Most of the thrust generated by a rocket engine is due to the expansion of gases through the nozzle. The nozzle accelerates the gases produced in the combustion chamber and converts their heat and pressure energy into kinetic energy so that these gases leave the nozzle at supersonic speeds. Along the way, both the temperature and the pressure of the gas are lowered, which also helps in increasing thrust. This article will try and explain how a nozzle works in simple terms.
Most rocket engines use asymmetrical, hourglass-shaped convergent-divergent nozzles. These were first developed in the 19th century for steam jet pumps and turbines. They were first used in a rocket by Robert Goddard, credited with building the world’s first liquid-fueled rocket in 1926.
The nozzle works as follows:
· The fuel (typically kerosene, alcohol, liquid hydrogen) and oxidizer (liquid oxygen, nitric acid, or nitrogen tetroxide) are combined and ignited in a chemical reaction in the combustion chamber, and the hot exhaust gas enters the nozzle.
· As it travels through the converging section, it is pinched (“converges”) down to the minimum area, or throat, of the nozzle. The size of this throat is designed to restrict (“choke”) the flow and accelerate it to the speed of sound (Mach 1).
· When the exhaust gas expands (“diverges”) after reaching sonic velocity in the throat, it expands to a supersonic speed. The expansion of this supersonic flow also causes the pressure and temperature to decrease.
The ultimate exhaust velocity depends on the area ratio of the exit to the throat, as well as the pressure and temperature of the gas at the exit. The design of the nozzle, therefore, determines all the elements that make up thrust — the exit velocity, pressure, and (because of flow choking in the throat) the mass flow rate through the propulsion system.
The key to the nozzle’s operation relies on the differing properties of a gas flowing at subsonic, sonic, and supersonic speeds, and specifically the relationship between the velocity of the gas, its density, and the speed of sound (Mach 1.0, about 330 m/s or 760 mph at sea level).
To understand how it works, let’s start with the law of conservation of mass, which states that mass cannot either be created or destroyed. This means the mass flow rate (mass passing through a particular cross-sectional area per unit time, or density x velocity x cross-sectional area) must remain constant regardless of where it is in the system.
When combustion first occurs, the exhaust gas that enters the nozzle is moving at a subsonic speed. It flows through the converging section of the nozzle in which the area of the nozzle decreases, pinching the gas. At this point, the gas is largely incompressible, i.e., its density is relatively constant. As a result, when the area decreases, the gas is forced to accelerate (increase velocity) so that the mass flow rate remains constant. The narrowest point (the throat) is designed so that the maximum velocity thus attained is the speed of sound. This has the effect of maximizing the flow rate across the nozzle, and this maximized flow is referred to as being ‘choked.’
At this choke point, when the gas becomes sonic (has a speed of Mach 1), heat and pressure energy now start getting converted into kinetic energy, and the gas becomes compressible. As a result, its density will now change as it continues to flow through the nozzle. Because of this, an interesting thing starts happening as the nozzle starts to expand in what’s called the diverging section. Instead of decreasing in velocity (because of the increase in area) to keep the mass flow rate constant, the gas starts increasing rapidly to supersonic speeds.
Why does the gas switch from being incompressible to compressible with an increase in speed? Think of the speed of sound as the speed at which information travels across the molecule of the gas. At lower speeds (typically Mach 0.4 or below), the information travels much faster than the actual movement of the gas molecules. This allows the gas molecules in front to react and in some ways, anticipate the push of the gas molecules from behind. As the flow speed increases to Mach 1, the pace of information flow is the same or slower than the speed of the gas molecules themselves. Shockwaves are generated, and the molecules in front are ‘shocked’ by the unexpected movement of the molecules from behind. This causes the molecules to bump together and compress, thus making the gas compressible and increasing density, and converting heat and pressure energy into kinetic energy. As a result, both temperature and pressure fall as shown below.
