Verification of thermodynamic parameters of a mixture of generator gas on oxygen-hydrogen fuel with an excess of one of the fuel components

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Introduction

Achieving carbon neutrality is underway in many countries around the world. Despite the low percentage of air pollution from launch vehicles compared to emissions of pollutants from industrial enterprises, the rocket industry is subject to some restrictions, forcing them to become more environmentally friendly.

One of the main tools for achieving carbon neutrality is alternative energy, the promising fuel of which is hydrogen due to its chemical kinetics [1]. Thus, back in the last century, hydrogen paired with oxygen was successfully used as fuel for liquid rocket engines [2; 3]. Liquid rocket engines developed in the Soviet Union [4], operating on hydroxygen, cannot compete with modern engines in terms of efficiency [5].

Following environmental trends [6] and taking into account the high energy content of hydrogen, the question arises of designing new [7] or modifying existing liquid propellant engines operating on this fuel [8]. At the same time, most modern liquid propellant propulsion systems contain liquid gas generators, in which, based on exothermic processes of decomposition or combustion of the corresponding substances, generator gas is produced with a relatively low temperature of the order of 500–1300 K [9]. The presence of a gas generator in the engine circuit allows throttling by regulating the ratio of fuel components in the gas generator [10], thus changing the thermodynamic parameters of the gas that drives the turbocharger turbine.

A feature of the LGG working process is that it occurs with a small supply of thermal energy to the fuel. Due to this, chemical reactions proceed more slowly than in a liquid-propellant rocket engine chamber [11]. As a result, high-temperature bundles may appear [12], which are characterized by increased temperatures with a disordered composition of fuel components [13], the presence of which has a negative effect on turbine blades [14]. Accordingly, the composition of combustion products is nonequilibrium. At the same time, modern programs for analyzing the thermodynamic parameters of combustion products (such as RPA and Astra) allow calculations only at equilibrium composition. Based on this, the question arises of obtaining reliable values of the parameters of the generator gas, which can be answered by creating mathematical models [15] that take into account the nonequilibrium composition [16].

The use of hydroxygen fuel should allow one to avoid the procedure for creating mathematical models due to the smaller number of chemical reactions occurring during the combustion process. In this regard, it is necessary to verify the calculated values of the thermodynamic parameters of the generator gas and the data obtained in programs for determining the equilibrium characteristics.

The use of oxygen and hydrogen as components of liquid propellant rocket engines makes it possible to achieve high values of specific thrust impulse (STI). At the same time, it becomes possible to use these engines as part of reusable rocket and space systems [17].

The advantage of reductive (RGG) and oxidative (OGG) RGGs based on oxygen-hydrogen fuel components is the chemical kinetics of the fuel itself, which makes it possible to drive turbines and achieve high values of adiabatic work at a sufficiently low or high excess oxidant ratio (EOR). At the same time, PSs provide high gas efficiency, as well as sufficient convergence of experimental data with thermodynamic calculations [18].

Calculation of the thermodynamic parameters of the LGG mixture using oxygen-hydrogen fuel

The thermodynamic parameters of the generator gas were calculated using the Rocket Propulsion Analysis (RPA) and Astra programs. These programs allow you to obtain the properties of combustion products at equilibrium gas composition. The Astra program was created at the Moscow State Technical University named after N. E. Bauman and is intended to determine the characteristics of equilibrium, phase and chemical composition of arbitrary systems, including for the thermodynamic calculation of liquid propellant engines [19].

RPA is a multi-platform analysis tool designed for use in the conceptual and preliminary design of chemical rocket engines [20]. RPA uses an expandable chemical library based on the NASA thermodynamic database and the L.V. Gurvich thermodynamic database, which includes data on numerous types of combustibles and oxidizers.

Table 1 [9] presents the thermodynamic parameters of the oxidizing generator gas [21], corresponding to the equilibrium composition and not taking into account the real working process.

Table 2 shows the calculated values of the reducing generator gas.

Comparison of the calculated parameters of the generator gas in the Astra and RPA programs with the values ​​from Tables 1 and 2 were carried out according to the following parameters: R is gas constant; T is temperature in the GG; k is the expansion isentropic index corresponding to the degree of gas expansion; C* is characteristic speed.

