CIELO EXTROVERT ADVANCED CONCEPT EXPLORATION ADL P Jennifer Bayard, Traci Thomason

Transcription

1 EXTROVERT ADVANCED CONCEPT EXPLORATION ADL P Jennifer Bayard, Traci Thomason Georgia Institute of Technology School of Aerospace Engineering CIELO Runway- Based Space Launch System Aerodynamics May 2, 2013

2 EXTROVERT ADVANCED CONCEPT EXPLORATION 2 Publishing Information We gratefully acknowledges support under the NASA Innovation in Aerospace Instruction Initiative, NASA Grant No. NNX09AF67G, to develop the techniques that allowed such work to be done in core courses, and the resources used to publish this. Tony Springer is the Technical Monitor. Copyright except where indicated, is held by the authors indicted on the content. Please contact the indicated authors komerath@gatech.edu for information and permission to copy. Disclaimer Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Aeronautics and Space Administration.

3 Cielo Runway-Based Space Launch System Aerodynamics AE3021A Jennifer Bayard Traci Thomason Professor: Dr. Narayanan Komerath Daniel Guggenheim School of Aerospace Engineering Georgia Institute of Technology Atlanta GA Spring 2013

4 2 Chapter 0

5 Contents 1 Summary 3 2 Historical Efforts 5 3 Initial Sizing Vehicle Staging Shape and Dimensions Speed Variations Sizing Iteration Wing Loading Aerodynamic Calculations Angle of Attack Aspect Ratio Subsonic Lift and Drag Supersonic Shock-Expansion Method Hypersonic Modified Newtonian Method Hypersonic Skin Friction Drag Wave Drag Thrust Available Turbojet Engines Liquid Air Cycle Engines Analysis of Aerodynamics and Thrust Available 35 7 Cielo Structure Structure Materials Retractable Engines Fuel Storage Mission Architecture Launch Sites Trajectory Conclusion Bibliography 43 3

6 Contents Chapter 0 4

7 List of Figures 2.1 HOTOL Skylon Rockwell X Rockwell X SpaceShipOne and White Knight Reaction Engines A X X-43 and B Boeing X Cielo Sizing Supersonic Flow Shock-Expansion Reynolds Number versus Chord Position for Varying Freestream Velocity Skin Friction Drag versus Chord Position Sears-Haack Body Turbojet Layout Retractable Trubojet Engine Cielo Trajectory

8 List of Figures Chapter 0 6

9 List of Tables 2.1 Heavy-Lift Aerodynamic Vehicles Take-off Weights and Wing Spans General Staging Details Wing Dimensions V and Isp Values Space Stage Sizing Iteration Hypersonic Stage Sizing Iteration Aircraft Stage Sizing Iteration Wing Loading Incompressible Subsonic Lift Coefficient Compressible Subsonic Lift Coefficient Subsonic Drag Coefficient Supersonic Expansion Analysis Supersonic Oblique Shock Analysis Supersonic Lift and Drag Coefficients from Shock Expansion Theory Results of Modified Newtonian Aerodynamics Sears-Haack Wave Drag Calculation Assumptions For Thrust Calculations Thrust Available Results LACE Engine Thrusts Excess Thrust Analysis Fuel Volume

10 List of Tables Chapter 0 2

11 Chapter 1 Summary Space Solar Power (SSP) is one method currently of interest by which fossil power on Earth may be replaced. To ensure to viability of this option in replacing fossil power, at least 1 kw of electric power delivered on Earth per kilogram of mass placed in orbit must be achieved. Therefore, 4 billion kilograms of mass would need to be delivered to orbit to generate the 4 TW of SSP needed to replace fossil power. This corresponds to 1000 payloads of 100,000 kg each year delivered to orbit over a 40 year time span. Cielo will be a horizontal runway-based space launch system that will reach orbit in three stages. The first will be a subsonic and supersonic stage in which two turbojet engines will be used, similar to the engines used on Concorde. This stage is referred to as the Aircraft Stage. The second stage will be a Hypersonic Stage in which four Liquid Air Cycle Engines (LACE) will be used, similar to the SABRE engines used on Skylon. During this stage, air taken from the atmosphere will be utilized with this engine. The final stage will be the Space Stage which will also use the LACE engines, but will use oxygen stored on board. Finally, Cielo will utilize a glide landing approach. The turbojet engines will be retracted at the start of the hypersonic stage and therefore will be protected upon reentry. First, a sizing iteration was conducted to find an appropriate estimate for Cielo, based on the payload mass and the payload fraction. Next, aerodynamics were examined for each stage. For the subsonic part of the Aircraft Stage, thin airfoil theory and slender wing theory were used for incompressible and compressible analysis, respectively. For the supersonic part of the Aircraft Stage, shock expansion theory was used while modeling Cielo as a flat plate. Additionally, skin friction drag and wave drag were also calculated for both the supersonic and hypersonic aerodynamics. During the Hypersonic Stage, aerodynamics were further evaluated by using modified Newtonian aerodynamics. Thrust available was evaluated for each stage, using turbojet propulsion analysis and published LACE engine results. The aerodynamics were first evaluated to ensure Cielo would have enough thrust available to overcome the drag of the system, in order to lift the payload to orbit. The trajectory was analyzed and finally fuel amounts were calculated to ensure mission success. As Cielo is capable of carrying this amount of fuel required, it was found that Cielo is capable of carrying its payload to orbit. 3

