Notes-Elements of Aerospace Engineering.pdf

Name of Institution Elements of Aerospace Engineering 1  Name of Institution Basic fluid dynamics The basics of the fluid dynamics are required to esti...

Name of Institution Elements of Aerospace Engineering 1  Name of Institution Basic fluid dynamics The basics of the fluid dynamics are required to estimate the flow characteristics over an aircraft wings. Proper understanding of aerodynamics allows us to calculate the flow properties, such as lift and drag on the airplane. The basic principles of aerodynamics allow us to calculate the exit flow velocity and pressure, which in turn allow us to calculate the thrust. Figure: Forces on the airplane 2  Name of Institution Airfoil Nomenclature Consider the wing of an airplane, as sketched in Figure. The cross-sectional shape obtained by the intersection of the wing with the perpendicular plane shown in Figure is called an airfoil. Figure: Sketch of wing and airfoil 3  Name of Institution Airfoil Nomenclature (Cont’d) Mean camber line: It is the locus of points halfway between the upper and lower surfaces as measured perpendicular to the mean camber line itself. Figure: Basic nomenclature of airfoil 4  Name of Institution Airfoil Nomenclature (Cont’d) Camber: The camber is the maximum distance between the mean camber line and the chord line, measured perpendicular to the chord line. 5  Name of Institution Airfoil Nomenclature (Cont’d) Angle of attack: The angle between the relative wind and the chord line is the angle of attack a of the airfoil. Figure: Sketch showing AOA, drag and lift 6  Name of Institution Airfoils Airfoils, the cross-sectional shapes of wings and control surfaces, are crucial in determining the aerodynamic performance of an aircraft. Two common types of airfoils are symmetric and cambered airfoils. These airfoils differ in shape, which directly influences their aerodynamic properties, such as lift, drag, and stability. Understanding these characteristics is essential for selecting the appropriate airfoil type for different parts of an aircraft. 7  Name of Institution Symmetric Airfoil Symmetric Airfoils: A symmetric airfoil has identical upper and lower surfaces, meaning that its shape is mirrored across the chord line (the straight line connecting the leading and trailing edges of the airfoil). This results in no inherent camber, or curvature, to the airfoil. 8  Name of Institution Symmetric Airfoils Characteristics Zero Lift at Zero Angle of Attack: Because the upper and lower surfaces are identical, a symmetric airfoil produces zero lift when the angle of attack (the angle between the chord line and the oncoming airflow) is zero. Balanced Performance: Symmetric airfoils provide a balanced performance in terms of lift and drag across a wide range of angles of attack. Stability: Due to their balanced lift characteristics, symmetric airfoils tend to offer predictable and stable aerodynamic behavior. They generate lift by adjusting the angle of attack, which makes them well-suited for control surfaces where precise and reversible lift generation is required. 9  Name of Institution Symmetric Airfoils Uses Control Surfaces: Symmetric airfoils are commonly used in control surfaces such as elevators, rudders, and ailerons. These surfaces need to generate lift in both directions (up and down or left and right) depending on the control input from the pilot. The symmetric design ensures that the response to control inputs is linear and predictable. 10  Name of Institution Cambered Airfoils A cambered airfoil has an asymmetrical shape, where the upper surface is more curved than the lower surface. This curvature introduces a camber, which is a measure of the airfoil’s deviation from being symmetric. 11  Name of Institution Cambered Airfoils Characteristics Positive Lift at Zero Angle of Attack: Due to the curved upper surface, cambered airfoils generate lift even at zero or small negative angles of attack. The curvature causes the airflow to travel faster over the upper surface, reducing pressure and generating lift. Higher Lift Coefficient: Cambered airfoils generally have a higher lift coefficient compared to symmetric airfoils. This means they can generate more lift at a given angle of attack, making them more efficient in producing lift. Increased Drag: While cambered airfoils are efficient at generating lift, they also tend to produce more drag compared to symmetric airfoils, 12 especially at higher angles of attack.  Name of Institution Symmetric Airfoils Uses Main Wings: Cambered airfoils are typically used for the main wings of aircraft, where maximizing lift is crucial for flight. The higher lift coefficient and ability to generate lift at lower angles of attack make cambered airfoils ideal for sustaining flight, especially during takeoff and landing when lift is most critical. High-Lift Devices: In addition to main wings, cambered airfoils are also used in high-lift devices such as flaps and slats, which are deployed during takeoff and landing to increase the effective camber and thereby increase lift. 13  Name of Institution Forces Lift: The lift L is always defined as the component of the aerodynamic force perpendicular to the relative wind. Drag: The drag D is always defined as the component of the aerodynamic force parallel to the relative wind. Aerodynamic Center: The aerodynamic center is the point at which the pitching moment coefficient for the airfoil does not vary with angle of attack, thus, this points makes analysis simpler for the engineer. dcm dcm =0 =0 d dcL 14  Name of Institution Continuity Equation Continuity equation works on the basic principle of physics that mass can neither be created nor destroyed. Let A1 be the cross- sectional area of the