scholarly journals Sensitivity of wavepackets in jets to nonlinear effects: the role of the critical layer

2016 ◽  
Vol 811 ◽  
pp. 95-137 ◽  
Author(s):  
Gilles Tissot ◽  
Mengqi Zhang ◽  
Francisco C. Lajús ◽  
André V. G. Cavalieri ◽  
Peter Jordan
Keyword(s):  
Linear Models ◽  
Nonlinear Effects ◽  
Turbulent Jets ◽  
Building Blocks ◽  
Linear Instability ◽  
Critical Layer ◽  
Potential Core ◽  
Instability Waves ◽  
Reduced Order ◽  
Modelling Framework

Linear instability waves, or wavepackets, are key building blocks for the jet-noise problem. It has been shown in previous work that linear models correctly predict the evolution of axisymmetric wavepackets up to the end of the potential core of subsonic turbulent jets. Beyond this station, linear models fail, and nonlinearity is the likely missing piece. The essential underlying nonlinear mechanisms are unknown, and it remains unclear how these should be incorporated in a reduced-order model. The nonlinear interactions are considered in this work as an ‘external’ harmonic forcing added to the standard linear model. This modelling framework is explored using a locally parallel resolvent analysis to determine optimal forcing and associated responses, and a global approach based on 4D-Var data assimilation aimed at finding the optimal forcing of the parabolised stability equations that would minimise errors in the predictions of wavepackets. In all of the problems considered, the critical layer is found to be relevant: it is the position where sensitivity of wavepackets to nonlinearity is greatest. It is seen that disturbances are forced around the critical layer, and tilted by shear as they are advected, in a manner suggestive of an Orr-like mechanism. The ensemble of results suggests that critical-layer effects play a central role in the dynamics of wavepackets in subsonic turbulent jets, and that inclusion of such effects may remedy the shortcomings of linear reduced-order models.

Interaction of oblique instability waves with a nonlinear plane wave

1994 ◽  
Vol 264 ◽  
pp. 343-372 ◽  
Author(s):  
David W. Wundrow ◽  
Lennart S. Hultgren ◽  
M. E. Goldstein
Keyword(s):  
Growth Rate ◽  
Parametric Resonance ◽  
Wave Interaction ◽  
Adverse Pressure Gradient ◽  
Linear Instability ◽  
Critical Layer ◽  
Spanwise Direction ◽  
Instability Waves ◽  
Resonance Effects ◽  
Nonlinear Plane

This paper is concerned with the downstream evolution of a resonant triad of initially non-interacting linear instability waves in a boundary layer with a weak adverse pressure gradient. The triad consists of a two-dimensional fundamental mode and a pair of equal-amplitude oblique modes that form a subharmonic standing wave in the spanwise direction. The growth rates are small and there is a well-defined common critical layer for these waves. As in Goldstein & Lee (1992), the wave interaction takes place entirely within this critical layer and is initially of the parametric-resonance type. This enhances the spatial growth rate of the subharmonic but does not affect that of the fundamental. However, in contrast to Goldstein & Lee (1992), the initial subharmonic amplitude is assumed to be small enough so that the fundamental can become nonlinear within its own critical layer before it is affected by the subharmonic. The subharmonic evolution is then dominated by the parametric-resonance effects and occurs on a much shorter streamwise scale than that of the fundamental. The subharmonic amplitude continues to increase during this parametric-resonance stage – even as the growth rate of the fundamental approaches zero – and the subharmonic eventually becomes large enough to influence the fundamental which causes both waves to evolve on the same shorter streamwise scale.

