Return to Learning Curriculum

LS1: Introduction to liquid propulsion

Lecture Zoom Recording

Original Author: Matt Morningstar '21, matt_m@mit.edu

  • Note: There are many, many good introductory resources online for learning about rockets and rocket engines. This introductory packet is not meant to replace them, but to supplement them w/ concise descriptions and example problems. 

What is a Rocket?

Put simply, a rocket is a vehicle used to launch people or things into space. Rockets propel themselves by expelling exhaust at a high velocity. This is, at its core, the same way that many propulsive devices work for a variety of vehicles. Aircraft/submarine propellers accelerate the surrounding fluid, leading to the production of thrust. Jet engines intake air, mix it with fuel, burn it, and expel the exhaust at a high velocity. Contrary to popular misconception, you do not need to push “against” anything to produce thrust! Rocket engines work perfectly well in the vacuum of space (in fact, they work even better there than they do on the ground! We’ll talk about why that is in a later LSET). 

As stated earlier, a rocket engine accelerates exhaust gas to a high velocity. By Newton’s second law, we know that this requires a force! And by Newton’s 3rd law, we know that the force that the rocket exerted on the exhaust gas is the same force that the gas exerted on the vehicle. In other words, thrust! The faster the rocket expels the exhaust gas, the greater the thrust force on the rocket. Similarly, the more exhaust (per second) that the rocket expels, the greater the thrust force. This relationship is clearly shown by the following equation:

 

 

Note: For those unfamiliar, a dot above a variable represents the derivative of that variable w/ respect to time. In this case the “m” with a dot over it (pronounced “m-dot”) represents the mass that flows through the engine every second, commonly known as the mass flow rate (commonly shown in kg/s).

The first half of this equation shows exactly what we just discussed: rocket thrust is proportional to the mass flow rate (mdot) and the exhaust velocity (V_e). This product of mdot and V_e is commonly referred to as “momentum thrust”. 

There is also another term on the right-hand side that deals with pressure and area. It states that thrust is also produced from the area at the exit of the nozzle (A_e) multiplied by the difference of the exit pressure (more specifically, the pressure of the exhaust as it exits the nozzle) and the ambient pressure of the surrounding atmosphere. This product is commonly referred to as “pressure thrust”. For the vast majority of rocket engines, pressure thrust plays a small role in the overall thrust production as compared to momentum thrust. It turns out that the most efficient nozzle design is actually one that produces zero pressure thrust. This may seem counterintuitive now, but we will discuss this interesting result in later psets when we deal w/ flow dynamics. Also, note that this quantity can be negative if the ambient pressure is larger than the exit pressure.

There are many different types of rocket engines, but this equation holds true for all of them. Whether we are dealing with solid rocket motors, liquid rocket engines, or cold gas thrusters, the fundamental principle at work is the same.


Types of Rocket Engines

Cold gas thruster:

A cold gas thruster is a simple form of rocket engine. A reservoir of high-pressure gas feeds into a nozzle, where the gas is then expanded/accelerated and expelled. They are very simple and are often used for small thrust requirements (e.g. orienting a satellite in space) where a simple, low part count, low mass solution is desired. 

Monopropellant thruster

A monopropellant thruster is another relatively simple type of engine used for simple, low thrust applications. A monopropellant thruster typically utilizes a gaseous pressurant (a fluid that is designed to pressurize the actual propellant). The propellant flows into the combustion chamber, where it then reacts chemically with a catalyst. This increases the temperature of the gas in the thrust chamber. The flow is then expanded/accelerated in the nozzle.   

Solid rocket motor

A solid rocket motor is arguably the simplest form of rocket engine. Instead of a liquid or gaseous propellant(s) flowing into a combustion chamber, a solid propellant grain burns and produces the exhaust gas which is then expanded through a nozzle. This is the type of rocket engine that MIT Rocket Team’s rockets have used. These engines are simpler than liquid rocket engines and generally have lower efficiency. Because of their reliability and simplicity, they are often used as side boosters to help lift rockets out of the lower atmosphere. Once ignited, there is no way to “turn off” the engine, because the grain will continue to combust.

 

Bipropellant Liquid Rocket Engines

Finally! We’ve saved the best for last. Bipropellant liquid rocket engines are the most widely used (and most complicated) type of rocket engine in modern launch vehicles because of their high efficiency and throttle-bility (the ability to change the thrust output during engine operation). 

Any combustion reaction requires a fuel and an oxidizer (e.g. for a candle, fuel = wax, oxidizer=air). Aircraft w/ jet engines carry their own fuel and use the surrounding air as the oxidizer. In the vacuum of space, there is no air, so a rocket must carry both the fuel and oxidizer (these, collectively, are the two propellants...hence ‘bi-propellant’). A bipropellant liquid engine works by injecting the fuel and oxidizer into a combustion chamber, where they then mix, combust, and flow out of the nozzle. The diagram below shows a specific variety of bipropellant engines where the propellants are pressurized with a pressurant. Other types of engines use pumps to increase the pressure of the propellants before they are fed to the combustion chamber. We will talk in a later LSET about why having the propellants at a high pressure is desired.


