Resolvent-based modeling of turbulent jet noise

Pickering, Ethan; Towne, Aaron; Jordan, Peter; Colonius, Tim

doi:10.1121/10.0006453

Cited by 26 publications

(19 citation statements)

References 36 publications

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“…Within the linearized equation, we use a turbulent Reynolds number of Re T = 1760, three orders of magnitude less than the true Reynolds number. This choice is motivated by recent work showing that using an eddy-viscosity model or reduced effective Reynolds number improves both the near-field (Pickering et al 2021a) and far-field (Pickering et al 2021b) predictions in free-shear flows.…”

Section: Dipole Forcing Of a Quiescent Fluidmentioning

confidence: 99%

Efficient global resolvent analysis via the one-way Navier–Stokes equations

et al. 2022

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Resolvent analysis is a powerful tool for modelling and analysing transitional and turbulent flows and, in particular, for approximating coherent flow structures. Despite recent algorithmic advances, computing resolvent modes for flows with more than one inhomogeneous spatial coordinate remains computationally expensive. In this paper we show how efficient and accurate approximations of resolvent modes can be obtained using a well-posed spatial marching method for flows that contain a slowly varying direction, i.e. one in which the mean flow changes gradually. First, we derive a well-posed and convergent one-way equation describing the downstream-travelling waves supported by the linearized Navier–Stokes equations. The method is based on a projection operator that isolates downstream-travelling waves. Integrating these one-way Navier–Stokes (OWNS) equations in the slowly varying direction, which requires significantly less CPU and memory resources than a direct solution of the linearized Navier–Stokes equations, approximates the action of the resolvent operator on a forcing vector. Second, this capability is leveraged to compute approximate resolvent modes using an adjoint-based optimization framework in which the forward and adjoint OWNS equations are marched in the downstream and upstream directions, respectively. This avoids the need to solve direct and adjoint globally discretized equations, therefore bypassing the main computational bottleneck of a typical global resolvent calculation. The method is demonstrated using the examples of a simple acoustics problem, a Mach 1.5 turbulent jet and a Mach 4.5 transitional zero-pressure-gradient flat-plate boundary layer. The optimal OWNS results are validated against corresponding global calculations, and the close agreement demonstrates the near-parabolic nature of these flows.

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Section: Dipole Forcing Of a Quiescent Fluidmentioning

confidence: 99%

Efficient global resolvent analysis via the one-way Navier–Stokes equations

et al. 2022

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“…Here, Orr modes, which are sensitive to the forcing, dominate [18,20]. This mismatch, which extends to higher frequencies at higher azimuthal wavenumbers due to the appearance of streaks [19,20], has motivated the investigation of improved forcing models for resolvent analysis of the jet based on analysis of the LES data [35,36], sparse sampling strategies [37,38], and eddy viscosity models [39].…”

Section: Modeling Coherent Structures Via Spectral Pod and Resolvent ...mentioning

confidence: 99%

A Database for Reduced-Complexity Modeling of Fluid Flows

Towne¹,

Dawson²,

Brès³

et al. 2022

Preprint

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We present a publicly accessible database designed to aid in the conception, training, demonstration, evaluation, and comparison of reduced-complexity models for fluid mechanics. Availability of high-quality flow data is essential for all of these aspects of model development for both data-driven and physics-based methods. The database contains time-resolved data for six distinct datasets: a large eddy simulation of a turbulent jet, direct numerical simulations of a zero-pressure-gradient turbulent boundary layer, particle-image-velocimetry measurements for the same boundary layer at several Reynolds numbers, direct numerical simulations of laminar stationary and pitching flat-plate airfoils, particle-image-velocimetry and force measurements of an airfoil encountering a gust, and a large eddy simulation of the separated, turbulent flow over an airfoil. These six cases span several key flow categories: laminar and turbulent, statistically stationary and transient, tonal and broadband spectral content, canonical and application-oriented, wall-bounded and free-shear flow, and simulation and experimental measurements. For each dataset, we describe the flow setup and computational/experimental methods, catalog the data available in the database, and provide examples of how these data can be used for reduced-complexity modeling. All data can be downloaded using a browser interface or Globus. Our vision is that the common testbed provided by this database will aid the fluid mechanics community in clarifying the distinct capabilities of new and existing methods.for reduced-complexity modeling. Finally, in §VIII we conclude the paper with a brief recap of the database and a discussion of our vision for its future applications and extensions. II. Turbulent jet large eddy simulationThe first flow included in the database is a turbulent jet. A jet is a canonical example of a free shear flow, i.e., a flow containing mean velocity gradients but unaffected by walls. Despite the geometrical simplicity of a jet -consisting of a fast inner stream that mixes with a slow outer stream -turbulent jets contain a diverse set of physics. Large-scale coherent structures created by the Kelvin-Helmholtz instability of the annular shear layer, along with their emitted acoustic radiation, have been studied continuously since the 1960s with increasingly sophisticated tools [16,17]. More recently, the important role of other physical mechanisms, including the Orr mechanism [18], streaks generated by the lift-up effect [19,20], and acoustic waves trapped within the core of the jet [21], have been identified and explored. This diverse, coexisting set of physics makes a turbulent jet an excellent testbed for reduced-complexity models. The available dataset contains 10,000 time-resolved snapshots of the jet computed via LES and other quantities derived from these data. A. SetupThis dataset corresponds to an subsonic turbulent jet issued from a contoured convergent-straight nozzle [22]. The jet Mach number is 𝑀 𝑗 = 𝑈 𝑗 /𝑐 𝑗 = 0.9 and the jet is isot...

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“…Following Schmidt et al [5], we use a turbulent Reynolds number of Re T = 30000 within the linearized equations. This choice is motivated by recent work showing that using an eddy-viscosity model or reduced effective Reynolds number within linear models improves both near-field [46] and far-field [47] predictions in free-shear flows.…”

Section: Turbulent Jetmentioning

confidence: 99%

Recursive one-way Navier Stokes equations with PSE-like cost

Zhu¹,

Towne²

2021

Preprint

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Spatial marching methods, in which the flow state is spatially evolved in the downstream direction, can be used to produce low-cost models of flows containing a slowly varying direction, such as mixing layers, jets, and boundary layers. The parabolized stability equations (PSE) are popular due to their extremely low cost but can only capture a single instability mode; all other modes are damped or distorted by regularization methods required to stabilize the spatial march, precluding PSE from properly capturing non-modal behavior, acoustics, and interactions between multiple instability mechanisms. The one-way Navier-Stokes (OWNS) equations properly retain all downstream-traveling modes at a cost that is a fraction of that of global methods but still one to two orders of magnitude higher than PSE. In this paper, we introduce a new variant of OWNS whose cost, both in terms of CPU time and memory requirements, approaches that of PSE while still properly capturing the contributions of all downstream-traveling modes. The method is formulated in terms of a projection operator that eliminates upstream-traveling modes. Unlike previous OWNS variants, the action of this operator on a vector can be efficiently approximated using a series of equations that can be solved recursively, i.e., successively one after the next, rather than as a coupled set. In addition to highlighting the improved cost scaling of our method, we derive explicit error expressions and elucidate the relationship with previous OWNS variants. The properties, efficiency, and accuracy of our method are demonstrated for both free-shear and wall-bounded flows.

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Resolvent-based modeling of turbulent jet noise

Cited by 26 publications

References 36 publications

Efficient global resolvent analysis via the one-way Navier–Stokes equations

Efficient global resolvent analysis via the one-way Navier–Stokes equations

A Database for Reduced-Complexity Modeling of Fluid Flows

Recursive one-way Navier Stokes equations with PSE-like cost

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