Statistically steady states of forced isotropic turbulence in thermal equilibrium and non-equilibrium

2016 ◽  
Vol 797 ◽  
pp. 181-200 ◽  
Author(s):  
Diego A. Donzis ◽  
Agustin F. Maqui
Keyword(s):  
Turbulent Flows ◽  
Thermal Equilibrium ◽  
Degrees Of Freedom ◽  
Isotropic Turbulence ◽  
Vibrational Energy ◽  
Relaxation Times ◽  
Steady States ◽  
Laminar Flows ◽  
Vibrational Modes ◽  
Non Equilibrium

We investigate statistically steady states of turbulent flows when molecular degrees of freedom, in particular vibration, are taken into account. Unlike laminar flows initially in thermal non-equilibrium which asymptotically relax towards thermal equilibrium, turbulent flows present persistent departures from thermal equilibrium. This is due to fluctuations in temperature and other thermodynamic variables, which are known to increase with turbulent Mach number. Analytical results are compared to direct numerical simulations at a range of Reynolds and Mach numbers as well as molecular parameters such as relaxation times. Turbulent fluctuations are also shown to disrupt the distribution of energy between translational–rotational–vibrational modes even if thermal equilibrium is attained instantaneously relative to turbulence time scales, an effect that increases with characteristic relaxation times. Because of the nonlinear relation between temperature and vibrational energy in equilibrium, the fluctuation of the latter could be strongly positively skewed with long tails in its probability density function. This effect is stronger in flows with strong temperature fluctuations and when vibrational modes are partially excited. Because of the finite-time relaxation of vibration, departures from equilibrium result in very strong transfers of energy from the translational–rotational mode to the vibrational mode. A simple spectral model can explain the stronger departures from thermal equilibrium observed at the small scales. The spectral behaviour of the instantaneous vibrational energy can be described by classical phenomenology for passive scalars.

scholarly journals The flame spectrum of carbon monoxide, II. Application to 'afterburning'

1941 ◽  
Vol 178 (972) ◽  
pp. 61-73 ◽  
Keyword(s):  
Carbon Monoxide ◽  
Absorption Spectrum ◽  
Degrees Of Freedom ◽  
Vibrational Energy ◽  
Radiative Lifetime ◽  
Relaxation Times ◽  
Latent Energy ◽  
Essentially Normal ◽  
Infra Red ◽  
Effect Of Moisture

In a previous paper it has been shown, from a study of the spectrum of the carbon monoxide flame, that the molecules of CO 2 formed by the combustion are initially in a highly excited state of internal vibration. An attempt is made here to derive approximate values for the lifetimes of these vibrationally activated molecules. The orders of magnitude of the radiative lifetime for the three types of vibration are derived. From data obtained from supersonic dispersion in CO 2 the relaxation times, or collision lifetimes, are discussed with especial emphasis on the effect of moisture on the collision-life of the activated molecules. A section is also devoted to the possibility of the close resonance between the vibrations v 1 and v 2 of CO 2 resulting in a high percentage of dissociation after the combustion of the dry gas. The results give a good interpretation of the experiments of Garner and colleagues on the marked effect of moisture and other catalysts on the infra-red emission of the flame, and the general failure to observe a strong emission band at 14.9 μ . The results of the theory go far towards explaining the latent energy of the combustion observed by David and colleagues. The lifetime of the activated molecules is calculated to be not more than a few tenths of a second, but dissociation and recombination processes might lengthen this time. For moist gases the lifetime will be very much less, and the infra-red radiation from the flame and the latent energy of the products should similarly be much reduced, in agreement with experiment. The vibrationally activated molecules are to be regarded as essentially normal molecules of CO 2 in which the vibrational energy has not had time to reach equipartition with the energy in other degrees of freedom; spectroscopically there is no evidence to show that they are electronically excited or peculiar in any other way. Experiments on the absorption spectrum of a long length of burning gas show strong absorption due to hot oxygen, this being particularly marked when the gases are dry. This is interpreted as being due to transfer of the vibrational energy from the CO 2 to the O 2 molecules, the absorption spectrum of which is thereby shifted to longer wave-lengths.

scholarly journals Bubbly and Buoyant Particle–Laden Turbulent Flows

2020 ◽  
Vol 11 (1) ◽  
pp. 529-559 ◽  
Author(s):  
Varghese Mathai ◽  
Detlef Lohse ◽  
Chao Sun
Keyword(s):  
Turbulent Flows ◽  
Isotropic Turbulence ◽  
Laminar Flows ◽  
Future Research ◽  
Vortical Structures ◽  
Fluid Turbulence ◽  
Thermally Driven ◽  
Dynamical Regimes ◽  
Liquid Flows ◽  
Present Understanding

