Two-Equation k-s Turbulence Model: Application to a Supersonic Base Flow

Benay, R.; Servel, Patrick

doi:10.2514/2.1350

Cited by 31 publications

(9 citation statements)

References 12 publications

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“…The supersonic wake flow has also been studied numerically using approaches ranging from various Reynolds-averaged Navier-Stokes (RANS) models 8,9 via detached-eddy simulations (DES) 10,11 and large-eddy simulations (LES) 12 to direct numerical simulations (DNS). [13][14][15] RANS models were found to be suitable only for the prediction of the attached flow and failed to provide accurate results concerning the low pressure recirculation area behind the base.…”

Section: Introductionmentioning

confidence: 99%

Analysis of pressure perturbation sources on a generic space launcher after-body in supersonic flow using zonal turbulence modeling and dynamic mode decomposition

et al. 2015

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A sparsity promoting dynamic mode decomposition (DMD) combined with a classical data-based statistical analysis is applied to the turbulent wake of a generic axisymmetric configuration of an Ariane 5-like launcher at Ma∞ = 6.0 computed via a zonal Reynolds-averaged Navier-Stokes/large-eddy simulation (RANS/LES) method. The objective of this work is to gain a better understanding of the wake flow dynamics of the generic launcher by clarification and visualization of initially unknown pressure perturbation sources on its after-body in coherent flow patterns. The investigated wake topology is characterized by a subsonic cavity region around the cylindrical nozzle extension which is formed due to the displacement effect of the afterexpanding jet plume emanating from the rocket nozzle (Mae = 2.52, pe/p∞ = 100) and the shear layer shedding from the main body. The cavity region contains two toroidal counter-rotating large-scale vortices which extensively interact with the turbulent shear layer, jet plume, and rocket walls, leading to the shear layer instability process to be amplified. The induced velocity fluctuations in the wake and the ultimately resulting pressure perturbations on the after-body feature three global characteristic frequency ranges, depending on the streamwise position inside the cavity. The most dominant peaks are detected at SrD r3 = 0.85 ± 0.075 near the nozzle exit, while the lower frequency peaks, in the range of SrD r2 = 0.55 ± 0.05 and SrD r1 = 0.25 ± 0.05, are found to be dominant closer to the rocket’s base. A sparse promoting DMD algorithm is applied to the time-resolved velocity field to clarify the origin of the detected peaks. This analysis extracts three low-frequency spatial modes at SrD = 0.27, 0.56, and 0.85. From the three-dimensional shape of the DMD modes and the reconstructed modulation of the mean flow in time, it is deduced that the detected most dominant peaks of SrD r3 ≈ 0.85 are caused by the radial flapping motion of the shear layer, while the middle-frequency range of SrD r2 ≈ 0.55 is found to be associated with its swinging motion. The less intensive peaks of SrD r1 ≈ 0.25 pronounced on the base wall are caused by the low-frequency longitudinal pumping of the two toroidal large-scale vortices inside the cavity.

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Section: Introductionmentioning

confidence: 99%

Analysis of pressure perturbation sources on a generic space launcher after-body in supersonic flow using zonal turbulence modeling and dynamic mode decomposition

et al. 2015

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“…There have been various CFD studies for the prediction of base flows and most of them used Reynolds-averaged Navier-Stokes (RANS) simulations with RANS turbulence models to handle high Reynolds number flows. Many investigations with various RANS turbulence models have tried to predict the supersonic cylindrical base flow [13][14][15][16], an axisymmetric truncated plug nozzle [17,18], and blunted cone cylinder [19]. Some improvements of the predictability have been made, but unfortunately the RANS simulations have failed to produce quantitative prediction of the base flow.…”

mentioning

confidence: 98%

Time-Series and Time-Averaged Characteristics of Subsonic to Supersonic Base Flows