 

Table 1. Parameters of oxidizing generator gas of oxygen-hydrogen fuel

pгг, MPa	Parameter	αгг
		8	9	10	11	13	14	15	16
10…25	T, К	1,449	1,313	1,199	1,103	945	881	824	773
	R, J/(Kg∙K)	287.9	284.8	282.3	280.3	277.2	275.9	274.9	274
	ккр	1.282	1.29	1.297	1.304	1.317	1.323	1.328	1.334
	C*, m/s	974	920	873	833	764	735	709	684

 

Table 2. Chemical composition and parameters of reducing generator gas oxygen-hydrogen fuel

pгг, МПа	Parameter	αгг
		0.07	0.08	0.09	0.1	0.12	0.14	0.16	0.18
0,1…50	mH2O	0.402	0.435	0.467	0.496	0.545	0.593	0.639	0.662
	mH2	0.598	0.565	0.533	0.504	0.455	0.407	0.361	0.338
	R, Дж/ (Кг∙К)	2,665	2,540	2,415	2,313	2,131	1,954	1,868	1,698
0,1	T, К	553	631	709	785	935	1,081	1,220	1,355
	ккр	1.389	1.382	1.379	1.375	1.36	1.35	1.331	1.321
	к100	1.407	1.402	1.401	1.399	1.388	1.38	1.363	1.355

 

The end of Table 2

pгг, MPa	Parameter	αгг
		0.07	0.08	0.09	0.1	0.12	0.14	0.16	0.18
10	T, К	564	642	720	797	948	1,094	1,234	1,369
	ккр	1.393	1.386	1.381	1.377	1.361	1.349	1.331	1.321
	к100	1.41	1.405	1.402	1.4	1.386	1.376	1.36	1.352
50	T, К	606	686	766	847	999	1,148	1,290	1,427
	ккр	1.392	1.385	1.379	1.373	1.358	1.341	1.327	1.314
	к100	1.408	1.403	1.399	1.395	1.382	1.367	1.355	1.344

 

Based on the EOR values for the operation of two-component OGG and RGG according to the data in Table. 1, 2 calculations were carried out in the ranges 0,07 ≤ α ≤ 0,18 and 8 ≤ α ≤ 16.

Comparison of the results of calculations of the thermodynamic parameters of the RGG mixture in the RPA and Astra programs

When analyzing the results of calculating mass fractions obtained in the Astra program, the convergence of the data was confirmed with an average error of no more than 0.54 % (Fig. 1). While the values obtained in RPA (Fig. 2) have an average error of no more than 0.69 %.

 

Рис. 1. Химический состав генераторного газа при низких КИО, полученный в программе «Астра»

Fig. 1. Chemical composition of generator gas at low EOR obtained in the Astra program

 

Рис. 2. Химический состав генераторного газа при низких КИО (RPA)

Fig. 2. Chemical composition of generator gas at low EOR (RPA)

 

Figure 3 shows the dependence of the gas constant R on the oxidizer excess coefficient, which does not correspond to the calculated values by 0.7 and 1.3 % in the Astra and RPA programs, respectively.

 

Рис. 3. Значения газовой постоянной при низких КИО

Fig. 3. Values of the gas constant at low EOR

 

At pressures of 0.1 and 10 MPa (Fig. 4), temperature values were obtained with an average error of no more than 0.5 %. The temperatures obtained at a pressure of 50 MPa differ from the calculated temperatures by 6 % in both programs.

 

Рис. 4. Температуры генераторного газа при давлении 10 МПа и низких КИО

Fig. 4. Generator gas temperatures at a pressure of 10 MPa and low EOR

 

Figure 5 shows the values of the expansion isentropic index corresponding to the critical pressure difference (pgg/pa = 2) obtained in the RPA and Astra programs. When analyzing the values, it was revealed that they have close convergence (no more than 0.57 %) with the calculated data.

The values of the expansion isentropic index k100 obtained in RPA have a discrepancy of 10 % with the calculated data, and the results obtained using the ASTRA-M program show qualitative convergence (Fig. 6). The average error of thermodynamic calculations is given in table 3.

