Preview

Journal of «Almaz – Antey» Air and Space Defence Corporation

Advanced search

On the question of solid-propellant rocket engine design preventing unstable operation in the combustion chamber

https://doi.org/10.38013/2542-0542-2017-4-63-72

Abstract

The paper presents results of a numerical investigation concerning the effect that the flow duct shape and combustion rate equation have on the gas dynamic vortex flow pattern and self-excited pressure oscillations in the combustion chamber of a solid-propellant rocket engine. We provide guidelines on upgrading solid-propellant rocket engines in order to decrease the magnitude of pressure pulses in the case of pulsating combustion.

For citation:


Glebov G.A., Vysotskaya S.A. On the question of solid-propellant rocket engine design preventing unstable operation in the combustion chamber. Journal of «Almaz – Antey» Air and Space Defence Corporation. 2017;(4):63-72. https://doi.org/10.38013/2542-0542-2017-4-63-72

Spontaneous occurrence of intense pressure oscillations in the combustion chamber, resulting in considerable thrust oscillations, pose a serious problem in development of solid-propellant rocket engines (SPRE). The experience of development of SPREs, such as Titan III (U.S.), Space Shuttle (U.S.), Ariane 5 (France), S-300V (USSR), goes to show that unstable operation would be caused by formation of powerful toroidal vortices in the air-gas channel of the combustion chamber.

Fig. 1 shows diagrams of the combustion chambers of the above-mentioned engines where the formation of intense toroidal (circular) vortices is observed. In particular, the following is shown: a – diagram of vortex formation in the air-gas channels of solid-propellant boosters of the Space Shuttle reusable spacecraft and Titan III launch vehicle [1], [2]; b – results of the computational estimate of vortex formation in the air-gas channel of solid-propellant booster of the Space Shuttle reusable spacecraft [3]; c – results of the estimate of vortex formation in the air-gas channel of solid-propellant booster of the Ariane 5 heavylift launch vehicle [4]; d – diagram of vortex formation in the SPRE air-gas channel with sudden expansion of charge channel [5]; e – diagrams of vortex formation and standing pressure and velocity waves in the air-gas channel of the launch stage of the S-300V anti-aircraft missile system [6],[7],[8]. As a rule, the frequency of formation of such vortices corresponds to the first mode of longitudinal pressure and velocity oscillations. Periodic toroidal vortex shedding appears to be a feedback for maintaining self-excited pressure oscillations.

 

 

 

The study [6] experimentally validates formation of toroidal vortices in the area of the nozzle inlet lip and states that the behaviour of acoustic process taking place in the SPRE combustion chamber resembles the processes taking place in a pipe with both ends closed. Fig. 1, e shows a typical shape of the first mode of standing pressure and velocity wave.

Notably, refinement of the above engines for the purpose of eliminating unstable (pulsating, vibrating) combustion conditions lasted from 8 to 12 years. As concerns the launch stages of surfaceto-air missile (SAM) of the S-300V system, the following methods for reducing the intensity of pressure and thrust oscillations can be identified:
• application of reactive pressure oscillation dampers such as the Helmholtz resonator;
• installation of micro-nozzles on the rear bottom to release acoustic energy.

The first method did not yield satisfactory results, while application of the second method resulted in certain reduction of pressure and thrust pulses. However, this method had to be rejected due to substantial two-phase losses of the specific impulse and added complexity of the engine design.

Fig. 2 shows some diagrams of upgraded SPRE with a recessed nozzle intended to suppress unstable operation conditions. The designs were proposed in 1986 by Kazan Aviation Institute (KAI) (now Kazan National Research Technical University named after A. N. Tupolev) and Kazan Experimental Design Bureau “Soyuz” (KOKB “Soyuz”) [9]. The main goal of these design solutions was to reduce acoustic and gas-dynamic interaction between combustion products delivered from part of the solid propellant charge combustion surface, located directly above the recessed section of the nozzle, and combustion products delivered from the main (remaining) surface part of solid propellant charge combustion. The diagram shown in Fig. 2, a, with developed combustion surface in the middle section of the charge, is remarkable in that this solution leads to a significant increase of mass flux in the velocity antinode area. In the authors’ opinion, this is supposed to reduce the intensity of standing wave oscillations in compliance with the Rayleigh criterion [10]. An increase of combustion products mass flux in the pressure antinode area contributes to formation of pulsating combustion conditions.

 

Fig. 2. Diagrams of design solutions proposed jointly by KAI and KOKB “Soyuz” at the SPRE development stage

 

To achieve the same goal, engine configurations may feature discharge of combustion products into the pre-expansion nozzle area (Fig. 2, b), as well as special ribs installed outside of the nozzle inlet lip (Fig. 2, c, d). It is known that such ribs allow to destroy a large-scale transverse vortex and transform it into a system of smaller longitudinal vortices of the Taylor-Görtler type.

