It is impossible to imagine the design of any rocket engine without a nozzle – a technical device that serves to accelerate gas flow passing through it to speeds exceeding the speed of sound. The main types of nozzle profiles are shown in Figure 1.
The most widely used are Laval nozzles due to their high efficiency in accelerating gas flow.
Increasing the efficiency of liquid propellant rocket engines (LPRE) requires increasing the pressure and temperature in the combustion chamber, as well as ensuring the safety of the material part of the engine from the damaging effect of high temperatures.
The challenge of nozzle cooling is relevant due to the high combustion temperature (<3000 K) which threatens the thermal destruction of the engine. In an LRE, fuel components are used to provide wall cooling of the combustion chamber and nozzle and to protect them from the effects of high-temperature gas flow.
Conversely in a solid-fuel engine, the fuel itself cannot be used for cooling. Instead, a specially designed fluid is used for cooling, and significantly increasing the weight of the engine and rocket. Therefore, liquid cooling is not used in a solid fuel engine where the temperature of the engine chamber continuously increases during operation. Normally, such an engine can operate for about 25 seconds without destruction. In the best-case scenarios, this duration increases to 50 seconds.
There are several methods for cooling the walls of the chamber in LREs:
- Flow cooling – based on the creation of a cavity in the walls of the chamber (a “cooling jacket”) through which one of the fuel components passes and cools the chamber wall. If the heat with the cooling flow is returned back to the chamber, then such a system is called “regenerative”. If the removed heat does not enter the combustion chamber and instead is moved to the outside, this is called the “independent” method of cooling.
- Film cooling – method of chamber cooling in which a relatively cold protective layer (film) of liquid or gas is created at the inner walls, washed by a stream of hot gases, moving in the same direction as the main stream. The cooling effect is due both to the absorption of heat during the evaporation of the film and also to the fact that the cooler vapors enter the boundary layer and increase its thickness, therefore reducing heat transfer to the wall.
- Transpiration cooling – based on the use of porous materials and forcing coolant on the surface of the firewall. This method is in principle similar to the film cooling method.
- The ablation method of cooling – carried out by applying a special heat-protective coating to the walls of the combustion chamber and nozzles. The coating at high temperatures passes from a solid to a gaseous state. As a result of the phase transition, a large part of the heat is absorbed.
Designing efficient nozzle cooling systems is not an easy task for an engineer. As was mentioned, both an oxidizer and a fuel component for nozzle cooling can be used. Speaking about the oxidizing components, it should be noted that in some cases the engineer cannot use this component of the fuel. For example, if oxygen is used as an oxidizing agent, it is not suitable for cooling, because it has a boiling point of 183 ° С.
A very important role in the removal of heat from the nozzle walls is played by structural materials usage. Aluminum is one of the engineer’s favorite materials in aircraft construction and is also widely used in rocket science. Pure aluminum is three times lighter than steel and fairly ductile. However, in terms of thermal conductivity and melting point – it loses to copper – the base metal of thermal technology. Copper often is used as inner wall material. Comparing copper with another structural material, steel (a metal used in every application), it should be noted that the melting temperature differs by only a third, while thermal conductivity differs by a factor of ten. Thus, steel wall burns faster than copper.
The critical cross-section of the nozzle is the most thermally loaded part and works under the most difficult conditions. This is due to the fact that the gas flow rate in this section increases, as a result, the heat transfer rate increases, and the heat transfer by the radiation remains the same as in the combustion chamber. In the expanding part of the nozzle, the flow rate continues to increase, but the temperature and density are lower than in the combustion chamber. Thus, in the expanding part of the nozzle, the heat flux from the gas to the wall is decreased as a result of convective and radiant heat transfer.
The design of the cooling system implies the application of effective cooling of the nozzle and especially the sections that are adjacent to the critical section of the nozzle. One of the methods is to reduce the flow area of the cooling channel. In this case, the speed of the cooling component increases, the heat transfer becomes more intense and the temperature difference between the wall and fuel decreases.
Working with companies in the Space Exploration industry, we have also run into challenges related to the cooling nozzle. For a preliminary assessment and analysis of the influence of the geometry of the cooling channels, determination of wall and cooler temperatures, and analysis of heat transfer coefficients, the thermal-fluid network software AxSTREAM NET™ was used. The application allows the engineer to accurately divide the cooling system into sections and thus obtain the distribution along the nozzle of the necessary values for future calculations in the next iteration.
The versatility of AxSTREAM NET allows you to work out in detail the various options for the geometry parameters of the “cooling jacket” in order to choose the most effective one under specific boundary conditions. AxSTREAM NET also enables users to model/calculate transient behaviors experienced in liquid rocket engines. Figure 3 shows a thermal-fluid network of the nozzle in AxSTREAM NET.
An analysis of the wall temperatures and heat transfer coefficients obtained in AxSTREAM NET™ allows engineers to go to the next step – the static thermal solution for assessing thermal stresses. If the assessment of thermal stresses does not satisfy the strength conditions, the ease of installing new boundary conditions in the thermal-fluid network allows you to quickly obtain new values (for example, a change in wall material from the side of hot gases or changing cross-section type). Figure 4 shows different types of cross-sections.
Designing and improving the efficiency of LREs requires an integrated process. In the case of unsatisfactory results, designers often find themselves going back to the drawing board so to speak, and starting from scratch. Using such applications as AxSTREAM NET™ enables engineers to quickly change the input boundary conditions and get new results, which speeds up the design process as a whole. If you want to learn more about how to efficiently simulate rocket nozzle cooling systems, please contact the SoftInWay team by emailing us at Sales@SoftInWay.com
- KudryavtsevM. “Fundamentals of the theory and calculation of liquid rocket engines”, 1993.
- Rocket materials online article
- Nozzles calculation of modern rocket engines – online article
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