Kawai

Fujii

2007

AIAA Journal

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Physics of cylindrical base flows ranging from subsonic to supersonic speeds at zero angle of attack are computationally investigated. Time-series and time-averaged investigations of base flows show distinctive characteristics at subsonic, transonic, and supersonic regimes. Normalized time-averaged base pressure decreases proportionally with respect to increasing freestream dynamic pressure in the subsonic regime of M 1 < 0:8. The base pressure begins to fall rapidly in the transonic regime and then settles down and decreases gradually toward an asymptotic value at M 1 > 1:5. Normalized base pressure fluctuations sharply increase at transonic speeds, whereas they decrease with increasing freestream Mach number at subsonic and supersonic speeds. Appearance of unsteady local shock waves change the characteristics of base pressure distinctively at the transonic speeds. Spectra of the base pressure show one clear peak at subsonic speeds (related to the shear layer dynamics), two clear peaks at transonic speeds (related to the shear layer dynamics and its subharmonic), and three major peaks at supersonic speeds (related to the shear layer dynamics, its subharmonic, and an additional mechanism). Instability of the free shear layers has dominant influence on the overall base flowfield over a wide range of Mach numbers ranging from subsonic to supersonic speeds. However, at supersonic speeds, an additional mechanism of instability within the recirculating region is possibly at work and has dominant influence on the flowfield. The dominant mechanisms significantly cause the strong Mach number dependence of the high-pressure region which is strongly related to the base pressure. The spectrum analysis suggests that the substantial base pressure fluctuations are caused by the pulsing of the flow inside the recirculating region. Nomenclature a = sonic speed C K = Yoshizawa model coefficientfrom closest wall to blending position d wall = distance from closest wall M = local Mach number Pr t = turbulent Prandtl number p = local static pressure q = local dynamic pressure q j = heat flux vector R = cylinder base radius Re = Reynolds number S ij = strain rate tensor Sr = Strouhal number T = temperature u = axial velocityx, y, z = Cartesian coordinates x j = coordinate vector = ratio of specific heats filter = filter length scale t = integration time x, y, z = step size of the grid in x, y, z directions ij = Kronecker delta t = turbulent eddy viscosity = kinematic eddy viscosity = density = blending function Superscripts LES = quantity in large-eddy simulation formulation RANS = quantity in Reynolds-averaged Navier-Stokes formulation = dimensional quantity = spatial-filtered or ensemble-averaged quantitỹ = Favre-filtered or Favre-averaged quantity = wall unit quantity Subscripts 1 = freestream quantity

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“…Numerical investigations of the turbulent wakes range from various RANS model based solutions [5,6] via detached-eddy simulations (DES) [7,8] and LES [9] to direct numerical simulations (DNS) [10,11]. The base §ow and the base pressure, however, have not always been predicted with su©cient accuracy.…”

Section: Introductionmentioning

confidence: 99%

Experimental and numerical investigation of the turbulent wake flow of a generic space launcher configuration

Statnikov

Saile

Meiss

et al. 2015

Progress in Flight Physics – Volume 7

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The turbulent wake of a generic space launcher at cold hypersonic freestream conditions is investigated experimentally and numerically to gain detailed insight into the intricate base §ow phenomena of space vehicles at upper stages of the §ight trajectory. The experiments are done at Ma ∞ = 6 and Re D = 1.7 · 10 6 m −1 by the German Aerospace Center (DLR) and the corresponding computations are performed by the Institute of Aerodynamics Aachen using a zonal Reynolds-averaged Navier Stokes / Large-Eddy Simulation (RANS/LES) approach. Two di¨erent aft-body geometries consisting of a blunt base and an attached cylindrical nozzle dummy are considered. It is found that the wind tunnel model support attached to the upper side of the main body has a nonnegligible impact on the wake along the whole circumference, albeit on the opposite side, the e¨ects are minimal compared to an axisymmetric con¦guration. In the blunt-base case, the turbulent supersonic boundary layer undergoes a strong aftexpansion on the model shoulder leading to the formation of a con¦ned low-pressure (p/p ∞ ≈ 0.2) recirculation region. Adding a nozzle dummy causes the shear layer to reattach on the its wall at x/D ∼ 0.6 and the base pressure level to increase (p/p ∞ ≈ 0.25) compared to the blunt-base case. For both con¦gurations, the pressure §uctuations on the base wall feature dominant frequencies at Sr D ≈ 0.05 and Sr D ≈ 0.2 0.27, but are of small amplitudes (p rms /p ∞ = 0.02 0.025) compared to the main body boundary layer. For the nozzle dummy con¦guration, when moving downstream along the nozzle extension, the wall pressure is increasingly in §uenced by the reattaching shear layer and the periodic low-frequency behavior

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Two-Equation k-s Turbulence Model: Application to a Supersonic Base Flow

Cited by 31 publications

References 12 publications

Analysis of pressure perturbation sources on a generic space launcher after-body in supersonic flow using zonal turbulence modeling and dynamic mode decomposition

Analysis of pressure perturbation sources on a generic space launcher after-body in supersonic flow using zonal turbulence modeling and dynamic mode decomposition

Time-Series and Time-Averaged Characteristics of Subsonic to Supersonic Base Flows

Experimental and numerical investigation of the turbulent wake flow of a generic space launcher configuration

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