is called induced drag; it is simply another source of pressure drag on the body.
Finally, we note that if the body is moving at speeds near and above the speed of sound (transonic and supersonic speeds), shock waves will occur that increase the pressure on the front portions of the body, contributing an additional source of pressure drag called wave drag.
In summary, the principal sources of drag on a body moving through a fluid are skin friction drag,
form drag, induced drag, and wave drag. In terms of drag coefficients, we can write: where C D is the total drag coefficient, C D, f is the skin friction drag coefficient, C D, p is the form drag coefficient (pressure drag due to flow separation), C D, i is the induced drag coefficient, and C D, w is the wave drag coefficient.
The large pressure drag associated with blunt bodies such as the sphere, leads to the design concept of streamlining. Consider a body of cylindrical cross section of diameter d with the axis of the cylinder oriented perpendicular to the flow, as shown in Figure 6a. There will be separated flow on the back face of the cylinder, with a relatively fat wake and with the associated high pressure drag. The bar to the right of the cylinder denotes the total drag on the cylinder; the shaded portion of the bar represents skin friction drag, and the open portion represents the pressure drag. Note that for the case of a blunt body, the drag is relatively large, and most of this drag is due to pressure drag. However, look at what happens when we wrap a long, mildly tapered after-body on the back of the cylinder, creating a teardrop-shaped body sketched in Figure 6b. This shape is a streamlined bod, of the same thickness d as the cylinder. Flow separation on the streamlined body will be delayed until much closer to the trailing edge, with an attendant, much smaller wake. As a result, the pressure drag of the streamlined body will be much smaller than that for the cylinder. Indeed, as shown by the bar to the right of Figure 6b, the total drag of the streamlined body will be almost a factor of 10 smaller than that of the cylinder of same thickness. The friction drag of the streamlined body will be larger due to its increased surface area, but the pressure drag is so much less that it dominates this comparison.
Streamlining has a major effect on the energy efficiency of bodies moving through a fluid. For example, a bicycle with its odd shaped surfaces, has a relatively large drag coefficient. In contrast, a streamlined outer shell used for recumbent bicycles reduces the drag and has allowed the speed record to reach 67 mph. Streamlining is a cardinal principle in airplane design, where drag reduction is so important.
Streamlining has a strong influence on the lift-to-drag ratio (L/D, or C L/C D) of a body. Lift-to-drag ratio is a measure of aerodynamic efficiency. For example, the Boeing 747 jumbo-jet has a lift-to-drag ratio of about 20. This means it can lift 20 lb at the cost of only 1 pound of drag—quite a leverage. In airplane design, an increase in L/D is usually achieved by a decrease in D rather than an increase in L. Vehicles that have a high L/D are that way because they are low-drag vehicles.
DRAG AND ENERGY
We now make the connection between aerodynamic drag and energy consumption, The drag of a moving vehicle must be overcome by the thrust from a propulsive mechanism in order to keep the vehicle in sustained motion. The time rate of energy consumption is defined as power, P. The power required to keep the vehicle moving at a given speed is the product of drag times velocity,
That is, the power required varies as the cube of the
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velocity, and directly as the drag coefficient. This clearly indicates why, as new vehicles are designed to move at higher velocities, every effort is made to reduce C D. Otherwise, the velocity-cubed variation may dictate an amount of energy consumption that is prohibitive. Note that this is one of the realities facing civil transport airplanes designed to fly at super-sonic speeds. No matter how you look at it, less drag means more energy efficiency.
The effect of aerodynamics on the energy consumption of transportation vehicles can be evaluated by using the dimensionless specific energy consumption, E, defined as E = P/WV, where P is the power required to move at velocity V and W is the weight of the vehicle, including its payload (baggage, passengers, etc.). Although power required increases as the cube of the velocity, keep in mind that the time required to go from point A to point B is inversely proportional to V, hence a faster vehicle operates for less time between two points. The quantity E = P/WV is the total energy expended per unit distance per unit weight; the smaller the value of E, the smaller the amount of energy required to move 1 lb a distance of 1 ft (i.e., the more energy efficient the vehicle). Representative values of E for different classes of vehicles (trains, cars, airplanes) are given in Figure 7. Using E as a figure of merit, for a given long distance trip, trains such as the Amtrak Metroliner and the French high-speed TGV are most efficient, airplanes such as the Boeing 747, are next, and automobiles are the least efficient.
DRAG OF VARIOUS VEHICLES
Let us examine the drag of various representative vehicles. First, in regard to airplanes, the evolution of streamlining and drag reduction is clearly seen in Figure 8, which gives the values of drag coefficient based on wing planform area for a number of different aircraft, plotted versus years. We can identify three different periods of airplanes, each with a distinctly lowered drag coefficient: strut-and-wire biplanes, mature propeller-driven airplanes, and modem jet airplanes. Over the past century, we have seen a 70 percent reduction in airplane drag coefficient. Over the same period, a similar aerodynamic drag reduction in automobiles has occurred. By 1999, the drag coefficients for commercialized vehicles have been reduced to values as low as 0.25. There are experimental land vehicles with drag coefficients on par with jet fighters; for example, the vehicles built for the solar challenge races, and some developmental electric vehicles.
The generic effect of streamlining on train engines is similar, with the drag coefficient again based on frontal area. The high-speed train engines of today have drag coefficients as low as 0.2.
For motorcycles and bicycles, the drag coefficient is not easy to define because the proper reference area is ambiguous. Hence, the drag is quoted in terms of the "drag area" given by D/q, where q is the dynamic pressure; q = 1⁄2ρ ∞ V ∞2. A typical drag area for a motorcycle and rider can be reduced by more than fifty percent by wrapping the motorcycle in a streamlined shell.
Aerodynamics is one of the applied sciences that plays a role in the overall consideration of energy. We have explained some of the more important physical aspects of aerodynamics, and illustrated how aerodynamics has an impact on energy efficiency.
John D. Anderson, Jr.
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Anderson, J. D., Jr. (1997). A History of Aerodynamics, and Its Impact on Flying Machines. New York: Cambridge University Press.
Anderson, J. D., Jr. (2000). Introduction to Flight, 4th ed. Boston: McGraw-Hill.
Tennekes, H. (1992). The Simple Science of Flight. Cambridge, MA: MIT Press.
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Gale Document Number: GALE|CX3407300013