Aerodynamics and Propulsion Principles - Research Paper Example

?Aerodynamics and Propulsion Principles Any object moving inside or through a fluid will experience a force. This force may be along the direction ofthe motion or perpendicular or at a certain angle to the motion of that object inside the fluid. If the direction is only along the motion, it is called drag. Perpendicular force is generally termed as lift. Objects having symmetric shapes or those moving at an angle to the flow thus creating a non-symmetric flow field around themselves create the lift force (Munson, Young and Okiishi). The idea behind a lift force is non-symmetric flow field around an object causes non-symmetric pressure distribution. The easiest example is that of an aerofoil. Figure 1 shows a non-symmetric object known as an aerofoil. An important point to notice is that the length of the bottom and the top are not the same. Since the length at the bottom is less than the length at the top, air flowing beneath the aerofoil must travel slower to ensure that the displacement is equal to the displacement of the air moving above. Using Bernouilli’s equation, we know that slower velocity results in higher pressure to keep the energy of the open volume system constant. Figure 1: Generation of a lift force (Adapted from Science & Engineering Encyclopaedia , 2010) Since the pressure at the bottom is higher than the pressure above, the force acting in the vertically up direction is greater than the downward force, hence generating a net upward lift force. The active cross-sectional area remains the same on the top and bottom surfaces since only the vertical components on the forces contribute to lift, while the horizontal component contributes to drag, which is termed as induced drag (Munson, Young and Okiishi). Generally, every object has a ‘lift coefficient’, which is related to the lift force as follows: Where is the lift coefficient, L is the lift force, is the fluid density, U is the relative speed between the object and the fluid and A is the cross-sectional area (Munson, Young and Okiishi). As seen from the above equation, under similar conditions, the lift coefficient will determine the lift force. The lift coefficient itself is a function of the following: Where Re is the Reynolds Number, Fr is the Froude number, Ma is the Mach number, and is a measure of surface roughness (Munson, Young and Okiishi). In summary, the fluid density, viscosity, speed, the smoothness of the surface and shape, all contribute to the lift coefficient and determine the lift force. Taking the example of an aircraft and how changes in some of these parameters affect the lift force. A lower temperature would mean higher density and hence, greater the lift force since the lift is directly proportional to the density of the fluid, in this case, air. However, since air has a mass which is influenced by the gravity of earth, its density closer to the surface is higher and decreases with increasing altitude. As the aircraft moves up in the atmosphere, this factor dominates over the effect of lower temperature and the resulting density is lower and results in smaller lift force. As mentioned before, lift is generated for non-symmetrical objects or symmetric objects kept at an angle in a fluid flow field. The angle between the object and fluid motion is called angle of attack. Symmetric aerofoil and other objects can generate lift by changing the angle of attack. An example of this is during takeoff of an aircraft, where the aircraft lifts its nose up, hence increasing the angle of attack, which greatly increases the lift force generated allowing it to quickly climb and gain altitude (Munson, Young and Okiishi). Drag generally opposes motion and slows down objects moving inside a fluid, or slows down the speed of a fluid moving past a fixed object. Hence, aircrafts and cars are designed to minimize drag and help improve fuel efficiency. Just like the lift force, the drag force and drag coefficient can be written as: Thus, in general, as an object goes fast and faster, the drag force is exponentially likely to increase due to higher velocity (Munson, Young and Okiishi). Using the argument of symmetry, we should be able to say that for a perfectly symmetric object, for example, a ball, there should be no lift or drag force induced upon it. This is ofcourse, not true. While there may not be a lift force, there is always a drag force. Physically, there are two types of drag forces. The first is the due to shearing stresses creating near the interface of the fluid and solid due to viscous effects of the fluid. When a fluid particle comes into contact with the surface of the ball, it sticks to it, and causes a slowing down effect on the fluid participles around it. This is called the boundary layer phenomenon, where the particle at the interface is stationary while particles infinitely away from the interface are moving at the maximum fluid velocity. Hence, stress