In this article we investigate an innovative thermodynamic scheme to recover some of the large drying energy in the superior form of mechanical work at the cost of a small reduction of drying rate. ...To define properties of this thermodynamic scheme we analyze the performance of a nonisothermal, drying-driven engine in terms of heat and mass fluxes flowing to/from solid and gaseous phases as energy reservoirs. Due to chemical potentials involved in power production, this type of engine can be qualified as a chemical engine. Essential variables in determining the performance of drying-driven engines are efficiency, total power output, and moisture flux. The problem naturally arising is that of power limits for the drying-driven engines, both steady and unsteady. The steady-state model refers to the case when both (gas and solid) reservoirs are infinite, whereas an unsteady model treats a dynamical case with the finite solid reservoir and gradually decreasing chemical potential of the liquid moisture. In the dynamical case the power integral (total work) is maximized at constraints that take into account rates of mass transport and efficiency of power generation. For low rates and large solid moisture content X the function describing optimal drying rate that maximizes total work is approximately constant in time. In an arbitrary situation, however, optimal rates are state dependent to preserve the constancy of the optimization Hamiltonian.
In this paper power limits and other performance indicators are investigated in various power generation systems with downgrading or upgrading of resources. Energy flux (power) is created in a power ...generator located between a resource fluid (‘upper’ fluid 1) and the environmental fluid (‘lower’ fluid, 2). Transfer phenomena, fluid properties and conductance values of dissipative layers or conductors influence the rate of power yield. While temperatures Ti of participating media are only necessary variables to describe purely thermal systems, in the present work both temperatures and chemical potentials μk are essential. This case is associated with engines propelled by fluxes of both energy and substance (chemical and electrochemical engines).
Optimization methods are applied to determine power generation limits which are important performance indicators for various energy converters, such as thermal, solar, chemical, and electrochemical engines. Methodological similarity is shown when analysing power limits in thermal machines and fuel cells. Numerical approaches are based on the methods of dynamic programing (DP) or Pontryagin’s maximum principle. In view of the limitation of DP to systems with low dimensionality of state vector, we focus here on the Pontryagin’s method, which involves discrete canonical algorithms derived from the process Hamiltonian. Some new or relatively unknown properties of these algorithms are described in the context of their application to power systems.
In fuel cells and other electrochemical systems downgrading or upgrading of resources may also occur. However, we restrict here to the steady-state fuel cells. An approximate (topology-ignoring) analysis shows that, in linear systems, only at most 1/4 of power dissipated in the natural transfer process can be transformed into mechanical or electric power. This indicator may be viewed as a new form of the second law efficiency. The relevant experimental data obtained at the institute of Power Engineering are also presented in this paper.
This work analyzes contemporary trends in thermodynamics of energy generators, heat pumps, separators, and other practical devices that are driven by thermal and solar energy. We focus on ...applications in which the optimal control theory plays an essential role. We consider devices of engine type (generators) and of heat pump or separator type (consumers), each driven either by radiative heat or by exchanged energy or mass. We outline difficulties in defining energy limits for transformation or consumption of solar energy. We also stress their links with classical problem of maximum work and exergy analysis of thermal systems.
We develop a thermodynamic theory for a difficult class of chemical processes undergoing in irreversible power-producing systems that yield mechanical work and are characterized by multiple ...(vectorial) efficiencies. Obtained efficiency formulas are applied for chemical machines working at maximum production of power. Steady-state model describes a chemical system in which two reservoirs are infinite, whereas an unsteady model treats a dynamical system with finite upper reservoir and gradually decreasing chemical potential of a key fuel component. In the considered chemical systems total power output is maximized at constraints which take into account dynamics of mass transport and efficiency of power generation. Dynamic optimization methods, in particular variational calculus, lead to optimal functions that describe integral power limits and extend reversible chemical work
W
rev to finite rate situations. Optimization results quantify effects of chemical rates and transport phenomena. Legendre transform of a local power function is an effective tool to obtain an optimal path in a dynamical process of power yield.
Thermodynamics is applied in mathematical simulation and optimization of nonlinear energy converters, in particular radiation engines, in steady and dynamical situations. Power is a cumulative effect ...maximized in a system with a nonlinear fluid, an engine or a sequence of engines, and an infinite bath. Dynamical state equations are applied to describe the resource temperature and work output in terms of a process control. Recent expressions for efficiency of imperfect converters are used to derive and solve Hamilton–Jacobi equations describing resource upgrading and downgrading. Various mathematical tools are applied in trajectory optimization with special attention given to the relaxing radiation. The radiation relaxation curve is non-exponential, characteristic of a nonlinear system. Power optimization algorithms in the form of Hamilton–Jacobi–Bellman equations lead to work limits and generalized availabilities. Converter's performance functions depend on end thermodynamic coordinates and a process intensity index,
h, in fact, the Hamiltonian of power optimization problem. As an example of limiting work from radiation, a finite rate exergy of radiation fluid is estimated in terms of finite rates quantified by Hamiltonian
h.
