👩🏼‍🚀Intro to Aerospace Engineering Unit 7 – Aerospace Propulsion: Jets and Rockets

Key Concepts and Terminology

• Propulsion generates force to move an object, typically by expelling mass in the opposite direction of motion
• Thrust is the force produced by a propulsion system, measured in newtons (N) or pounds-force (lbf)
• Specific impulse ($I_{sp}$) measures the efficiency of a propulsion system, expressed as the thrust per unit of propellant flow rate
  • Higher $I_{sp}$ indicates better fuel efficiency and performance
• Propellants are substances used to generate thrust, consisting of fuel and oxidizer
  • Liquid propellants (kerosene, liquid hydrogen) are commonly used in rockets and some jet engines
  • Solid propellants (ammonium perchlorate, aluminum) are used in solid rocket motors
• Nozzles are essential components that accelerate and direct the exhaust flow to generate thrust
  • Converging-diverging nozzles (De Laval nozzles) are used to achieve supersonic exhaust velocities

Fundamentals of Propulsion

• Newton's third law of motion states that for every action, there is an equal and opposite reaction, which is the basis for propulsion
• Propulsion systems generate thrust by expelling mass in the opposite direction of the desired motion
• Thrust equation: $F = \dot{m}v_e + (p_e - p_0)A_e$, where $F$ is thrust, $\dot{m}$ is mass flow rate, $v_e$ is exhaust velocity, $p_e$ and $p_0$ are exit and ambient pressures, and $A_e$ is nozzle exit area
• Specific impulse ($I_{sp}$) is a key performance metric for propulsion systems, defined as $I_{sp} = \frac{F}{\dot{m}g_0}$, where $g_0$ is standard gravity (9.81 m/s²)
  • $I_{sp}$ is often expressed in seconds, representing the duration a propulsion system can generate 1 unit of thrust per unit of propellant mass
• Propulsive efficiency ($\eta_p$) is the ratio of the useful propulsive power to the total power input, given by $\eta_p = \frac{F v_{\infty}}{\dot{m} (h_0 - h_e)}$, where $v_{\infty}$ is the vehicle velocity, and $h_0$ and $h_e$ are the total enthalpy at the inlet and exit, respectively

Jet Engine Types and Components

• Jet engines use air as the working fluid and generate thrust by accelerating the air through the engine
• Turbojet engines compress air using a compressor, burn fuel in a combustion chamber, and expand the hot gases through a turbine and nozzle
  • Suitable for high-speed applications (fighter aircraft) but have lower efficiency at lower speeds
• Turbofan engines add a large fan before the compressor, which accelerates a larger mass of air around the engine core
  • Bypass ratio is the ratio of the mass flow through the fan to the mass flow through the core
  • High-bypass turbofans (airliners) are more fuel-efficient at subsonic speeds, while low-bypass turbofans (military aircraft) offer better performance at supersonic speeds
• Turboprop engines use a turbine to drive a propeller, which accelerates a large mass of air to generate thrust
  • Efficient at lower speeds and altitudes (regional and cargo aircraft)
• Ramjet engines have no moving parts and rely on the forward motion of the vehicle to compress the incoming air
  • Operate efficiently at high supersonic speeds (Mach 3-6) but cannot generate static thrust

Rocket Propulsion Basics

• Rockets carry both fuel and oxidizer onboard, allowing them to operate in the vacuum of space
• Chemical rockets burn fuel and oxidizer in a combustion chamber to generate high-temperature, high-pressure gases that are expanded through a nozzle to produce thrust
• Rocket thrust equation: $F = \dot{m}v_e + (p_e - p_0)A_e$, where the second term (pressure thrust) becomes significant at high altitudes or in vacuum
• Specific impulse for rockets is higher than jet engines due to the absence of air drag and the ability to use more energetic propellants
  • Typical $I_{sp}$ values range from 200-300 seconds for solid rockets and 300-450 seconds for liquid rockets
• Staging is used to improve rocket performance by discarding empty propellant tanks and engines during flight
  • Multistage rockets (Saturn V, Falcon 9) can achieve higher payload mass ratios and reach higher velocities than single-stage rockets

