Feedback control of weakly nonlinear Rayleigh–Bénard–Marangoni convection

2001 ◽  
Vol 440 ◽  
pp. 27-47 ◽  
Author(s):  
A. C. OR ◽  
R. E. KELLY
Keyword(s):  
Feedback Control ◽  
Nonlinear Flow ◽  
Control Action ◽  
Control Analysis ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
Wide Range ◽  
Nonlinear Control Processes ◽  
Gas Layer ◽  
Rayleigh Benard

We study the effect of proportional feedback control on the onset and development of finite-wavelength Rayleigh–Bénard–Marangoni (RBM) convection using weakly nonlinear theory as applied to Nield's model, which includes both thermocapillarity and buoyancy but ignores deformation of the free surface. A two-layer model configuration is used, which has a purely conducting gas layer on top of the liquid. In the feedback control analysis, a control action in the form of temperature or heat flux is considered. Both measurement and control action are assumed to be continuous in space and time. Besides demonstrating that stabilization of the basic state can be achieved on a linear basis, the results also indicate that a wide range of weakly nonlinear flow properties can also be altered by the linear and nonlinear control processes used here. These include changing the nature of hexagonal convection and the amount of subcritical hysteresis associated with subcritical bifurcation.

The effects of boundary imperfections on convection in a saturated porous layer: near-resonant wavelength excitation

1989 ◽  
Vol 199 ◽  
pp. 133-154 ◽  
Author(s):  
D. A. S. Rees ◽  
D. S. Riley
Keyword(s):  
Porous Layer ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
Resonant Forcing ◽  
Saturated Porous Layer ◽  
The Stability ◽  
Spatially Varying ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Complementary Study

Weakly nonlinear theory is used to study the porous-medium analogue of the classical Rayleigh-Bénard problem, i.e. Lapwood convection in a saturated porous layer heated from below. Two particular aspects of the problem are focused upon: (i) the effect of thermal imperfections on the stability characteristics of steady rolls near onset; and (ii) the evolution of unstable rolls.For Rayleigh-Bénard convection it is well known (see Busse and co-workers 1974, 1979, 1986) that the stability of steady two-dimensional rolls near onset is limited by the presence of cross-roll, zigzag and sideband disturbances; this is shown to be true also in Lapwood convection. We further determine the modifications to the stability boundaries when small-amplitude imperfections in the boundary temperatures are present. In practice imperfections would usually consist of broadband thermal noise, but it is the Fourier component with wavenumber close to the critical wavenumber for the perfect problem (i.e. in the absence of imperfections) which, when present, has the greatest effect due to resonant forcing. This particular case is the sole concern of the present paper; other resonances are considered in a complementary study (Rees & Riley 1989).For the case when the modulations on the upper and lower boundaries are in phase, asymptotic analysis and a spectral method are used to determine the stability of roll solutions and to calculate the evolution of the unstable flows. It is shown that steady rolls with spatially deformed axes or spatially varying wavenumbers evolve. The evolution of the flow that is unstable to sideband disturbances is also calculated when the modulations are π out of phase. Again rolls with a spatially varying wavenumber result.

scholarly journals Statistical State Dynamics of Weak Jets in Barotropic Beta-Plane Turbulence

2019 ◽  
Vol 76 (3) ◽  
pp. 919-945 ◽  
Author(s):  
Nikolaos A. Bakas ◽  
Navid C. Constantinou ◽  
Petros J. Ioannou
Keyword(s):  
Second Order ◽  
Homogeneous Turbulence ◽  
Nonlinear Flow ◽  
Flow Forming ◽  
Ginzburg Landau ◽  
Linear Flow ◽  
Weakly Nonlinear ◽  
Zonal Jets ◽  
Statistical State ◽  
Wide Range

Abstract Zonal jets in a barotropic setup emerge out of homogeneous turbulence through a flow-forming instability of the homogeneous turbulent state (zonostrophic instability), which occurs as the turbulence intensity increases. This has been demonstrated using the statistical state dynamics (SSD) framework with a closure at second order. Furthermore, it was shown that for small supercriticality the flow-forming instability follows Ginzburg–Landau (G–L) dynamics. Here, the SSD framework is used to study the equilibration of this flow-forming instability for small supercriticality. First, we compare the predictions of the weakly nonlinear G–L dynamics to the fully nonlinear SSD dynamics closed at second order for a wide range of parameters. A new branch of jet equilibria is revealed that is not contiguously connected with the G–L branch. This new branch at weak supercriticalities involves jets with larger amplitude compared to the ones of the G–L branch. Furthermore, this new branch continues even for subcritical values with respect to the linear flow-forming instability. Thus, a new nonlinear flow-forming instability out of homogeneous turbulence is revealed. Second, we investigate how both the linear flow-forming instability and the novel nonlinear flow-forming instability are equilibrated. We identify the physical processes underlying the jet equilibration as well as the types of eddies that contribute in each process. Third, we propose a modification of the diffusion coefficient of the G–L dynamics that is able to capture the evolution of weak jets at scales other than the marginal scale (side-band instabilities) for the linear flow-forming instability.

