Second order nonlinear spatial stability analysis of compressible mixing layers

Ladeinde, Foluso; Wu, Jia

doi:10.1063/1.1492284

Cited by 7 publications

(5 citation statements)

References 32 publications

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“…While the real reason for this relaxation behavior is not entirely clear, it may be due to lower amplification ͑decay͒ rates that are usually associated with small amplitudes, from the view point of hydrodynamic stability. 40 ͑See Table II, cases III and VIII for the initial kinetic energy levels.͒ Note that, whereas Fig. 11 ͑or Table III͒ shows the most enhancement of the internal energy mode by f1-0-100, followed by f1-45-100, the spectra plots in Figs.…”

Section: Resultsmentioning

confidence: 91%

“…The calculations are limited to M a ϭ0.5. This choice is guided by the results in GM1 and from our own work, 35,40 in which the lower M a calculations (0.1рM a р0.3) gave results that were similar to those of the corresponding incompressible cases, and higher M a runs produced shocklets and other potentially discontinuous fields that require a different kind of analysis from the one presented in this paper. The effects of the initial hydrodynamic turbulent Reynolds number is also well known from previous work.…”

Section: Case Studiesmentioning

confidence: 99%

“…FЈ, GЈ, and HЈ are vectors of the inviscid fluxes while 38 and flow fields with shock waves. [39][40][41] With the compact schemes, the derivative uЈ for a generic variable u is obtained from the representation…”

Section: Numerical Solutionmentioning

confidence: 99%

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Magnetic Reynolds number effects in compressible magnetohydrodynamic turbulence

Ladeinde

Gaitonde

2004

Physics of Fluids

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The effects of the magnetic Reynolds number, Re , on decaying two-dimensional compressible magnetohydrodynamic ͑MHD͒ turbulence are investigated through direct numerical simulations. The initial relative intensities of, and the correlation between, the fluctuating velocity ͑u͒ and magnetic induction ͑b͒ fields are also varied, as measured with the respective parameters f and angle. The investigations cover the parameter ranges 1рRe р250, 0°рр90°, and 1р f р3. The results suggest that, at the lowest Re investigated, the magnetic field has a negligible impact on the evolution of the turbulence kinetic energy E k. At higher Re values, when magnetic effects are important, the magnetic field tends to accelerate the decay of the turbulence energy relative to non-MHD flows. On the other hand, the magnetic energy E b shows the opposite trend, being rapidly driven from its initial values to essentially zero very early in the transient at lower Re values, while higher Re values significantly retard this decay. An enhancement of density fluctuations is noted in the intermediate Re range. An interesting observation pertaining to the normalized cross helicity is the fast decay to zero of this quantity when Re ϭ1, independent of the values of and f. That is, the fluctuating u and b fields tend to be uncorrelated when the magnetic Reynolds number is low. In this case, the role of the magnetic field is passive, and it is merely convected by the velocity field. The conditions required to maintain a high correlation during the evolution are discussed. We have also seen that the E b decay mode is less sensitive to the value of than that of E k. The relative contribution of E k , E b , and the internal energy E i to the total energy E t is discussed in relation to the values of f, , and Re .

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Section: Resultsmentioning

confidence: 91%

Section: Case Studiesmentioning

confidence: 99%

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Magnetic Reynolds number effects in compressible magnetohydrodynamic turbulence

Ladeinde

Gaitonde

2004

Physics of Fluids

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“…An exponential initial growth curve is overplotted for both patterns. Ladeinde & Wu (2002). Table 3 shows the maximum amplitude, H max , of all five instabilities.…”

Section: Characteristics Of Kelvin-helmholtz Instabilitiesmentioning

confidence: 98%

Interfacial waves in two-layer exchange flows downslope of a bottom sill

Fouli

Zhu

2011

J. Fluid Mech.

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An experimental study was conducted to examine the interfacial waves in twolayer exchange flows downslope of a bottom sill. The objective of the study was to understand the generation mechanisms of different interfacial waves and the generation conditions and development of Kelvin-Helmholtz (KH) instabilities in spatially varying flow field. During the flow regime of the steady maximal exchange, low-frequency oscillation of the density interface above the sill crest was observed, which resulted in periodic piling and releasing of the lower-layer fluid. This lowfrequency oscillation led to the development of large-scale downslope waves that caused significant interfacial entrainment. The periodic time of those piling and releasing events was found to be inversely proportional to the square root of the reduced gravitational acceleration and to be related to the baroclinic forcing of the basin internal seiching. During late sub-maximal exchange, regular and frequent KH instabilities were generated at the interface down the slope at bulk Richardson number of approximately 0.07-0.21, which is considerably larger than previous theoretical predictions for parallel flows with a sharp density interface. Two different growth patterns of those KH instabilities were observed. Measurements of their initial growth rate and the wavelength were also obtained and compared to the theoretical predictions.

