Instabilities and pressure oscillations in solid rocket motors

Fabignon, Yves; Dupays, Joel; Avalon, G.; Vincent, François; Lupoglazoff, Nicolas; Casalis, Grégoire; Prévost, Michel

doi:10.1016/s1270-9638(02)01194-x

Cited by 145 publications

(71 citation statements)

References 15 publications

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“…This may be owed to its association with several studies involving hydrodynamic instability [23][24][25][26][27][28], acoustic instability [29][30][31][32][33][34][35], wave propagation [36][37][38][39], particle-mean flow interactions [40], and rocket performance measurements [41][42][43]. The Taylor-Culick solution was originally verified to be an adequate representation of the expected flowfield in SRMs both numerically by Sabnis et al [44] and experimentally by Dunlap et al [45,46], thereby confirming its character in a nonreactive chamber environment.…”

Section: Doi: 102514/1j055949mentioning

confidence: 95%

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Viscous Mean Flow Approximations for Porous Tubes with Radially Regressing Walls

Saad

Majdalani

2017

AIAA Journal

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The mean gaseous motion in solid rocket motors has been traditionally described using an inviscid solution in a porous tube of fixed radius and uniform wall injection. This model, usually referred to as the Taylor-Culick profile, consists of a rotational solution that captures the bulk gaseous motion in a frictionless rocket chamber. In practice, however, the port radius increases as the propellant burns, thus leading to time-dependent effects on the mean flow. This work considers the related problem in the context of viscous motion in a porous tube and allows the radius to be time dependent. By implementing a similarity transformation in space and time, the incompressible Navier-Stokes equations are first reduced to a nonlinear fourth-order ordinary differential equation with four boundary conditions. This equation is then solved both numerically and asymptotically, using the injection Reynolds number Re and the dimensionless wall regression ratio α as primary and secondary perturbation parameters. In this manner, closedform analytical solutions are obtained for both large and small Reynolds number with small-to-moderate α. The resulting approximations are then compared with the numerical solution obtained for an equivalent third-order ordinary differential equation in which both shooting and the irregular limit that affects the fourth-order formulation are circumvented. This code is found to be capable of producing the stable solutions for this problem over a wide range of Reynolds numbers and wall regression ratios.

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Section: Doi: 102514/1j055949mentioning

confidence: 95%

“…For example, we elect to use Eq. (30) for the numerical solution because it requires less memory storage and fewer Runge-Kutta integrations. On the other hand, Eq.…”

Section: Similarity In Timementioning

confidence: 99%

Viscous Mean Flow Approximations for Porous Tubes with Radially Regressing Walls

Saad

Majdalani

2017

AIAA Journal

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“…Full numerical approaches must be used, in providing insight into oscillatory flow fields and must become irreplaceable tools to predict motor stability. After more than ten years of sustained CFD research in ONERA, CFD methods are available to build a detailed understanding of the instability mechanisms 17,18 . An unsteady quasi-onedimensional flow solver with higher-order numerical solutions for simulating internal ballistics and axial acoustic fluctuations in solid rocket motors is developed by Chakravarthy 19 , et al The characteristic frequencies, corresponding mode shapes, and damping rates is estimated for cylindrical grain geometry.…”

Section: Introductionmentioning

confidence: 99%

Computational Fluid Dynamics Simulation of Combustion Instability in Solid Rocket Motor : Implementation of Pressure Coupled Response Function

Saha

Chakraborty

2016

Def. Sc. Jl.

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Combustion instability in solid propellant rocket motor is numerically simulated by implementing propellant response function with quasi steady homogeneous one dimensional formulation. The convolution integral of propellant response with pressure history is implemented through a user defined function in commercial computational fluid dynamics software. The methodology is validated against literature reported motor test and other simulation results. Computed amplitude of pressure fluctuations compare closely with the literarture data. The growth rate of pressure oscillations of a cylindrical grain solid rocket motor is determined for different response functions at the fundamental longitudinal frequency. It is observed that for response function more than a critical value, the motor exhibits exponential growth rate of pressure oscillations.

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“…This is especially true in applications that require an analytical mean-flow formulation. Among the relevant examples, one may cite those studies concerned with vorticoacoustic wave propagation Majdalani 2001b) and hydrodynamic instability treatment in porous chambers with (Féraille & Casalis 2003) and without particle interactions (Ugurtas et al 2000;Fabignon et al 2003;Chedevergne et al 2006).…”

Section: Introductionmentioning

confidence: 99%

On the Lagrangian optimization of wall-injected flows: from the Hart–McClure potential to the Taylor–Culick rotational motion

Saad

Majdalani

2009

Proc. R. Soc. A.

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The Taylor-Culick solution for a porous cylinder is often used to describe the bulk gas motion in idealized representations of solid rocket motors. However, other approximate solutions may be found that satisfy the same fundamental constraints. In this vein, steeper or smoother profiles may be observed in either experimental or numerical tests, particularly in the presence of intense levels of acoustic energy. In this study, we use the Lagrangian optimization principle to arrive at multiple solutions that can help to explain the practically observed motions. We then search for the extreme states that display either the least or the most kinetic energy. These are derived and found to be dependent on the chamber's aspect ratio. By assuming a slender case, simple expressions are retrieved from which both the rotational Taylor-Culick and the irrotational HartMcClure solutions are recovered as special cases. At the outset, a new family of flow approximations is derived extending from purely potential to highly rotational fields. These are constructed, verified and catalogued based on their kinetic energies. To help understand the tendency of a motion to shift energy states, a second law analysis is performed and used to rank these solutions based on their entropy content. Interestingly, the Taylor-Culick profile is found to represent an equilibrium state entailing the most energy and entropy among those starting from the rest. A formal extension of Kelvin's minimum energy theorem to an open region is then pursued, followed by a direct implementation to the problem at hand. Three other flow motions with open boundaries are examined to further exemplify the application of Kelvin's extended criteria. Our efforts illustrate the overarching harmony that exists between Lagrange's minimization principle and Kelvin's minimum energy theorem; both converge on the potential solution as the least kinetic energy bearer even when the velocity at the open barrier is finite.

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Instabilities and pressure oscillations in solid rocket motors

Cited by 145 publications

References 15 publications

Viscous Mean Flow Approximations for Porous Tubes with Radially Regressing Walls

Viscous Mean Flow Approximations for Porous Tubes with Radially Regressing Walls

Computational Fluid Dynamics Simulation of Combustion Instability in Solid Rocket Motor : Implementation of Pressure Coupled Response Function

On the Lagrangian optimization of wall-injected flows: from the Hart–McClure potential to the Taylor–Culick rotational motion

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