A New Stability Approach for the Flow Induced by Wall Injection

Casalis, Grégoire; Chedevergne, F.; Feraille, Th.; Avalon, G.

doi:10.1007/1-4020-4159-4_9

Cited by 2 publications

(2 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Numerical procedure Equation (3.2) can be solved directly for (x, r) ∈ [0, X e ] × [0, 1] provided that a suitable outflow condition is made available at x = X e . We follow Theofilis (2003, 2011), Theofilis, Duck & Owen (2004 and Casalis et al (2004), who utilize a simple linear extrapolation relation. Thus, given a number of discretization points N x in the streamwise direction, we set, for all r:…”

Section: Hydrodynamic Instability Eigenmodesmentioning

confidence: 99%

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

2012

Self Cite

View full text Add to dashboard Cite

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 steadystate 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 † Instability waves in solid rocket motors 191 secondary eigenmode. Unlike the original eigenmode, the latter materializes naturally in the computed flow without being artificially seeded. This natural occurrence may be ascribed to a nonlinear modal interplay in the form of internal, eigenmode-toeigenmode coupling instead of an external, eigenmode pairing with acoustic modes. As a result of these interactions, large amplitude oscillations are induced.

show abstract

Section: Hydrodynamic Instability Eigenmodesmentioning

confidence: 99%

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

2012

Self Cite

View full text Add to dashboard Cite

show abstract

“…After several attempts, the chosen exit condition is a simple linear extrapolation, written at x = X e . With this condition, the computational results are independent of the value of X e , see [10]. Finally, the set of boundary condition is as follows :…”

Section: Linear Stability Analysismentioning

confidence: 99%

A Theoretical Approach of Thrust Oscillations in S...

Chedevergne

Casalis

2005

56th International Astronautical Congress of the International Astronautical Federation, the International Academy of Astronaut

Self Cite

View full text Add to dashboard Cite

Solid rocket motors present thrust oscillations at the end of their firings. These oscillations are due to flow instabilities which cause pressure fluctuations. Several possible sources of instabilities have been identified. Among them, the hydrodynamic instabilities of the main flow is believed to play a major role. However, the first hydrodynamic stability studies, based on a classical linear stability analysis, led to a model which is not consistent. Thus, the linear stability of the mean flow has been revisited thanks to a more general approach. The results are compared to measurements coming from cold-gas and reduced scale live motors set-ups. The obtained excellent agreements (in both cases) lead to significant changes in the understanding of the thrust oscillations arising. * The two main ARIANE 5 propellant grains are conical

show abstract

A New Stability Approach for the Flow Induced by Wall Injection

Cited by 2 publications

References 5 publications

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

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

A Theoretical Approach of Thrust Oscillations in S...

Contact Info

Product

Resources

About