12 4 Chapter 1

13 Chapter 2 Historical Efforts To begin the development of a horizontal takeoff space access vehicle, first previous efforts were considered and analyzed for their validity of design. These efforts are described below. Also investigated and shown in Table 2.1 are some heavy-lift aerodynamic vehicles takeoff weights and wing spans. 1. HOTOL The HOTOL aircraft, which stands for Horizontal Take-Off and Landing, was an effort to create a single-stage-to-orbit space access vehicle. It was developed by Rolls Royce with British support between 1982 and As the name suggests, it was designed to have horizontal takeoff and landing. The horizontal takeoff was assisted by a rocket propelled trolley. Once HOTOL reached a Mach number between 5 and 6, it would be propelled to orbit purely using rocket propulsion. HOTOL was designed to use 3 Rolls-Royce RB545 engines. These engines used air/liquid hydrogen/liquid oxygen as propellant, but essentially they were rockets that used the oxygen obtained from the atmosphere during the air breathing ascent. To land, it was planned that HOTOL would use a glide landing. The engines and wings were designed to be at the rear of the fuselage. This resulted in a discrepancy between the location of the center of pressure and the center of mass, as the center of mass would have been behind the center of pressure. To fix this discrepancy, design changes were made that severely limited the amount of payload that could be carried, making the project economically unsustainable. HOTOL was designed to have a span of 28.3 m, a length of meters, a diameter of 7 m, and maximum payload of 8,000 kg. Additionally, this project was designed to be unmanned. The HOTOL aircraft is shown in Figure Skylon SKYLON is a project currently being developed by the British company, Reaction Engine Limited, or REL. It is marketed as a reusable spaceplane. REL plans for this vehicle to be reused up to 200 times and be able to carry 15,000 kg into orbit. It will be a single-stage-to-orbit vehicle and will use two SABRE engines, designed by REL. This engine has combined air breathing and rocket cycles. It is a liquid hydrogen/liquid oxygen engine. During the air breathing phase of the ascent, the engine uses the oxygen in the atmosphere. Once a Mach number of 5.4 is reached, the onboard liquid oxygen is used to propel the vehicle to orbit. SKYLON is de- 5

14 Chapter 2 Courtesy of Figure 2.1: HOTOL signed to have no pilot, but will have passenger carry capabilities. This project is extremely similar to HOTOL, except, among other differences, SKYLON will not use a trolley as an aid for takeoff and the engines and wings will be located near the center of the vehicle, not near the rear. SKYLON will have a length of 83.3 m, and a wingspan of 25.4 m. The Skylon concept is shown in Figure NASP/Rockwell X-30 The Rockwell X-30, as shown in Figure 2.3, was a single-stage-to-orbit vehicle concept developed between 1990 and 1993 for the National Aero-Space Plane, or NASP. This vehicle was never developed past the conceptual phase. The ultimate goal was to use a scramjet engine. The fuselage was designed to be shaped like a shovel, which would create shocks at the front of the fuselage to compress the air entering the scramjet. The rear fuselage would then expand the exhaust leaving the engine. Additionally, the vehicle used the concept of compression lift to fly. This involved using the shock waves generated in flight as a lifting surface to improve the drag-to-lift ratio. This design worked well for supersonic flight, but poorly for subsonic flight, including takeoff and landing. This vehicle was not designed to carry large payloads or many, if any depending on the development stage, people. The vehicle was projected to have a length of 48.8 m and a wingspan of 22.6 m. 4. Lynx The Lynx spaceplane, as shown in Figure 2.4, is a vehicle under development by the American company, XCOR, that will be a single-stage-to-orbit reusable commercial launch vehicle. This vehicle is designed to carry a pilot and one passenger, therefore payload capabilities are extremely small, estimated to be 120 kg. This vehicle will be propelled to orbit from runway using four LOX-Kerosene rocket engines at the rear of the fuselage. The Lynx wingspan measures 7.5 meters, while it is 9 meters in length. 6

15 Chapter 2 Courtesy of the UK Space Agency Figure 2.2: Skylon Courtesy of the Space Literacy Foundation Figure 2.3: Rockwell X-30 7

