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Faculty of Science and Engineering, Curtin University ENGR2000 – Fluid Mechanics Semester 1 2019 GROUP MINI-PROJECT HIGH-SPEED FLIGHT

Summary A maximum of half a page that describes the most important outcomes of the investigation. Do not insert any table of contents after the summary. 1

1 Theory of Flight 1.1 Principles Aircrafts designed to approach the speed of sound look different from most aircrafts. Before an Airplane can be designed and constructed, engineers are required to consider the fundamental principles of flight. By not doing so, planes that weighs upward of 300 metric tons could not take off the ground and fly effectively over vast distances (MacCormick, 1995). To understand flight of a plane, one must understand the four forces of flight. These being thrust, lift, drag and weight (Hoover 2018). Lift is what opposes weight and is the key aerodynamic force that is able to maintain a plane in the air. The weight, also known as gravity, is a force that acts vertically down. The two forces work opposable to each other, with the weight dictating how strong the lift will need to be. Thrust is the force that is produced by the engines, and is what makes the forward movement possible for an aircraft. Lastly drag, the opposing force to thrust, whereby is it generated by the contact of an object moving through a medium, such as liquid or gas. Figure 1.1 – Four forces of flight (Hull 2010) 1.2 History Adolf Busemann, a German Aerodynamism was one of the first people to study the characteristics of high-speed flight in 1933. Busemann used a wind tunnel which could reach Mach 1.5 (1.5 times the speed of sound), the findings clearly suggest the benefits of using an aerofoil with a thin leading edge at supersonic speeds. Busemann, also recommended the use of thin aerofoils to postpone subsonic drag rise. During the second world war, German scientists where far ahead of the world in deriving a possible solution to what they called the “limiting Mach Number” (Whitford 1998). The ratio of the aircraft’s true airspeed to the speed of sound of where its flying, is called Mach number. Subsonic flight has a Mach 2

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number below 1.0, while supersonic has a Mach number above 1.0 (Hull 2010). The Mach number has a great influence on an aircraft, as it determines the way it gets designed. The first official aircraft to travel at Mach speed was the Bell X-1 Rocket-powered aircraft in 1946. It was on the 13 th run of the aircraft when the sound barrier was broken by reaching a speed of Mach 1.06. Ballistic study was a major influence in the design of the X-1. The body of the aircraft was shaped like a 0.5 caliber bullet to help reduce drag (Whitford 1998). While the wing was a mid-mounted, roughly elliptical platform with diagonally clipped tips as shown in Figure 1.2 Figure 1.2 – Design of wing (Houghton et al., 2013) 2 Design 2.1 Purpose A concerning problem from supersonic flight in the early design stages was the control and stability at high speeds. The majority of the work by Busemann and other German aerodynamicist was regarding that issue. After extensive study in that field, aerodynamicists realised the major problem of the sudden drag increase when an aircraft reaches Mach speeds. At just beyond Mach 1, it appeared that the rate of change of drag with speed becomes infinite. This meant that there was theoretically and maximum limit to the speed at which planes could fly. An Investigation conducted by the National Advisory committee for aeronautics in 1947, revealed an unusual occurrence of a flow phenomenon that occurs at the leading edge of supersonic air-foils at higher Mach speeds. Elimination of an extensive separated flow condition over the leading edge of the aerofoil, causes a sudden increase in normal-force coefficient and in some cases showed a decrease in the drag coefficient (Lindsey et al. 1947). Flow separation is when streamlines detach from the surface of the object and forms eddies and vortices within the flow (Islam et al. 2013). This occurs after the boundary layer of a fluid travels away from an adverse pressure gradient. Which in result changes the pressure gradient of the speed of the boundary layer relative to the object to fall to almost to zero. The Reynolds number ( Re ) is used to measure different flow phenomena including flow 3