stream tube at point 1, and V1 be the flow velocity at point 1. At a given instant in time, consider all the fluid elements that are momentarily in the plane of A1. After a lapse of time dt, these same fluid elements all move a distance Vi Figure: Stream tube with mass dt; as shown in Figure. conservation 15  Name of Institution Continuity Equation (Cont’d) In so doing, the elements have swept out a volume ( A1V1 dt) downstream of point 1. The mass of gas, dm, in this volume is equal to the density times the volume, i.e., dm = 1 ( AV 1 1dt ) …(1) …(2) Also, the mass flow through A2 , bounded by the same streamlines that go through the circumference of A1, is obtained in the same fashion, as …(3) 16  Name of Institution Continuity Equation (Cont’d) Applying the condition that mass is same for both the points, and equate the equation (2) and (3): …(4) The above equation (4) is known as continuity equation. 17  Name of Institution Compressible flow The flow in which the density of the fluid element changes from point to point is called compressible flow. The variability of density in aerodynamic flows is particularly important at high speeds, such as for high-performance subsonic aircraft, all supersonic vehicles, or rocket engines. Indeed, all real-life flows, strictly speaking, are compressible. 1  2 …(5) 18  Name of Institution Incompressible flow The flow in which the density of the fluid elements is always constant. The continuity equation for the incompressible flow can be written as: 1 = 2 …(6) Incompressible flow is a myth. It can never actually occur in nature, as discussed above. However, for those flows in which the actual variation of density is negligibly small, it is convenient to make the assumption that density is constant in order to simplify our analysis. 19  Name of Institution Convergent Duct If the incompressible flow is passing through a convergent duct, the continuity equation is expressed as: …(7) If A 2 is less than A1, then the velocity increases as the water flows through the nozzle, as desired. The same principle is used in the design of nozzles for subsonic wind tunnels built for aerodynamic testing. Figure: Incompressible flow in a convergent duct 20  Name of Institution Convergent Duct (Cont’d) 21  Name of Institution Bernoulli's theorem Bernoulli's equation is one of the most fundamental equations in fluid mechanics. It is derived from the Euler’s equation: …(8) If flow is incompressible, density is assumed to be constant. Integrating the above equation (8) between points 1 and 2, following equations are obtained: …(9) Figure: Two points along the streamline 22  Name of Institution Bernoulli's theorem (Cont’d) Bernoulli’s relation can be expressed as: …(10) The following important points should be noted:. Equation(10) is valid for inviscid, and incompressible flow. Equation(10) relation gives the properties along the streamline. 23  Name of Institution Bernoulli's theorem Bernoulli’s Principle states that an increase in the velocity of a fluid (air, in this case) leads to a decrease in pressure. This principle is crucial for understanding lift generation over an airfoil (the cross-sectional shape of a wing). Airfoil Shape: An airplane wing is typically designed with a curved upper surface and a flatter lower surface. This shape is called an airfoil. When air flows over the wing, the shape of the airfoil causes the air above the wing to travel faster than the air below it. 24  Name of Institution Bernoulli's theorem Velocity and Pressure Relationship: According to Bernoulli’s Principle, since the air on the upper surface of the wing is moving faster, the pressure above the wing decreases. In contrast, the slower-moving air under the wing has a higher pressure. Pressure Difference: The difference in pressure between the upper and lower surfaces of the wing creates a net upward force, which is lift. 25  Name of Institution Bernoulli's theorem 26  Name of Institution Mach Number Mach number is one of the most powerful quantities in aerodynamic. Mach number is the ratio of flow velocity to the speed of sound. …(18) With respect to the Mach number, flow regime are categorized into 3 different categories: If M1, flow is supersonic 27  Name of Institution CL vs Alpha graph The slope of the linear portion of the lift curve is designated as. when a = 0, there is still a positive value of c1, that is, there is still some lift even when the airfoil is at zero angle of attack to the flow. This is due to the positive camber of the airfoil. All airfoils with such camber have to be pitched to some negative angle of attack before zero lift is obtained. 28  Name of Institution CL vs Alpha graph 29  Name of Institution CL vs Alpha graph For large values of a, the linearity of the lift curve breaks down. As a is increased beyond a certain value, CL peaks at some maximum value, CL_max and then drops precipitously as a is further increased. In this situation, where the lift is rapidly decreasing at high a, the airfoil is stalled. 30  Name of Institution CL vs Alpha graph 31  Name of Institution CL vs Alpha graph 32  Name of Institution CL vs Alpha graph 33  Name of Institution Wing-Tip Vortices 34  Name of Institution Wing-Tip Vortices 35  Name of Institution Wing-Tip Vortices 36  Name of Institution Wing-Tip Vortices 37  Name of Institution Wing-Tip Vortices 38  Name of Institution Induced Drag These wingtip vortices downstream of the wing induce a small downward component of air velocity in the neighborhood of the wing itself. This can be seen intuitively from given Figure; the two wingtip vortices tend to drag the surrounding air around with them, and this secondary movement induces a small velocity component in the downward direction at the wing. This downward component is called downwash, given by the symbol w. 39  Name of Institution Induced Drag 40  Name of Institution Induced Drag 41  Name of Institution Induced Drag This has several consequences: 1. The angle of attack of the airfoil sections of the wing is effectively reduced in comparison to the angle of attack of the wing referenced to V 2. There is an increase in the drag. The increase is called induced drag, which has at least three physical interpretations. 