Applying the common mathematical procedure of thermodynamic optimization the paper offers a synthesizing or generalizing modeling of power production in various energy generators, such as thermal, ...solar and electrochemical engines (fuel cells). Static and dynamical power systems are investigated. Dynamical models take into account the gradual downgrading of a resource, caused by power delivery. Analytical modeling includes conversion efficiencies expressed in terms of driving fluxes. Products of efficiencies and driving fluxes determine the power yield and power maxima. While optimization of static systems requires using of differential calculus and Lagrange multipliers, dynamic optimization involves variational calculus and dynamic programming. In reacting mixtures balances of mass and energy serve to derive power yield in terms of an active part of chemical affinity. Power maximization approach is also applied to fuel cells treated as flow engines driven by heat flux and fluxes of chemical reagents. The results of power maxima provide limiting indicators for thermal, solar and SOFC generators. They are more exact than classical reversible limits of energy transformation.
•Systematic evaluation of power limits by optimization.•Common thermodynamic methodology for engine systems.•Original, in-depth study of power maxima.•Inclusion of fuel cells to a class of thermodynamic power systems.
A Fermat-like principle of minimum time is formulated for nonlinear steady paths of fluid flow in inhomogeneous isotropic porous media where fluid streamlines are curved by a location dependent ...hydraulic conductivity. The principle describes an optimal nature of nonlinear paths in steady Darcy’s flows of fluids. An expression for the total path resistance leads to a basic analytical formula for an optimal shape of a steady trajectory. In the physical space an optimal curved path ensures the maximum flux or shortest transition time of the fluid through the porous medium. A sort of “law of bending” holds for the frictional fluid flux in Lagrange coordinates. This law shows that—by minimizing the total resistance—a ray spanned between two given points takes the shape assuring that a relatively large part of it resides in the region of lower flow resistance (a ‘rarer’ region of the medium).
Power optimization approaches are unified for various energy converters, such like: thermal, solar, chemical, and electrochemical engines. Thermodynamics leads to converter’s efficiency and limiting ...power. Efficiency equations serve to solve problems of upgrading and downgrading of resources. While optimization of steady systems applies the differential calculus and Lagrange multipliers, dynamic optimization involves variational calculus and dynamic programming. In reacting systems chemical affinity constitutes a prevailing component of an overall efficiency, so that power is analyzed in terms of an active part of chemical affinity. The main novelty of the present paper in the energy yield context consists in showing that the generalized heat flux
Q (involving the traditional heat flux
q plus the product of temperature and the sum products of partial entropies and fluxes of species) plays in complex cases (solar, chemical and electrochemical) the same role as the traditional heat
q in pure heat engines.
The presented methodology is also applied to power limits in fuel cells as to systems which are electrochemical flow engines propelled by chemical reactions. The performance of fuel cells is determined by magnitudes and directions of participating streams and mechanism of electric current generation. Voltage lowering below the so-called idle run voltage is a proper measure of cells imperfection. The voltage losses, called polarization, include three main sources: activation, ohmic and concentration polarization. Examples show power maxima in fuel cells and prove the suitability of the thermal machine theory to chemical and electrochemical systems. The main novelty of the present paper in the FC context consists in introducing the effective or reduced Gibbs free energy change between products
p and reactants
s which take into account the decrease of voltage and power decrease caused by the incomplete conversion of the overall electrochemical reaction.
In power production problems maximum power and minimum entropy production and inherently connected by the Gouy–Stodola law. In this paper various mathematical tools are applied in dynamic ...optimization of power-maximizing paths, with special attention paid to nonlinear systems. Maximum power and/or minimum entropy production are governed by Hamilton–Jacobi–Bellman (HJB) equations which describe the value function of the problem and associated controls. Yet, in many cases optimal relaxation curve is non-exponential, governing HJB equations do not admit classical solutions and one has to work with viscosity solutions. Systems with nonlinear kinetics (e.g. radiation engines) are particularly difficult, thus, discrete counterparts of continuous HJB equations and numerical approaches are recommended. Discrete algorithms of dynamic programming (DP), which lead to power limits and associated availabilities, are effective. We consider convergence of discrete algorithms to viscosity solutions of HJB equations, discrete approximations, and the role of Lagrange multiplier
λ associated with the duration constraint. In analytical discrete schemes, the Legendre transformation is a significant tool leading to original work function. We also describe numerical algorithms of dynamic programming and consider dimensionality reduction in these algorithms. Indications showing the method potential for other systems, in particular chemical energy systems, are given.
We present a thermodynamic approach to simulation and modeling of nonlinear energy converters, in particular radiation engines. Novel results are obtained especially for dynamical engines when the ...temperature of the propelling medium decreases in time due to a continual decrease of the medium's internal energy caused by the power production. Basic thermodynamic principles determine the converter's efficiency and work limits in terms of the entropy production. The real work is a cumulative effect obtained in a system of a resource fluid, a sequence of engines, and an infinite bath. Nonlinear modeling involves dynamic optimization in which the classical expression for efficiency at maximum power is generalized to endoirreversible machines and nonlinear transfer laws. The primary result is a finite-rate generalization of the classical, reversible work potential (exergy). The generalized work function depends on thermal coordinates and a dissipation index,
h, i.e. a Hamiltonian of the minimum entropy production problem. This generalized work function implies stronger bounds on work delivered or supplied than the reversible work potential. The role of the nonlinear analyses and dynamic optimization is shown especially for radiation engines. As an example of the kinetic work limit, generalized exergy of radiation fluid is estimated in terms of finite rates, quantified by the Hamiltonian
h.
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