JANNAF Standard¶
In 1975, the John Hopkins University, Applied Physics Laboratory published CPIA 246 in conjunction with JANNAF (Joint Army-Navy-NASA-Air Force) titled Rocket Engine Performance Test Data Acquisition and Interpretation Manual
CPIA 246 JANNAF Rocket Engine Performance Prediction and Evaluation Manual established a US national standard for the analytical and experimental evaluation of the performance of liquid propellant rocket engines and is a result of the work by the Interagency Chemical Rocket Propulsion Group (ICRPG) formed in 1962. In 1973, NASA-CR-131519 was published to discuss the history of the ICRPG meetings that led to CPIA 246 and to summarize the selected model approaches.
In 1977, Aerojet Liquid Rocket Company (ALRC), now known as Aerojet Rocketdyne, published an update to CPIA 246 entitled Analysis of rocket engine injection combustion processes that reflects on-going improvements to the models and software used to implement the “standard” JANNAF model. The Aerojet report also indicates that, in 1977, the JANNAF model, in general, could not yet achieve a 1% accuracy on predicting Isp without the help of test data.
There are two model approaches offered by JANNAF, a rigorous model and a simplified model.
Rigorous Model¶
The rigorous model is intended for the detailed analysis of an engine that is preparing for a hardware production design; either test or flight hardware.
The rigorous model requires many more resources and much more technical expertise than can be presented here.
Since 1977, much has changed in how aerospace companies conduct rigorous performance analysis. The rigorous approach has evolved. The advent of Computational fluid dynamics (CFD) has given rise to analysis approaches like the NASA Space Launch System (SLS) at NASA Ames Research Center and NASA Marshall Space Flight Center (MSFC). Such models require super computers or large computer clusters in order to complete a single run in a reasonable time (often several days of run time).
Simplified Model¶
The simplified model is intended more for preliminary analysis where general trends and influences are more important than low-level design details.
The simplified model can be performed with some first-order efficiency models and the python project RocketCEA (RocketCEA wraps the NASA FORTRAN CEA code that calculates One Dimensional Equilibrium Isp)
Rocketisp will focus on a simplified model of performance prediction.
NASA-CR-131519 describes the simplified model for calculating delivered Isp (\(Isp_{del}\)) as having 3 basic assumptions:
1 One-dimensional isentropic expansion (ODE)
2. Simple nozzle geometry
3. A system of correction losses to the ODE value
a. Mixture ratio distribution
b. Chamber friction
c. Chamber heat transfer
d. Energy release efficiency
e. Nozzle friction
f. Nozzle heat transfer
g. Nozzle geometry
h. Kinetics
i. Mass distribution
j. Two-phase flow
k. Nonstandard inlet conditions
In its most simplified form, the delivered Isp (\(Isp_{del}\)) of a liquid propellant rocket engine with a conventional nozzle is just the One Dimensional Equilibrium Isp (\(Isp_{ODE}\)) generated by RocketCEA multiplied times each of the efficiencies (\(\eta_i\)) described by the correction losses, a through k, above.
The above efficiencies are usually separated into two groups; those that happen in the chamber and those that happen in the nozzle.
Nozzle Losses¶
The Isp losses in the nozzle are more simple to model than the chamber losses and are usually more consequential to the delivered Isp.
Rocketisp calculates overall nozzle efficiency from:
effDiv = Divergence Efficiency of Nozzle
effKin = Kinetic Efficiency of Nozzle
effBL = Boundary Layer Efficiency of Nozzle
effTP = Two Phase Efficiency of Nozzle
Chamber Losses¶
Chamber losses are usually more difficult to model than losses in the nozzle and they are usually more subject to detailed design features.
That said, the combined chamber losses are usually small in production engines. For example, 98% efficiency is a very typical value for all the combined chamber losses.
Rocketisp calculates overall chamber efficiency from:
effMix = Inter-Element Mixing Efficiency of Injector
effEm = Intra-Element Mixing Efficiency of Injector
effVap = Vaporization Efficiency of Injector
effHL = Heat Loss Efficiency of Chamber
effFFC = Fuel Film Cooling Efficiency of Chamber
effPulse = Pulsing Efficiency of Thruster
Mixing loss results from less than ideal mixing between the fuel and the oxidizer. Vaporization loss results when the fuel and/or oxidizer do not completely vaporize to enable full combustion. Those losses combined with any inability of combustion to reach equilibrium chemistry are lumped to yield the injector losses, sometimes referred to as combustion efficiency or energy release losses.
The most universally used parameter to characterize an injector is the characteristic velocity (\(c^*\)).
Rocket Propulsion Elements, defines \(c^*\), pronounced “cee-star”, as:
The characteristic velocity (\(c^*\)) is easily determined from measured data of mass flow rate (\(\dot m\)), chamber pressure (\(P_c\)), and throat area (\(A_t\)). It relates to the efficiency of the combustion and is essentially independent of nozzle characteristics.
\(c^*\) is often used as a measure of the injector excellence since fully mixed and reacted propellants generally have higher \(c^*\) than poorly-mixed and partially-reacted propellants.
The most direct measurement of energy release efficiency (\(\eta_{ERE}\)) is the measured \(c^*\) efficiency (\(\eta_{c^*}\)) of the thrust chamber. If the \(c^*\) efficiency is used to back out energy release efficiency , then the effect of the nozzle discharge coefficient \(C_D\) must be taken into account.
In other words, for a perfect injector: \(\Large{\eta_{c^*_{PI}} = 1 / C_D}\)
For a real injector: \(\Large{\eta_{c^*} = \eta_{ERE} / C_D}\)
such that the energy release efficiency can be calculated as:
Note that, In general, the use of empirical data is required to predict the energy release efficiency. – D.E. Coats
