Evolution of large eddies in compressible shear layers

Papamoschou, Dimitri; Bunyajitradulya, Asi

doi:10.1063/1.869230

Cited by 76 publications

(51 citation statements)

References 33 publications

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“…We remark that the present study yields temporal linear growth rates, whereas experiments measure the spatial growth of the mixing layer. Our results and those of Papamoschou & Bunyajitradulya (1996) indicate a distinct lack of interaction between eddies in supersonic shear layers. Their slow evolution may be due a combinations of decreased growth rates and this lack of interaction.…”

Section: Comparison With Experimentssupporting

confidence: 62%

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Structure and stability of the compressible Stuart vortex

O'Reilly¹,

Pullin

2003

J. Fluid Mech.

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The structure and two-and three-dimensional stability properties of a linear array of compressible Stuart vortices (CSV;Stuart 1967;Meiron et al. 2000) are investigated both analytically and numerically. The CSV is a family of steady, homentropic, two-dimensional solutions to the compressible Euler equations, parameterized by the free-stream Mach number M ∞ , and the mass flux inside a single vortex core. Known solutions have 0 < M ∞ < 1. To investigate the normal-mode stability of the generally spatially non-uniform CSV solutions, the linear partial-differential equations describing the time evolution of small perturbations to the CSV base state are solved numerically using a normal-mode analysis in conjunction with a spectral method. The effect of increasing M ∞ on the two main classes of instabilities found by Pierrehumbert & Widnall (1982) for the incompressible limit M ∞ → 0 is studied. It is found that both two-and three-dimensional subharmonic instabilities cease to promote pairing events even at moderate M ∞ . The fundamental mode becomes dominant at higher Mach numbers, although it ceases to peak strongly at a single spanwise wavenumber. We also find, over the range of investigated, a new instability corresponding to an instability on a parallel shear layer. The significance of these instabilities to experimental observations of growth in the compressible mixing layer is discussed. In an Appendix, we study the CSV equations when is small and M ∞ is finite using a perturbation expansion in powers of . An eigenvalue determining the structure of the perturbed vorticity and density fields is obtained from a singular Sturm-Liouville problem for the stream-function perturbation at O( ). The resulting small-amplitude steady CSV solutions are shown to represent a bifurcation from the neutral point in the stability of a parallel shear layer with a tanh-velocity profile in a compressible inviscid perfect gas at uniform temperature.

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Section: Comparison With Experimentssupporting

confidence: 62%

“…However, the plan views from Papamoschou & Bunyajitradulya (1996) show that the chaotic patterns reveal every possible oblique angle to the free-stream flow. A possible explanation for this may be found in figures 13(a), 9 and 12.…”

Section: Comparison With Experimentsmentioning

confidence: 99%

Structure and stability of the compressible Stuart vortex

O'Reilly¹,

Pullin

2003

J. Fluid Mech.

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“…Anticipating our discussion later on, we first define a key compressibility parameter; the convective Mach number M c = ⌬U / ͑a 1 + a 2 ͒, where ⌬U is the velocity change across the initial constant-pressure mixing shear layer, and a 1 and a 2 are the corresponding speeds of sound. The convective Mach number is considered as an appropriate parameter to scale the effects of compressibility in supersonic shear flows, and even though a single parameter may not be universally applicable, 34 it is still considered a useful parameter to delineate the effects of compressibility and will be used for this purpose in the present work.…”

