Cold-flow simulation of a two-dimensional nozzleless solid rocket motor

Traineau, J. C.; Hervat, Pierre; Kuentzmann, P.

doi:10.2514/6.1986-1447

Cited by 93 publications

(70 citation statements)

References 6 publications

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“…This finding is consistent with the axial steepening observed in compressible models of solid rocket motors (e.g. Traineau, Hervat & Kuentamann 1986;Balakrishnan, Liñán & Williams 1992;Wasistho, Balachandar & Moser 2004;Majdalani 2007a;Maicke & Majdalani 2008;Akiki & Majdalani 2012, 2016. Contrary to the aforementioned studies, no net amplification of the axial velocity may be noted here, aside from a reshaping of the profile itself.…”

Section: Compressible Velocity Steepeningsupporting

confidence: 44%

On the compressible bidirectional vortex in a cyclonically driven Trkalian flow field

2017

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In this study, the Bragg-Hawthorne equation (BHE) is extended in the context of a steady, inviscid and compressible fluid, thus leading to an assortment of partial differential equations that must be solved simultaneously. A solution is pursued by implementing a Rayleigh-Janzen expansion in the square of the reference Mach number. The corresponding formulation is subsequently used to derive a compressible approximation for the Trkalian model of the bidirectional vortex. The approximate solution is compared to a representative computational fluid dynamics simulation in order to validate the modelling assumptions under realistic conditions. The latter is found to exhibit an appreciable steepening of the axial velocity profile, which is accompanied by an axial dependence in the mantle location that is somewhat reminiscent of the radial shifting of mantles reported in some experimental trials and simulations. In this context, flows with a strong swirl intensity do not seem to be significantly affected by the introduction of compressibility. Rather, as the swirl intensity is reduced the effects of compressibility become more noticeable, especially in the axial and radial velocity components. It may also be realized that imparting a progressively larger swirl component stands to promote the axisymmetric distribution of flow field properties, and these include an implicit resistance to dilatational effects in the tangential direction. From a broader perspective, this study provides a viable approximation to the Trkalian motion associated with cyclonic flows, while serving as a limited proof of concept for the compressible Bragg-Hawthorne procedure applied to a steady, axisymmetric and inviscid fluid.

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Section: Compressible Velocity Steepeningsupporting

confidence: 44%

On the compressible bidirectional vortex in a cyclonically driven Trkalian flow field

2017

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“…Furthermore, flow approximations exhibiting smoother or steeper profiles than the cold flow equilibrium state have been studied in connection with their energy content by Majdalani & Saad (2007a) and Saad & Majdalani (2008). In what concerns compressible flow effects, these have been first investigated by Traineau, Hervat & Kuentzmann (1986) in the context of two-dimensional porous tubes and channels with sidewall injection. Using either nitrogen or air as the working substance, these investigators have reported rich characteristics of the spatially developing motion, which has been shown to depict appreciable steepening beyond the Taylor-Culick baseline (Taylor 1956;Culick 1966).…”

mentioning

confidence: 99%

“…In fact, a variant of this technique was used by Traineau et al (1986), who introduced, in a precursor to the present study, a rotational and compressible integral equation, which can be solved in a planar, two-dimensional, and viscous-free setting. In the same context, two related extensions appeared, given by Balakrishnan, Liñan & Williams (1991) and Akiki & Majdalani (2012).…”

mentioning

confidence: 99%

“…In complementing ongoing efforts to obtain closed-form solutions for the flow in porous cylinders, it is the purpose of this study to extend the integral formulation developed initially by Traineau et al (1986) and later reconstructed by Balakrishnan, Liñan & Williams (1992). Our objective is to produce a complete pseudo-twodimensional approximation that would not be limited to homentropic flow conditions, and that would obviate the need for numerical integration, at least in some well-defined cases of interest.…”

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confidence: 99%

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Compressible integral representation of rotational and axisymmetric rocket flow

Akiki

Majdalani

2016

J. Fluid Mech.

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This work focuses on the development of a semi-analytical model that is appropriate for the rotational, steady, inviscid, and compressible motion of an ideal gas, which is accelerated uniformly along the length of a right-cylindrical rocket chamber. By overcoming some of the difficulties encountered in previous work on the subject, the present analysis leads to an improved mathematical formulation, which enables us to retrieve an exact solution for the pressure field. Considering a slender porous chamber of circular cross-section, the method that we follow reduces the problem's mass, momentum, energy, ideal gas, and isentropic relations to a single integral equation that is amenable to a direct numerical evaluation. Then, using an Abel transformation, exact closed-form representations of the pressure distribution are obtained for particular values of the specific heat ratio. Throughout this effort, Saint-Robert's power law is used to link the pressure to the mass injection rate at the wall. This allows us to compare the results associated with the axisymmetric chamber configuration to two closed-form analytical solutions developed under either one-or two-dimensional, isentropic flow conditions. The comparison is carried out assuming, first, a uniformly distributed mass flux and, second, a constant radial injection speed along the simulated propellant grain. Our amended formulation is consequently shown to agree with a one-dimensional solution obtained for the case of uniform wall mass flux, as well as numerical simulations and asymptotic approximations for a constant wall injection speed. The numerical simulations include three particular models: a strictly inviscid solver, which closely agrees with the present formulation, and both k-ω and Spalart-Allmaras computations.

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“…Swirling motion in rockets 267 (Traineau, Hervat & Kuentzmann 1986;Balakrishnan, Liñan & Williams 1992;Akiki & Majdalani 2012.…”

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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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Cold-flow simulation of a two-dimensional nozzleless solid rocket motor

Cited by 93 publications

References 6 publications

On the compressible bidirectional vortex in a cyclonically driven Trkalian flow field

On the compressible bidirectional vortex in a cyclonically driven Trkalian flow field

Compressible integral representation of rotational and axisymmetric rocket flow

On the swirling Trkalian mean flow field in solid rocket motors

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