16 Chapter 2 Courtesy of the Space Literacy Foundation Figure 2.4: Rockwell X SpaceShipOne SpaceShipOne was the first privately funded vehicle to reach sub-orbital space, in Horizontal takeoff was accomplished while the vehicle was attached to White Knight, its mother ship. The vehicle is designed for flights to 100 km altitude. During reentry, the vehicle enters its feathered configuration, allowing for high-drag. In this configuration, the rear half of the wing is folded upward. It is designed to carry payloads up to 3175 kg. It had a wingspan of 25 m. While the White Knight used two turbojet engines, SpaceShipOne uses a hybrid engine. This hybrid engine was a hybrid of solid and liquid rocket engines. SpaceShipOne won the Ansari X Prize by flying to a 100 m altitude twice in two weeks, carrying the weight of three people onboard. While not designed for very high loads, Space- ShipOne proved the possibility of a fast turnaround time for space access vehicles. SpaceShipOne is shown in Figure Reaction Engines A2 The Reaction Engines Limited A2, as shown in Figure 2.6, is a vehicle currently being designed that would serve as a hypersonic airliner. The airliner is projected to weigh at maximum 400,000 kg, which is less than a Boeing 747. It is designed to be able to take off and land using conventional runways. The engines used are similar to the SABRE engines developed by the company for use on SKYLON. The 8

17 Chapter 2 Courtesy of Virgin Galactic Figure 2.5: SpaceShipOne and White Knight Courtesy of Reaction Engines Figure 2.6: Reaction Engines A2 engines used here are the Scimitar engines, which are similar to a ramjet. It is not a rocket engine. The wingspan is projected to be 41 meters, while the length is 143 meters. It is intended to carry 300 passengers and have a cruise speed of 5.2 Mach. 7. X-15 The X-15, as shown in Figure 2.7, is a hypersonic vehicle that has reached what is classified as the border of space, 100 km altitude, two times in its flight history. The X-15 was carried to an altitude of 13.7 km by a B-52 mother ship, Balls 8. The X-15 used two different rocket engines over its lifetime. The first was two XLR11 engines, which were driven by ammonia and liquid oxygen propellant. The second engine used was the XLR99, which was driven by ethyl alcohol and liquid oxygen propellant. It has a wingspan of 6.8 meters and a length of meters. It was designed to carry one pilot. 9

18 Chapter 2 Courtesy of Figure 2.7: X X-43 The X-43, as shown in Figure 2.8, is an unmanned hypersonic vehicle designed by NASA, which has flown up to a Mach number of It was designed for a single use and all three tests of this design have crashed intentionally into the ocean. The X-43 is attached to a B-52 carrier plane to about 13 km. The X-43 is attached to a rocket, the first stage of the Pegasus rocket. After 13 km, the plane and rocket are detached from the carrier plane. The rocket is then used to propel the aircraft to hypersonic speeds. The rocket is detached following this procedure and the scramjet on the X-43 is used at hypersonic speeds. The scramjet was used for a maximum of 10 seconds in flight during testing. The X-43 uses a lifting body design and is 3.7 meters in length. 9. Boeing X-51 The Boeing X-51, as shown in Figure 2.9, is an unmanned hypersonic aircraft that successfully flew in 2010, achieving a Mach number of 6. This vehicle is known as the WaveRider because it uses compression lift to generate lift from shock waves. Similar to the X-43, it is carried to an altitude of 15.2 km by a B-52 carrier plane. Once detached from the carrier plane, it uses solid rocket booster to achieve a Mach number of 4.5. Once the booster is dumped, the X-51 uses a Pratt and Whitney SJY61 scramjet engine to achieve a Mach of 6. It can carry a payload of 120 kg and has a length of 7.62 meters. 10

19 Chapter 2 Courtesy of Spaceflight Now Figure 2.8: X-43 and B-52 Couresty of Flight Global Figure 2.9: Boeing X-51 11

20 Chapter 2 Table 2.1: Heavy-Lift Aerodynamic Vehicles Take-off Weights and Wing Spans Heavy-Lift Aerodynamic Vehicle Payload (kg) Wing Span (m) B-52B 31, Lockheed C-5 Galaxy 771, Antonov An-225 Mriya 440, Airbus A F 320, Boeing F 308,

21 Chapter 3 Initial Sizing 3.1 Vehicle Staging The conceptual design is to use a multistage approach for the horizontal takeoff and landing space access vehicle. There will be a total of three aircraft stages: the Aircraft Stage, the Hypersonic Stage, and the Space Stage. Each stage is described below. Stage 1: Aircraft Stage Cielo will be equipped with two turbojet engines as well as four LACE engines. During the aircraft stage, the vehicle will takeoff horizontally and reach a maximum of Mach 4 with the turbojet engines. Stage 2: Hypersonic Stage During the hypersonic stage (Mach 4 to Mach 15), the turbojet engines will be retracted into the wing and the LACE engines will be used instead. This retraction of the turbojet is required to acquire the aerodynamic shape needed for a glide landing. The LACE engines will be air-breathing hypersonic engines. They will draw oxygen from the atmosphere to use in conjunction with stored hydrogen in order to propel the vehicle. Stage 3: Space Stage After Mach 15 is reached, the Space Stage will begin in which the LACE engines will then switch to using stored oxygen until Low Earth Orbit (LEO) is reached. Next, the payload will be released appropriately. The vehicle will then reenter the atmosphere and undergo a glide landing. This is proposed to be an unmanned procedure. Additional information about the conditions at each stage is shown in Table Shape and Dimensions Cielo will have a long, slender body with delta wings. The turbojet engines will be located on the underside of the wings and will be raised into the wings prior to reentry. The LACE engines will be located on the ends of the wings. The general shape of the aircraft is displayed in Figure 3.1, where all dimensions are in meters. Additionally, specific wing dimension information is shown in Table

