Improved time-dependent flowfield solution for solid rocket motors

Majdalani, J.; Moorhem, W. K. Van

doi:10.2514/3.13804

Cited by 10 publications

(22 citation statements)

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“…With the instability eigenfunctions already in hand, the vorticoacoustic waves remain to be determined, and these have been systematically investigated by Majdalani and co-workers in a variety of geometries and flow configurations (see, for example, Majdalani & Van Moorhem 1998;Majdalani 1999;Majdalani 2001a,b;Majdalani 2009). Unlike the instability waves, which cannot be obtained except by computer, the vorticoacoustic framework leads to closed-form approximations that can be used to directly describe the oscillatory waves driven by pressure fluctuations.…”

Section: Vorticoacoustic Modesmentioning

confidence: 99%

“…For example, DNS results will be used to: (a) verify the dependence of the temporal growth rate on the domain size; (b) reproduce the same frequencies and growth rates predicted by the stability eigensolver; and (c) confirm the nonlinear coupling between stability eigenmodes and acoustic modes, a mechanism that leads to the emergence of secondary eigenmodes in the flow. Additionally, the oscillatory velocity components obtained through DNS will be shown to match the corresponding stability eigenfunctions when properly augmented by the vorticoacoustic solution of Majdalani & Van Moorhem (1998), and a properly modelled viscous dissipation function that must be applied to the inviscid acoustic amplitudes.…”

Section: Introductionmentioning

confidence: 98%

“…A simpler closed-form expression may be obtained, as shown by Majdalani & Van Moorhem (1998), using the concept of composite scales. The so-called 'CST' technique is a variant of multiple scales theory and applies to the treatment of some problems with nonlinear scales (see Majdalani 1998Majdalani , 2001a.…”

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confidence: 99%

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

2012

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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.

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Section: Vorticoacoustic Modesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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

2012

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“…The acoustic wave is now replaced by a longitudinal acoustic mode in a pipe (a closed-form solution that accounts for the interaction with the Taylor-Culick flow and the lateral walls can be found in Majdalani & Van Moorhem (1998)). If again an elongated defect of rectangular shape is considered, the problem should be equivalent, as in the boundary-layer case, to a large-scale forcing of rectangular shape.…”

Section: Comparison With Experimental Studymentioning

confidence: 99%

Eigenvalue sensitivity, singular values and discrete frequency selection mechanism in noise amplifiers: the case of flow induced by radial wall injection

Cerqueira

Sipp

2014

J. Fluid Mech.

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We have performed linearized direct numerical simulations (DNS) of flow induced by radial wall injection forced by white-noise Gaussian forcings. We have shown that the frequency spectrum of the flow exhibits low-frequency discrete peaks in the case of a spatial structure of the forcing that is large scale. On the other hand, we observed that the spectrum becomes smooth (with no discrete peaks) if the spatial structure of the forcing is of a smaller extent. We have then tried to analyse these results in the light of global stability analyses. We have first computed the eigenvalue spectrum of the Jacobian and shown that the computed eigenvalues in the frequency range of interest were strongly damped and extremely sensitive to numerical discretization choices if large domains in the axial direction were considered. If shorter domains are used, then the eigenvalues are more robust but still extremely sensitive to the location of the upstream and downstream boundaries. Analysis of the -pseudo-spectrum showed that eigenvalues located in a region displaying 'background' values of below 10 −12 were extremely sensitive and confirmed that all values in this region of the spectrum were actually quasi-eigenvalues. The eigenvalues are therefore ill-behaved and cannot be invoked to explain the observed discrete frequency selection mechanism. We have then performed a singular value decomposition of the global resolvent matrix to compute the leading optimal gains, optimal forcings and optimal responses, which are robust quantities, insensitive to numerical discretization details. We showed that the frequency response of the flow with the large-scale forcing can accurately be reproduced by an approximation based on the leading optimal gain/forcing/response. Analysis of this approximation showed that it is the projection coefficient of the forcing onto the leading optimal forcing that is responsible for the discrete frequency selection mechanism in the case of the large-scale forcing. From a more physical point of view, such a discrete behaviour stems from the streamwise oscillations of the leading optimal forcings, whose wavelengths vary with frequency, in combination with finite extent forcings (which start or end at locations where the leading optimal forcings are strong). Experimental results in the literature are finally discussed in light of these findings.

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“…First, several researches have been focused entirely on the evolution of assumed irrotational (acoustic) velocity and pressure disturbances, to the exclusion of rotational flow (vorticity) transients. Secondly, several investigators developed a competitive linear theory to demonstrate that accurate descriptions of internal flow dynamics frequently require the presence of co-existing rotational and irrotational velocity fields (see for example, Flandro [13], Majdalani and Van Moorhem [14,15]). Finally, systematic nonlinear asymptotic modeling, valid for larger amplitude disturbances, shows formally that the basic velocity and pressure fields are decoupled from thermal processes (see for example, Staab et al [9], Zhao et al [11,12]).…”

Section: Introductionmentioning

confidence: 99%

Vorticity generation and acoustic resonance of simulated solid rocket motor chamber with high wave number wall injection

Hegab

2009

Computers & Fluids

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Improved time-dependent flowfield solution for solid rocket motors

Cited by 10 publications

References 0 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

Eigenvalue sensitivity, singular values and discrete frequency selection mechanism in noise amplifiers: the case of flow induced by radial wall injection

Vorticity generation and acoustic resonance of simulated solid rocket motor chamber with high wave number wall injection

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