Determining Sources of Unsteady Energy Transfer in Time-Accurate Computational Fluid Dynamics

Jacob, Eric J.; Batterson, Joshua W.

doi:10.2514/1.b35215

Cited by 5 publications

(6 citation statements)

References 25 publications

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“…Both the increased injection velocity and its companion vorticity seem to magnify the damping rate as the flow speed is increased. At this point, it is useful to note that while former studies have invariably considered flow turning to be an acoustic damping mechanism, 34,42,66 recent work by Batterson 17 and Jacob and Batterson 58 have shown multiple cases where flow turning can appear as an acoustic driving mechanism, although its overall effect remains less appreciable than other energy pathways.…”

Section: A Flow Turningmentioning

confidence: 97%

“…A more complete listing of energy transfer pathways and a discussion of their physical contexts is found in a study by Jacob and Batterson. 58 American Institute of Aeronautics and Astronautics…”

Section: Quantifying Unsteady Energy Transfermentioning

confidence: 99%

“…58 Accordingly, pathways facilitating the transfer of energy between the mean flow and the unsteady field can be quantified by:…”

Section: Quantifying Unsteady Energy Transfermentioning

confidence: 99%

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Transverse Vortico-Acoustic Waves in the Presence of Strong Mean Flow Shear Layers

Kovacic¹,

Batterson²,

Majdalani³

2015

51st AIAA/SAE/ASEE Joint Propulsion Conference

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Several analytical models describing the formation of resonant waves in simple geometric configurations are available in the open literature. Their solutions are predicated on several limiting assumptions, namely, that the mean flow velocity is uniform and that the wall injection Mach number is sufficiently small to justify asymptotic reductions to the governing equations. When considering acoustic waves in a convecting medium where 1 M  , the effect of mean flow motion appears at 2 ( ) M which, from an asymptotic standpoint, represents a higher-order correction that is traditionally dismissed with no afterthought. Naturally, the ensuing truncation leads to a simple Helmholtz-type wave equation. In practice though, the influence of the mean flow appears at leading order when accounting for acoustic boundary layers. Acoustic boundary layers, when strongly coupled with the mean flow, give rise to the so-called vorticity (or vortical) waves. When combined with the acoustic wave motion, the resulting pair constitutes what is typically referred to as a vortico-acoustic wave. By strictly enforcing the 1 M  condition, analytical solutions can be recovered for vortico-acoustic waves in simple planar and axisymmetric chambers. The present study focuses on a numerical approach that resolves the unsteady field equations computationally for the threefold purpose of verifying existing analytical solutions, providing practical bounds for their applicability, and extending their predictive capabilities to more complex configurations. In particular, the interaction between acoustic waves and a strong mean flow shear layer is investigated by computationally resolving the vortico-acoustic field developing behind a backward facing step. In this context, deviations from the analytical solutions are reported both at high injection Mach numbers and when considering the emergence of acoustically-synchronized vortex cells around a shear layer. These vortex cells exhibit a spatial instability that continues to grow as the flow is further accelerated. Lastly, the temporal stability of the flow is quantified by computing the rate of energy transfer into the unsteady field. Similarly to the spatial instability, the increased vorticity at higher injection velocities tends to drive temporal instability as well. Nomenclature a = chamber radius or half-height [m] s a = speed of sound [m/s] j = mode number M = injection Mach number, / inj s U a p = pressure [Pa] R = specific gas constant [J/kg-K] j R = pressure amplitude for mode j [Pa] r = spatial coordinate, , , r z  T = temperature [K] inj U = injection velocity [m/s] u = velocity vector [m/s] j u = velocity associated with mode j [m/s] Symbols  = acoustic velocity potential [m 2 /s]  = dynamic viscosity [N-m/s]  = density [kg/m 3 ] Ω = steady vorticity [1/s] ω = unsteady vorticity [1/s] j  = circular frequency of mode j [rad/s] Superscripts and Subscripts 0 = denotes a mean flow variable 1= denotes an unsteady flow variable , , m n l = denotes the tangential, radial, and axial acoust...

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Section: A Flow Turningmentioning

confidence: 97%

Section: Quantifying Unsteady Energy Transfermentioning

confidence: 99%

See 1 more Smart Citation

Transverse Vortico-Acoustic Waves in the Presence of Strong Mean Flow Shear Layers

Kovacic¹,

Batterson²,

Majdalani³

2015

51st AIAA/SAE/ASEE Joint Propulsion Conference

Self Cite

View full text Add to dashboard Cite

show abstract

“…Jacob and Batterson [43] created a theory based on the premise of instability manifesting as periodic behavior such as acoustic resonance or hydrodynamic vortex shedding. Their approach is based on decomposing the flow-field into a steady and unsteady modal fluctuation.…”

Section: Introductionmentioning

confidence: 99%

“…Their approach is based on decomposing the flow-field into a steady and unsteady modal fluctuation. Jacob and Batterson [43] argue that there is a modified Rayleigh criterion (see their Equation ( 26)). A puzzling aspect of the work of Jacob and Batterson [43], and works similar that have come before, resides in the fact that all acoustic energy radiates into modes of the geometric acoustic field.…”

Section: Introductionmentioning

confidence: 99%

Analytical Equations for Thermoacoustic Instability Sources and Acoustic Radiation from Reacting Turbulence

Miller

2020

International Journal of Aerospace Engineering

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We seek to ascertain and understand source terms that drive thermoacoustic instability and acoustic radiation. We present a new theory based on the decomposition of the Navier-Stokes equations coupled with the mass fraction equations. A series of solutions are presented via the method of the vector Green’s function. We identify both combustion-combustion and combustion-aerodynamic interaction source terms. Both classical combustion noise theory and classical Rayleigh criterion are recovered from the presently developed more general theory. An analytical spectral prediction method is presented, and the two-point source terms are consistent with Lord Rayleigh’s instability model. Particular correlations correspond to the source terms of Lighthill, which represent the noise from turbulence and additional terms for the noise from reacting flow.

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Parallel Calculation of Random Vibration for Reentry Vehicles in Fluctuating Pressure Environment

Fan

Liang

Wang

et al. 2021

Shock and Vibration

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The reentry vehicle is in an unconstrained free-flight state during the reentry process. The pressure of air fluctuations acts on the external surface of the vehicle and induces a random vibration environment with a wide-frequency range, which makes great influences on the structural dynamic properties of vehicles. This paper aims at the parallel calculation of the wide-frequency random vibration problems for the free body under multipoint fluctuating pressure loads. The calculation method is based on the self-developed JAUMIN framework and PANDA platform. The novel algorithm based on the modal superposition method reduces the computational complexity, realizes the parallel calculation, and achieves the maximum numerical simulation calculation capacity of 1.045 billion degrees of freedom (DOFs) while improving the calculation efficiency and the accuracy of the results. Finally, this article also uses typical examples to verify the correctness and parallel scalability of algorithms and programs.

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Determining Sources of Unsteady Energy Transfer in Time-Accurate Computational Fluid Dynamics

Cited by 5 publications

References 25 publications

Transverse Vortico-Acoustic Waves in the Presence of Strong Mean Flow Shear Layers

Transverse Vortico-Acoustic Waves in the Presence of Strong Mean Flow Shear Layers

Analytical Equations for Thermoacoustic Instability Sources and Acoustic Radiation from Reacting Turbulence

Parallel Calculation of Random Vibration for Reentry Vehicles in Fluctuating Pressure Environment

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