Section: Introductionmentioning

confidence: 99%

Unsteady flow organization of compressible planar base flows

2007

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The unsteady flow features of a series of two-dimensional, planar base flows are examined, within a range of low-supersonic Mach numbers in order to gain a better understanding of the effects of compressibility on the organized global dynamics. Particle image velocimetry is used as the primary diagnostic tool in order to characterize the instantaneous near wake behavior, in combination with data processing using proper orthogonal decomposition. The results show that the mean flowfields are simplified representations of the instantaneous flow organizations. Generally, each test case can be characterized by a predominant global mode, which undergoes an evolution with compressibility, within the Mach number range considered. ͑The term "global mode" is defined herein as an organized global dynamical behavior of the near wake region, recognizing that the near wake dynamics may be describable in terms of several global modes.͒ At Mach 1.46, the predominant global mode can be characterized by a sinuous or flapping motion. With increasing compressibility, this flapping mode decreases, and the predominant global mode evolves into a pulsating motion aligned with the wake axis at Mach 2.27. These global modes play an important role in the distributed nature of the turbulence properties. The turbulent mixing processes become increasingly confined to a narrower redeveloping wake with increasing compressibility. Global maximum levels of the streamwise turbulence intensity and the kinematic Reynolds shear stress occur within the vicinity of the mean reattachment location, and show no systematic trend with compressibility. In contrast, the global maximum level of the vertical turbulence intensity moves upstream from the redeveloping wake toward the mean reattachment location. The vertical turbulence intensity decays thereafter more slowly than the other turbulence quantities. Overall, the local maximum levels of the turbulence properties decrease appreciably with increasing compressibility.

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“…Further work on turbulent mixing-layers was done by Elliott et al (1995) who used single and double pulsed visualizations to track the evolution of the largescale structures. In their work, Papamoschou & Bunyajitradulya (1996) addressed the following observations: For increasing convective Mach number, not only does the growth rate of the shear layer decline but the turbulence becomes less organized (shows less 2-D coherence) and 3-D disturbances become more amplified. Some analytical work, validated with numerical simulations, was done by Sarkar et al (1991) who focused on the effect of the dilatational terms on compressible turbulence.…”

Section: Coherent Structuresmentioning

confidence: 99%

Simulation of Supersonic Base Flows: Numerical Investigations Using DNS, LES, and URANS

Fasel¹,

Sandberg²

2006

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Public Reporting Burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comment regarding this burden estimate or any other aspect of this collection of information, including suggesstions for reducing this burden, Simulation of Supersonic Base Flows: Numerical Investigations Using DNS, LES, and URANS Report Title ABSTRACTTransitional and turbulent supersonic axisymmetric wakes were investigated by conducting various numerical experiments. The main objective was to identify hydrodynamic instability mechanisms in the flow at Mach number M = 2.46 for several Reynolds numbers, and relating these to coherent structures that are found from various visualization techniques. The premise for this approach is the assumption that flow instabilities lead to the formation of coherent structures. The effect of these structures on the mean flow is of particular interest, as they strongly affect the base drag. Three high-order accurate compressible codes were developed in cylindrical coordinates for this research: A spatial Navier-Stokes (N-S) code to conduct Direct Numerical Simulations (DNS), a linearized N-S code for linear stability investigations using two-dimensional basic states, and a temporal N-S code for performing local stability analyses. The ability of numerical simulations to deliberately exclude physical effects is exploited. This includes intentionally eliminating certain azimuthal/helical modes by employing DNS for various circumferential domain-sizes. With this approach, the impact of structures associated with certain modes on the global wake-behavior can be scrutinized. It is concluded that azimuthal modes with low wavenumbers are responsible for a flat mean base-pressure distribution and that k=2 and k=4 are the dominant modes in the trailing wake, producing a four-lobe wake pattern. Complementary spatial and temporal calculations are carried out to investigate whether instabilities are of local or global nature. Circumstatial evidence is presented that absolutely unstable global modes within the recirculation region coexist with convectively unstable shear-layer modes. The flow is found to be absolutely unstable with respect to modes k>0 for Re_D > 5,000 and with respect to the axisymmetric mode for Re_D>100,000. Furthermore, it is investigated whether flow control measures designed to weaken the naturally most significant modes can decrease the base drag. Finally, the novel Flow Simulation Methodology (FSM), using state-of-the-art turbulence closures, was shown to reproduce DNS results at a fraction of the computational cost.

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Evolution of large eddies in compressible shear layers

Cited by 76 publications

References 33 publications

Structure and stability of the compressible Stuart vortex

Structure and stability of the compressible Stuart vortex

Unsteady flow organization of compressible planar base flows

Simulation of Supersonic Base Flows: Numerical Investigations Using DNS, LES, and URANS

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