Fluid turbulence is commonly associated with stronger drag, greater heat transfer, and more efficient mixing than in laminar flows. In many natural and industrial settings, turbulent liquid flows contain suspensions of dispersed bubbles and light particles. Recently, much attention has been devoted to understanding the behavior and underlying physics of such flows by use of both experiments and high-resolution direct numerical simulations. This review summarizes our present understanding of various phenomenological aspects of bubbly and buoyant particle–laden turbulent flows. We begin by discussing different dynamical regimes, including those of crossing trajectories and wake-induced oscillations of rising particles, and regimes in which bubbles and particles preferentially accumulate near walls or within vortical structures. We then address how certain paradigmatic turbulent flows, such as homogeneous isotropic turbulence, channel flow, Taylor–Couette turbulence, and thermally driven turbulence, are modified by the presence of these dispersed bubbles and buoyant particles. We end with a list of summary points and future research questions.

The influence of non-equilibrium transient effects on measurements of vibrational relaxation times and of dissociation rate constants

1982 ◽  
Vol 60 (23) ◽  
pp. 2927-2942 ◽  
Author(s):  
Heshel Teitelbaum
Keyword(s):  
Rate Constants ◽  
Vibrational Relaxation ◽  
Vibrational Energy ◽  
Relaxation Times ◽  
Dissociation Rate ◽  
Harmonic Oscillators ◽  
Dissociation Limit ◽  
Transient Effects ◽  
Rate Law ◽  
Non Equilibrium

A semi-empirical analysis based on a rate law for vibrational relaxation of dissociating simple harmonic oscillators allows for a detailed study of measurements of vibrational relaxation times τ and of steady dissociation rate coefficients k0. It is shown that non-equilibrium populations of vibrational energy levels prevent attainment of the thermodynamically expected equilibrium energy. Even under near-isothermal and mild conditions, [Formula: see text], serious experimental errors result when the Bethe–Teller relaxation rate law is used. Closed form expressions are given which permit evaluation of these errors. Measurements should be analyzed using the rate law[Formula: see text]where ε is the vibrational energy per molecule, τ the relaxation time, kd the non-equilibrium rate coefficient, ετ the thermodynamically expected vibrational energy at temperature T, and (ε* + hv) the energy just above the dissociation limit. It is also shown that if[Formula: see text]a local minimum and maximum are predicted for measured density gradients in shock tube dissociations of diatomic molecules, where tine is the incubation time, D′ the effective dissociation energy, and x0 the mole fraction of dissociating molecules in an inert diluent. Expressions are given for extracting incubation times and rate constants from such studies when [Formula: see text]. Analysis of experimental data actually showing such phenomena (J. Chem Phys. 55, 4017 (1971)) is carried out. There are indications that any analysis which does not explicitly account for transient effects could result in errors in measured k0's of factors of 2 or more.

scholarly journals Matrix Product State Simulations of Non-Equilibrium Steady States and Transient Heat Flows in the Two-Bath Spin-Boson Model at Finite Temperatures

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 77
Author(s):  
Angus J. Dunnett ◽  
Alex W. Chin
Keyword(s):  
Finite Temperature ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Steady States ◽  
Matrix Product ◽  
Open Quantum ◽  
Matrix Product State ◽  
Wide Range ◽  
Boson Model ◽  
Non Equilibrium

Simulating the non-perturbative and non-Markovian dynamics of open quantum systems is a very challenging many body problem, due to the need to evolve both the system and its environments on an equal footing. Tensor network and matrix product states (MPS) have emerged as powerful tools for open system models, but the numerical resources required to treat finite-temperature environments grow extremely rapidly and limit their applications. In this study we use time-dependent variational evolution of MPS to explore the striking theory of Tamascelli et al. (Phys. Rev. Lett. 2019, 123, 090402.) that shows how finite-temperature open dynamics can be obtained from zero temperature, i.e., pure wave function, simulations. Using this approach, we produce a benchmark dataset for the dynamics of the Ohmic spin-boson model across a wide range of coupling strengths and temperatures, and also present a detailed analysis of the numerical costs of simulating non-equilibrium steady states, such as those emerging from the non-perturbative coupling of a qubit to baths at different temperatures. Despite ever-growing resource requirements, we find that converged non-perturbative results can be obtained, and we discuss a number of recent ideas and numerical techniques that should allow wide application of MPS to complex open quantum systems.

Stochastic pumping of non-equilibrium steady-states: how molecules adapt to a fluctuating environment

2018 ◽  
Vol 54 (5) ◽  
pp. 427-444 ◽  
Author(s):  
R. D. Astumian
Keyword(s):  
Steady States ◽  
Absolute Amount ◽  
Fluctuating Environment ◽  
The Absolute ◽  
Non Equilibrium

Fluctuations favour state B = (B,B′) based on kinetic asymmetry combined with moderate dissipation rather than state A = (A,A′) in which the absolute amount of dissipation is greater but where there is no kinetic asymmetry.