 A (slightly) Deeper Dive into Bipropellant Liquid Engines

Liquid rocket engines used in industry today are extremely complicated machines, often containing thousands of individual parts and taking years (if not decades) to develop. These engines deal with extremely high pressures, temperatures, and mechanical loads, and require the intersection of many engineering disciplines to avoid becoming a pile of rubber. Luckily, the Liquid Propulsion subteam deals with much simpler variants of liquid rocket engines. 

All bipropellant liquid engines share, at the very least, a few important components.

Injector

The injector is the first stop for our propellants as they begin the journey to the exit of the engine. The purpose of the injector is to inject the 2 propellants into the combustion chamber in such a manner that they mix thoroughly. Thorough mixing of the two propellants is very important, as better mixing leads to more complete combustion. To be clear, the mixing itself occurs in the combustion chamber. The injector serves as a tool to inject the fuel and oxidizer into the combustion chamber in a very specific pattern to facilitate mixing. A very common injector design is one that forces the fuel and oxidizer to flow through a series of small holes (called orifices). The small streams of fuel and oxidizer then collide, or impinge, upon one another, causing the two to mix.

Combustion Chamber

After the propellants exit the injector and mix, they combust inside the combustion chamber. The combustion chamber must deal with the high pressures of the gas, as well as the high temperatures. 

Nozzle

After the propellants fully mix and combust, they flow into the nozzle. The nozzle features a converging and diverging section, as shown in the above image. This pattern accelerates the flow to supersonic speeds (you will learn why that is in a later lset). The primary goal of the nozzle is to accelerate the flow to a high velocity. As we discussed, a higher exit velocity means more thrust (and, as you will find out, higher efficiency). 

Note: The combustion chamber and nozzle are not always two separate parts, and are sometimes manufactured in one piece.

 

The Ideal Rocket Equation

As discussed, rockets must bring their propellants with them. This means that throughout the burn, the rocket will get lighter, as it is expelling the propellants. A lighter rocket means it can be accelerated more with the same force (Newton’s 2nd law: a = F/m). Because the rocket does not have a constant acceleration, the formula for the change in velocity achieved by a rocket is not totally trivial. 

The Ideal Rocket Equation (shown above) describes the change in a rocket’s velocity as a function of two inputs (the fraction of initial to final mass, and the exhaust velocity). We are not going to go through the derivation of this equation in this document (although you will in 8.01), but there are many resources online that will go through that derivation (and we recommend you go through that on your own). This equation assumes that no other forces are acting on the spacecraft.

Delta-v is an important quantity for launch vehicle and spacecraft design. In order to reach certain ‘destinations’, a certain amount of delta-v is required. For example, reaching low earth orbit from the earth’s surface requires ~10,000 m/s of delta-v. Getting from a low earth orbit to a low lunar orbit takes an additional 900 m/s of delta V. It doesn’t matter how large or small the vehicle is. The delta-v requirement is the same. 

(Delta-v budgets for different destinations)

This ideal rocket equation shows two very important relations. First, delta-v is directly proportional to the exhaust velocity. This tells us that engine efficiency is highly important. Second, delta-v is proportional to the natural log of the mass ratio, which is the initial mass over the final (dry) mass. This shows that a rocket that has a very low dry mass will achieve a greater delta-v. The greater your propellant / stuff ratio (“stuff” includes the structure, engines, tanks, etc.), the better performance you will achieve. In launch vehicle design, this is one of the most important principles: every pound of non-propellant weight you add is a drop in performance.

Note: You may be wondering why the rocket equation does not depend on thrust. If a rocket has an engine twice as powerful, shouldn’t it be able to achieve twice the delta-v? Nope. To illustrate why, consider the example of two identical cars that fill up gas at the same station, and drive down a highway until they run out of gas. One car drives at 60 mph, while the other drives at 30mph. Will the car driving at 60 mph go twice the distance before running out of fuel? No, because it is the fuel efficiency (mpg) and the amount of fuel (size of gas tank) that matter. The 60 mph car will simply exhaust its fuel and go the distance quicker. The same is true for rockets. Our exhaust velocity is analogous to fuel efficiency. A more powerful engine with the same exhaust velocity will simply exhaust the spacecraft’s propellants quicker. That being said, thrust output still matters in many scenarios. For example, rockets launching from the ground must be able to overcome the earth’s gravity, so their thrust must be greater than their weight at takeoff. There is a delta-v penalty associated with this need to overcome gravity. It is referred to as “gravity losses”. There is also a penalty associated with drag. It is called “drag losses”.


Return to Learning Curriculum


  • No labels