Laminar cold-flow model for the internal gas dynamics of a slab rocket motor

Majdalani, Joseph; Moorhem, W. K. Van

doi:10.1016/s1270-9638(01)01095-1

Cited by 29 publications

(23 citation statements)

References 24 publications

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“…Traditionally, terms due to the pseudopressure are ignored because of the small contribution of p. 33,36 At present, the corresponding integrals will be evaluated before a decision is made. Our motivation stems from recent numerical and experimental studies that have emphasized the importance of the pseudopressure in the global analysis.…”

Section: H Eighth Factor: Pseudoacoustical Correctionmentioning

confidence: 99%

“…In the process, special attention will be given to the pseudopressure corrections which have been found to be important in recent experimental and numerical rocket motor simulations. [36][37][38][39][40] Furthermore, the unsteady energy crossing the exit plane will be accounted for. This will lead to a loss term that causes the cancellation of the pseudorotational growth rate.…”

Section: Introductionmentioning

confidence: 99%

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Some rotational corrections to the acoustic energy equation in injection-driven enclosures

2005

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This article presents rotational corrections to the energy stability equation in injection-driven porous enclosures used to simulate solid rocket motors. The evaluation of stability growth rate factors is carried out both numerically and asymptotically. Analytical expressions for the energy stability factors are obtained over a spectrum of physical parameters encompassing solid rocket motor operation. For all representative motors under investigation, the analytical estimates are shown to exhibit negligible errors compared to their numerical values. Both numerics and asymptotics converge in predicting less stable systems than projected by purely irrotational stability theory. The differences can be ascribed to the dismissal of time-dependent rotational coupling in some past formulations. The current study unravels the details of six additional growth rate corrections not accounted for previously. These include the rotational flow, inviscid vortical, viscous, pseudoacoustical, pseudorotational, and unsteady nozzle growth rate factors. The fourth and fifth terms are due to acoustical and vortical interactions with the often neglected pseudopressure. The sixth is due to the energy associated with the unsteady rotational flow exiting the porous enclosure. This study enables us to explain the influence of distinct flow variables on stability. Based on asymptotic approximations for individual growth rates, explicit criteria are presented in the form of critical Mach numbers, penetration numbers, or motor lengths that must not be exceeded in prevention of system instability. The net rotational corrections have been recently appended to the widely used Standard Stability Prediction code.

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Section: H Eighth Factor: Pseudoacoustical Correctionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Some rotational corrections to the acoustic energy equation in injection-driven enclosures

2005

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“…The asymptotic approximations obtained previously were also shown to agree favorably with experimental data obtained in cold-flow simulations of transpiring surfaces. [39][40][41][42] Although the physical nature of the problem changes when suction is introduced, the assumptions used in reducing the governing equations remain valid, regardless of the inflow or outflow boundary conditions. By analogy with the injection-driven problem, one can expect a comparable level of agreement between the asymptotic formulations given here and either numerical or experimental studies of the model at hand.…”

Section: A a Formerly Tested Methodologymentioning

confidence: 99%

“…It may be interesting to note that these distinguished limits are dissimilar from those realized in the injection flow analog, [37][38][39][40][41][42] including those arising in the rectangular cavity. 1,2 The disparity can be attributed to the reversal in the physics of the problem, namely, in the relocation of the viscous boundary layer to the vicinity of the suction wall.…”

Section: ͑39͒mentioning

confidence: 99%

Vortical and acoustical mode coupling inside a porous tube with uniform wall suction