22 3.2. Shape and Dimensions Chapter 3 Table 3.1: General Staging Details Stage Altitude (km) Temperature (K) ρ (kg/m 3 ) Mach Velocity (m/s) Final Space E Initial Space Final Hypersonic Initial Hypersonic Final Aircraft Initial Aircraft Figure 3.1: Cielo Sizing Table 3.2: Wing Dimensions Wing Length (m) Wingspan (m) Wing Area (m)

23 Chapter Speed Variations 3.3 Speed Variations Variations in speed at each stage of flight are proposed in Table 3.1. The highest expected Mach Numbers for Hypersonic and Aircraft Stages are 15 and 4, respectively, as constrained by the LACE and turbojet engines. The velocities at these stages were calculated based on the temperature and speed of sound at each altitude. The Mach number at the Final Space stage was calculated using the expected velocity in Low Earth Orbit of 7780 m/s. 3.4 Sizing Iteration In order to effectively conduct vehicle sizing, several iterations were taken by varying different initial properties. The properties varied were both the payload mass and the payload fraction. These were varied between 150,000-50,000 kg and percent for the payload mass and fraction, respectively. The Isp values used for the sizing iteration are based on industry standard values and are shown in Table 3.3. Additionally, the V values for each stage are also shown in this table, and were found using the speed variations shown in Table 3.1. Table 3.3: V and Isp Values V Space (m/s) V Hypersonic (m/s) Isp Space (s) Isp Hypersonic (s) The final mass of the Space Stage was found by adding the combined payload mass and structure mass as well as a 7,000 kg mass per turbojet engine, and an estimated 15,000 kg mass per LACE engine. Using this final mass of the space stage, the initial mass of the space stage could be found using the rocket equation as shown in Equation 3.1. m i m f = e V Isp g 0 (3.1) The iteration of the Space Stage is shown in Table 3.4. The bolded values represent the values of payload mass and payload fraction which are the best combination of ideal and realistic values. Using these values, the initial mass of the Space Stage was calculated using the values shown in Equation m s 400s 9.81 m i = kg e m s 2 = kg (3.2) Equation 3.1 was then used to find the initial mass of the hypersonic stage, while assuming the initial space stage mass is equal to the final hypersonic stage mass. The iteration of the Hypersonic Stage is shown in Table 3.5. To use the bolded values as an example, the values used in the rocket equation to find the initial hypersonic mass are shown below in Equation

24 3.5. Wing Loading Chapter m s 2000s 9.81 m i = kg e m s 2 = kg (3.3) Once the initial hypersonic stage mass was found, this was assumed to equal the final aircraft stage mass. An assumed fuel percentage of 30 percent of the final aircraft mass was used to then calculate the initial aircraft mass. The iteration of the Aircraft Stage is shown in Table 3.6. As seen in this table, the initial total mass corresponding to the design point of Cielo is estimated to be 748,053.8 kg. 3.5 Wing Loading Wing loading was determined based on the dimensions of the delta wing shape shown in Table 3.2. The total mass of the aircraft at each stage divided by the wing area yielded the wing loading. The wing loading at each stage is displayed in Table

25 Chapter Wing Loading Total Payload (kg) Table 3.4: Space Stage Sizing Iteration Payload Fraction Structure Mass (kg) Final Mass Space (kg) Initial Mass Space (kg)

26 3.5. Wing Loading Chapter 3 Table 3.5: Hypersonic Stage Sizing Iteration Final Mass Hypersonic (kg) Initial Mass Hypersonic (kg)

27 Chapter Wing Loading Table 3.6: Aircraft Stage Sizing Iteration Final Mass Aircraft (kg) Initial Mass Aircraft (kg)

28 3.5. Wing Loading Chapter 3 Table 3.7: Wing Loading Total Mass (kg) Wing Loading (kg/m 2 ) Final Space Initial Space Final Hypersonic Initial Hypersonic Final Aircraft Initial Aircraft

29 Chapter 4 Aerodynamic Calculations This chapter outlines predictions for lift, drag, and thrusts at each of the stages. 4.1 Angle of Attack During the subsonic and supersonic phases of this mission, α is assumed to be 12 degrees. During the hypersonic phase, α is assumed to be 7 degrees. 4.2 Aspect Ratio Aspect ratio was calculated using Equation 4.1 where b (wingspan) and S (wing area) are obtained from Table 3.2. Aspect Ratio was found to be approximately AR = b2 S (4.1) 4.3 Subsonic Lift and Drag Thin Airfoil Theory Thin airfoil theory was used for lift analysis between Mach numbers 0 to 0.3, representing incompressible flow. For this analysis, Equation 4.2 was used. As stated previously, the angle of attack for this subsonic phase is 12. The results of this analysis are shown in Table 4.1. C l = 2πα = 2π ( ) 12 π 180 (4.2) 1 M 2 1 M 2 Table 4.1: Incompressible Subsonic Lift Coefficient M C l

