There is a lot that comes into play when designing a rocket motor – whether it be a liquid, solid, or hybrid motor – many assumptions must be made during the design phase. From experience, these assumptions greatly ease the design process along and is a fundamental set of knowledge that anyone venturing into rocket engineering should know about.
The Assumptions of The Ideal Rocket:
As summarized from Sutton (2010)
- The working substance, the products of the combustion from the propellant(s), is homogeneous.
- All species of the working substance are gaseous. There are in reality solid and liquid (condensed) phases coming out of the business end of the rocket but are negligible.
- The working substance obeys the perfect gas law!
- The flow is adiabatic, we neglect heat transfer across the nozzle walls etc.
- Friction and boundary layer effects are neglected.
- Inside the nozzle there are no shock waves or discontinuities.
- The flow and expansion are steady, constant, without vibration. Transients (startup and tail-0ff) are neglected.
- All exhaust gasses have axially directed velocity. This must be corrected for conical nozzles and is a simple trig function and will be covered in a future post.
- As our assumptions deal with quasi-one-dimensional flow, the gas velocity, pressure, temperature, and density are considered to be uniform at any cross-section of the nozzle normal to its axis.
- Chemical equilibrium is established in the combustion chamber. This is the “Frozen Flow” assumption meaning the gas composition doesn’t change as it moves through the nozzle.
- Propellants are at room temperature. The exemption is for cryogenic propellants, these are considered to be at their boiling points.
But how much error will result from these assumptions? For a chemical rocket, the measured performance is, according to Sutton (2010), is only 1% to 6% below the ideal value! Personally, I think this is incredible
So why do these assumptions cause such small errors? Based on the temperature inside the combustion chamber is so high (generally above 2000 K) all the species of combustion products are above saturation conditions and thus follow closely the perfect gas law and also allow the second and 10th assumption. Neglecting friction and heat loss, as well as assuming the lack of discontinuities allows the use of isentropic flow relations for the expansion of the gas within the nozzle. In real world measurements, friction loss is usually negligible and the heat loss to the duct walls is usually <1% and thus allows the neglection of heat loss in our calculations. Transients happen very quickly and thus due to the sheer velocity of the flow, allow for the steady and uniform assumption. Boundary layer effects are ignored for one amazing reason, these flow is too fast. That’s right, the flow is fast enough that the Reynolds number is so high that all boundary leyer effects will be localized very very close to the nozzle wall and thus can be ignored!
For further and more detailed information see chapter three of the source given below. This is a very good text and is considered one of the bibles of rocketry.
Sutton, G. P., & Biblarz, O. (2010). Rocket Propulsion Elements. Hoboken, NJ: John Wiley & Sons Inc.