The role of nonlinear critical layers in boundary layer transition

1995 ◽  
Vol 352 (1700) ◽  
pp. 425-442 ◽  
Keyword(s):  
Asymptotic Methods ◽  
Nonlinear Effects ◽  
Boundary Layer Transition ◽  
Critical Layer ◽  
Mean Flow ◽  
Layer Transition ◽  
Instability Waves ◽  
Laminar Boundary Layers ◽  
Instability Modes ◽  
Critical Layers

Asymptotic methods are used to describe the nonlinear self-interaction between pairs of oblique instability modes that eventually develops when initially linear spatially growing instability waves evolve downstream in nominally two-dimensional laminar boundary layers. The first nonlinear reaction takes place locally within a so-called ‘critical layer’, with the flow outside this layer consisting of a locally parallel mean flow plus a pair of oblique instability waves - which may or may not be accompanied by an associated plane wave. The amplitudes of these waves, which are completely determined by nonlinear effects within the critical layer, satisfy either a single integro-differential equation or a pair of integro-differential equations with quadratic to quartic-type nonlinearities. The physical implications of these equations are discussed.

On the growth and propagation of linear instability waves in compressible turbulent jets

2009 ◽  
Vol 21 (5) ◽  
pp. 054106 ◽  
Author(s):  
Prasun K. Ray ◽  
Lawrence C. Cheung ◽  
Sanjiva K. Lele
Keyword(s):  
Turbulent Jets ◽  
Linear Instability ◽  
Instability Waves

scholarly journals A coherence-matched linear source mechanism for subsonic jet noise

2015 ◽  
Vol 776 ◽  
pp. 235-267 ◽  
Author(s):  
Yamin B. Baqui ◽  
Anurag Agarwal ◽  
André V. G. Cavalieri ◽  
Samuel Sinayoko
Keyword(s):  
Linear Models ◽  
Hydrodynamic Instability ◽  
Near Field ◽  
Jet Noise ◽  
Turbulent Jets ◽  
Single Frequency ◽  
Linear Wave ◽  
Far Field ◽  
Potential Core ◽  
Subsonic Jet

We investigate source mechanisms for subsonic jet noise using experimentally obtained datasets of high-Reynolds-number Mach 0.4 and 0.6 turbulent jets. The focus is on the axisymmetric mode which dominates downstream sound radiation for low polar angles and the frequency range at which peak noise occurs. A linearized Euler equation (LEE) solver with an inflow boundary condition is used to generate single-frequency hydrodynamic instability waves, and the resulting near-field fluctuations and far-field acoustics are compared with those from experiments and linear parabolized stability equation (LPSE) computations. It is found that the near-field velocity fluctuations closely agree with experiments and LPSE computations up to the end of the potential core, downstream of which deviations occur, but the LEE results match experiments better than the LPSE results. Both the near-field wavepackets and the sound field are observed directly from LEE computations, but the far-field sound pressure levels (SPLs) obtained are more than an order of magnitude lower than experimental values despite close statistical agreement of the near hydrodynamic field up to the potential core region. We explore the possibility that this discrepancy is due to the mismatch between the decay of two-point coherence with increasing distance in experimental flow fluctuations and the perfect coherence in linear models. To match the near-field coherence, experimentally obtained coherence profiles are imposed on the two-point cross-spectral density (CSD) at cylindrical and conical surfaces that enclose near-field structures generated with LEEs. The surface pressure is propagated to the far field using boundary value formulations based on the linear wave equation. Coherence matching yields far-field SPLs which show improved agreement with experimental results, indicating that coherence decay is the main missing component in linear models. The CSD on the enclosing surfaces reveals that the application of a decaying coherence profile spreads the hydrodynamic component of the linear wavepacket source on to acoustic wavenumbers, resulting in a more efficient acoustic source.

scholarly journals Active control of liquid film flows: beyond reduced-order models

2021 ◽  
Vol 104 (1) ◽  
pp. 267-287
Author(s):  
Radu Cimpeanu ◽  
Susana N. Gomes ◽  
Demetrios T. Papageorgiou
Keyword(s):  
Liquid Film ◽  
Information Transfer ◽  
Analytical Models ◽  
Feedback Controls ◽  
Reduced Order ◽  
Modelling Framework ◽  
Theoretical Approaches ◽  
Active Feedback ◽  
Feedback Strategies ◽  
Set Up