Shown in Fig. 2, e is a method for reducing the intensity of counter-flow from behind the recessed part of the nozzle due to perforation of the recessed nozzle. The tests showed that the use of perforation makes it possible to reduce the level of thrust pulses by 7…14 %. Relatively low effectiveness of this method can be explained by small area of the perforation.

The application of a convergent nozzle tip designed as shown in Fig. 2, f allowed to achieve the best possible result – to reduce the pressure pulsation amplitude by 3 times and thrust oscillation amplitude by 75 % approximately within the entire operation time of the SPRE. Relevant recommendations for selecting the nozzle tip design and the best suitable size of a circular slot between the inlet lip of a recessed nozzle and a convergent nozzle tip are given in [6].

Experimental development of these technical solutions on the basis of the manufactured product prototype requires substantial material and time resources. Taking into account the contemporary political environment, we need to strive for cost reduction in development of new systems and equipment. Cost saving can be achieved by using advanced methods of mathematical simulation and computing equipment.

Papers [7], [8] propose a method for computing vortex structures and amplitude of self-excited pressure oscillations in SPRE combustion chamber, developed on the basis of ANSYS Fluent software package. Given below are the basic assumptions made in the computational method.
1. The flow is 2D axisymmetrical.

2. The thermodynamic properties of solidpropellant combustion products are determined in approximation of the equilibrium composition of a two-phase mixture [11]:
Tг =Tz , Uг = Uz,
where Тг – temperature of the gaseous products of solid propellant combustion (K);
Тz – temperature of condensed particles of Al2O3 formed as a result of composite solid propellant combustion (K);
Uг – outflow velocity of the gaseous products of solid propellant combustion (m/s);
Uz – outflow velocity of condensed particles of Al2O3 formed as a results of composite solid propellant combustion (m/s).

3. To resolve the flow eddy field, so as to save computational resources, a quasi-LES method (i.e. large-eddy simulation (LES) as a beta option of ANSYS Fluent) is used in the case of 2D axisymmetrical flow) [7], [8].

4. The solid propellant combustion rate law is quasi-steady-state. This assumption is based on the results of R. E. Sorkin’s study [12], where it is shown that at relatively low frequencies of pressure pulses the solid propellant combustion rate law can be considered quasi-steady-state.

5. Entrainment of thermal protection coating material with respect to engine operation time is not considered. The temperature of the structure walls is taken equal to the temperature of composite material (carbon-fibre composite EPAN-25) destruction, i.e. 940 K.

The computational method attempts to solve the following problem: determining the presence and intensity of coherent vortex structures in the engine air-gas channel based on the given pressure field in the form of a longitudinal standing wave using the numerical method. From the viewpoint of the lowest values of pressure pulses in the combustion chamber, the best configuration or shape of the air-gas channel will apparently be such under which the probability of occurrence of transient vortices and their intensity will be the minimal. A computation block diagram is given in Fig. 3.

 

Fig. 3. Block diagram for computing transient processes in SPRE combustion chamber

 

Fig. 3 features the following notations:
f – frequency of longitudinal pressure oscillations (Hz);
n – oscillation mode 1, 2, 3…;
а – sound velocity (m/s);
L – SPRE combustion chamber length (m);
P (x,τi ) – pressure value on the solid propellant charge combustion surface at the moment of time τi (Pa);
P′ – amplitude of pressure pulses (Pa);
Pк ном – pressure value in the SPRE combustion chamber (Pa) obtained from steady-state computation;
Uгор – solid propellant combustion rate (m/s);
B (Tн) = B (T0)(1 + au )(Tн - T0)– term accounting for the influence of charge initial temperature Tн ;
au – temperature sensitivity coefficient;
ν – combustion law exponent;
ṁ – combustion products mass flux from the solid propellant charge combustion surface (kg/s);
ρт – propellant density (kg/m3 );
F – solid propellant charge combustion surface area (m2 ).

The frequency of longitudinal self-excited pressure oscillations is determined in linear acoustics approximation (1). The shape of a longitudinal standing wave is given as a periodic function (2). With account of the combustion rate law (3), the inflow (mass flux) of combustion products from the solid propellant combustion surface is determined (4). Then, using the Navier – Stokes equations (URANS and URANS/LES), transient velocity and pressure fields in the air-gas channel of the SPRE combustion chamber are calculated. The initial conditions with regard to the amplitude of pressure oscillations at the standing wave ends Р'(0, 0) = -Р'(0, L) = 0,1 Рк ном correspond to the so-called hard mode of self-excitation of pressure oscillations.

