Local stability analysis of a low-dissipation cyclic refrigerator

2021 ◽  
Author(s):  
Kai Li ◽  
Jie Lin ◽  
Jian-Hui Wang
Keyword(s):  
Steady State ◽  
Local Stability ◽  
Figure Of Merit ◽  
Coefficient Of Performance ◽  
Stable Steady State ◽  
Local Stability Analysis ◽  
Low Dissipation ◽  
Internal Dissipation ◽  
The Stability

Abstract We study the local stability near the maximum figure of merit for the low-dissipation cyclic refrigerator, where the irreversible dissipation occurs not only in the thermal contacts but also the adiabatic strokes. We find that the bounds of the coefficient of performance at maximum figure of merit or maximum cooling rate in presence of internal dissipation are identical to corresponding those in absence of internal dissipation. Using two different scenarios, we prove the existence of a single stable steady state for the refrigerator, and clarify the role of internal dissipation on the stability of thermodynamic steady state, showing that the speed of system evolution to the steady state decreases due to internal dissipation.

Stability Analysis of an Endoreversible Heat Engine with Stefan-Boltzmann Heat Transfer Law Working in Maximum-Power-Like Regime

2006 ◽  
Vol 13 (01) ◽  
pp. 43-53 ◽  
Author(s):  
J. C. Chimal-Eguía ◽  
M. A. Barranco-Jiménez ◽  
F. Angulo-Brown
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Local Stability ◽  
Heat Engine ◽  
Relaxation Times ◽  
Stability Study ◽  
Maximum Power ◽  
Working Fluid ◽  
Local Stability Analysis ◽  
The Stability

A local stability study of an endoreversible Stefan-Boltzmann (SB) engine, working in a maximum-power-like regime, is presented. This engine consists of a Carnot engine that exchanges heat with heat reservoirs T1 and T2, (T 1 > T2) through a couple of thermal links, both having the same conductance g. In addition, the working fluid has the same heat capacity C in the two isothermal branches of the cycle. From the local stability analysis we conclude that the SB engine is stable for every value of g, C and τ = T2/T1. After a small perturbation, the system decays to the steady state with either of two different relaxation times; both being proportional to C/g, and τ. Finally, when we plot some of the thermodynamic properties in the steady state versus τ, we find how an increment of τ can improve the stability of the system, at the same decreasing the efficiency and the power of the system. This suggests a compromise between the stability and the energetic properties of the engine driven by τ.

Local Stability of an Endoreversible Heat Engine Working in an Ecological Regime

2007 ◽  
Vol 14 (04) ◽  
pp. 411-424 ◽  
Author(s):  
J. C. Chimal-Eguía ◽  
I. Reyes-Ramírez ◽  
L. Guzmán-Vargas
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Stability Analysis ◽  
Local Stability ◽  
Heat Engine ◽  
Relaxation Times ◽  
Local Stability Analysis ◽  
The Stability ◽  
Qualitative Phase ◽  
Ecological Regime

We present a local stability analysis of an endoreversible engine working in an ecological regime, for three common heat transfer laws. From our local stability analysis we conclude that the system is stable for every value of the heat conductivity g, the heat capacity C and the ratio of temperatures τ = T2/T1 with T1 > T2. After a small perturbation the system decays exponentially to the steady state determined by two different relaxation times. We observe that the stability of the system improves as r increases whereas the steady-state energetic properties of the engine decline. Moreover, we compare the stability properties of the engine working in the ecological regime and under maximum power output. Finally, qualitative phase-space portraits for the evolution of the system are presented for representative cases.

scholarly journals Optimization and Stability of Heat Engines: The Role of Entropy Evolution

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 865 ◽  
Author(s):  
Julian Gonzalez-Ayala ◽  
Moises Santillán ◽  
Maria Santos ◽  
Antonio Calvo Hernández ◽  
José Mateos Roco
Keyword(s):  
Local Stability ◽  
Production Efficiency ◽  
Basin Of Attraction ◽  
Heat Engine ◽  
Time Constraints ◽  
Thermal Gradients ◽  
Heat Engines ◽  
Low Dissipation ◽  
The Basin Of Attraction

Local stability of maximum power and maximum compromise (Omega) operation regimes dynamic evolution for a low-dissipation heat engine is analyzed. The thermodynamic behavior of trajectories to the stationary state, after perturbing the operation regime, display a trade-off between stability, entropy production, efficiency and power output. This allows considering stability and optimization as connected pieces of a single phenomenon. Trajectories inside the basin of attraction display the smallest entropy drops. Additionally, it was found that time constraints, related with irreversible and endoreversible behaviors, influence the thermodynamic evolution of relaxation trajectories. The behavior of the evolution in terms of the symmetries of the model and the applied thermal gradients was analyzed.