Jankowski

Majdalani

2005

The Journal of the Acoustical Society of America

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This paper considers the oscillatory motion of gases inside a long porous tube of the closed-open type. In particular, the focus is placed on describing an analytical solution for the internal acoustico-vortical coupling that arises in the presence of appreciable wall suction. This unsteady field is driven by longitudinal oscillatory waves that are triggered by small unavoidable fluctuations in the wall suction speed. Under the assumption of small amplitude oscillations, the time-dependent governing equations are linearized through a regular perturbation of the dependent variables. Further application of the Helmholtz vector decomposition theorem enables us to discriminate between acoustical and vortical equations. After solving the wave equation for the acoustical contribution, the boundary-driven vortical field is considered. The method of matched-asymptotic expansions is then used to obtain a closed-form solution for the unsteady momentum equation developing from flow decomposition. An exact series expansion is also derived and shown to coincide with the numerical solution for the problem. The numerically verified end results suggest that the asymptotic scheme is capable of providing a sufficiently accurate solution. This is due to the error associated with the matched-asymptotic expansion being smaller than the error introduced in the Navier-Stokes linearization. A basis for comparison is established by examining the evolution of the oscillatory field in both space and time. The corresponding boundary-layer behavior is also characterized over a range of oscillation frequencies and wall suction velocities. In general, the current solution is found to exhibit features that are consistent with the laminar theory of periodic flows. By comparison to the Sexl profile in nonporous tubes, the critically damped solution obtained here exhibits a slightly smaller overshoot and depth of penetration. These features may be attributed to the suction effect that tends to attract the shear layers closer the wall.

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“…These start with the classical laboratory measurements acquired by Taylor (1956) and evolve through a plethora of computational (Dunlap, Willoughby & Hermsen 1974;Baum, Levine & Lovine 1988;Sabnis, Gibeling & McDonald 1989;Apte & Yang 2000), experimental (Yamada et al 1976;Dunlap et al 1990;Casalis et al 1998;Avalon & Josset 2006) and theoretical studies (Clayton 1996;Barron, Van Moorhem & Majdalani 2000;Majdalani & Van Moorhem 2001;Zhou & Majdalani 2002) for both cylindrically shaped and planar rocket configurations. Most of these endeavours tend to confirm the suitability of the TC model in approximating the bulk flow in a simulated SRM (Kuentzmann 1991), although many seem to recognize the natural tendency of the flow to develop a non-zero swirl component, and, hence, axial vorticity, in a sufficiently long chamber with circular cross-section (Dunlap et al 1990;Balachandar et al 2001;Najjar et al 2006).…”

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confidence: 99%

On the swirling Trkalian mean flow field in solid rocket motors

Fist

Majdalani

2017

J. Fluid Mech.

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In this work, an exact Euler solution is derived under the fundamental contingencies of axisymmetric, steady, rotational, incompressible, single-phase, non-reactive and inviscid fluid, which also stand behind the ubiquitously used mean flow profile named 'Taylor-Culick.' In comparison with the latter, which proves to be complex lamellar, the present model is derived in the context of a Trkalian flow field, and hence is capable of generating a non-zero swirl component that increases linearly in the streamwise direction. This enables us to provide an essential mathematical representation that is appropriate for flow configurations where the bulk gaseous motion is driven to swirl. From a procedural standpoint, the new Trkalian solution is deduced directly from the Bragg-Hawthorne equation, which has been repeatedly shown to possess sufficient latitude to reproduce several existing profiles such as Taylor-Culick's as special cases. Throughout this study, the fundamental properties of the present model are considered and discussed in the light of existing flow approximations. Consistent with the original Taylor-Culick mean flow motion, the Trkalian velocity is seen to exhibit both axial and tangential components that increase linearly with the distance from the headwall, and a radial component that remains axially invariant. Furthermore, the Trkalian model is shown to form a subset of the Beltramian class of solutions for which the velocity and vorticity vectors are not only parallel but also directly proportional. This characteristic feature is interesting, as it stands in sharp contrast to the complex-lamellar nature of the Taylor-Culick motion, where the velocity and vorticity vectors remain orthogonal. By way of verification, a numerical simulation is carried out using a finite-volume solver, thus leading to a favourable agreement between theoretical and numerical predictions.

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Laminar cold-flow model for the internal gas dynamics of a slab rocket motor

Cited by 29 publications

References 24 publications

Some rotational corrections to the acoustic energy equation in injection-driven enclosures

Some rotational corrections to the acoustic energy equation in injection-driven enclosures

Vortical and acoustical mode coupling inside a porous tube with uniform wall suction

On the swirling Trkalian mean flow field in solid rocket motors

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