To set up a computational grid, the ICEM CFD grid generator is used. The computational grid is structured. The element size is 0.002 m, with accumulation towards the wall up to 0.0004 m; the number of elements is ~300,000. The appearance of a structured grid for computations by the quasi-LES method is shown in Fig. 4.

 

Fig. 4. Appearance of computational grid in the recessed-nozzle inlet lip area: а – standard recessed nozzle; b – recessed nozzle with annular convergent tip

 

Given in Fig. 5 are the results of computation of the flow vortex structure inside the combustion chamber for three values of pressure oscillation phases. It can be seen that the acoustic wave propagating from left to right “enters” the area above the recessed nozzle part, while decelerating the counter-flow and generating vortex A (Fig. 5, a). At a change of acoustic wave direction (Fig. 5, b, c), vortex A moves towards the nozzle inlet lip, with further periodic passing through the nozzle. The periodicity of vortex A formation corresponds to the first mode of longitudinal oscillations of the combustion chamber’s gas column. According to the computation data [8], the maximum amplitude of pressure pulses is Р'= ±5.7 kgf/cm2 , and that of thrust pulses R'/Rном = ±45.2 %. 

Fig. 6 shows a flow pattern represented as flow lines in case a circular convergent tip is installed at the recessed nozzle inlet. It can be seen that no toroidal vortices are formed in this case. The nozzle tip divides the main flow of combustion products and the flow from behind the recessed nozzle part into two separated areas, which prevents gas-dynamic and acoustic interaction between them. In so doing, the maximum amplitude of pressure pulses is reduced to Р'=±1.1 kgf/cm2 , with thrust pulses dropping down to R'/Rном = ±8.75 %.

 

Fig. 6. Flow lines in the nozzle inlet lip area for engine with a convergent nozzle tip depending on pressure oscillation phase:
а – φ=0 ; b – φ ≈ π

 

Based on the computation data analysis, we managed to obtain a qualitative representation of the mechanism of acoustic energy release through the nozzle (Fig. 7). It is worth mentioning that the pulsation amplitude of the axial velocity component U′ is normalised to a dimensionless form as a result of division by sound velocity a across the minimum nozzle cross-section. When using a nozzle with tip, significant pulsations of axial velocity up to 4 % of the critical velocity can be observed at the annular slot outlet between the nozzle inlet lip and the tip. This is a proof to essential release of acoustic energy, which leads to a decrease in pressure pulses in the combustion chamber and thrust pulses of the engine.

 

Fig. 7. Amplitude profile of axial velocity pulses in the minimum nozzle cross-section area

 

In its time, installation of a convergent tip at the nozzle inlet of the engine under consideration raised serious doubts and disputes among the designers. Firstly, the nozzle tip is a technologically complex structural element of the nozzle unit, and, secondly, it is located in the area exposed to fairly high mechanical and thermal loads. For these reasons, within the scope of the proposed method, the intensities of convective heat flux relative to its surface were estimated by the authors. Fig. 8 shows a layout diagram of check points in which the value of heat transfer coefficient was calculated.

 

Fig. 8. Layout diagram of check points for computing the coefficient of heat transfer to structural elements of the nozzle unit: 1 – outer wall; 2 – convergent nozzle tip; 3 – inner wall; 4 – nozzle inlet lip

 

The heat transfer computation results are given in Figs. 9, 10. The check point numbers are plotted on the abscissa axis, and the ordinate axis features the ratio of the calculated values of heat transfer coefficient to the maximum heat transfer value in a standard nozzle in the minimal (critical) nozzle cross-section area. According to the computations performed, the maximum heat flux is ~30…40 MW/m2 .

 

 

With a convergent nozzle tip installed, the intensity of convective heat flux at the recessed nozzle inlet lip decreased two-fold (Fig. 10). The heat transfer intensity on the nozzle tip surface is 20…40 % of the maximum heat transfer of a standard nozzle (Fig. 10), which is confirmed by years-long failure-free operation of the nozzle tip.

Papers [7], [8] provide the results of numerical investigations of the influence of charge channel shape and exponent in the solid propellant combustion law on the intensity of pressure and thrust pulses. The following engine modifications were considered:
1) standard engine (ν=0.7);
2) standard engine (ν=0.4);
3) standard engine (ν=0.1);
4) engine with convergent nozzle tip (ν=0.4);
5) engine without projection in the front part of the charge (ν=0.4).