separation. Flow separation usually occurs at low Reynolds numbers and usually starts at R e = 2.0 (Islam et al. 2013). Early research in Laminar Flow Control ( LFC ) was conducted in the 1950’s where suction was utilised to eliminate or reduce cross-flow instability that was created from swept wings. This research leads to the discovery that transition could be delayed for substantial distances with a large decrease in viscous drag. Turbulent Drag Reduction ( TDR ) is one of the main researched areas in aeronautics, as it decreases the turbulent streamlines on the wings and thus reduces overall drag. During the 1930’s till the 1960’s, research in surface roughness reduction was one of the main TDR’s achieved. Reducing surface friction might seem very simple, flow separation can provide negative surface friction, however, it creates a very large pressure drag that exceeds the original friction drag (Bushnell 2003). Figure 2.1 – Side profile of a Cambered Aerofoil (Houghten et al. 2013) The thickness to chord ratio ( t/c ) as shown in Figure 2.1, is one of the biggest influences on the wave drag of a straight wing. The reduction of the wings thickness causes the critical Mach number to increase. However, at supersonic speeds, thin wings provide a large reduction in wing drag, which may be considered the largest contributor to total drag. At supersonic speeds, the wave drag is proportional to almost the square of t/c . The first supersonic aircraft, Bell X-1, had a biconvex, sharp-edged aerofoil, with a 4.9% thickness at the leading edge and 7.5% thickness at the trailing edge. This incredibly thin design of the wing was necessary to decrease drag as much as possible since the available engines at the time were very inefficient and were lacking in thrust production (Whitford 1998). 2.2 Materials Used Material selection for an aircraft is one of the most important procedures when designing the plane. Materials for each section must possess certain characteristics to ensure the flight goes according to plan especially at high speeds such as supersonic flight. Considerations needed to be deliberated when selecting materials for an aircraft. These regard to specific strength, strength to weight ratio, tensile properties, fatigue strength, heat resistance, fabricability, as well as many others. Long-term operation at high speeds usually means high friction for a long period of time, which results in heat build-up. As can be seen in Table 2.1, long-term operation at speeds above Mach 3.5 can cause the aircraft to increase its temperature up to 300 °C. 4

Speed (Mach Number) Skin Temperature (°C) 2.0 100 2.5 150 3.0 200 3.5 300 4.0 370 Table 2.1: Aircraft Skin Temperatures at Various Speeds (Huda and Edi 2013) From the relationship between Mach number and skin temperature, it can be suggested that as surface temperature increases as the speed increases, a result of the increased friction will also occur. It must be noted that most supersonic aircrafts are strictly designed for military based purposes. Supersonic aircrafts mainly use a lightweight Carbon-Fiber-Reinforced Polymer ( CFRP ). This material possesses high strength, fatigue strength, corrosion resistance, high creep strength, and most importantly its very lightweight (Huda and Edi 2013). When designing both military and commercial supersonic aircrafts temperatures, loads, moisture, radiation, maintenance, and environmental conditions must also be considered. Aluminium alloys are also other materials used in the construction of supersonic aircraft due to its light weight and relatively high strength, as well as very useful fabrication features. Material development and selection when designing a supersonic aircraft is very important. Not only does it help reduce weight while maintaining strength, it also ensures that materials can be manufactured to the specific engineering requirement. As stated above, surface roughness is a major contributor to LFC reduction, therefore a material must be chosen which can be easily smoothed out to help achieve the desired effect. 2.3 Comparison of Conventional and Supersonic Aircrafts A conventional aircraft wing produces lift by forcing air to move faster over its smooth, curved upper surface, and slower underneath along the flat, angled bottom of the wing. The lift force is simply increased by increasing the length of the wing, creating a larger area over which the pressure difference accumulates. Drag on a conventional wing is largely caused by the trailing edge of the wing, which creates an area of extreme low pressure along the back edge of the wing as the aircraft moves at speed through the air. This area generates a turbulent flow in the wing’s wake, as seen in Figure 2.2, producing a large drag force on the aircraft. In order to combat this, aircraft wings are designed with a slow taper towards the trailing edge 5

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of the wing, allowing the passing air to gradually return to normal pressure and decreasing the drag force on the plane (Yousefi 2018). Figure 2.2: Turbulent flow with streamlines (Yousefi 2018) In addition to the wing, the body of a conventional aircraft will also generate a drag force, and must be designed with smooth transitions where air will begin and end its contact with the body surface. This transitioning will reduce low pressure points along the craft, preventing unnecessary drag forces from generating. These principles of aerodynamic aircraft design, while still holding true for supersonic aircraft, are greatly exaggerated at the incredibly high speeds reached, and therefore must be accommodated for through the alteration of the wing’s design. In addition to this, the conditions faced also allow for the formation of shock waves, which increase drag exponentially. Firstly, in order to restrict the formation of shock waves, the body of supersonic aircraft must be designed as uniformly as possible. This uniformity is achieved through the long taper of the aircraft’s nose which pierces the air, forcing streamlines to form along the outside of the craft, along with the avoidance of any sudden size changes along the body. While a longer wing is desirable for conventional flight, as it allows for a larger lift force to generate, it greatly hinders the ability of flight as an aircraft approaches and reaches the speed of sound (Roohani and Skews 2009). This is due to the shock waves, which form along the wing, generating an enormous drag force as they move along the wing and break up into a turbulent wake. In order to combat this, the horizontal wingspan of a supersonic aircraft must be reduced, minimising drag caused by shock waves along the wing. Shock waves generated at subsonic speed compared to supersonic speed can be seen in Figure 2.3. 6