AbstractThe ability to robustly and efficiently control the dynamics of nonlinear systems lies at the heart of many current technological challenges, ranging from drug delivery systems to ensuring flight safety. Most such scenarios are too complex to tackle directly, and reduced-order modelling is used in order to create viable representations of the target systems. The simplified setting allows for the development of rigorous control theoretical approaches, but the propagation of their effects back up the hierarchy and into real-world systems remains a significant challenge. Using the canonical set-up of a liquid film falling down an inclined plane under the action of active feedback controls in the form of blowing and suction, we develop a multi-level modelling framework containing both analytical models and direct numerical simulations acting as an in silico experimental platform. Constructing strategies at the inexpensive lower levels in the hierarchy, we find that offline control transfer is not viable; however, analytically informed feedback strategies show excellent potential, even far beyond the anticipated range of applicability of the models. The detailed effects of the controls in terms of stability and treatment of nonlinearity are examined in detail in order to gain understanding of the information transfer inside the flows, which can aid transition towards other control-rich frameworks and applications.

Numerical Study of the Mean and Filtered Characteristics of Turbulent Jets Impinging on Convex and Flat Surfaces Using LES

2012 ◽  
Author(s):  
Adra Benhacine ◽  
Zoubir Nemouchi ◽  
Lyes Khezzar ◽  
Nabil Kharoua
Keyword(s):  
Convex Surface ◽  
Numerical Study ◽  
Three Dimensional ◽  
Turbulent Jets ◽  
Scale Model ◽  
Wall Jet ◽  
Potential Core ◽  
Flat Surfaces ◽  
Free Jet ◽  
Eddy Simulation

A numerical study of a turbulent plane jet impinging on a convex surface and on a flat surface is presented, using the large eddy simulation approach and the Smagorinski-Lilly sub-grid-scale model. The effects of the wall curvature on the unsteady filtered, and the steady mean, parameters characterizing the dynamics of the wall jet are addressed in particular. In the free jet upstream of the impingement region, significant and fairly ordered velocity fluctuations, that are not turbulent in nature, are observed inside the potential core. Kelvin-Helmholtz instabilities in the shear layer between the jet and the surrounding air are detected in the form of wavy sheets of vorticity. Rolled up vortices are detached from these sheets in a more or less periodic manner, evolving into distorted three dimensional structures. Along the wall jet the Coanda effect causes a marked suction along the convex surface compared with the flat one. As a result, relatively important tangential velocities and a stretching of sporadic streamwise vortices are observed, leading to friction coefficient values on the curved wall higher than those on the flat wall.

scholarly journals An evaluation of linear instability waves as sources of sound in a supersonic turbulent jet

2002 ◽  
Vol 14 (10) ◽  
pp. 3593-3600 ◽  
Author(s):  
Kamran Mohseni ◽  
Tim Colonius ◽  
Jonathan B. Freund
Keyword(s):  
Linear Instability ◽  
Turbulent Jet ◽  
Instability Waves

Active control of instability waves in excited and nonexcited turbulent jets

2017 ◽  
Author(s):  
Victor Kopiev ◽  
Georgy Faranosov ◽  
Oleg Bychkov ◽  
Mikhail Zaytsev ◽  
Vladimir Kopiev ◽  
...  
Keyword(s):  
Active Control ◽  
Turbulent Jets ◽  
Instability Waves

Global scale hydrological modelling at 100 m, 1 h resolution, in Python

2021 ◽  
Author(s):  
Kor de Jong ◽  
Marc van Kreveld ◽  
Debabrata Panja ◽  
Oliver Schmitz ◽  
Derek Karssenberg
Keyword(s):  
Large Scale ◽  
Model Building ◽  
Flow Direction ◽  
Building Blocks ◽  
Global Scale ◽  
Data Availability ◽  
Hydrological Models ◽  
Continental Scale ◽  
Modelling Framework ◽  
Scale Models