The computation results of the flow vortex structure and time-dependent pressure pulses in the combustion chamber of engines 2, 5, 3, respectively, are given in Fig. 11. It can be seen that the amplitude of pressure pulses and the intensity of flow vorticity substantially depend on the charge channel shape and the exponent in the combustion law.

The computation results of pressure pulses in the front bottom area for the five considered SPRE modifications are given in Fig. 12. It can be seen that the lowest values of pressure pulsation amplitude are demonstrated by engine modifications 3–5.

 

Fig. 12. Amplitude of pressure pulses for considered SPRE modifications

 

The presented computation data concerning the influence of charge channel geometry, nozzle unit design, and other factors on the gas-dynamic and acoustic processes in an SPRE with recessed nozzle may be helpful for the developers of combustion chamber designs.

References

1. Данлэп Р., Браун Р. С. Экспериментальное исследование акустических пульсаций, возбуждаемых периодическим срывом вихрей // Ракетная техника и космонавтика. 1981. № 4. С. 142–143.

2. Brown R. S., Dunlap R., Young S. W., Waugh R. C. Vortex shedding as an additional source of acoustic energy in segmented solid propellant rocket motors // AIAA/SAE/ASME 16 th Joint Propulsion Conference, USA, Hartfold, 1980. DOI 10.2514/6.1980-1092

3. Mason D., Morstadt R., Cannon S., Gross E., Nielsen D. Pressure oscillations and structural vibration in space shuttle RSRM and ETM-3 Motors // 40 th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 11–14 July 2004, Fort Launderdale, Florida. 2004. Pp. 1–17.

4. Anthoine J. Experimental and Numerical Study of Aeroacoustic Phenomena in Large Solid Propellant Boosters. Germany: Von Karman Institute for Fluid Dynamics, 2009. 237 p.

5. Flandro J. A. Vortex driving mechanism in oscillatory rocket flows // Journal of Propulsion and Power. 1986. Vol. 2. No. 3. Pp. 206–214.

6. Моделирование рабочих процессов в РДТТ. Труды семинара. Вып. XXIII. Казань, Физ.техн. ин-т КФ АН СССР, 1989. 68 с.

7. Глебов Г. А., Высоцкая С. А. К вопросу о влиянии геометрии канала заряда и свойств топлива на неустойчивость рабочего процесса в камере РДТТ // Вестник Концерна ВКО «Алмаз – Антей». 2017. № 1. С. 67–75.

8. Глебов Г. А., Высоцкая С. А. Моделирование когерентных вихревых структур и автоколебаний давления в камере сгорания РДТТ // Вестник Концерна ВКО «Алмаз – Антей». 2016. № 4. С. 41–48.

9. Глебов Г. А., Высоцкая С. А. Неустойчивость рабочего процесса в РДТТ с утопленным соплом и способы ее подавления // VIII Научная конференция Волжского регионального центра РАРАН «Современные методы проектирования и отработки ракетно-артиллерийского вооружения», ФГУП «РФЯЦ-ВНИИЭФ», Саров, 4–6 июня 2013. Т. 2. С. 256–263.

10. Стрет Дж. В. (Лорд Рэлей). Теория звука. Т. II. М.: Гос. изд-во техн.-теор. лит., 1955. 475 с.

11. Термодинамические и теплофизические свойства продуктов сгорания: в 6 т. Т. 1. Методы расчета / В. Е. Алемасов, А. Ф. Дрегалин, А. П. Тишин, В. А. Худяков; под ред. В. П. Глушко. М.: ВИНИТИ, 1971. 267 с.

12. Соркин Р. Е. Газотермодинамика ракетных двигателей на твердом топливе. М.: Наука, 1967. 368 с.


About the Authors

G. A. Glebov
Kazan National Research Technical University named after A. N. Tupolev
Russian Federation

Glebov Gennadiy Aleksandrovich – Doctor of Engineering Sciences, Associate Professor, Professor, Department of Jet Engines and Power Plants. Science research interests: gas dynamic and thermal processes in rocket engines, unstable operation of rocket engines, pulsating combustion.

Kazan



S. A. Vysotskaya
Joint Stock Company “Kazan Experimental Design Bureau “Soyuz”
Russian Federation

Vysotskaya Svetlana Abdulmyanafovna – Candidate of Engineering Sciences, Chief Designer. Science research interests: gas dynamic computations of power plant parameters.

Kazan



Review

For citation:


Glebov G.A., Vysotskaya S.A. On the question of solid-propellant rocket engine design preventing unstable operation in the combustion chamber. Journal of «Almaz – Antey» Air and Space Defence Corporation. 2017;(4):63-72. https://doi.org/10.38013/2542-0542-2017-4-63-72

Views: 470


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 2542-0542 (Print)