Shock discontinuity zone effect: the main factor in the explosive decomposition detonation process

1992 ◽  
Vol 339 (1654) ◽  
pp. 355-364 ◽  
Keyword(s):  
Degrees Of Freedom ◽  
Thermal Ionization ◽  
Relaxation Processes ◽  
Explosive Decomposition ◽  
Time Duration ◽  
Active Particles ◽  
Condensed Explosives ◽  
Discontinuity Zone ◽  
Electronically Excited ◽  
Non Equilibrium

A new qualitative conception of the detonation mechanism in condensed explosives has been developed on the basis of experimental and numerical modelling data. According to the conception the mechanism consists of two stages: non-equilibrium and equilibrium. The mechanism regularities are explosive characteristics and they do not depend on explosive charge structure (particle size, nature of filler in the pores, explosive state, liquid or solid, and so on). The tremendous rate of loading inside the detonation wave shock discontinuity zone ( ca. 10 -13 s) is responsible for the origin of the non-equilibrium stage. For this reason, the kinetic part of the shock compression energy is initially absorbed only by the translational degrees of freedom of the explosive molecules. It involves the appearance of extremely high translational temperatures for the polyatomic molecules. In the course of the translational-vibrational relaxation processes (that is, during the first non-equilibrium stage of ca. 10 -10 s time duration) the most rapidly excited vibrational degrees of freedom can accumulate surplus energy, and the corresponding bonds decompose faster than behind the front at the equilibrium stage. In addition to this process, the explosive molecules become electronically excited and thermal ionization becomes possible inside the translational temperature overheat zone. The molecules thermal decomposition as well as their electronic excitation and thermal ionization result in some active particles (radicals, ions) being created. The active particles and excited molecules govern the explosive detonation decomposition process behind the shock front during the second equilibrium stage. The activation energy is usually low, so that during this stage the decomposition proceeds extremely rapidly. Therefore the experimentally observed dependence of the detonation decomposition time for condensed explosives is rather weak.

scholarly journals On the different contributions of coherent structures to the spectra of a turbulent round jet and a turbulent boundary layer

2001 ◽  
Vol 448 ◽  
pp. 367-385 ◽  
Author(s):  
T. B. NICKELS ◽  
IVAN MARUSIC
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Turbulent Flows ◽  
Coherent Structures ◽  
Isotropic Turbulence ◽  
Structural Models ◽  
Spectral Measurements ◽  
Round Jet ◽  
Good Account ◽  
Single Size

This paper examines and compares spectral measurements from a turbulent round jet and a turbulent boundary layer. The conjecture that is examined is that both flows consist of coherent structures immersed in a background of isotropic turbulence. In the case of the jet, a single size of coherent structure is considered, whereas in the boundary layer there are a range of sizes of geometrically similar structures. The conjecture is examined by comparing experimental measurements of spectra for the two flows with the spectra calculated using models based on simple vortex structures. The universality of the small scales is considered by comparing high-wavenumber experimental spectra. It is shown that these simple structural models give a good account of the turbulent flows.

The Effects of Turbulence Length Scale on the Performance of Piezoelectric Harvesters

2015 ◽  
Author(s):  
Yiannis Andreopoulos ◽  
Amir H. Danesh-Yazdi ◽  
Oleg Goushcha ◽  
Niell Elvin
Keyword(s):  
Turbulent Flows ◽  
Power Output ◽  
Isotropic Turbulence ◽  
Spatial Scales ◽  
Mechanical Energy ◽  
Relative Size ◽  
Analytical Description ◽  
Length Scale ◽  
Linear Effect ◽  
Turbulence Length

Turbulent flows carry mechanical energy distributed over a range of temporal and spatial scales and their interaction with a thin immersed piezoelectric beam results in a strain field which generates electrical charge. This energy harvesting method can be used for developing self-powered electronic devices such as flow sensors. In the present experimental work, various energy harvesters were placed in a turbulent boundary layer or inside a decaying flow field of homogeneous and isotropic turbulence. The role of large instantaneous turbulent structures in this rather complex fluid-structure interaction is discussed in interpreting the electrical output results. The forces acting on the vibrating beams have been measured dynamically and a theory has been developed which incorporates the effects of mean local velocity, turbulence intensity, the relative size of the beam’s length to the integral length scale of turbulence, the structural properties of the beam and the electrical properties of the active piezoelectric layer to provide reasonable estimates of the mean electrical power output. Experiments have been carried out in which these fluidic harvesters are immersed first in inhomogeneous turbulence like that encountered in boundary layers developing over solid walls and homogeneous and isotopic turbulence for which a simplified analytical description exists. It was found that there is a non-linear effect of turbulence length scales on the power output of the fluidic harvesters.

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