Aerodynamics and propulsion - Research Paper Example

?Aerodynamics and Propulsion Principles a) Explain how lift force is generated (include a sketch of a typical cambered aerofoil)? Lift is a force generally associated with an object moving inside the fluid, with the direction being either vertical or in some cases, perpendicular to the direction of motion. A classic example of where lift is used is the wings of an aircraft. As the aircraft moves horizontally, the shape of the wings create a pressure gradient beneath its top and bottom surface, hence creating a vertically upwards force (Munson, Young and Okiishi). When an object moves through a fluid, it mostly experiences a force due to the pressure forces acting on the body. If the forces are acting on opposite ends of different magnitudes, they tend to create a net pressure force. For a symmetric object moving in a fluid, with its line of symmetry being parallel to the direction of motion of the fluid, no lift would be generated because the forces would cancel each other. Hence, to create a lift force, a symmetric object must have its line of symmetry at an angle to the direction of motion, or be non-symmetric. Non-symmetric objects may also move at an angle inside the fluid, and this angel is called the angle of attack (Munson, Young and Okiishi). In the case of an aerofoil which is depicted below, it can be seen that the section of the top surface over which air is flowing is greater than the area of the bottom surface. To ensure that conservation of mass is not violated, the speed of the air at the top is increased so that the total horizontal displacement of the air at the top and bottom are the same (Abhinav). We know from Bernoulli’s equation, that an increase in velocity results in decrease in pressure. Using this argument, the pressure on the top surface is lower than the pressure at the bottom surface. Since the lift is only caused by force acting in the vertically up direction, only the horizontal cross-sectional area creates the vertically upward force due to non-symmetric pressure distribution on the top and bottom surface. This is called lift (Munson, Young and Okiishi). Figure 1 : An Aerofoil (Abhinav) The mathematical expression to calculate lift is given as follows: Where is the lift coefficient, usually calculated empirically, 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). The lift coefficient is a key factor for objects that create lift. It depends on shape, the fluid properties and the surface roughness. A general expression for this coefficient is given as: Where Re is the ratio of inertial forces to viscous forces; Fr is the Froude number, the ration between inertia forces and gravitational forces; Ma is the speed of the fluid relative to the speed of sound in that fluid; and is a measure of surface roughness (Munson, Young and Okiishi). In other words, the fluid’s temperature, density, speed, viscosity, as well as the shape of the object, surface roughness and angle of attack, amongst other things, have a say in the determination of the lift forces. b) Describe how atmospheric parameters (temperature, pressure, density) affect the generation of lift and drag as an aircraft gains altitude? As discussed previously, the fluid’s temperature, density, speed, viscosity, as well as the shape of the object, surface roughness and angle of attack, amongst other things, have a say in the determination of the lift forces. Let us now discuss the effects of a few these parameters on the lift force and lift coefficient. Coming back to the case of the aircraft: as the aircraft moves at a higher altitude, where the air is thinner and less dense because of the gravitational effects forcing the mass of air to move downwards, the lift force, which is directly proportional to the density of the fluid, decreases with the decrease in density. Another factor is temperature. At higher elevations, the temperature of the air is lower, which creates an increase in density, the lift force is likely to increase. However, gravitational effect outweighs the effect of temperature and air does get thinner with higher altitudes giving aircraft less lift. Also, as the aircraft moves at higher altitudes air pressure also decreases, and thus, the differential pressure gradient created by the aerofoil wings decreases and creates less lift (Munson, Young and Okiishi). As mentioned before, the vertical force is known as lift. The horizontal force, either created by pressure differences or viscous shearing effects, is known as drag force. Drag causes retardation to motion, and for most applications, is an undesirable force, just like friction. Plane tickets would be much cheaper if drag was not a factor of aerodynamics. The major difference between drag and lift forces is that drag forces are always present, regardless of the symmetry of the object or zero angle of attack (Abhinav). Unlike lift, there are two kinds of drag forces. The first is the drag caused by non-symmetric fluid field of an object creating pressure differences, just like the lift force. The mathematical expression for this kind of drag is given as: Where is the drag coefficient, comparable to the lift coefficient (Munson, Young and Okiishi). If this is the case, a symmetric ball, moving in air, should show no retardation since the pressure fields on both sides would cancel each other out. This is not true due to the presence of shearing forces. When an object moves in air, viscous forces from the fluid cause a retardation effect on the object. In most cases, the viscous forces also cause the separation of the fluid from the surface of the object, creating higher pressure differential forces. The aerofoils are streamlined to minimize this effect (Munson, Young and Okiishi). a) As lift is generated