1,996 research outputs found
A filter-less LES model based on the local minimization of the entropy generation rate: model description
No full textThe paper discusses a novel LES turbulent model, first presented in a linearized version in 2019. The model, named “ESS-LES” (for Entropy Smoothing at Sub-grid-scales LES), is based on the local minimization of the entropy generation rate in each single cell. We present here the theoretical background in some detail. First, the exact entropy generation equation is written in each cell in terms of the instantaneous velocities U,V,W. Then, a set of explicit differential equation for the subgrid scale velocities u,v,w is obtained from the Lagrangian minimization of the entropy generation rate, and a closed form solution is derived in the form of an infinite sinh*sin series. By solving them and truncating the series at the relevant Kolmogorov scales, a formal integration of the uu, vv, ww within each cell provides the subgrid stress tSGS terms that can be added into the resolved Stokes-Navier equations that are in turn solved iteratively. The physical correctness of the model is first analyzed by studying the effect of the model on a number of externally imposed wavelike velocity solutions, to verify the congruency of the resulting shapes of the subgrid stresses. Some preliminary results (not described here in detail) indicate that the model is in a good agreement with the DNS solution and appears to be competitive with other “classical” LES models. A fully-3D simulation is being developed to validate the model on realistic geometries against available LES and DNS results, to verify that it properly reproduces the energy dynamics of turbulence
A general model for the evolution of non-equilibrium systems
No full textThe paper addresses the problem of the evolution of systems that are initially in a state of non-equilibrium. The model we propose leads to an equation of motion that starts from a rephrasing of the classical non-equilibrium Ginzburg-Landau equation by reinterpreting in the sense of an exergy evolution paradigm. This paper may be considered as a logical corollary to -and at the same time as an e conceptual extension of-the solution to the problem of the existence and quantification of a non-equilibrium exergy presented in previous articles by the present Authors. In previous papers it was shown that, if both energy and exergy are considered a priori concepts, the evolution of the exergy of a solid body subject to a sufficiently smooth relaxation process can be calculated for arbitrary initial temperature or concentration distributions with an accuracy that depends only on the information about the initial distribution of the system properties at the initial time and on the availability of proper material relations. It was shown that the non-equilibrium exergy, i.e., the extra ideal work that can be extracted from the body, relaxes to zero as the system tends to its equilibrium state, so that the total exergy content (given by the sum of non-equilibrium and equilibrium exergy) attains the value given by its classical definition. The evolution history depends of course on the imposed b.c. and on the “gradient” that drives the relaxation. In this paper, we formalize the dependence of the non-equilibrium exergy on its possible drivers (pressure, temperature or concentration gradients) and derive a general “equation of motion” that links the former to the latter. The solution is analytical, and therefore there is no need to postulate local equilibrium, as long as we are dealing with a continuum (scales sufficiently removed from the atomic ones). A few applications to ideal and real processes are presented and discussed, while the application of the method to more complex and industrially relevant cases is left for later studies. The paradigm is theoretically simple and the resulting model of relatively easy implementation: we therefore hope that applications of the proposed framework may be systematically developed in the fields of engineering and natural science, to gain a better insight into real non-equilibrium processe
An Exergy-based analysis of the co-evolution of different species sharing common resources
No full text
On the Quantification of Non-equilibrium Exergy for Thermodynamic Systems Evolving According to Cattaneo’s Equation
No full textThis paper is a follow-up of previous work aimed at the identification and quantification of the exergy of macroscopic non-equilibrium systems. Assuming that both energy and exergy are a priori concepts, it is possible to show that a system in an initial non-equilibrium state relaxes to equilibrium releasing (or absorbing) an additional amount of exergy, called non-equilibrium exergy, which is fundamentally different from Gibbs’ Available Energy and depends on both the initial state and the imposed boundary conditions. The existence of such a quantity implies that all iso-energetic non-equilibrium states can be ranked in terms of their non-equilibrium exergy content, any point of the Gibbs plane corresponding therefore to a possible initial distribution, each one with its own exergy-decay history. The non-equilibrium exergy is always larger than its equilibrium counterpart and constitutes the “real” total exergy content of the