Calculation of Electrification of Nozzles of Liquid Rocket Engines

One of the most important tasks in modern spacecraft launches is the development of efficient and at the same time economical engines. Losses in the wall layer associated with the friction of the flow against the nozzle wall cause the appearance of an electric potential on it. Electrification by friction of the flow against the nozzle wall (engine electrification) also affects the occurrence of inhomogeneities in the flow [1]. As a consequence of these processes, the occurrence of a transverse current in the flow of combustion products. These processes lead to the accumulation of potential on the body of the isolated engine and its effect on the rest of the spacecraft units, the occurrence of electrical discharges on board the aircraft, interference with control systems and radio communications and other effects that negatively affect the normal operation of the propulsion system and the spacecraft as a whole.

The conversion of chemical energy into thermal energy in the channels of rocket engines occurs through the combustion of fuel and is characterized by the primary generation of charged components (ions and electrons) and exothermic recombination reactions occurring mainly behind the flame front. The fuel combustion products are located in the combustion chamber (CC) at high pressures (up to 25 MPa) and temperatures (more than 3500 K) characteristic of liquid propellant rocket engines (LRE) (kerosene and oxygen) and can be considered as partially ionized plasma. An ambipolar region is formed near the wall, in which the main losses occur, the calculation model of which is given by the authors of this article.

The paper considers the electrification of the nozzle by the flow of combustion products of liquid fuel (kerosene-oxygen combination) in the RD-191 LRE at three different pressures in the combustion chamber: 10, 15 and 25 MPa.

Based on the TERRA software package [4], the main characteristics of the flow (pressure, temperature, velocity, concentrations of electrons, ions and neutral components) and their distribution along the length of the nozzle in accordance with its specified configuration are determined. The initial parameters were the pressure in the combustion chamber, the enthalpy of the fuel, as well as a number of ratios of nozzle diameters to its critical diameter in order to set the cross sections under study.

According to the results of the calculation of the software package, 30 different components of the flow of neutral particles, 16 ions (both positively and negatively charged) and electrons were used for calculations.

In accordance with the literature [3], the distribution of ion concentrations in the wall region was assumed to be constant, and the electron distributions were approximated and estimated according to known dependencies – the electron concentration decreases, the value of the ambipolar region was determined, which was about 3 mm, in which the values of the resulting linear current and voltage drops were estimated and shown.

The calculation grid consisted of splitting the nozzle into 344 equal sections with a width of 5 mm. In each section, the current and voltage drop were calculated according to the obtained values, in which the distributions of the desired values were constructed along the length of the supercritical part of the nozzle.

Thus, the current value at the beginning of the nozzle (at the critical section) reached up to 25 mA, and closer to the output section it turned out to be close to zero. The total current generated along the entire length of the supercritical part of the nozzle was 55, 90 and 150 mA for pressures of 10, 15 and 25 MPa in the combustion chamber, respectively.

Distributions of the total voltage drop associated only with ambipolar diffusion were obtained both in the wall region and along the entire length of the supercritical part of the nozzle. So, in the first sections, the magnitude of the voltage drop was about 3 V, and closer to the output section it decreased to almost 1.5 V. This pattern is characteristic of all the studied pressures.

A further assessment of the electron mobility and electrical conductivity allowed us to carry out calculations and calculate the values of the ohmic part of the voltage drop, which reached 3, 4.5 and 7.5 V (for pressures in the combustion chamber of 10, 15 and 25 MPa, respectively) at the critical section and dropped quite sharply below 1 V after 0.5 m of the nozzle, and at the outlet of its the value was about 0.1 V.

In the work, the distributions of currents and voltage drops in the supersonic flow of partially ionized liquid propellant combustion products along the length of the supercritical part of the nozzle were obtained. The construction and approximation of graphs were carried out in the program «Microsoft Excel».

The occurrence of a potential can have a significant impact on the structural elements if the engine is electrically isolated. In this regard, it is necessary to adjust the length of the supercritical part taking into account the potential formed by the flow of combustion products on the engine body.

The work was supported by the program №075-2020-444 fundamental Research of the Ministry of Science and Higher Education of the Russian Federation.