Figure 2.3: Shock wave transition during flight (https://www.businessinsider.com.au/awesome-nasa-photos-of-supersonic-flight-2015-10? r=US&IR=T) Since supersonic aircraft require a short wingspan, the wing must be extended further backwards in order to allow for an appropriate surface for the lift to generate along. This led to the implementation of a swept wing, which works to both minimise and delay shock wave drag forces. A short horizontal wingspan, however, proved detrimental to the aircraft’s performance during take-off and subsonic travel, as the wings didn’t generate enough lift at the lower speeds. To allow for travel at both subsonic and supersonic speeds the Delta Wing and variable-sweep designs were implemented (Takahashi 2006). The Delta-Wing design, which resembles an upside-down triangle from below, generates appropriate lift along its large surface area, combined with a more powerful jet engine. Alternately, the Variable-Sweep design enables subsonic and supersonic flight by extending the lower portions of the wing outwards during low speed flight, increasing the lift generated, before retracting into a swept wing for high speed flight, avoiding excessive shock wave generation and propagation (Takahashi 2006). 3 Bernoulli Effect Pressure variations created by flowing air are best signified by the Bernoulli equation. Where: P + 1 2 ∗ ρ ∗ V 2 . Where P = pressure, ρ = density of fluid, V = velocity of object. Bernoulli’s equation is for non-viscous flows only. When considering this equation for a steady non-viscous compressible flow, energy is conserved along any streamline of a flow. 3.1 Changes from Compressible Air When considering subsonic aerodynamics, lift is created by forces that are exerted on a body and the air, being gas, from which it is immersed in. With a speed of around ~300mph, the air is considered to be incompressible where, at a set altitude, its density is approximately the same whereas its pressure will vary (Richards 2008). Based upon this assumption, water and air are acting the same therefore air can be classified as a fluid. Viscosity effects are said to be negligible when referring to subsonic theory and from this the result is the prevention of motion of a certain part of the fluid with respect to another. From this, it can be seen that air is classified as an ideal fluid, so it conforms to the principles of ideal fluid aerodynamics which include continuity, circulation and Bernoulli’s Theory. Of course, this is only theoretical, and the air is compressible and viscous in reality. When considering low speeds these effects are negligible, but when speed increases the effects of compressibility become much more important and must be considered. It is very important to notice the effects of compressibility and also viscosity when the speed is higher and approaching the speed of sound. At these higher speeds, the density of the air surrounding the object is altered due to the compressibility effects present (Richards 2008). 7

As has been discussed in this report, accelerating airflow passing over the top surface of the wing creates lift. Although the aircraft may only be at subsonic speed, this is not true for the accelerated air which reaches supersonic speed. Having supersonic and subsonic airflows at the same time is possible when an aircraft is in flight. When the flow velocities achieve sonic speeds at certain locations, mainly at the area of maximum camber of the wing, even more acceleration is shown with the compressibility effects. These take form in shock waves, buffeting, drag increases, stability along with trouble controlling. At speeds above this point, the subsonic flow principles can be disregarded. 3.2 Aerodynamic Forces Aerodynamic forces are dependent on the viscosity of the gas, although it is through a complex way. When an object moves through a gas, molecules from the gas stick to the surface of the object. When this occurs, the result is called a boundary layer, which is a layer of air near the object’s surface. As a result of this, the shape of the object is changed. The gas that flows past the boundary layer reacts with it as if it were a physical surface being part of the object. When analysing a boundary layer during flight, it may be undistinguishable when the boundary layer separates from the body, as it creates a new shape which is vastly different from the original shape of the object (Glenn 2006). Along with this, the interaction of the flow and the boundary layer are considered to be unsteady. This in turn means it changes with time. When considering the drag of an object, the boundary layer becomes very important. Whilst trying to predict these conditions, it is vital to use a wind tunnel with controlled variables. This is since to test desired parameters along with a sophisticated computer evaluation, a high level of accuracy is needed to be carried out. 3.3 Compressibility The compressibility of the gas is completely dependent on the aerodynamic forces. When the object moves through and or past the gas, the molecules of the gas shift around the object. When this occurs at low speeds, from 320 km/h or less, the density for the fluid will be the same throughout (Woodward 1968). For subsonic speeds, the object is compressed and takes away some of the energy to do so. By this happening, this then changes the density, as well as the force on the object. As the speed continues to increase the effects of compressibility become more evident and important. The air pressure changes on an aircraft can be seen from Figure 3.1. With purple showing low pressure, and blue showing high pressure. When speeds reach around and past the speed of sound, it is important to understand the effects of compressibility, and how it correlates with the density of the air around the aircraft. 8