system, i.e., the real maximum work extractable (or absorbable) from the system. The application of the method to heat conduction problems led to the calculation of a “relaxation curve”, i.e., to the determination of the time-history of the relaxation towards equilibrium that takes place in finite rather than infinite time interval. In our previous works, use was made of the Fourier heat diffusion equation. In this study, the Cattaneo heat transfer equation is used instead, in an attempt to extend the validation range of the procedure. Cattaneo introduced in 1948 a second time derivative term that renders the diffusion equation hyperbolic and avoids an infinite speed of propagation. A finite propagation velocity of thermal disturbances affects the value of the non-equilibrium exergy: this paper presents the new results and offers a discussion of the implication
Exergy for systems in thermal non-equilibrium evolving according to Cattaneo’s equation
No full textThis paper is a follow-up of previous work aimed at the identification and quantification of the exergy of
macroscopic non-equilibrium systems. Assuming that both energy and exergy are a priori concepts, it is
possible to show that a system in an initial non-equilibrium state relaxes to equilibrium releasing (or absorbing)
an additional amount of exergy, called the non-equilibrium exergy, which is fundamentally different from Gibbs’
Available Energy and depends on both the initial state and the imposed boundary conditions. The existence
of such a quantity implies that all iso-energetic non-equilibrium states can be ranked in terms of their nonequilibrium exergy content, each point of the Gibbs plane corresponding therefore to a possible initial
distribution, each one with its own exergy-decay history. The non-equilibrium exergy is always larger than its
equilibrium counterpart and constitutes the “real” total exergy content of the system, i.e., the real maximum
work extractable (or absorbable) from the system. The application of the method to heat conduction problems
led to the calculation of a “relaxation curve”, i.e., to the determination of the time-history of the relaxation
towards equilibrium that takes place in finite rather than infinite time interval. In our previous works, use was
made of the Fourier heat diffusion equation. In this study, the Cattaneo heat transfer equation is used instead,
in an attempt to extend the validation range of the procedure. Cattaneo introduced in 1948 a second time
derivative term that renders the diffusion equation hyperbolic and avoids an infinite speed of propagation. A
finite propagation velocity of thermal disturbances affects the value of the non-equilibrium exergy: this paper
presents the new results and offers a discussion of the implication
A thermodynamic model for plant growth,validated with Pinus sylvestris data
No full textPlants are open, irreversible and non-equilibrium systems that live via mass- and energy exchanges with the environment, and therefore, are amenable to a thermodynamic treatment: in fact, they may be considered “energy converters” because their metabolism is nothing else than a controlled ability to transform energy from one form (solar) into another (chemical energy suitable to cell metabolism) and to activate and maintain reactions at cellular- and molecular level -promoting the plant growth. This paper presents an original model based on mass conservation and on the First- and Second Law of Thermodynamics, which results in a set of equations that allow for the calculation of the Primary Productivity (NPP) and consequently lead to a measure of the plant growth. The model is lumped, steady-state and totally deterministic, because no primary process is modelled in detail: the control volume is a portion of the universe that contains the plant and its immediate surroundings (atmosphere and the relevant portion of the soil), and the solution is strongly depending on the imposed boundary conditions. In such a formulation, the tree is considered as a non-equilibrium system evolving at a steady rate, and the only implicit assumption is the local equilibrium hypothesis. The general evolution equations are derived, and their steady-state form is analysed in detail. The approach is based on the calculation of the exergy in- and outflows from the control volume. Based on reasonably accurate empirical data, the exergy budget shows that the overall exergy conversion efficiency is quite low in plants and is very sensitive to even small changes in the environmental condition and to the adopted evapotranspiration model, as it would have been expected. The model is applied to a mature specimen of Pinus sylvestris and the results are compared with some literature data: despite neglecting the real chemo-physical details, the model reproduces the most salient characters of the tree growth. The sensitivity of the results to the tree age as well to the main model parameters is also calculated. The application of the same model to different species may reveal asymmetries in the “adaptability” of certain genotypes to different environments. On the more specific engineering side, the model may see an immediate application in the estimate of CO2 capture by plants
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