30 4.4. Supersonic Shock-Expansion Method Chapter 4 Slender Wing Theory Slender Wing Theory was used to analyze subsonic flows in the compressible Mach number region from 0.3 to 1. To do so, Equation 4.3 was used. In this equation, the angle of attack is 12 and the aspect ratio is as given in Equation 4.4. In Equation 4.4, AR 0 represents the incompressible aspect ratio, given previously as The results of this analysis are shown in Table 4.2. C L = π ARα (4.3) 2 AR = AR 0 1 M 2 (4.4) Table 4.2: Compressible Subsonic Lift Coefficient M AR 0 C L Subsonic Drag For subsonic speeds, Drag Coefficient was calculated using a lift-to-drag ratio of 20. This number was obtained from lift to drag ratios of similar heavy lift vehicles. The drag coefficient for subsonic Mach numbers is shown in Table 4.3. Table 4.3: Subsonic Drag Coefficient M C D

31 Chapter Supersonic Shock-Expansion Method Figure 4.1: Supersonic Flow Shock-Expansion 4.4 Supersonic Shock-Expansion Method For the sake of simplicity, the wing for this aircraft was modeled as a flat plate for supersonic aerodynamic calculations. As shown in Figure 4.1, this flat pate experiences a shock expansion over the upper surface, and an oblique shock on the lower surface. By iterating over a range of Mach numbers from 1 to 4, the Lift and Drag of this airfoil could be found for an angle of attack of 12. Expansion Over Upper Surface First, the expansion over the upper surface of the airfoil was evaluated in order to find the pressure on the upper surface. First, the value of ν 1 was calculated using Equation 4.5. In this equation, γ is 1.4 and M 1 is the freestream Mach value iterated over a range of Mach numbers from 1 to 4. ν 1 = γ + 1 γ 1 γ 1 tan 1 γ + 1 (M 1 2 1) tan 1 M1 2 1 (4.5) The next step was to find ν 2. This was done by using the relationship that ν 2 = ν 1 + θ. Once this was obtained, values for M 2, the Mach number after expansion, could be found by using shock tables. Then, using both M 1 and M 2, P 01 P 1 and P 02 P 2, could be found by using the relation shown in Equation 4.6. ( P 0 P = 1 + γ 1 M 2 ) γ γ 1 (4.6) Once these values were known, then P 2 P 1 could be found by using Equation 4.7. In this equation, P 02 P 01 is equal to one since the shock is isentropic in expansion. The values of P 2 P 1, as well as the others found in the analysis of the expansion over the upper surface are listed in Table 4.4. ( ) ( ) ( ) P 2 P2 P02 P01 = P 1 P 02 P 01 P 1 (4.7) Oblique Shock Over Lower Surface Next, the oblique shock on the lower surface was evaluated. First, β was found using a β-θ-m chart, where θ is equal to α, or 12. Next, M 1N was found using the relationship that M 1N = M 1 sin β. Finally, P 3 P 1 could be found by using Equation 4.8. The values found during this analysis of the oblique shock over the lower surface are shown in Table

32 4.4. Supersonic Shock-Expansion Method Chapter 4 Table 4.4: Supersonic Expansion Analysis M 1 ν 1 (rad) ν 2 (rad) ν 2 ( ) M 2 P 01 P 1 P 02 P 2 P 2 P

33 Chapter Supersonic Shock-Expansion Method P 3 = 1 + 2γ ( M 2 P 1 γ + 1 1N 1 ) (4.8) Table 4.5: Supersonic Oblique Shock Analysis M 1 β ( ) β (rad) M 1N P 3 P Lift and Drag Lift and drag per unit span were then found by using Equations 4.9 and In these equations, an average value of 30 meters was used for the chord, c. L = D = ( P3 P ) 2 P 1 c cos α (4.9) P 1 P 1 ( P3 P ) 2 P 1 c sin α (4.10) P 1 P 1 The lift and drag coefficients were then found using Equations 4.11 and

34 4.5. Hypersonic Modified Newtonian Method Chapter 4 C l = L 1 γ(p )M 2 2 A (4.11) C d = D 1 γ(p )M 2 2 A (4.12) Table 4.6 shows the lift and drag coefficients for the varying supersonic Mach numbers. Table 4.6: Supersonic Lift and Drag Coefficients from Shock Expansion Theory M C l C d Hypersonic Modified Newtonian Method Newtonian Aerodynamics was used to derive values for lift and drag coefficients at hypersonic speeds. This is under the assumption that at a very high speed and altitude molecules do not interact. Also, the shocks occur so close to the surface that the normal force on the body is very close to the normal drag on the body. The modified version of Newtonian Aerodynamics was the preferred method since it accounts for the change 26

