Lesson 3 : Ideal Rocket Nozzle


Topics/Contents:

  • Assumptions for Ideal rocket

  • Isentropic flow through the nozzle

          • Area - Mach Number - Velocity Relationship

          • Choking of Nozzle

          • Nozzle Area Ratio

  • Flow Separation in Nozzles

          • Under expanded and over expanded nozzles

        • Rocket Nozzle Configurations

Introduction to Nozzles

A nozzle converts the chemical energy of the propellant to kinetic energy without any moving parts. Rocket nozzle channelize and accelerate the combustion products produced by the burning propellant inside the rocket, in such a way that it maximizes the velocity of the exhaust at the exit to the supersonic velocity. Generally, nozzles are used to control the flow rate, direction, mass, speed, shape, and pressure of the exhaust stream.

Assumptions of Ideal Rocket

The following are the assumptions considered for the conceptualizing of Ideal Rocket for expressing basic thermodynamics equations in terms of simple mathematical expressions.

  • The working substance is homogeneous.

  • All the species of the working fluid are in the gaseous state, any other phases are negligible when compared with the total mass.

  • The working substance obeys the perfect gas law.

  • There is no heat transfer across the rocket walls, therefore the flow is adiabatic.

  • There is no appreciable friction and all the boundary layer effects are neglected.

  • There are no shock waves or discontinuities in the nozzle flow.

  • The propellant flow is steady and constant.

  • The expansion of the working fluid is uniform and steady, without vibration.

  • Transient effects (i.e. the start and shutdown) are of very short duration and may be neglected.

  • All exhaust gases leaving the rocket have an axially directed velocity.

  • The gas velocity, pressure, temperature, and density are all uniform across any section normal to the nozzle axis.

  • Chemical equilibrium is established within the rocket chamber and the gas composition does not change in the nozzle.

Ref: Biblarz, O., Sutton, G. P. (2016). Rocket Propulsion Elements. United Kingdom: Wiley.

Isentropic Flow through the Nozzle

Choking of Nozzle

Nozzle Area Ratio

Nozzle

Flow Separation in Nozzles

A rocket traverses different altitudes and the different ambient pressure decreases as the rocket moves away from the surface of the earth. If the area ratio of the nozzle is designed for optimum conditions at a given altitude of operation, it will be operating in an “under-expanded” condition for altitudes higher than design altitude. Whereas it will function as an “over-expanded” nozzle for lower altitudes.

In an over expanded nozzle, the pressure towards the exit of the nozzle falls below the ambient pressure. The flow within the nozzle divergent section being supersonic, the flow cannot sense the conditions ahead of it, the flow abruptly changes through a discontinuity called shock and becomes subsonic to match the ambient pressure.


The sudden compression by the shock is associated with separation of flow from the walls . The zone of separation depends on the local pressure and the rate of acceleration and is influenced by the nozzle divergence.


In an ideal case, the separated flow would be helpful as it provides higher pressure at the nozzle wall and therefore the nozzle can adapt to the altitude. The thrust from a nozzle with flow separation is more than the thrust corresponding to the same area ratio for which the flow separation has not taken place.