# Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles1 Nozzle Expansion Conditions Not all nozzles are created equal. In the ideal case, we’d like.

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Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles1 Nozzle Expansion Conditions Not all nozzles are created equal. In the ideal case, we’d like the pressure of the exhaust coming out of the nozzle to equal the pressure of the atmosphere outside. But what happens when exit pressure doesn’t equal the pressure of the outside atmosphere? When this happens, we have a rocket that’s not as efficient as it could be.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles2 Nozzle Expansion Conditions (cont’d) We can consider two possible situations: – Over-expansion: the exit pressure is less than the pressure of the outside atmosphere. – Under-expansion: the exit pressure is greater than the pressure of the outside atmosphere. Nozzle Expansion

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles 3 Nozzle Expansion Conditions (cont’d) Over-expansion: – This is when the exit pressure is less than the pressure of the outside atmosphere. – This is often the case for a rocket at lift-off because many launch pads are near sea level, where atmospheric pressure is at a maximum. – This atmospheric pressure can cause shock waves to form at the nozzle’s lip. – These shock waves represent areas where kinetic energy turns back into heat and pressure. In other words, they rob kinetic energy from the flow, lowering the exhaust velocity and thus decreasing the overall thrust.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles 4 Nozzle Expansion Conditions (cont’d) Under-expansion: – In this case, the exhaust gasses haven’t expanded as much as they could have within the nozzle. Thus, there’s a “loss” in the sense that we’ve not converted all the heat and pressure we could have into velocity. – This is the normal case for a rocket operating in a vacuum because the exit pressure is always higher than the pressure of the atmosphere. The pressure of the atmosphere is 0 in the vacuum of space. – Unfortunately, we’d need an infinitely long nozzle to expand the flow to zero pressure, so in practice we must accept some loss in efficiency.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles5 Expansion Ratio The total expansion in the nozzle depends on its design. We define the nozzles expansion ratio as the ratio between the nozzle’s exit area and the throat area.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles 6 Thermodynamic Impulse A thermodynamic rocket’s efficiency depends on only two things: the temperature in the combustion chamber and the molecular mass of the propellants. Molecular mass is a measure of the mass per molecule of propellant. – To improve the specific impulse for thermodynamic rockets, we try to produce the highest combustion temperature while keeping the propellant’s molecular mass as low as possible.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles 7 Thermodynamic Impulse (cont’d) Hydrogen is often the fuel of choice because it has the lowest possible molecular mass and burns at high temperatures. The efficiency measured by specific impulse of a thermodynamic rocket goes up as the combustion temperature goes up or as the molecular mass of propellant goes down.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles8 Thermodynamic Rocket System Figure 12-11 is an expanded view of a thermodynamic rocket system. We can see the various inputs, processes, and outputs.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles9 Cold-gas Rockets A cold-gas rocket uses thermodynamic energy in the form of pressurized propellant as its energy source. It’s similar to the toy balloon we talked about earlier. A Cold-gas Thruster

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles10 Cold-gas Rockets (cont’d) A coiled spring stores mechanical energy that can be converted to work. An example is an old fashioned watch. Cross-section of a typical thruster

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles11 Cold-gas Rockets (cont’d) Cold-gas rockets are very reliable and can be turned on and off repeatedly. This produces very small, finely controlled thrust pulses called impulse bits. A good example of them is the MMU which uses compressed nitrogen and many small thrusters. Manned Maneuvering Unit (MMU)

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles 12 Table 12-1 Summary of Cold-gas Rockets Operating PrincipleUses the thermodynamic energy in a compressed gas and expands the gas through a nozzle, producing high-velocity exhaust PropellantsHelium (He), Nitrogen (N2), Carbon dioxide (CO2), or almost any compressed gas Advantages Extremely simple Reliable Safe, low-temperature operation Short impulse bit (thrust pulses) DisadvantagesLow specific impulse compared to other types of rockets

