Nonlinear characteristics of the triggering combustion instabilities in solid rocket motors

Wang, Zhuopu; Liu, Peijin; Jin, Bingning; Ao, Wen

doi:10.1016/j.actaastro.2020.06.022

Cited by 19 publications

(5 citation statements)

References 39 publications

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“…The FDM treatment, using the backward time central space (BTCS) algorithm, is proposed in [12], which has been used in the combustion instability research in solid rocket motors [3]. The spectral method treatment, using the Laguerre polynomial expansion, is proposed by [13], which has also been used in the combustion instability research in solid rocket motors [4,5].…”

Section: Resultsmentioning

confidence: 99%

“…Due to the complex structures and chemical compositions of the oxidizers, binders and other additives, there are a series of complicated physical and chemical processes in the combustion of solid propellants [1,2]. Fortunately, research shows that some simplified models can capture the dynamic characteristics of the complex system well [3][4][5]. A widely adopted simplification is to assume that the propellants are homogeneous and the combustion is one-dimensional.…”

Section: Introductionmentioning

confidence: 99%

“…However, it has been shown that the proper inclusion of the nonlinear effects is necessary for the correct modeling of the combustion instability of SRMs, especially the important triggering phenomenon [11]. In the modeling of thermoacoustic oscillations in SRMs, the unsteady combustion is modeled by the numerical solution [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

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A Discontinuous Galerkin–Finite Element Method for the Nonlinear Unsteady Burning Rate Responses of Solid Propellants

Wang,

Yu,

Liu

2024

Aerospace

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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.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Discontinuous Galerkin–Finite Element Method for the Nonlinear Unsteady Burning Rate Responses of Solid Propellants

Wang,

Yu,

Liu

2024

Aerospace

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“…The unsteady combustion model used by Mariappan and Sujith [7] is the quasi-steady homogeneous one-dimensional (QSHOD) model equipped with a flame model, named the Krier-T'ien-Sirignano-Summerfield (KTSS) model [8], where the flame is in the gas phase, which is assumed to be a uniform one in a region above the burning surface. The author of the present paper finds that the Zel'dovich-Novozhilov(ZN) model serves better, and investigates the triggering instability and bi-stable region thoroughly in a previous work [9,10].…”

Section: Introductionmentioning

confidence: 91%

A Phenomenological Model for the Unsteady Combustion of Solid Propellants from a Zel’dovich-Novzhilov Approach

Wang,

Zhang,

Liu

2023

Aerospace

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Solid rocket motors are prone to combustion instabilities, which may lead to various problems for the rockets, from unexpected oscillations, precision decreasing, to explosion. The unsteady combustion dynamics of the propellants play a crucial role in most solid rocket motors experiencing combustion instabilities. A modeling framework for the unsteady combustion of the solid propellant is constructed via the Zel’dovich-Novozhilov (ZN) phenomenological perspective. The overall unsteady combustion features of a quasi-steady homogeneous one-dimensional (QSHOD) model are investigated. The phenomenological ZN parameters are then calculated. Compared with the traditional ZN-QSHOD linear equivalence relation, the new calculated system yields better results for the pressure coupling response, especially in the non-linear regime. The proposed phenomenological modeling provides a new methodology for the model reduction of the complex flame models.

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“…We come across many studies in the past that are dedicated to understand the phenomenon of triggering in thermoacoustic systems [2,14,44,48,56,62,68,77,95,100,101,108,109]. Triggering has mostly been observed in the solid and liquid rocket motors [3,11,99]. Zinn and Lieuwen [109] remarked in the context of gas turbine engines that "although large-amplitude disturbances are generally required to initiate unstable oscillations in nonlinearly unstable systems, a system may be nonlinearly unstable at low-amplitude disturbances that are of the order of the background noise level".…”

Section: Triggering In Thermoacoustic Systemsmentioning

confidence: 99%

Bifurcation to Limit Cycle Oscillations in Laminar Thermoacoustic Systems

Sujith

Pawar

2021

Springer Series in Synergetics

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In this chapter, we study the bifurcation characteristics of a laminar thermoacoustic system through the application of dynamical system theory. We restrict our discussions to two simple prototypes of real thermoacoustic systems (known as Rijke-type thermoacoustic systems): a horizontal Rijke tube with an electrical heater and a ducted premixed flame combustor, both having a laminar flow field. We describe the transition of a thermoacoustic system from a state of stable operation (called stable fixed point) to unstable operation (called stable limit cycle) on variation of any control parameter. First, we will present the dynamical transitions and characteristics of the dynamical states observed in laminar thermoacoustic systems in the absence of any stochastic background fluctuations in the flow field. Subsequently, we will study the effect of external stochastic perturbations on the occurrence of different dynamical transitions in such systems. These investigations performed on simple laminar thermoacoustic systems can be considered as a baseline study before we attempt to understand the complex dynamics exhibited by turbulent thermoacoustic systems in Chap. 6.As mentioned in Chap. 1, the occurrence of thermoacoustic instability has been a concern for most practical combustion systems used in power generating units and propulsion engines. Traditionally, both linear and nonlinear methodologies have been used to explain the occurrence and the characteristics of thermoacoustic oscillations observed in such systems. In linear analysis, the equations describing flame-acoustic interactions are subjected to small amplitude perturbations for calculating the eigenvalues [12]. When all the eigenvalues are negative, the system is considered to be linearly stable, and when one of the eigenvalues is positive, the system is considered to be linearly unstable. For a linearly unstable system, an infinitesimally small perturbation introduced in the system grows in time and asymptotically approaches another stable state that is different from the initial state. As seen in Chap. 2, for the case of subcritical Hopf bifurcation, a finite amplitude perturbation (or initial condition) in the regime of bistability (hysteresis) can alter

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Nonlinear characteristics of the triggering combustion instabilities in solid rocket motors

Cited by 19 publications

References 39 publications

A Discontinuous Galerkin–Finite Element Method for the Nonlinear Unsteady Burning Rate Responses of Solid Propellants

A Discontinuous Galerkin–Finite Element Method for the Nonlinear Unsteady Burning Rate Responses of Solid Propellants

A Phenomenological Model for the Unsteady Combustion of Solid Propellants from a Zel’dovich-Novzhilov Approach

Bifurcation to Limit Cycle Oscillations in Laminar Thermoacoustic Systems

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