Simcenter Amesim comes with the Liquid Propulsion library which contains a set of components specific to cryogenic engines, such as pumps, turbines, combustion chambers and nozzles. This library is an extension of the Two-Phase Flow and Gas Mixture libraries which address the physical phenomena linked to dynamic gas mixture, combustion and phase change transition such as boiling and condensation.
Components from other libraries, for instance shafts with inertia, gearboxes, electrical generators or heat exchangers, can be combined with the Liquid Propulsion library components to allow the modeling of any rocket engine architecture and any integrated system.
Several liquid rocket engine architectures have been used during the decades as pressure-fed cycle, gas-generator cycle, expander cycle or staged combustion cycle.Each architecture has its own benefits and drawbacks and at the beginning of rocket engine development, analysis must be done to choose the one which fits with the vehicle and rocket requirements.
Thanks to the Simcenter Amesim modular approach, a plant model of any of these cycles can be created.
In this article, we will focus on one of these cycles: the staged combustion cycle.
The staged combustion cycle is an engine cycle where the propellants are burned in several stages (pre-burner and main combustion), improving fuel efficiency. Indeed, this closed cycle improves the fuel efficiency compared to an open cycle like gas generator where the gas driving the pump is exhausted overboard.
This type of cycle allows to reach the higher chamber pressure; this makes it a good candidate when high performance is required. However, one of the main disadvantages is the engineering complexity.
In this specific staged combustion cycle, shown in Figure 3, the engine uses two separate pre-combustion chambers (fuel rich pre-burners), each mounted directly on a separate main turbopump. Two additional turbopumps provide a boost pressure to the main pumps. These are not driven by combustion gases: one booster pump high-pressure liquid oxygen while the other is driven by evaporated hydrogen.
As for the expander cycle (b picture in Figure 2), the fuel coolant flows through the cooling jacket around the expander nozzle. Finally, the products of the combustion are accelerated in the rocket nozzle to generate thrust.
The model that reproduces this cycle is shown in Figure 2, and it is based on :
In the Simcenter Amesim sketch, you can see different typical components of a rocket engine as the combustion chambers, the turbomachines, the cooling jacket or the valves and control systems.
In the staged combustion cycle, rockets burn fuel and oxidizer in several stages: there is a first combustion chamber where a small portion of propellant is burned and the main combustion chamber where the propellants are completely burned.
In terms of simulation, you might need to answer the following questions:
If you have this kind of questions, please take a look at this subchapter:
In this case, combustion burns H2 and O2 as propellants.
The choice between the two approaches depends on the combustion conditions. In the case of the pre-burners on this particular engine, the temperatures of the chambers are sufficiently low to ignore the dissociation process.
If the dissociation process is not taken into account during the combustion, the combustion reaction can be written as follows:
However, this assumption is less accurate when the combustion temperatures get higher, due to the intermediate endothermic reactions of the dissociation process. In fact, at high temperatures other combustion products should be taken into account (as for example H, O, HO2 and OH).
To demonstrate this, two combustion submodels have been used:
We imposed different mixture ratios to both chambers.
Figure 7 shows the comparison of the combustion chamber temperature as a function of the mixture ratio obtained with the two submodels. LPCCP00 overestimates the maximum temperature with respect to LPCCP01 (where dissociation is considered). This is due to the increase of the combustion products fractions of OH, O, H and HO2 as shown in Figure 8.
Being said that, how can we apply our last analysis to this staged-combustion example?
Since the temperatures in the pre-burner chambers are sufficiently low (Figure 10), the dissociation process can be ignored. For this reason, LPCCP00 is used for pre-burners and LPCCP01 is used for the main combustion chamber.
In this rocket engine example, there are 4 turbomachines:
The main advantage of the low-pressure turbopumps is that they boost the liquid oxygen and hydrogen from low pressure to the high-pressure turbopumps. During engine operation, the low-pressure turbopumps allow the high-pressure turbopumps to operate at high rotary speeds avoiding cavitation.
In terms of modeling, pumps are modeled using Suter curves formalism. It allows us to describe centrifugal or axial pump that may experience reversal in flow, inversion of rotational speed, torque and/or differential pressure during a transient event.
Suter curve formalism uses dimensionless standard curves coming from experimental results, as pictured in Figure 11. The dimensionless quantities are as a function of a reference pump characteristics or Best Efficiency Point (BEP).
The usage of these curves can be different depending on the information the user has from their turbopump:
For this example, the following valves have been considered:
The valves follow a sequence of start reported in . The next figure shows this sequence:
During the engine run phase, most of the valves run schedules, while the FPOV switched from an open-loop control to a closed-loop control to control the mixture ratio of the pre-burners and therefore, the mixture ratio of the main combustion chamber.
The engine controller can be found in the following supercomponent:
In this case, a simple proportional controller has been used but more robust control strategy can be modeled. For more details, please take a look at how MHI and Churyo Engineering modeled and validated (MiL) the control system of their LE-9 engine u... and its standard interface allows co-simulation with controller models.
We have seen how to assess the behavior of a staged combustion rocket engine, and we have considered different assumptions and modeling strategies that can be used. The Simcenter Amesim model also shows how to couple the plant model with the control system.
For more information, please open the “Staged combustion cycle rocket engine start up” demonstrator in Simcenter Amesim and watch the how-to video:
: Modern Engineering for Design of Liquid-Propellant Rocket Engines.
: Rocketdyne Propulsion & Power, Space Shuttle Main Engine Orientation.
: Sanford Gordon and Bonnie J. McBride. Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications I. Analysis.
 Wylie, E., Streeter, V. and Suo, L. (1993). Fluid transients in systems. Englewood Cliffs, NJ: Prentice Hall.
David Jiménez Mena is 1D presales system simulation consultant based in France. After more than 5 years as a simulation engineer, he joined the system simulation technical team of EMEA Center of Excellence.
Before he worked as a simulation engineer focused on the development of the aerospace propulsion specific applications of Simcenter Amesim.