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Figure 3.1 Air pressure change on a Boeing 747 during flight (https://howthingsfly.si.edu/aerodynamics) 9

Conclusion Provide a set of brief conclusions that encapsulate the findings of your investigation. Flight is something that is experienced throughout the world, with the aerodynamics that relates to it being extremely important. The aerodynamics of flight deals with the motion of air, and focuses of the principles governing it. This in turn is a subset of fluid dynamics. As well as being designed for aircrafts, there are many other uses for aerodynamics. Aerodynamics is significant when understanding the designs of construction buildings, vehicles, and bridges. ⚠ Summary + Main Body + Conclusion = 10 pages maximum! 10

References Bushnell, D. M. 2003. "Aircraft Drag Reduction--a Review." Proceedings of the Institution of Mechanical Engineers 217 (1): 1. https://search-proquest- com.dbgw.lis.curtin.edu.au/docview/213200250?accountid=10382. MacCormick, B. 1995. “Aerodynamics, aeronautics, and flight mechanics”. New York: Wiley Glenn, Valerie D. 2006. "NTRS: NASA Technical Reports Server200695ntrs: NASATechnical Reports Server. Washington, DC: National Aeronautics And Space Administration 1994 ‐ . Gratis Last Visited July 2005 URL: http://Ntrs.Nasa.Gov/". Reference Reviews 20 (2): 40-41. doi:10.1108/09504120610647500. Hoover, Todd. 2018. “Disequilibrium: Flight and The Bernoulli Effect”. Science Scope 042 (01). Doi:10.2505/4/ss18_042_01_12. Houghton, E., Carpenter, P., Collicott, S. and Valentine, D. (2013). Aerodynamics for engineering students . 6th ed. Elsevier, p.25-28. Huda, Zainul, and Prasetyo Edi. 2013. "Materials Selection In Design Of Structures And Engines Of Supersonic Aircrafts: A Review". Materials & Design 46: 552-560. doi: 10.1016/j.matdes.2012.10.001. Hutchinson, John R. 1996. “Vertebrate Flight – The physics of flight.” UCMP. Hull, D. 2010. “Fundamentals of airplane flight mechanics”. Berlin: Springer. Islam, Toukir, S. M. R. Hassan, and Mohammad Ali. 2013. "FLOW SEPARATION PHENOMENA FOR STEADY FLOW OVER A CIRCULAR CYLINDER AT LOW REYNOLDS NUMBER." International Journal of Automotive and Mechanical Engineering 8 (Jul): 1406-1415. doi: http://dx.doi.org.dbgw.lis.curtin.edu.au/10.15282/ijame.8.2013.28.0116. https://search- proquest-com.dbgw.lis.curtin.edu.au/docview/1774318736?accountid=10382. Lindsey, W., Daley, B. and Humphreys, M. (1947). The Flow and Force Characteristics of Supersonic Airfoils at High Subsonic Speeds. Reference Reviews , pp.40-41. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930081941.pdf Mechanical & Mechatronic Engg. 2005. "Separation Of Flow". Www-Mdp.Eng.Cam.Ac.Uk . http://www- mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/fprops/introvisc/ node9.html. Richards, Louise M. 2008. "NASA Technical Reports Server (NTRS)2008364NASA Technical Reports Server (NTRS). Washington, DC: NASA Center For Aerospace Information Last Visited June 2008. Gratis URL: Http://Ntrs.Nasa.Gov/". Reference 11

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Reviews 22 (8): 40-41. doi:10.1108/09504120810914619. WOODWARD, F. A. 1968. "Analysis And Design Of Wing-Body Combinations At Subsonic And Supersonic Speeds.". Journal Of Aircraft 5 (6): 528-534. doi:10.2514/3.43979. Whitford, Ray. 1998. "Supersonic Man is Fifty." Aircraft Engineering and Aerospace Technology 70 (1): 15. https://search-proquest- com.dbgw.lis.curtin.edu.au/docview/213778007?accountid=10382. Roohani, Hamed, and B. W. Skews. 2009. "The Influence Of Acceleration And Deceleration On Shock Wave Movement On And Around Aerofoils In Transonic Flight". Shock Waves 19 (4): 297-305. doi:10.1007/s00193-009-0207-9. Yousefi, Kianoosh. 2018. Turbulence in the Atmospheric Wave Boundary Layer. Sites.Udel.Edu. https://sites.udel.edu/kyousefi/research/ Takashashi, Thimothy. 2006. Aircraft Preformance and Sizing. 12