there is production of induced drag. What is induced drag and how can its affect be seen on an aircraft? When an object is moving with an angle of attack inside a fluid, depending on the shape and desired type of force required, that might not always be the case. Consider a non-symmetric aerofoil at an angle in air. Due to the angle, the lift will not be vertical but also at an angle. The effective lift will be the vertical component of this true lift, while the horizontal component, will create drag, also known as induced drag (Munson, Young and Okiishi). b) Describe how drag varies with airspeed and the generation of lift. Drag will always be present on a moving body, even though lift is not produced. What do we call this type of drag and how does shape affect it? Unlike lift, there are two kinds of drag forces. The first is the drag caused by non-symmetric fluid field of an object creating pressure differences, just like the lift force. The second kind of drag is due to presence of viscous effects in a fluid, since no fluid has zero viscosity. When an object moves in air, viscous forces from the fluid cause a retardation effect on the object. In most cases, the viscous forces also cause the separation of the fluid from the surface of the object, creating higher pressure differential forces. The aerofoils are streamlined to minimize this effect (Munson, Young and Okiishi), but there is eventually some drag present during motion due to viscous effects. The following diagram shows the effect of increasing speed and its contribution to the drag. As the speed increases, due to the exponential variation of the total drag with speed, the curve is as follows; The drag generated in this case is termed as parasite drag. The mathematical expression for drag is given as: Where is the drag coefficient, comparable to the lift coefficient (Munson, Young and Okiishi). It is very much dependent on the shape of the object and orientation. A blunt object would have larger drag while a sharper or smooth object would have less drag. Round objects tend to have less drag than rectangular objects. Generally, objects that allow smooth flow over them without creating flow restrictions or prevent velocity separation, have low drag and drag coefficients. c) The drag versus velocity curve is often known as a drag polar. The drag polar is often used to link in with aircraft power curves. How are the power required curves and the drag polar linked? If we compare the two general formulas for lift coefficient and drag coefficient presented in this document, we can see their similarities, as well as the fact that they are dependent on the same factors, and only the orientation of the motion being the dividing factors between these two forces. Hence, they can be related to each other and this dependence of the coefficient of drag and coefficient of lift is known as the drag polar (Munson, Young and Okiishi). Figure 3: Drag Polar The following graph on the next page shows that as the air speed, given in non-dimensional form of Reynolds number, increases, the drag coefficient decreases, and this provides the link between drag polar, and the power curve. Figure 4: Drag Coefficient vs. Reynolds Number (Eccomoder) d) Describe the operation of supersonic wind tunnels explain why the size of the working area is so small. As Aircraft materials and technology become more advanced the ability of an aircraft to ravel faster continues, how have designers changed their approach to testing new designs to keep pace with the higher operation speeds now possible? Wind tunnels are used to study the effects of different parameters on the tested object, such as a car model or an aircraft model, instead of actually building the car or aircraft and hence, saving millions of dollars. The drag and lift coefficients are empirical results, and hence, to build an actual aircraft and then optimize the shape to reduce drag and increase lift would amount to momentous costs. Hence, wind tunnels help reduce the cost of design and testing. Since these coefficients are dependent on dimensionless quantities, to obtain accurate results, these dimensionless quantities must be duplicated in the wind tunnel as to what they would be in actual operations. Take for example the Reynolds’s number, which is a multiple of speed and object dimensions. To reduce the cost of the model, we reduce the size of the aircraft, and hence, to keep the Reynolds’s number the same, the velocity of the air moving past must be increased. This is why wind tunnels are generally supersonic or even hypersonic. As the size of the object tested gets smaller, the wind rating of a wind tunnel increases (Munson, Young and Okiishi). In this advanced age, the focus has been on developing lighter, stronger and more durable materials. This has allowed aircraft to be made of lighter, engines more efficient and thus allowing them to travel larger distances. The reduced weight has the advantage of allowing the aircraft to travel at higher altitudes, where there is less drag and increasing the fuel economy as well. However, the modern day research on aircraft has not been on speed, but on economy. The reason behind this is simple. Higher speeds mean higher drag forces and hence, more fuel costs and pollution. It is a trade-off between time and money, and so far, most of the work is done in decreasing the cost, while the speed of aircraft has been kept just under the sound barrier. Works Cited Abhinav, Addala Sai. "Aerofoil." 23 November 2010. KNowledge of Aeronautics. 30 January 2011 . Eccomoder. A Crash Course in Aerodynamics and an Introduction to Turbulence. 21 February 2008. 30 January 2011 . Munson, Bruce Roy, Donald F. Young and Theodore H. Okiishi. Fundamentals of Fluid Mechanics. Wiley Publications, 2008. Read More