Exhaust Gas Velocity

Description

A rocket engine nozzle is a propelling nozzle (usually of the de Laval type) used in a rocket engine to expand and accelerate the combustion gases produced by burning propellants so that the exhaust gases exit the nozzle at hypersonic velocities.

A de Laval nozzle (or convergent-divergent nozzle, CD nozzle or con-di nozzle) is a tube that is pinched in the middle, making a carefully balanced, asymmetric hourglass-shape. It is used to accelerate a hot, pressurized gas passing through it to a higher speed in the axial (thrust) direction, by converting the heat energy of the flow into kinetic energy. Because of this, the nozzle is widely used in some types of steam turbines, and rocket engine nozzles. It also sees use in supersonic jet engines.

Similar flow properties have been applied to jet streams within astrophysics

concepts and simplifying assumptions: – The combustion gas is assumed to be an ideal gas. – The gas flow is isentropic i.e., at constant entropy, as the result of the assumption of non-viscous fluid, and adiabatic process. – The gas flow is constant (i.e., steady) during the period of the propellant burn. – The gas flow is non-turbulent and axisymmetric from gas inlet to exhaust gas exit (i.e., along the nozzle’s axis of symmetry) – The flow behavior is compressible since the fluid is a gas.

As the gas enters a nozzle, it is moving at subsonic velocities. As the throat contracts, the gas is forced to accelerate until at the nozzle throat, where the cross-sectional area is the smallest, the axial velocity becomes sonic. From the throat the cross-sectional area then increases, the gas expands and the axial velocity becomes progressively more supersonic.

The linear velocity of the exiting exhaust gases can be calculated using the equation shown.

Some typical values of the exhaust gas velocity ve for rocket engines burning various propellants are:

– 1,700 to 2,900 m/s (3,800 to 6,500 mph) for liquid monopropellants, – 2,900 to 4,500 m/s (6,500 to 10,100 mph) for liquid bipropellants, – 2,100 to 3,200 m/s (4,700 to 7,200 mph) for solid propellants.

As a note of interest, ve is sometimes referred to as the ideal exhaust gas velocity because it based on the assumption that the exhaust gas behaves as an ideal gas.

As an example calculation using the shown equation, assume that the propellant combustion gases are: at an absolute pressure entering the nozzle p = 7.0 MPa and exit the rocket exhaust at an absolute pressure pe = 0.1 MPa; at an absolute temperature of T = 3500 K with an isentropic expansion factor γ = 1.22 and a molar mass M = 22 kg/kmol. Using those values in the above equation yields an exhaust velocity ve = 2802 m/s, or 2.80 km/s, which is consistent with above typical values.
The technical literature can be very confusing because many authors fail to explain whether they are using the universal gas law constant R, which applies to any ideal gas, or whether they are using the gas law constant Rs, which only applies to a specific individual gas. The relationship between the two constants is Rs = R/M.

Related formulas

Variables

veexhaust velocity at nozzle exit (m/s)
Tabsolute temperature of inlet gas (K)
Rmolar gas constant
Mgas molecular mass (kg/mol)
γisentropic-heat expansion factor (typical value for dry air : 1.398) (dimensionless)
peabsolute pressure of exhaust gas at nozzle exit (pascal)
pabsolute pressure of inlet gas (pascal)