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“…Planché and Reynolds 25 observe that heating favor the outer instability modes in linear, small-amplitude disturbance theory. The linear stability studies in Ref [24] were extended to the nonlinear case by Ladeinde and Wu, 26 whereby second-order nonlinear spatial stability to the three-dimensional perturbation waves is analyzed by expanding the perturbations into amplitude-dependent harmonic waves and truncating the Landau equation to the second term. Ragab and Wu 27 examine the viscous and inviscid stability, from which they conclude that the disturbance could be calculated accurately from the inviscid theory if the Reynolds number was greater than 1000.…”

Section: Theoretical Foundationmentioning

confidence: 99%

A Critical Review of Scramjet Combustion Simulation (Invited)

Ladeinde

2009

47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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A review of scramjet combustion simulation is provided in this paper. The topics covered include the fundamental problem of supersonic mixing layers, high-speed combustion modeling efforts, and actual calculations of realistic scramjet combustors. The review shows that the RANS approach dominates the turbulence modeling of the system, with only a handful of LES work. Also, virtually all the numerical works are based on low-order schemes, and the combustion models that have been used for realistic simulations solve the species evolution equations with assumed PDF closures, although there seems to be a growing use of the flamelet methods. Spray modeling for scramjet combustion has not received enough attention.2 for high-speed combustion applications, emphasizing on the salient features and shortcomings of the averaged equation set. Some of the models in Ref [1] have been implemented in VULCAN, a widely-used, multi-grid, fluxdifference-split, finite-volume code, developed by the Air Force and NASA for high-speed (ramjet, scramjet) reacting flow simulation. The precise models and solution procedure in this code are documented in White and Morrison. 2 Tishkoff et al. 3 presents the state of supersonic combustion research, including modeling and simulation, as an outcome of a joint AFRL/NASA meeting in May of 1996, in which the state-of-the-art in hydrocarbon and/or hydrogen-fueled scramjet research was examined, with suggestions for the future direction and needs of basic research in support of scramjet technology.Other relevant reviews, albeit applicable mostly to low-speed combustion, include Givi, 4 who provides a review of the state-of-the-art in subgrid scale modeling as required for large-eddy simulation (LES) of turbulent combustion. Closure complexities caused by chemical reactions are the focus, while Givi 5 presents a review devoted primarily to subgrid scale (SGS) closure based on the filtered density function (FDF), which is a method that is analogous to the probability density function (PDF) modeling. A more recent review of the FDF method is provided in Ref [6]. Heinz 7 highlights the fundamental differences between the Reynolds-averaged Navier-Stokes (RANS) and LES combustion models for premixed and non-premixed turbulent combustion.Finally, Grinstein 8 addresses modeling issues relevant to CFD of turbulent non-premixed jet flames, including subgrid and supergrid modeling. Transitional jet diffusion flames of the hydrogen/air and propane/air types are reviewed, while the jets studied involve laminar initial conditions, preferential diffusion effects, weak axial forcing, negligible streamwise vorticity, and negligible azimuthal non-uniformities, as well as the impact of aspect ratiodependent vortex topological and dynamical features on the development of the jet diffusion flame. Models for turbulence, chemical reactions, volume expansion, and heat release are discussed, as are models for the dominant features of the couplings between the various phenomena.Unlike the foregoing reviews, which either did n...

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Second order nonlinear spatial stability analysis of compressible mixing layers

Cited by 7 publications

References 32 publications

Magnetic Reynolds number effects in compressible magnetohydrodynamic turbulence

Magnetic Reynolds number effects in compressible magnetohydrodynamic turbulence

Interfacial waves in two-layer exchange flows downslope of a bottom sill

A Critical Review of Scramjet Combustion Simulation (Invited)

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