Propellants and Fuel Systems

• Liquid propellants are stored in separate tanks and pumped into the combustion chamber
  • Bipropellant systems use separate fuel (kerosene, liquid hydrogen) and oxidizer (liquid oxygen) tanks
  • Monopropellant systems use a single propellant that decomposes when heated (hydrazine)
• Solid propellants are pre-mixed and cast into a solid grain that burns from one end to the other
  • Consist of an oxidizer (ammonium perchlorate), fuel (aluminum), and binder (HTPB)
  • Simpler and more reliable than liquid propellant systems but offer less control over thrust
• Cryogenic propellants (liquid hydrogen, liquid oxygen) offer high specific impulse but require insulated tanks and careful handling
• Propellant feed systems can be pressure-fed or pump-fed
  • Pressure-fed systems use pressurized gas to force propellants into the combustion chamber, suitable for small engines
  • Pump-fed systems use turbopumps to deliver propellants at high pressure, necessary for large engines (Space Shuttle Main Engine)

Thrust and Performance Calculations

• Thrust is calculated using the rocket thrust equation: $F = \dot{m}v_e + (p_e - p_0)A_e$
  • Mass flow rate ($\dot{m}$) depends on propellant density, combustion chamber pressure, and nozzle throat area
  • Exhaust velocity ($v_e$) is a function of the specific heat ratio, combustion temperature, and pressure ratio across the nozzle
• Specific impulse is calculated as $I_{sp} = \frac{F}{\dot{m}g_0}$ and represents the efficiency of a rocket engine
  • Affected by factors such as propellant combination, combustion chamber pressure, and nozzle expansion ratio
• Tsiolkovsky rocket equation describes the relationship between velocity change ($\Delta v$), specific impulse, and initial and final mass: $\Delta v = I_{sp} g_0 \ln \frac{m_0}{m_f}$
  • Determines the payload capacity and range of a rocket based on the available propellant mass
• Thrust-to-weight ratio (TWR) is the ratio of the rocket's thrust to its weight and determines its acceleration and ability to overcome gravity
  • TWR > 1 is necessary for a rocket to lift off from the launch pad

Design Considerations and Challenges

• Rocket engines must withstand extreme temperatures, pressures, and vibrations during operation
  • Regenerative cooling circulates cryogenic propellant around the nozzle and combustion chamber to prevent overheating
  • Ablative cooling uses a sacrificial material (silica phenolic) that chars and erodes to dissipate heat
• Throttling and thrust vectoring are used to control the rocket's trajectory and attitude
  • Throttling adjusts the thrust level by varying the propellant flow rate or combustion chamber pressure
  • Thrust vectoring deflects the exhaust flow using movable nozzles or injection of secondary fluids
• Combustion instability can occur due to pressure oscillations in the combustion chamber, leading to increased heat transfer and structural damage
  • Acoustic cavities, baffles, and injector design are used to dampen instabilities
• Propellant sloshing in the tanks can affect the rocket's stability and control
  • Baffles and anti-slosh diaphragms are used to minimize sloshing effects

Real-World Applications and Future Trends

• Rockets are used for space launch vehicles (SpaceX Falcon, ULA Atlas), spacecraft propulsion (satellites, deep space probes), and military applications (intercontinental ballistic missiles)
• Electric propulsion systems (ion engines, Hall thrusters) use electricity to accelerate propellant, offering high specific impulse but low thrust
  • Suitable for long-duration missions (Dawn spacecraft) and satellite station-keeping
• Nuclear thermal rockets heat a propellant (hydrogen) using a nuclear reactor, providing higher specific impulse than chemical rockets
  • Potential for faster interplanetary travel and manned missions to Mars
• Scramjet (supersonic combustion ramjet) engines enable air-breathing propulsion at hypersonic speeds (Mach 5+)
  • Challenges include efficient fuel injection, mixing, and combustion in supersonic flow
• Reusable rocket technology (SpaceX Falcon 9, Blue Origin New Shepard) aims to reduce launch costs by recovering and refurbishing rocket stages
  • Vertical takeoff and landing (VTVL) and parachute recovery are the main approaches being developed