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles13 Electromagnetic Acceleration Besides thermodynamic acceleration through a nozzle, a second way to accelerate propellants is gaining wider use on spacecraft—electrodynamic acceleration. The force of attraction (or repulsion) between charges depends on the strength of the charges involved and the distance between them. The higher the charge, or the closer the charges are, the higher the force of attraction (or repulsion). Unlike charges attract; like charges repel each other.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles 14 Electromagnetic Acceleration (cont’d) An electric field exists when there is a difference in charge between two points. That is when a large imbalance exists between positive and negative charges in a confined region. – Electrical potential is the energy an electric field can transmit to a unit charge, described in terms of volts per meter. – The resulting force on a unit charge is called an electrostatic force.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles15 Electrodynamic Rockets Figure 12-14 illustrates this principle of imbalance. Notice, the direction of the force is parallel to the electric field. Electrodynamic rockets use this principle to create thrust. In the simplest use, they need only some charged propellant and an electric field. As with any rocket, the two key performance parameters are thrust, and specific impulse.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles 16 Electrodynamic Rockets (cont’d) In an electrodynamic rocket, we get high mass flow rate by having a high density of charged propellant. High exhaust velocity comes from having a strong electric field or from applying the electrostatic force for a longer time. We can summarize these effects on performance as follows: – Higher charge density → higher mass flow rate → higher thrust. – Stronger electric field → stronger electrostatic force on the propellant → higher acceleration → higher exhaust velocity → higher specific impulse.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles 17 Electrodynamic Rockets (cont’d) Charge density is limited by the nature of the propellant and how it is charged. An ion is a positively charged propellant molecule that has had one or more electrons “stripped off.” Ions are handy in that they are simple to accelerate in an electric field. Compacted ions in a small, confined space tend to repel each other.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles 18 Electrodynamic Rockets (cont’d) One way around this density limit is to create a plasma with the propellant. – A plasma is an electrically neutral mixture of ions and free electrons. – Common florescent lamps or neon lights create a plasma when turned on.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles 19 Electrodynamic Rockets (cont’d) When a gas, such as neon, is in a strong electric field, the electrons become only weakly bound to the molecules, thus creating a “soup” of ions and free electrons. The glow is from electrons jumping back and forth between energy states within the molecule. Because it is electrically neutral, a plasma can contain a much higher charge density than a collection of ions alone.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles SECTION 12.2 20 Propulsion Systems Elements of Propulsion Systems Propellant Management Thermodynamic Rockets Electrodynamic Rockets System Selection and Testing Exotic Propulsion Methods

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles21 Elements of Propulsion Systems A propulsion subsystem uses the desired end state (specific thrust at a specific time), plus inputs from sensors, to determine commands for the propellant-management and energy-control systems to produce the system’s output: thrust. Figure 12-15 is a block diagram of a complete propulsion subsystem.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles 22 Propellant Management Propellant management is storing propellant and getting it where it needs to go at the right time. This part of a propulsion subsystem has four main tasks: – Propellant storage – Pressure control – Temperature control – Flow control

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles23 Pressure-fed Systems A pressure-fed propellant system (Figure 12-16) relies on either a gas propellant stored under pressure or a separate tank attached to the main tank. This separate tank is full of an inert, pressurized gas, such as nitrogen or helium, that pressurizes and expels a liquid propellant.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles 24 Pressure-fed Systems (cont’d) The high-pressure gas “squeezes” the liquid propellant out of the storage tank at the same pressure as the gas, like blowing water out of a straw.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles 25 Pressure-fed Systems (cont’d) Mechanical regulators are used to regulate the high pressure for propellant delivery. As high-pressure gas flows into a regulator, the gas pushes against a carefully designed diaphragm. The diaphragm is a thin part inside the regulator. The resulting balance of forces maintains a constant flow rate at a much lower output pressure.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles26 Pump-fed Systems Pump-fed delivery systems (Figure 12- 17) rely on pumps to take low-pressure liquid and move it toward the combustion chamber at high pressure. Pumps give kinetic energy to the propellant flow, increasing its pressure.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles27 Pump-fed Systems (cont’d) The Space Shuttle Main Engines (SSMEs) (Figure 12-18) use turbine pumps to feed liquid hydrogen and oxygen to the combustion chamber.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles 28 Pump-fed Systems (cont’d) Regardless of the propellant-delivery system, the pressure of propellants and pressuring gases must be monitored all the time. Pressure sensors are small electromechanical devices used to measure the pressure at different points throughout the system.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles29 Propellant Thermal Management On launch vehicles, propellant thermal management often has the problem of maintaining liquid oxygen and liquid hydrogen at temperatures hundreds of degrees below 0 ° Celsius.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles30 Propellant Thermal Management (cont’d) Using insulation helps control the temperature. We need to plan for some “boil off” of propellants, which usually happens before launch. Cryogenic propellants on the shuttle must remain hundreds of degrees below zero.

Unit 3, Chapter 12, Lesson 12: Rockets and Launch Vehicles 31 Pressure Sensors Propellant-management subsystems must control the flow of gases and liquids through valves. Pressure-relief valves automatically release gas if the pressure rises above a preset value. Check valves let liquid flow in only one direction.

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