scholarly journals Experimental observation of the origin and structure of elastoinertial turbulence

2021 ◽  
Vol 118 (45) ◽  
pp. e2102350118
Author(s):  
George H. Choueiri ◽  
Jose M. Lopez ◽  
Atul Varshney ◽  
Sarath Sankar ◽  
Björn Hof
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Shear Layers ◽  
Viscoelastic Flows ◽  
Inertial Forces ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
Wide Range ◽  
Maximum Drag Reduction ◽  
Striking Contrast

Turbulence generally arises in shear flows if velocities and hence, inertial forces are sufficiently large. In striking contrast, viscoelastic fluids can exhibit disordered motion even at vanishing inertia. Intermediate between these cases, a state of chaotic motion, “elastoinertial turbulence” (EIT), has been observed in a narrow Reynolds number interval. We here determine the origin of EIT in experiments and show that characteristic EIT structures can be detected across an unexpectedly wide range of parameters. Close to onset, a pattern of chevron-shaped streaks emerges in qualitative agreement with linear and weakly nonlinear theory. However, in experiments, the dynamics remain weakly chaotic, and the instability can be traced to far lower Reynolds numbers than permitted by theory. For increasing inertia, the flow undergoes a transformation to a wall mode composed of inclined near-wall streaks and shear layers. This mode persists to what is known as the “maximum drag reduction limit,” and overall EIT is found to dominate viscoelastic flows across more than three orders of magnitude in Reynolds number.

The effects of boundary imperfections on convection in a saturated porous layer: non-resonant wavelength excitation

1989 ◽  
Vol 421 (1861) ◽  
pp. 303-339 ◽  
Keyword(s):  
Porous Layer ◽  
Three Dimensional ◽  
Resonant Interaction ◽  
Mean Values ◽  
Weakly Nonlinear ◽  
Special Cases ◽  
Wide Range ◽  
Saturated Porous Layer ◽  
Convection Patterns ◽  
Rayleigh Benard

The onset of Rayleigh-Bénard convection in a horizontally unbounded saturated porous layer is considered when the temperatures of both horizontal boundaries vary periodically in one direction about their respective mean values. Attention is focused on small-amplitude thermal modulations with a wavenumber not close to the critical value for the perfect layer. A stability analysis of weakly nonlinear convection is performed and the effects of different wavenumbers and symmetries of the thermal modulations are deduced systematically. It is shown that there are many special cases to be considered and that the convection patterns depend crucially on the particular configuration. Intuitively it might be expected that one-dimensional thermal modulation would always stimulate a two-dimensional motion. Surprisingly, however, for a wide range of modulation wavenumber a three-dimensional motion with a rectangular planform results from a resonant interaction between a pair of oblique rolls and the boundary forcing.

scholarly journals Portable near Infrared Spectroscopy as a Tool for Fresh Tomato Quality Control Analysis in the Field

2021 ◽  
Vol 11 (7) ◽  
pp. 3209
Author(s):  
Karla R. Borba ◽  
Didem P. Aykas ◽  
Maria I. Milani ◽  
Luiz A. Colnago ◽  
Marcos D. Ferreira ◽  
...  
Keyword(s):  
Citric Acid ◽  
Near Infrared ◽  
Prediction Models ◽  
Quality Attributes ◽  
Internal Quality ◽  
Control Analysis ◽  
Tomato Quality ◽  
Wide Range ◽  
Different Types ◽  
Fresh Tomato