scholarly journals Suppression of marine ice sheet instability

2018 ◽  
Vol 857 ◽  
pp. 648-680 ◽  
Author(s):  
Samuel S. Pegler
Keyword(s):  
Steady State ◽  
Rapid Assessment ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Stable Steady State ◽  
Ice Shelf ◽  
West Antarctic Ice Sheet ◽  
West Antarctic ◽  
Grounding Line ◽  
The Stability

A long-standing open question in glaciology concerns the propensity for ice sheets that lie predominantly submerged in the ocean (marine ice sheets) to destabilise under buoyancy. This paper addresses the processes by which a buoyancy-driven mechanism for the retreat and ultimate collapse of such ice sheets – the marine ice sheet instability – is suppressed by lateral stresses acting on its floating component (the ice shelf). The key results are to demonstrate the transition between a mode of stable (easily reversible) retreat along a stable steady-state branch created by ice-shelf buttressing to tipped (almost irreversible) retreat across a critical parametric threshold. The conditions for triggering tipped retreat can be controlled by the calving position and other properties of the ice-shelf profile and can be largely independent of basal stress, in contrast to principles established from studies of unbuttressed grounding-line dynamics. The stability and recovery conditions introduced by lateral stresses are analysed by developing a method of constructing grounding-line stability (bifurcation) diagrams, which provide a rapid assessment of the steady-state positions, their natures and the conditions for secondary grounding, giving clear visualisations of global stabilisation conditions. A further result is to reveal the possibility of a third structural component of a marine ice sheet that lies intermediate to the fully grounded and floating components. The region forms an extended grounding area in which the ice sheet lies very close to flotation, and there is no clearly distinguished grounding line. The formation of this region generates an upsurge in buttressing that provides the most feasible mechanism for reversal of a tipped grounding line. The results of this paper provide conceptual insight into the phenomena controlling the stability of the West Antarctic Ice Sheet, the collapse of which has the potential to dominate future contributions to global sea-level rise.

scholarly journals Local stability analysis and eigenvalue sensitivity of reacting bluff-body wakes

2016 ◽  
Vol 788 ◽  
pp. 549-575 ◽  
Author(s):  
Benjamin Emerson ◽  
Tim Lieuwen ◽  
Matthew P. Juniper
Keyword(s):  
Stability Analysis ◽  
Acoustic Waves ◽  
Local Stability ◽  
Bluff Body ◽  
Density Ratio ◽  
Global Mode ◽  
Eigenvalue Sensitivity ◽  
Local Stability Analysis ◽  
Measured Time ◽  
The Stability

This paper presents an experimental and theoretical investigation of high-Reynolds-number low-density reacting wakes near a hydrodynamic Hopf bifurcation. This configuration is applicable to the wake flows that are commonly used to stabilize flames in high-velocity flows. First, an experimental study is conducted to measure the limit-cycle oscillation of this reacting bluff-body wake. The experiment is repeated while independently varying the bluff-body lip velocity and the density ratio across the flame. In all cases, the wake exhibits a sinuous oscillation. Linear stability analysis is performed on the measured time-averaged velocity and density fields. In the first stage of this analysis, a local spatiotemporal stability analysis is performed on the measured time-averaged velocity and density fields. The stability analysis results are compared to the experimental measurement and demonstrate that the local stability analysis correctly captures the influence of the lip-velocity and density-ratio parameters on the sinuous mode. In the second stage of the analysis, the linear direct and adjoint global modes are estimated by combining the local results. The sensitivity of the eigenvalue to changes in intrinsic feedback mechanisms is found by combining the direct and adjoint global modes. This is referred to as the eigenvalue sensitivity throughout the paper for reasons of brevity. The predicted global mode frequency is consistently within 10 % of the measured value, and the linear global mode shape closely resembles the measured nonlinear oscillations. The adjoint global mode reveals that the oscillation is strongly sensitive to open-loop forcing in the shear layers. The eigenvalue sensitivity identifies a wavemaker in the recirculation zone of the wake. A parametric study shows that these regions change little when the density ratio and lip velocity change. In the third stage of the analysis, the stability analysis is repeated for the varicose hydrodynamic mode. Although not physically observed in this unforced flow, the varicose mode can lock into longitudinal acoustic waves and cause thermoacoustic oscillations to occur. The paper shows that the local stability analysis successfully predicts the global hydrodynamic stability characteristics of this flow and shows that experimental data can be post-processed with this method in order to identify the wavemaker regions and the regions that are most sensitive to external forcing, for example from acoustic waves.

scholarly journals The effect of a lifted flame on the stability of round fuel jets

2008 ◽  
Vol 609 ◽  
pp. 275-284 ◽  
Author(s):  
JOSEPH W. NICHOLS ◽  
PETER J. SCHMID
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Local Stability ◽  
Premixed Flame ◽  
Absolute Instability ◽  
Low Mach Number ◽  
Lifted Flame ◽  
Local Stability Analysis ◽  
The Stability ◽  
Globally Stable