35 Chapter Hypersonic Skin Friction Drag in stagnation pressure through the leading edge shock. First, Equation 4.13 was used to solve for c p,max. In this Equation, γ is equal to 1.4. [ c p,max = 4 γ + 1 (γ + 1) 2 4γ ] γ γ 1 (4.13) Next, Equation 4.14 was used to solve for c p. In this equation, θ is equal to the angle of attack which is 7 degrees in the hypersonic stage. c p = c p,max sin θ 2 (4.14) The coefficient of lift and drag were then found using the relations shown in Equations 4.15 and The results of this analysis are shown in Table 4.7. c L = c p,max cos θ (4.15) c D = c p,max sin θ (4.16) Table 4.7: Results of Modified Newtonian Aerodynamics c p,max c p c d c l Hypersonic Skin Friction Drag The temperature reference method was used to calculate skin friction drag for the hypersonic phase of this mission. First, it was desired to know when the flow became turbulent. Reynolds number was plotted for various freestream velocities as a function of chord position. This plot is shown in Figure 4.2. The solid red line indicates where the flow transitions from laminar to turbulent, which occurs at a Reynolds number of 500,000. A reference temperature, or T, of 288 K was used, and a reference viscosity, or µ, of 1.8x10 5 was assumed. T 1 was taken to be 217 K, while ρ 1 was taken to be kg, which correspond to stratosphere conditions. Additionally, the relationships shown m 3 in Equations 4.17 and 4.18 were used in the skin friction drag calculation. ( ) 3 µ 1 µ = T1 4 T (4.17) ( ) ρ T1 = ρ 1 T To obtain the skin friction drag value for laminar flow, Equation 4.19 was used. 27 (4.18)

36 4.7. Wave Drag Chapter 4 Figure 4.2: Reynolds Number versus Chord Position for Varying Freestream Velocity c f = ( Re T1 ) ( ) (4.19) µ 1 x T µ To obtain the skin friction drag value for turbulent flow, Equation 4.20 was used. c f = ( T1 T ) ( ( ( ) ( ))) 2.45 T1 µ1 log Re x (4.20) T µ Figure 4.3 shows the variation in skin friction drag as a function of x position along the chord for varying velocities. This plot shows that at a Mach number of 4, the skin friction drag is approximately 3.04x10 4, and when the Mach number is 15, the skin friction drag is approximately 2.46x Wave Drag The method of calculating wave drag was based on the Sears-Haack Body concept. A Sears-Haack Body is displayed in Figure 4.4. First, the volume of the Sears-Haack Body was determined using Equation This value was then used in Equation 4.22 to calculate the wave drag. The results of these calculations are shown in Table 4.8. V = 3π2 16 R2 maxl = 3π2 16 (5m)2 (100m) = 4626m 3 (4.21) c d,w = 24 V 4626m3 = 24 l3 3 = (4.22) (100m) 28

37 Chapter Wave Drag Figure 4.3: Skin Friction Drag versus Chord Position Courtesy of the Triangulated Aerodynamics Suite Figure 4.4: Sears-Haack Body 29

38 4.7. Wave Drag Chapter 4 Table 4.8: Sears-Haack Wave Drag Calculation Wave Drag Volume (m 3 ) 4626 Length (m) 100 c d,w

39 Chapter 5 Thrust Available 5.1 Turbojet Engines A turbojet engine similar to that used on Concorde, the Rolls Royce Olympus 593 Turbojet Engine, will be used on Cielo for all of the Aircraft Stage. Figure 5.1 shows the numbering of each part of the turbojet engine so that they may be followed in the calculations. The available thrust, τ, was found using Equation 5.1 below, where m a is mass flow rate and u is flight velocity. In order to determine the exit velocity, u e, a number of calculations were necessary. The steps are outlined below in addition to the assumptions made shown in Table 5.1. τ = m a [(1 + f) u e u] (5.1) Table 5.1: Assumptions For Thrust Calculations Atmosphere Conditions Efficiencies,η Engine Parameters ) m Diffuser 0.8 P 03 P Inlet Area (m 3 ) 7.06 Compressor 0.9 T γ 1.4 Nozzle 0.97 Q R Ambient Pressure (Pa) Turbine 0.93 c p 1.1 Ambient Temperature (K) Burner 0.98 P 04 P ρ( kg Figure 5.1: Turbojet Layout 31

40 5.1. Turbojet Engines Chapter 5 a. Compressor Inlet Conditions ( T 02 = T a 1 + γ 1 ) M 2 ) 2 [ ( )] γ T02 γ 1 P 02 = P a 1 + η d 1 T a (5.2) (5.3) b. Compressor Outlet Conditions P 03 = P 02 P 03 P 02 (5.4) T 03 = P a [ η c ( P 03 P 02 γ 1 γ 1 )] (5.5) c. Turbine Inlet Pressure d. Turbine Outlet Conditions P 04 = P 03 P 04 P 03 (5.6) T 05 = T 04 T 03 + T 02 (5.7) [ P 05 = P ( 1 T )] γ γ 1 05 η d T 04 (5.8) e. Nozzle Inlet Conditions T 06 = T 05 (5.9) f. Nozzle Exit Velocity [ u e = γ 2ηn γ 1 RT 06 P 06 = P 05 (5.10) 1 P a P 06 ] γ 1 γ (5.11) g. Fuel-Air Ratio f = c p T 04 T 03 Q R (5.12) h. Thrust Specific Fuel Consumption T SF C = The results are displayed in Table 5.2. f (1 + f) u e u 32 (5.13)

