A Discontinuous Galerkin–Finite Element Method for the Nonlinear Unsteady Burning Rate Responses of Solid Propellants
The unsteady combustion of solid propellants under oscillating environments is the key to understanding the combustion instability inside solid rocket motors. The discontinuous Galerkin–finite element method (DG-FEM) is introduced to provide an efficient yet flexible numerical platform to investigat...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-01-01
|
| Series: | Aerospace |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2226-4310/11/1/97 |
| _version_ | 1797344846176845824 |
|---|---|
| author | Zhuopu Wang Kairui Yu Yuanzhe Liu |
| author_facet | Zhuopu Wang Kairui Yu Yuanzhe Liu |
| author_sort | Zhuopu Wang |
| collection | DOAJ |
| description | The unsteady combustion of solid propellants under oscillating environments is the key to understanding the combustion instability inside solid rocket motors. The discontinuous Galerkin–finite element method (DG-FEM) is introduced to provide an efficient yet flexible numerical platform to investigate the combustion dynamics of solid propellants. The algorithm is developed for the classical unsteady model, the Zel’dovich–Novozhilov model. It is then validated based on a special analytical solution. The DG-FEM algorithm is then compared with the classical spectral method based on Laguerre polynomials. It is shown that the DG-FEM works more efficiently than the traditional spectral method, providing a more accurate solution with a lower computational cost. |
| first_indexed | 2024-03-08T11:09:46Z |
| format | Article |
| id | doaj.art-d07e5a554c374df99c6e22ff037819fc |
| institution | Directory Open Access Journal |
| issn | 2226-4310 |
| language | English |
| last_indexed | 2024-03-08T11:09:46Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Aerospace |
| spelling | doaj.art-d07e5a554c374df99c6e22ff037819fc2024-01-26T14:14:23ZengMDPI AGAerospace2226-43102024-01-011119710.3390/aerospace11010097A Discontinuous Galerkin–Finite Element Method for the Nonlinear Unsteady Burning Rate Responses of Solid PropellantsZhuopu Wang0Kairui Yu1Yuanzhe Liu2National Key Laboratory of Solid Rocket Propulsion, Northwestern Polytechnical University, Xi’an 710072, ChinaNational Key Laboratory of Solid Rocket Propulsion, Northwestern Polytechnical University, Xi’an 710072, ChinaNational Key Laboratory of Solid Rocket Propulsion, Northwestern Polytechnical University, Xi’an 710072, ChinaThe unsteady combustion of solid propellants under oscillating environments is the key to understanding the combustion instability inside solid rocket motors. The discontinuous Galerkin–finite element method (DG-FEM) is introduced to provide an efficient yet flexible numerical platform to investigate the combustion dynamics of solid propellants. The algorithm is developed for the classical unsteady model, the Zel’dovich–Novozhilov model. It is then validated based on a special analytical solution. The DG-FEM algorithm is then compared with the classical spectral method based on Laguerre polynomials. It is shown that the DG-FEM works more efficiently than the traditional spectral method, providing a more accurate solution with a lower computational cost.https://www.mdpi.com/2226-4310/11/1/97discontinuous Galerkinnumerical algorithmsolid propellantunsteady responsecombustion instability |
| spellingShingle | Zhuopu Wang Kairui Yu Yuanzhe Liu A Discontinuous Galerkin–Finite Element Method for the Nonlinear Unsteady Burning Rate Responses of Solid Propellants Aerospace discontinuous Galerkin numerical algorithm solid propellant unsteady response combustion instability |
| title | A Discontinuous Galerkin–Finite Element Method for the Nonlinear Unsteady Burning Rate Responses of Solid Propellants |
| title_full | A Discontinuous Galerkin–Finite Element Method for the Nonlinear Unsteady Burning Rate Responses of Solid Propellants |
| title_fullStr | A Discontinuous Galerkin–Finite Element Method for the Nonlinear Unsteady Burning Rate Responses of Solid Propellants |
| title_full_unstemmed | A Discontinuous Galerkin–Finite Element Method for the Nonlinear Unsteady Burning Rate Responses of Solid Propellants |
| title_short | A Discontinuous Galerkin–Finite Element Method for the Nonlinear Unsteady Burning Rate Responses of Solid Propellants |
| title_sort | discontinuous galerkin finite element method for the nonlinear unsteady burning rate responses of solid propellants |
| topic | discontinuous Galerkin numerical algorithm solid propellant unsteady response combustion instability |
| url | https://www.mdpi.com/2226-4310/11/1/97 |
| work_keys_str_mv | AT zhuopuwang adiscontinuousgalerkinfiniteelementmethodforthenonlinearunsteadyburningrateresponsesofsolidpropellants AT kairuiyu adiscontinuousgalerkinfiniteelementmethodforthenonlinearunsteadyburningrateresponsesofsolidpropellants AT yuanzheliu adiscontinuousgalerkinfiniteelementmethodforthenonlinearunsteadyburningrateresponsesofsolidpropellants AT zhuopuwang discontinuousgalerkinfiniteelementmethodforthenonlinearunsteadyburningrateresponsesofsolidpropellants AT kairuiyu discontinuousgalerkinfiniteelementmethodforthenonlinearunsteadyburningrateresponsesofsolidpropellants AT yuanzheliu discontinuousgalerkinfiniteelementmethodforthenonlinearunsteadyburningrateresponsesofsolidpropellants |