The stability and dynamics of an axisymmetric lifted flame are studied by means of direct numerical simulation (DNS) and linear stability analysis of the reacting low-Mach-number equations. For light fuels (such as non-premixed methane/air flames), the non-reacting premixing zone upstream of the lifted flame base contains a pocket of absolute instability supporting self-sustaining oscillations, causing flame flicker even in the absence of gravity. The liftoff heights of the unsteady flames are lower than their steady counterparts (obtained by the method of selective frequency damping (SFD)), owing to premixed flame propagation during a portion of each cycle. From local stability analysis, the lifted flame is found to have a significant stabilizing influence at and just upstream of the flame base, which can truncate the pocket of absolute instability. For sufficiently low liftoff heights, the truncated pocket of absolute instability can no longer support self-sustaining oscillations, and the flow is rendered globally stable.

Numerical simulation of the absolutely and convectively unstable wake

1989 ◽  
Vol 199 ◽  
pp. 55-88 ◽  
Author(s):  
K. Hannemann ◽  
H. Oertel Jr
Keyword(s):  
Numerical Simulation ◽  
Steady State ◽  
Stability Analysis ◽  
Local Stability ◽  
Stokes Equations ◽  
Plate Thickness ◽  
Experimental Result ◽  
Quasi Steady State ◽  
Local Stability Analysis ◽  
Base Bleed

The development of the wake behind a flat plate at a supercritical Reynolds number (Re= 200, based on the plate thickness and free-stream velocity) is simulated numerically by solving the two-dimensional unsteady Navier-Stokes equations with a finite-difference Galerkin method. The intermediate quasi-steady state of the wake development is investigated with an Orr-Sommerfeld analysis for complex frequencies and wavenumbers. Based on this linear, local stability analysis it can be shown that the quasi-steady state can be divided into regions of local absolute and local convective instability. One goal of this work is to determine the validity of the linear, local stability theory by comparing the predictions of the Orr-Sommerfeld analysis to the results of a numerical wake simulation. Based on this comparison, for the investigated flow field, the frequency selection mechanisms recently proposed by several authors are discussed. Base bleed is applied in the numerical simulation of the wake as a control parameter, following the well-known experimental result that sufficient base bleed reduces the strength of the vortex street (see e.g. Wood 1964). It can be shown that from a critical base-bleed ratio, disturbances grow no longer in time but only in space, indicating a change of the global stability characteristics. In addition the linear, local stability analysis is used to investigate to what extent this global transition can be described.

Photobioreactor Stability by Phase Plane Technique Applied to Spirulina Maxima Growth

2003 ◽  
Vol 1 (1) ◽  
Author(s):  
Khaled Belkacemi ◽  
Safia Hamoudi
Keyword(s):  
Steady State ◽  
Phase Plane ◽  
Biologically Active ◽  
Raw Material ◽  
System Stability ◽  
Stable Steady State ◽  
Monod Kinetics ◽  
Spirulina Maxima ◽  
Plane Technique ◽  
The Stability

Spirulina maxima is a worthy multicellular filamentous micro-algae used as a food supplement and raw material for fine chemicals and biologically active compounds production. Intensive approach consisting of cultivating pure strains of this photoautotroph microorganism in photobioreactors is more desirable than extensive ones, largely incontrollable with regard to production stability. Determining the best reaction conditions to reach a steady state in the runway events is often needed in biological systems. For a biochemical engineer, knowing the system stability for an optimal bioreactor configuration is crucial to estimate the rate at which dependent variables grow or decay with the time reaction. The stability analysis becomes important in recycle processes in which possibility that these systems influence themselves exists. The aim of this work deals with the 1) description of the growth kinetics by a logistic and unstructured model based on Monod kinetics taking into account the maintenance in life of viable cells; 2) establishment of a dynamic growth model for Spirulina maxima cultivated in continuous lamellar photobioreactors using industrial manures as macro-nutrients; 3) determination of optimal culture conditions sustaining a stable growth of S. maxima in a system of two bioreactors in series; and 4) investigation of the dynamic stability of this multivariable system with nonlinear dynamics using phase plane technique (PPT). Although good mixing of the culture is essential for ensuring adequate supply of nutrients and prevention of the accumulation of toxic metabolites. Excessive agitation causes mechanical damage to Spirulina cells. An air flow rate of 2.5 L/min for airlift agitation represented a balance between the need to provide good mixing and to avoid cell damage. A stable steady state was achieved corresponding to a productivity of 10.8 g. m2/day when the system was supplied with 0.2 g N/L of minerals, at a dilution rate of 0.1 1/day, temperature of 30 °C under light intensity of 18 Klux. PPT as a powerful procedure successfully predicts the stability of such a complex system very well.

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