Statement of the problem of designing a liquid rocket engine dual bell nozzle of the maximum thrust using the direct method of the calculus of variations
A rocket engine with a standard single-section profiled nozzle provides maximum thrust only at a certain value of atmospheric pressure [1]. To expand the range of atmospheric pressure values at which the optimum engine operation mode is achieved, a dual bell nozzle can be used [2]. A typical diagra...
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Oles Honchar Dnipro National University
2023-06-01
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| Series: | Challenges and Issues of Modern Science |
| Online Access: | https://cims.fti.dp.ua/j/article/view/6 |
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| author | Ivan Dubrovskyi Valerii Bucharskyi |
| author_facet | Ivan Dubrovskyi Valerii Bucharskyi |
| author_sort | Ivan Dubrovskyi |
| collection | DOAJ |
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A rocket engine with a standard single-section profiled nozzle provides maximum thrust only at a certain value of atmospheric pressure [1]. To expand the range of atmospheric pressure values at which the optimum engine operation mode is achieved, a dual bell nozzle can be used [2]. A typical diagram of such a nozzle is shown in Fig. 1. Its main elements are three cross-sections a, b, c and two profiled section elements a-b, b-c bounded by them. The fig. 1 shows the general case of the contour of such a nozzle, for which a corner in the generatrix is located at points a and b. In addition, the section a coincides with the critical section of the engine chamber.
Let’s consider the principle of operation of such a nozzle. When operating at low altitude, with a high value of atmospheric pressure pe1, the thrust is generated only by the first profiled section a-b. With an increase in flight altitude and a corresponding drop in atmospheric pressure to pe2 (pe1 > pe2), the flow of combustion products expands, begins to flow around the second profiled section and create additional thrust. Thus, an engine with a dual bell nozzle will generate more average flight time thrust than an engine with a single nozzle designed to operate at one of the atmospheric pressures pe1 or pe2.
Usually, the method of characteristics [3] is used for profiling a dual bell nozzle. However, it has the following disadvantages:
• the inability to profile the maximum thrust nozzle with explicit restrictions on its dimensions, weight, etc.;
• the requirement for the absence of shock waves in the flow of combustion products inside the nozzle.
As an alternative to the method of characteristics, this paper proposes to use the direct method of calculus of variations [4] for profiling a dual bell nozzle.
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| format | Article |
| id | doaj-art-d562b50ab2794141b795cceea15b6b36 |
| institution | Kabale University |
| issn | 3083-5704 |
| language | English |
| publishDate | 2023-06-01 |
| publisher | Oles Honchar Dnipro National University |
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| series | Challenges and Issues of Modern Science |
| spelling | doaj-art-d562b50ab2794141b795cceea15b6b362025-02-11T09:58:31ZengOles Honchar Dnipro National UniversityChallenges and Issues of Modern Science3083-57042023-06-011Statement of the problem of designing a liquid rocket engine dual bell nozzle of the maximum thrust using the direct method of the calculus of variationsIvan Dubrovskyi0https://orcid.org/0000-0002-0707-0074Valerii Bucharskyi1https://orcid.org/0000-0002-8245-5652Oles Honchar Dnipro National UniversityOles Honchar Dnipro National University A rocket engine with a standard single-section profiled nozzle provides maximum thrust only at a certain value of atmospheric pressure [1]. To expand the range of atmospheric pressure values at which the optimum engine operation mode is achieved, a dual bell nozzle can be used [2]. A typical diagram of such a nozzle is shown in Fig. 1. Its main elements are three cross-sections a, b, c and two profiled section elements a-b, b-c bounded by them. The fig. 1 shows the general case of the contour of such a nozzle, for which a corner in the generatrix is located at points a and b. In addition, the section a coincides with the critical section of the engine chamber. Let’s consider the principle of operation of such a nozzle. When operating at low altitude, with a high value of atmospheric pressure pe1, the thrust is generated only by the first profiled section a-b. With an increase in flight altitude and a corresponding drop in atmospheric pressure to pe2 (pe1 > pe2), the flow of combustion products expands, begins to flow around the second profiled section and create additional thrust. Thus, an engine with a dual bell nozzle will generate more average flight time thrust than an engine with a single nozzle designed to operate at one of the atmospheric pressures pe1 or pe2. Usually, the method of characteristics [3] is used for profiling a dual bell nozzle. However, it has the following disadvantages: • the inability to profile the maximum thrust nozzle with explicit restrictions on its dimensions, weight, etc.; • the requirement for the absence of shock waves in the flow of combustion products inside the nozzle. As an alternative to the method of characteristics, this paper proposes to use the direct method of calculus of variations [4] for profiling a dual bell nozzle. https://cims.fti.dp.ua/j/article/view/6 |
| spellingShingle | Ivan Dubrovskyi Valerii Bucharskyi Statement of the problem of designing a liquid rocket engine dual bell nozzle of the maximum thrust using the direct method of the calculus of variations Challenges and Issues of Modern Science |
| title | Statement of the problem of designing a liquid rocket engine dual bell nozzle of the maximum thrust using the direct method of the calculus of variations |
| title_full | Statement of the problem of designing a liquid rocket engine dual bell nozzle of the maximum thrust using the direct method of the calculus of variations |
| title_fullStr | Statement of the problem of designing a liquid rocket engine dual bell nozzle of the maximum thrust using the direct method of the calculus of variations |
| title_full_unstemmed | Statement of the problem of designing a liquid rocket engine dual bell nozzle of the maximum thrust using the direct method of the calculus of variations |
| title_short | Statement of the problem of designing a liquid rocket engine dual bell nozzle of the maximum thrust using the direct method of the calculus of variations |
| title_sort | statement of the problem of designing a liquid rocket engine dual bell nozzle of the maximum thrust using the direct method of the calculus of variations |
| url | https://cims.fti.dp.ua/j/article/view/6 |
| work_keys_str_mv | AT ivandubrovskyi statementoftheproblemofdesigningaliquidrocketenginedualbellnozzleofthemaximumthrustusingthedirectmethodofthecalculusofvariations AT valeriibucharskyi statementoftheproblemofdesigningaliquidrocketenginedualbellnozzleofthemaximumthrustusingthedirectmethodofthecalculusofvariations |