Compressible Wall-Injection Flows in Laminar, Transitional, and Turbulent Regimes: Numerical Prediction

Wasistho, B.; Balachandar, S.; Moser, Robert D.

doi:10.2514/1.2019

Cited by 57 publications

(34 citation statements)

References 13 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: 43%

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: 43%

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

2017

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“…While the former group explored the merits of a one-dimensional theoretical model, the latter employed a pseudo-two-dimensional numerical approach. Given the relevance of an accurate mean-flow description to the study of hydrodynamic instability in simulated rocket motors, the problem was revisited by Venugopal, Najjar & Moser (2001) and, in complementary work, by Wasistho, Balachandar & Moser (2004). As a windfall, the compressible solutions engendered in these studies became valuable resources in the limiting process verification of Navier-Stokes solvers (Wasistho et al 2002;Najjar et al 2003).…”

mentioning

confidence: 99%

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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“…2 In terms of turbulence characterization in simulated rocket configurations, works by Beddini, 3 Beddini and Roberts, 4 Lee and Beddini,5,6 Apte and Yang, [7][8][9] Wasistho, Balachandar and Moser, 10 and numerous others have contributed significant advancements to our understanding of the corresponding unsteady flowfield. More recent studies by Casalis, Avalon, and Pineau, 11 Griffond, Casalis and Pineau, 12 Ugurtas et al, 13 Griffond and Casalis,14,15 Féraille and Casalis, 16 and Fabignon et al 17 have paid special attention to different hydrodynamic stability models and their ability to predict with varying degrees of accuracy the oscillatory motions observed in solid rocket motors.…”

Section: Introductionmentioning

confidence: 99%

Effect of Outflow Boundary Conditions on the Stability of Cylindrically-Shaped Hybrid Rockets

Elliott¹,

Majdalani²

2015

51st AIAA/SAE/ASEE Joint Propulsion Conference

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In this study, the biglobal stability approach, which is frequently used to characterize the hydrodynamic instability waves associated with parietal vortex shedding, is applied to a simulated rocket chamber with variable headwall injection. The analysis is motivated by the need to assess the viability of three dissimilar outflow boundary conditions that are relevant to the modeling of cylindrically-shaped solid and hybrid rocket chambers with headwall mass injection. To this end, three sets of boundary conditions are considered and discussed: first, an acoustically-closed chamber is assumed; second, an adjoint-compliant method is relied upon; and, third, a continual outflow requirement is imposed. The first set of boundary conditions is ubiquitously used in conjunction with the Local Nonparallel (LNP) formulation in rocket-flow problems that entail a choked chamber endwall (e.g., a nozzle throat). By suppressing velocity fluctuations, using axial symmetry, and setting the normal stress tensor at the exit boundary equal to zero, one arrives at a second unique set of conditions. These so-called adjoint-compliant requirements lead to a well-posed adjointconforming problem, which has been shown to be essential for simulations based on the finite element method. The final set of constraints is precipitated by the need to secure flow continuation at the exit, which may be achieved through linear extrapolation. As with previous implementations of the biglobal stability framework, we do not limit ourselves to a stream function formulation. Instead we consider the linearized Navier-Stokes equations and solve the resulting eigenvalue problem using pseudo-spectral methods. Although the stability spectrum for a solid rocket motor configuration with a non-injecting headwall may be recovered from our formulation as a special case, our main discussion concentrates on the hybrid rocket flow configuration with an order of magnitude difference between the headwall and sidewall injection speeds. Lastly, comparisons to previous investigations that rely on the stream function approach and the LNP technique are provided and discussed. Nomenclatureij A = operator matrix a = chamber radius ij B = the right-hand-side coefficient matrix of a matrix pencil N D = Chebyshev pseudo-spectral derivative matrix of size N d = weight coefficients for pseudo-spectral derivative matrices N I = identity matrix of size N L = chamber length M = base flow component M = instantaneous flow component m = general amplitude function m = acoustic fluctuation 2 m = unsteady hydrodynamic fluctuation m = vortical fluctuation = Landau order symbol P = base flow pressure p = pressure amplitude function p = hydrodynamic pressure fluctuation q = azimuthal integer wave number , rz = normalized radial and axial coordinates Re = Reynolds number N T = Chebyshev polynomial of the first kind U = base flow velocity, r U ,U  , z U u = velocity amplitude function u = hydrodynamic velocity fluctuation Greek  = gradient operator  = 1/ Re  = streamwise Chebyshev variables m...

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Compressible Wall-Injection Flows in Laminar, Transitional, and Turbulent Regimes: Numerical Prediction

Cited by 57 publications

References 13 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

Effect of Outflow Boundary Conditions on the Stability of Cylindrically-Shaped Hybrid Rockets

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