<p>Data availability at global scale is increasing exponentially. Although considerable challenges remain regarding the identification of model structure and parameters of continental scale hydrological models, we will soon reach the situation that global scale models could be defined at very high resolutions close to 100 m or less. One of the key challenges is how to make simulations of these ultra-high resolution models tractable ([1]).</p><p>Our research contributes by the development of a model building framework that is specifically designed to distribute calculations over multiple cluster nodes. This framework enables domain experts like hydrologists to develop their own large scale models, using a scripting language like Python, without the need to acquire the skills to develop low-level computer code for parallel and distributed computing.</p><p>We present the design and implementation of this software framework and illustrate its use with a prototype 100 m, 1 h continental scale hydrological model. Our modelling framework ensures that any model built with it is parallelized. This is made possible by providing the model builder with a set of building blocks of models, which are coded in such a manner that parallelization of calculations occurs within and across these building blocks, for any combination of building blocks. There is thus full flexibility on the side of the modeller, without losing performance.</p><p>This breakthrough is made possible by applying a novel approach to the implementation of the model building framework, called asynchronous many-tasks, provided by the HPX C++ software library ([3]). The code in the model building framework expresses spatial operations as large collections of interdependent tasks that can be executed efficiently on individual laptops as well as computer clusters ([2]). Our framework currently includes the most essential operations for building large scale hydrological models, including those for simulating transport of material through a flow direction network. By combining these operations, we rebuilt an existing 100 m, 1 h resolution model, thus far used for simulations of small catchments, requiring limited coding as we only had to replace the computational back end of the existing model. Runs at continental scale on a computer cluster show acceptable strong and weak scaling providing a strong indication that global simulations at this resolution will soon be possible, technically speaking.</p><p>Future work will focus on extending the set of modelling operations and adding scalable I/O, after which existing models that are currently limited in their ability to use the computational resources available to them can be ported to this new environment.</p><p>More information about our modelling framework is at https://lue.computationalgeography.org.</p><p><strong>References</strong></p><p>[1] M. Bierkens. Global hydrology 2015: State, trends, and directions. Water Resources Research, 51(7):4923–4947, 2015.<br>[2] K. de Jong, et al. An environmental modelling framework based on asynchronous many-tasks: scalability and usability. Submitted.<br>[3] H. Kaiser, et al. HPX - The C++ standard library for parallelism and concurrency. Journal of Open Source Software, 5(53):2352, 2020.</p>

A Physics-Based Dynamic Model for Boilers: Part 2 — Model Reduction in a Cogeneration Application

2017 ◽  
Author(s):  
Matthew J. Blom ◽  
Michael J. Brear ◽  
Chris G. Manzie ◽  
Ashley P. Wiese
Keyword(s):  
Model Reduction ◽  
Gas Turbine ◽  
Dynamic Model ◽  
Reduction Process ◽  
Singular Perturbation Theory ◽  
Reduced Order Models ◽  
Reduced Order ◽  
One Dimensional ◽  
Time Scale Separation ◽  
Modelling Framework

This paper is the second part of a two part study that develops, validates and integrates a one-dimensional, physics-based, dynamic boiler model. Part 1 of this study [1] extended and validated a particular modelling framework to boilers. This paper uses this framework to first present a higher order model of a gas turbine based cogeneration plant. The significant dynamics of the cogeneration system are then identified, corresponding to states in the gas path, the steam path, the gas turbine shaft, gas turbine wall temperatures and boiler wall temperatures. A model reduction process based on time scale separation and singular perturbation theory is then demonstrated. Three candidate reduced order models are identified using this model reduction process, and the simplest, acceptable dynamic model of this integrated plant is found to require retention of both the gas turbine and boiler wall temperature dynamics. Subsequent analysis of computation times for the original physics-based one-dimensional model and the candidate, reduced order models demonstrates that significantly faster than real time simulation is possible in all cases. Furthermore, with systematic replacement of the algebraic states with feedforward maps in the reduced order models, further computational savings of up to one order of magnitude can be achieved. This combination of model fidelity and computational tractability suggest suggests that the resulting reduced order models may be suitable for use in model based control of cogeneration plants.

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