41 Chapter Liquid Air Cycle Engines Table 5.2: Thrust Available Results M u f u e τ m a τ TSFC Liquid Air Cycle Engines After Mach 4, this concept utilizes the LACE engines. Therefore, values for thrust are available in the literature. The thrust values are shown in Table 5.3. This engine was chosen regardless of some of its drawbacks due to the high efficiency liquid hydrogen fuel. Hydrogen fuel is extremely lightweight and has a high density, making it ideal for missions such as this, as large amounts of hydrogen can be stored at relatively low masses. Additionally, liquid hydrogen fuel gives an extremely high Isp. Despite the lower thrust-to-weight ratio of similar engines, the LACE is ideal for this application because it is reusable, and when used for this mission, this technology will only be further developed which will, in turn, further develop the aerospace industry. Table 5.3: LACE Engine Thrusts LACE Engine Sea Level Space (vaccum) 1960 kn 2940 kn 33

42 5.2. Liquid Air Cycle Engines Chapter 5 34

43 Chapter 6 Analysis of Aerodynamics and Thrust Available The aerodynamics of each stage were evaluated against the thrust available at the beginning and end of each stage. The total drag for the supersonic aerodynamics was found by adding the drag found by shock-expansion analysis, the wave drag, and the skin friction drag for supersonic speeds. The total drag for the hypersonic aerodynamics was found by adding the drag found by modified Newtonian analysis with the skin friction drag for hypersonic speeds. Finally, the final drag of the Space Stage is zero as the drag is space is considered negligible. Thrust available was found keeping in mind that there will be two turbojet engines and four LACE engines on Cielo. Excess thrust was found by subtracted the total drag from the thrust available for each stage. Table 6.1 shows the available excess thrust for each stage. These excess thrust values support the possibility of this mission. Table 6.1: Excess Thrust Analysis Stage Final Space Initial Space Final Hypersonic Initial Hypersonic Final Aircraft Mach Total Drag Coeff Total Lift Coeff Total Drag (N) Total Lift (N) Thrust Available (N) Excess Thrust (N)

44 36 Chapter 6

45 Chapter 7 Cielo Structure 7.1 Structure Materials To keep the weight of Cielo to a minimum while maintaining a high level of structural integrity, the internal and external shell and frame will be made mostly from titanium and aluminum. Cielo will contain a series of stringers, frames, ribs and spars to reinforce the structure under the high loads it will be subjected to. 7.2 Retractable Engines In order to decrease drag incurred upon re-entry, the turbojet engines retract into the fuselage and wings. They are concealed by a mechanical door. This allows the undercarriage to be flush and smooth, enabling a glide landing- similar to the Space Shuttle. During the Hypersonic phase of flight, just as the transition to LACE engines is successfully completed, the hydraulically operated retraction system is signaled to begin retracting the turbojet engines. The mechanical doors are opened and a mechanical arm lifts the engines into the crevice between the wings and the fuselage. Once the engine is pulled into the designated area, known as the engine well, the doors closed over the area. This mechanism, including the turbojet engines, remains dormant for the remainder of flight. However, the reverse process is used on the ground to restore the engines for another flight. Figure 7.1 shows an example of the retractable engine schematic that will be used on Cielo. This figure shows the left half of Cielo as viewed from the nose of the vehicle. Figure 7.1: Retractable Trubojet Engine 37

46 7.3. Fuel Storage Chapter Fuel Storage The density of liquid hydrogen is kg/m 3. The density of liquid oxygen is 1140 kg/m 3. The ratio for liquid oxygen to liquid hydrogen fuel is 6:1. Comparing the final Hypersonic Stage mass with the initial Hypersonic Stage mass as shown in Table 3.5, the difference in mass due to fuel is kg of liquid hydrogen and liquid oxygen. Thus, the amount of liquid hydrogen fuel during the airbreathing Hypersonic Stage is kg, obtained by dividing kg by 6. Comparing the final Space Stage mass with the initial Space Stage mass as shown in Table 3.4, the difference in mass due to fuel is kg of liquid hydrogen and liquid oxygen. Using the same oxygen to hydrogen fuel ratio, this corresponds to kg of liquid hydrogen and kg of liquid oxygen. Therefore, the total amount of liquid hydrogen needed is kg, and the total liquid oxygen needed is kg. Using the densities previously stated, this corresponds to a total volume requirement of 1069 m 3. As discussed previously, through the use of Equation 4.21, the Sears-Haack body volume of Cielo is 4626 m 3. This corresponds to an excess volume on Cielo after fuel is added of 3557 m 3. This volume will be used to meet payload requirements. This information is shown below in Table 7.1. Table 7.1: Fuel Volume Mass (kg) Density (kg/m 3 ) Volume (m 3 ) Liquid Hydrogen Liquid Oxygen Total Volume 1069 Sears Haack Body Volume 4626 Excess Volume

