Direct numerical simulation and biglobal stability investigations of the gaseous motion in solid rocket motors

摘要

In this article,a biglobal stability approach is used in conjunction with direct numerical simulation(DNS)to identify the instability mode coupling that may be responsible for triggering large thrust oscillations in segmented solid rocket motors(SRMs). These motors are idealized as long porous cylinders in which a Taylor-Culick type of motion may be engendered. In addition to the analytically available steady-state solution,a computed mean flow is obtained that is capable of securing all of the boundary conditions in this problem,most notably,the no-slip requirement at the chamber headwall. Two sets of unsteady simulations are performed,static and dynamic,in which the injection velocity at the chamber sidewall is either held fixed or permitted to vary with time. In these runs,both DNS and biglobal stability solutions converge in predicting the same modal dependence on the size of the domain. We find that increasing the chamber length gives rise to less stable eigenmodes. We also realize that introducing an eigenmode whose frequency is sufficiently spaced from the acoustic modes leads to a conventional linear evolution of disturbances that can be accurately predicted by the biglobal stability framework. While undergoing spatial amplification in the streamwise direction,these disturbances will tend to decay as time elapses so long as their temporal growth rate remains negative. By seeding the computations with the real part of a specific eigenfunction,the DNS outcome reproduces not only the imaginary part of the disturbance,but also the circular frequency and temporal growth rate associated with its eigenmode. For radial fluctuations in which the vorticoacoustic wave contribution is negligible in relation to the hydrodynamic stability part,excellent agreement between DNS and biglobal stability predictions is ubiquitously achieved. For axial fluctuations,however,the DNS velocity will match the corresponding stability eigenfunction only when properly augmented by the vorticoacoustic solution for axially travelling waves associated with the Taylor-Culick profile. This analytical approximation of the vorticoacoustic mode is found to be quite accurate,especially when modified using a viscous dissipation function that captures the decaying envelope of the inviscid acoustic wave amplitude. In contrast,pursuant to both static and dynamic test cases,we find that when the frequency of the introduced eigenmode falls close to(or crosses over)an acoustic mode,a nonlinear mechanism is triggered that leads to the emergence of a assumption holds true as long as x<12. Under these conditions,ωi remains negative,thus implying the presence of temporal damping. However,as Xe continues to increase,nonlinearities in the flow will inevitably lead to strong amplification in the streamwise direction. The natural transition of the flow around x = 12 is likely to result from the existence of the eigenmodes discussed heretofore. This hypothesis has to be further explored in future work. So far,comparisons with cold and reactive gas experiments have confirmed the relevance of biglobal stability analysis in accurately estimating the temporally stable modes(see Chedevergne et al. 2006;Chedevergne & Casalis 2006a). The nature of these intrinsic instabilities has led to a coherent construct that explains the source of SRM thrust oscillations.