 

Рис. 5. Показатель изоэнтропы расширения при давлении в ГГ 10 МПа и низких КИО

Fig. 5. Isentropy of expansion at a pressure in GG of 10 MPa and low EOR

 

Рис. 6. k100 при давлении в ГГ 10 МПа и низких КИО

Fig. 6. k100 at a pressure in GG of 10 MPa and low EOR

 

Table 3. Average error relative to the calculated values of the reducing generator gas

Parameter	Error, %
	Astra	RPA
mH2O	0.47	0.55
mH2	0.61	0.82
R	0.7	1.3
T	2.51	2.60
ккр	0.69	0.23
k100	1.04	9.54

 

Comparison of the results of calculations of the thermodynamic parameters of the OGG mixture in the RPA and Astra programs

Figures 7–9 show graphs of the dependences of the gas constant, temperature, and characteristic velocity on the oxidizer excess coefficient. The dependences were obtained for oxidizing generator gas in the gas generator pressure range of 10–25 MPa. The results of thermodynamic calculations carried out in the Astra and RPA programs show sufficient convergence with the calculated values (Table 4). The maximum error of the parameters is no more than 0.21 %.

 

Рис. 7. Значения газовой постоянной при высоких КИО

Fig. 7. Values of the gas constant at high EOR

 

Рис. 8. Температуры генераторного газа при давлениях 10–25 МПа и высоких КИО

Fig. 8. Generator gas temperatures at pressures of 10.25 MPa and high EOR

 

Рис. 9. Зависимость характеристической скорости от КИО

Fig. 9. Dependence of the characteristic velocity on the EOR

 

Table 4. Average error relative to the calculated values of oxidizing generator gas

Parameter	Error, %
	Astra	RPA
T	0.59	0.10
R	0.02	0.02
ккр	0.04	0.09
C*	0.18	0.03

 

Conclusion

Verification of the parameters of the generator gas mixture on oxygen-hydrogen fuel at low and high EOR made it possible to establish that most of the values obtained in the Astra program have better agreement with the calculated data at low EOR and are 0.15% inferior to the RPA program at high EOR. The disadvantage of the Astra program is the inability to obtain mass fractions and the requirement for additional recalculation from other fractions.

The values of the thermodynamic parameters of the generator gas obtained in the RPA program also have sufficient convergence. The disadvantages of RPA include the inability to carry out calculations with an EOR equal to less than 0.1.

As a result, it was revealed that both programs can be used for engineering calculations and modeling of the thermodynamics of LGG. It was possible to confirm the sufficient convergence of calculations of the thermodynamic parameters of reducing and oxidizing gas generators using oxygen-hydrogen fuel to the values from calculations taking into account the nonequilibrium composition of the generator gas [22].

About the authors

Vladislav A. Belyakov

Moscow Aviation Institute (National Research University); Experimental Design Bureau “Crystal”

Email: titflavii@rambler.ru

Cand. Sc., Assistant of the Department 202: Rocket Engines; Leading Engineer

Russian Federation, Moscow; Moscow

Dmitry O. Vasilevsky

Nevsky Plant; Baltic State Technical University “Voenmeh” named after D. F. Ustinov

Author for correspondence.
Email: zudwa_dwesti_dwa@rambler.ru

Leading Designer; Cand. Sc., Associate Professor of Department A8: Aircraft Engines and Power Plants

Russian Federation, Saint Petersburg; Saint Petersburg

Daniil V. Maslov

State Scientific Center “Keldysh Center”

Email: davmaslov@mai.education

Technician

Russian Federation, Moscow

Artemy A. Kilyashov

University of Information Technologies, Mechanics and Optics

Email: artemy.kiliashov@gmail.com

Postgraduate Student

Russian Federation, Saint Petersburg

Roman V. Romashko

Moscow Aviation Institute (National Research University); Experimental Design Bureau “Crystal”

Email: roma.romashko2015@yandex.ru

Postgraduate Student; Engineer of Department 202: Rocket Engines; Category III Design Engineer

Russian Federation, Moscow; Moscow

References

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