Portable spectrometers are promising tools that can be an alternative way, for various purposes, of analyzing food quality, such as monitoring in a few seconds the internal quality during fruit ripening in the field. A portable/handheld (palm-sized) near-infrared (NIR) spectrometer (Neospectra, Si-ware) with spectral range of 1295–2611 nm, equipped with a micro-electro-mechanical system (MEMs), was used to develop prediction models to evaluate tomato quality attributes non-destructively. Soluble solid content (SSC), fructose, glucose, titratable acidity (TA), ascorbic, and citric acid contents of different types of fresh tomatoes were analyzed with standard methods, and those values were correlated to spectral data by partial least squares regression (PLSR). Fresh tomato samples were obtained in 2018 and 2019 crops in commercial production, and four fruit types were evaluated: Roma, round, grape, and cherry tomatoes. The large variation in tomato types and having the fruits from distinct years resulted in a wide range in quality parameters enabling robust PLSR models. Results showed accurate prediction and good correlation (Rpred) for SSC = 0.87, glucose = 0.83, fructose = 0.87, ascorbic acid = 0.81, and citric acid = 0.86. Our results support the assertion that a handheld NIR spectrometer has a high potential to simultaneously determine several quality attributes of different types of tomatoes in a practical and fast way.

Acoustic Energy Balance During the Onset, Growth and Saturation of Thermoacoustic Instabilities

2020 ◽  
Author(s):  
R. Gaudron ◽  
D. Yang ◽  
A. S. Morgans
Keyword(s):  
Energy Balance ◽  
Network Models ◽  
Acoustic Energy ◽  
Dimensionless Numbers ◽  
Weakly Nonlinear ◽  
Acoustic Damping ◽  
Thermoacoustic Instabilities ◽  
Wide Range ◽  
Acoustic Absorption Coefficient ◽  
Flame Describing Function

Abstract Thermoacoustic instabilities can occur in a wide range of combustors and are prejudicial since they can lead to increased mechanical fatigue or even catastrophic failure. A well-established formalism to predict the onset, growth and saturation of such instabilities is based on acoustic network models. This approach has been successfully employed to predict the frequency and amplitude of limit cycle oscillations in a variety of combustors. However, it does not provide any physical insight in terms of the acoustic energy balance of the system. On the other hand, Rayleigh’s criterion may be used to quantify the losses, sources and transfers of acoustic energy within and at the boundaries of a combustor. However, this approach is cumbersome for most applications because it requires computing volume and surface integrals and averaging over an oscillation cycle. In this work, a new methodology for studying the acoustic energy balance of a combustor during the onset, growth and saturation of thermoacoustic instabilities is proposed. The two cornerstones of this new framework are the acoustic absorption coefficient Δ and the cycle-to-cycle acoustic energy ratio λ, both of which do not require computing integrals. Used along with a suitable acoustic network model, where the flame frequency response is described using the weakly nonlinear Flame Describing Function (FDF) formalism, these two dimensionless numbers are shown to characterize: 1) the variation of acoustic energy stored within the combustor between two consecutive cycles, 2) the acoustic energy transfers occurring at the combustor’s boundaries and 3) the sources and sinks of acoustic energy located within the combustor. The acoustic energy balance of the well-documented Palies burner is then analyzed during the onset, growth and saturation of thermoacoustic instabilities using this new methodology. It is demonstrated that this new approach allows a deeper understanding of the physical mechanisms at play. For instance, it is possible to determine when the flame acts as an acoustic energy source or sink, where acoustic damping is generated, and if acoustic energy is transmitted through the boundaries of the burner.

High Flux Reactor Review and Reactivity Control Analysis

2021 ◽  
Author(s):  
Wang Lin ◽  
Xu Wei ◽  
Xie Fei
Keyword(s):  
Control Analysis ◽  
Control Mechanisms ◽  
General Description ◽  
High Flux ◽  
High Flux Reactor ◽  
Wide Range ◽  
Versatile Tool ◽  
Flux Reactor ◽  
Safety Operation ◽  
Reactivity Insertion

Abstract For over 60 years, research reactors have provided the world with a versatile tool to test materials and promote irradiation research, as well as to produce radioisotopes for medical treatments. The High Flux Reactor (HFR), as a water moderated and cooled, beryllium-reflected reactor has awarded more attention in recent years. There is a wide range of designs and applications for HFRs that based on their own situation to meet research requirements. For the purpose of reducing the volume and mass of the reactor, as well as ensuring the safety operation, it is necessary to determine the most effective reactivity control scheme, and analyze the corresponding reactivity insertion accidents. This paper is going to investigate typical high flux reactors within the same type with HFETR, summarize general description and characteristics, the uses of the high flux reactor, and reactivity control mechanisms. In addition, the associated reactivity insertion accidents were presented and analyzed. The analysis result will provide some references to further design and construction of high flux reactor.

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