42  Name of Institution Induced Drag First, the wingtip vortices simply alter the flow field about the wing in such a fashion as to change the surface pressure distributions in the direction of increased drag. An alternate explanation is that, because the local relative wind is canted downward, the lift vector itself is "tilted back," hence it contributes a certain component of force parallel to V , that is, a drag force. The induced drag coefficient can be written as: 43  Name of Institution Critical Mach Number Consider the flow of air over an airfoil. We know that, as the gas expands around the top surface near the leading edge, the velocity and hence the Mach number will increase rapidly. Indeed, there are regions on the airfoil surface where the local Mach number is greater than free stream Mach number. Imagine that we put a given airfoil in a wind tunnel where M = 0.3 and that we observe the peak local Mach number on the top surface of the airfoil to be 0.435. 44  Name of Institution Critical Mach Number (Cont’d) Figure: Flow over the airfoil at different Mach numbers 45  Name of Institution Critical Mach Number This is sketched in Figure. Imagine that we now increase free stream Mach to 0.5; the peak local Mach number will correspondingly increase to 0.772, as shown in Figure. If we further increase free stream Mach to a value of 0.61, we observe that the peak local Mach number is 1. Note that the flow over an airfoil can locally be sonic (or higher), even though the freestream Mach number is subsonic. By definition, that freestream Mach number at which sonic flow is first obtained somewhere on the airfoil surface is called the critical Mach number of the airfoil. 46  Name of Institution Drag on different phases of Flight Flight is divided into several phases, each characterized by different aerodynamic forces. The primary phases of flight include takeoff, climb, cruise, descent, and landing. The drag experienced by an aircraft varies across these phases, with different types of drag dominating depending on the specific flight conditions. 47  Name of Institution Drag on different phases of Flight 48  Name of Institution Drag on different phases of Flight Takeoff Phase Characteristics: The takeoff phase involves accelerating the aircraft to generate enough lift to leave the ground. The aircraft is typically in a high-lift configuration, with flaps extended. Dominant Drag: Induced Drag Reason: Induced drag is predominant during takeoff due to the high angle of attack needed to generate sufficient lift at low speeds. As the aircraft climbs, induced drag decreases as speed increases and the angle of attack decreases. 49  Name of Institution Drag on different phases of Flight Climb Phase Characteristics: During the climb phase, the aircraft continues to gain altitude. This phase requires a balance between lift and the aircraft's weight while overcoming the drag. Dominant Drag: Induced Drag Reason: Like takeoff, the climb phase involves higher angles of attack at lower speeds, where induced drag remains significant. The aircraft is also still in a high-lift configuration, contributing to induced drag. 50  Name of Institution Drag on different phases of Flight Cruise Phase Characteristics: The cruise phase is where the aircraft flies at a constant altitude and speed, usually at the most fuel-efficient conditions. Dominant Drag: Parasite Drag (Form and Skin Friction Drag) Reason: At cruise speeds, the aircraft operates at a lower angle of attack, minimizing induced drag. However, the higher speeds increase parasite drag, particularly form drag due to the aircraft's shape and skin friction drag due to the airflow over the surface. 51  Name of Institution Drag on different phases of Flight Descent Phase Characteristics: The descent phase involves the aircraft reducing altitude in preparation for landing. The speed is often reduced compared to the cruise phase. Dominant Drag: Parasite Drag Reason: During descent, the aircraft reduces speed, but parasite drag remains dominant due to the airflow over the aircraft's surfaces. Induced drag is less significant because the angle of attack is relatively low. 52  Name of Institution Drag on different phases of Flight Landing Phase Characteristics: The landing phase is the final phase where the aircraft reduces speed, extends landing gear and flaps, and prepares for touchdown. Dominant Drag: Induced Drag Reason: Similar to takeoff, induced drag becomes dominant during landing due to the high angle of attack and the use of high-lift devices such as flaps. The aircraft is moving at lower speeds, so induced drag is more prominent as it generates the required lift at these conditions. 53  Name of Institution Importance of understanding drag at various flight phase Induced Drag: Dominant at lower speeds, especially during takeoff, climb, and landing. It is directly related to the angle of attack and lift generation. Parasite Drag: Dominant at higher speeds, particularly during cruise and descent. It includes form drag (due to the aircraft's shape) and skin friction drag (due to the airflow over the surface). Understanding the dominant drag in each phase of flight is crucial for optimizing aircraft performance, fuel efficiency, and overall aerodynamic 54 design.  Name of Institution Thank You 55