47 Chapter 8 Mission Architecture 8.1 Launch Sites The majority of Cielo launches will be from Florida in order to take advantage of the Earth s rotation. This will also allow Cielo to break the sound barrier over the ocean, rather than over any residential areas. The rest of the launches will take place along the east coast of the United States. Cielo will not be limited to only launches from the US, but can be launched from additional launch sites around the world with international cooperation. The initial cost of Cielo is less than the payload of the Lockheed C-5 Galaxy as shown in Table 2.1. Additionally, the wingspan of Cielo is less than both the Airbus A F and the Boeing F. Therefore, in terms of wingspan, Cielo will be able to takeoff from any runway that can already accommodate the Airbus A F and the Boeing F. Cielo will also be able to takeoff from any runway that can already accommodate the Lockheed C-5 Galaxy. This includes most military runways. 8.2 Trajectory The trajectory that Cielo will follow will be broken into the distinct Aircraft Stage, Hypersonic Stage and Space Stages. During the Aircraft Stage, Cielo will climb at an angle of attack of 12 until an altitude of 10 km is reached. At this point, Cielo will accelerate until a Mach number of 4 is reached. This stage is estimated to take about 30 minutes. Following this stage, Cielo will initiate the Hypersonic Stage. During this stage, Cielo will climb at an angle of attack of 7 until an altitude of 22.9 km is reached. At this point, Cielo will accelerate until a Mach number of 15 is reached. This stage is estimated to take about 20 minutes. Next, the Space Stage will be initiated. During this stage, Cielo will continue to climb from an altitude of 22.9 km to LEO at 350 km. This stage is estimated to take approximately 10 minutes. This trajectory concept is shown in Figure

48 8.2. Trajectory Chapter 8 Figure 8.1: Cielo Trajectory 40

49 Chapter 9 Conclusion Initial aerodynamic analysis of Cielo shows that this vehicle will have enough thrust to overcome the drag forces acted on its body. These drag forces include drag found through shock-expansion theory, wave drag and skin friction drag in supersonic flight, as well as drag found through modified Newtonian theory and skin friction drag in hypersonic flight. The thrust available was found by analyzing the turbojet engines which will be used on Cielo, and by investigating published results on LACE engines. Cielo will use two turbojet engines and four LACE engines. This will provide Cielo with about seven million Newtons of excess thrust during the supersonic and hypersonic phases of this mission. Additional analysis was conducted to ensure the amount of fuel could fit into the body of Cielo, while still allowing room for the payload. Through the use of the rocket equation, the mass of fuel used during both Space and Hypersonic Stages was found. The liquid oxygen to liquid hydrogen fuel ratio was found to be about one to six. This, as well as the densities of liquid hydrogen and liquid oxygen, were then used to determine the amount of volume this fuel would require. Overall, the fuel volume required is 1069 m 3. The volume of the Sears-Haack Body of Cielo was found to be 4626 m 3. This allows for an excess volume of 3557 m 3 which can be used for payload on Cielo. Overall, this mission is possible within the constraints of the vehicle and mission analyzed. The thrust from the propulsion systems onboard Cielo overpower the drag forces acting on the body, found through aerodynamic analysis. Additionally, the fuselage of Cielo contains enough volume to hold both the fuel required for this mission, as well as the payload. Therefore, this design does close. 41

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51 Chapter 10 Bibliography Anderson, John David. Fundamentals of Aerodynamics. New York: McGraw-Hill, Print. Aerospaceweb.org Aircraft Museum - X-15. Aerospaceweb.org Aircraft Museum - X-15. N.p., n.d. Web. 21 Apr Array. Multimedia Album WhiteKnightOne and SpaceShipOne. N.p., n.d. Web. 21 Apr Hill, Phillip. Peterson, Carl. Mechanics and Thermodynamics of Propulsion (2nd Edition) [Hardcover]. Mechanics and Thermodynamics of Propulsion (2nd Edition): N.p., n.d. Web. 21 Apr HOTOL Resources. HOTOL Resources. N.p., n.d. Web. 21 Apr Komerath, Narayanan. AE 3021: High Speed Aerodynamics. Class Lectures. Georgia Institute of Technology, Atlanta, Georgia. Spring Reaction Engines Limited. Reaction Engines Limited. N.p., n.d. Web. 21 Apr Spaceflight Now Breaking News Scramjet Experiment Soars off California Coast. Spaceflight Now Breaking News Scramjet Experiment Soars off California Coast. N.p., n.d. Web. 21 Apr Why SLF? Space Literacy Foundation. N.p., n.d. Web. 21 Apr X-51A: Jury-rigged for Hypersonic Success. - The DEW Line. N.p., n.d. Web. 21 Apr html. XCOR Aerospace: Products Overview. XCOR Aerospace: Products Overview. N.p., 43