is created inside the fluid within the boundary layer just close to the surface causing drag (Munson, Young and Okiishi). The second kind of drag is due to fluid separation from the solid surface. This happens when a fluid streamline moves around an object, like a ball, does not have enough energy to move all the way along to the opposite end of the ball and hence separates, creating a much lower pressure at the backside of the object than at the front, creating pressure drag. An example of this can be bicycling up a hill. If one starts cycling up a hill with a initial speed such that the speed at the top of the hill is zero, when one comes down, the speed will not equal to the initial speed due to friction along the way. Same is the case with fluid particles. Aerofoils and cars are designed in such a way as to minimize flow separation and hence, reduce the drag force to just the drag caused by shearing stress. A combination of pressure and shearing drag is sometimes referred as the parasite drag (Munson, Young and Okiishi). Considering an aerofoil inside a horizontal flowfield with a small angle of attack, due to the non-symmetric nature of the flowfield, there will be a lift force created by the aerofoil, perpendicular to the direction of the wing cross-sectional area. Since this force is not upwards, the vertical component of this force will contribute to lift while the horizontal component will contribute to the drag. Hence, the total drag force will increase and this extra drag force is known as induced drag, since it was induced due to the presence of lift and not by shearing stresses. This kind of drag has a serious consequence on the aircraft. Generally, to gain more lift at lower speeds, the angle of attack is increased but this has a negative effect of increasing the drag too, so aircraft must use a tradeoff between higher drag and lower thrust. The following section discusses how different types of drag vary with airspeed. The curves show the power or thrust requirement increasing exponentially for increasing airspeed while the induced drag reduces with greater airspeed. The drag coefficient and the lift coefficient are both related to the angle of attack, and hence can be linked to each other as well. In other words, the drag coefficient is dependent upon the lift coefficient and this is known as the drag polar (Cavcar). Figure 4: Drag Polar (Adapted from Cavcar, 2004) Generally, the drag and lift coefficients decrease with increasing airspeed, and this allows us to link the drag polar to the aircraft power curve. The following graph shows us the drag coefficient, varying with Reynolds number, which is a non-dimensional estimate of the speed. Figure 5: Variation of Drag Coefficient with the Reynolds Number (Adapted form Wolfram Alpha, 2010) Windtunnels are generally used to estimate what kinds and magnitude of forces an object, such as a car or a plane, would undergo in real operations. The primary goal is to study these forces and to design the most optimum shape for the required purpose, such as minimizing drag. As mentioned before, the lift and drag coefficients are the unknown factors and depend on the shape of the aircraft or car, as well as non-dimensional numbers such as the Reynolds and Froude number. Hence, to make sure the wind tunnel tests are as accurate as possible, these numbers must be close to the actual numbers the car or the plane would experience in active duty. Considering the Reynolds number, which is Re = VD/µ. If we scale down the model of the aircraft, that is, decrease the dimensions, the velocity of the fluid must be increased to make sure that the Reynolds number does not change. Hence, as wind tunnels get smaller, the wind speeds become higher and the wind tunnels become supersonic or even hypersonic (Munson, Young and Okiishi). As technology has become more advanced, new stronger and lighter materials have been introduced which have allowed aircraft to become lighter and requiring less lift per volume. Thus, they can now fly at higher altitudes, which has reduced the drag force due to thinner atmosphere and increased fuel efficiency. All this has resulted in more air-travel and hence modernization of air-travel. Designers have focused on larger and more economical aircraft, flying just beneath the speed of sound than higher speeds which require much power due to increased drag and flying at lower altitude where the air is much thicker to provide more thrust. Works Cited Cavcar, Mustafa. AeroDynamic Forces and Drag Polar. 2004. 26 January 2011 . CFIT courses. Thrust, Drag, and the Power Curve. 2010. January 26 2011 . Munson, Bruce Roy, Donald F. Young and Theodore H. Okiishi. Fundamentals of Fluid Mechanics. Wiley Publications, 2008. Science & Engineering Encyclopaedia . "Aerofoil." 2010. Science & Engineering Encyclopaedia . 26 January 2011 . Wolfram Alpha. "Drag on a sphere." 17 May 2010. Computations by Wolfram|Alpha. 26 January 2011 . Read More