One-dimensional Non-equilibrium Model Research Articles

Study on the thermal storage performance of high-temperature molten salt spheres packed bed using different heat transfer fluids

The high-temperature packed bed latent heat thermal energy storage system (PBLHTES) system is regarded as the key to the efficient operation of concentrating solar power (CSP) system. The heat transfer and storage materials determine the thermal performance of the thermal energy storage (TES) system. In this study, a discrete scheme for the PBLHTES system has been programmed, and a one-dimensional non-equilibrium model has been established. The numerical results are in good agreement with the experimental findings of the references. Originally, the effects of different fluids' thermodynamic characteristics on thermal performance are studied. Three widely used heat transfer fluids for high temperature working conditions, namely mixed nitrate salt, mixed chloride salt, and thermal oil, are applied for the established packed bed system, respectively. Then, three systems are numerically simulated, and sensitivity analyses of the Reynolds number, Stefan number, and sphere diameter are performed. According to the results, raising the Reynolds and Stefan numbers improves the energy storage rate but leads to an increase in heat transfer temperature difference and a decrease in exergy efficiency. Increasing Stefan number enhances the thermal storage capacity of three systems but causes irreversible loss. Differently, increasing the particle diameter not only extends the thermal storage time and increases the heat transfer temperature difference in all three systems but also decreases the energy storage rate and exergy efficiency. Furthermore, the decreasing slope of exergy efficiency with an increase in Reynolds and Stefan numbers is slowing down in systems 1 and 2 but growing in system 3. With the increase in sphere diameter, the decline slope is decreasing in all three systems. Overall, it is critical to choose the suitable HTF in a traditional or novel PBLHTES system to optimize thermal storage performance.

Quasipotentials in the nonequilibrium stationary states or a method to get explicit solutions of Hamilton–Jacobi equations

We assume that a system at a mesoscopic scale is described by a field ϕ(x, t) that evolves by a Langevin equation with a white noise whose intensity is controlled by a parameter . The system stationary state distribution in the small noise limit (Ω → ∞) is of the form P st [ϕ] ≃ exp(−ΩV 0[ϕ]), where V 0[ϕ] is called the quasipotential. V 0 is the unknown of a Hamilton–Jacobi equation. Therefore, V 0 can be written as an action computed along a path that is the solution from Hamilton’s equation that typically cannot be solved explicitly. This paper presents a theoretical scheme that builds a suitable canonical transformation that permits us to do such integration by deforming the original path into a straight line and including some weights along with it. We get the functional form of such weights through conditions on the existence and structure of the canonical transformation. We apply the scheme to get the quasipotential algebraically for several one-dimensional nonequilibrium models as the diffusive and reaction–diffusion systems.

Thermal and Stability Analysis of Formed Platelet in Platelet Transpiration Cooling

Platelet transpiration cooling is one of the key techniques for the developing reusable launch vehicle. The thinner of the platelet, the better effect plate transpiration will gain. Meanwhile, the platelet unit may get wrinkled if thermal stress is large enough. One-dimensional non-equilibrium model is adopted to analyze the heat transfer characteristics of platelet transpiration cooling. The assumption of rectangular plate with three-side simple supported and one-side free is taken and Galerkin method is applied for analyzing the stability of platelet unit. Analysis indicates that as the heat transfer intensity increases, the thermal soaking depth decreases, while more coolant is needed to keep the heated wall at design temperature. Also, the critical thickness for the platelet not to get wrinkled gets larger with the increasing thermal soaking depth.

High-order well-balanced schemes and applications to non-equilibrium flow

The appearance of the source terms in modeling non-equilibrium flow problems containing finite-rate chemistry or combustion poses additional numerical difficulties beyond that for solving non-reacting flows. A well-balanced scheme, which can preserve certain non-trivial steady state solutions exactly, may help minimize some of these difficulties. In this paper, a simple one-dimensional non-equilibrium model with one temperature is considered. We first describe a general strategy to design high-order well-balanced finite-difference schemes and then study the well-balanced properties of the high-order finite-difference weighted essentially non-oscillatory (WENO) scheme, modified balanced WENO schemes and various total variation diminishing (TVD) schemes. The advantages of using a well-balanced scheme in preserving steady states and in resolving small perturbations of such states will be shown. Numerical examples containing both smooth and discontinuous solutions are included to verify the improved accuracy, in addition to the well-balanced behavior.

Matrix product states of three families of one-dimensional interacting particle systems

The steady states of three families of one-dimensional non-equilibrium models with open boundaries, first proposed in N. J. Phys. 5 (2003) 145.1, are studied using a matrix product formalism. It is shown that their associated quadratic algebras have two-dimensional representations, provided that the transition rates lie on specific manifolds of parameters. Exact expressions for the correlation functions of each model have also been obtained. We have also studied the steady-state properties of one of these models, first introduced in J. Phys. A: Math. Gen. A 36 (2003) 74, with more details. By introducing a canonical ensemble we calculate the canonical partition function of this model exactly. Using the Yang–Lee theory of phase transitions we spot a second-order phase transition from a power law to a jammed phase. The density profile of particles in each phase has also been studied. A simple generalization of this model in which both the left and the right boundaries are open has also been introduced. It is shown that double shock structures may evolve in the system under certain conditions.

Exact solution of a class of one-dimensional nonequilibrium stochastic models.

We consider various one-dimensional nonequilibrium models, namely, the diffusion-limited pair-annihilation and creation model (DPAC) and its unbiased version (the Lushnikov model), the DPAC model with particle injection, as well as (biased) diffusion-limited coagulation model (DC). We study the DPAC model using an approach based on a duality transformation and the generating function of the dual model. We are able to compute exactly the density and correlation functions in the general case with arbitrary initial states. Further, we assume that a source injects particles in the system. Solving, via the duality transformation, the equations of motion of the density, and the noninstantaneous two-point correlation functions, we see how the source affects the dynamics. Finally we extend the previous results to the DC model with help of a similarity transformation.

Experimental and theoretical study of combined solvent and steam stripping of 1,2,3,4,5,6-hexachlorocyclohexane (HCH) and mercury from contaminated natural soil

This paper reports on an experimental and theoretical study of the combined solvent and steam stripping of contaminated soil. First, feasibility experiments on the bench scale are reported concerning the stripping of soil contaminated with 1,2,3,4,5,6-hexachlorocyclohexane (HCH) and mercury. This natural soil, originating from a contaminated site, was packed and stripped in a glass column. The results of cleaning revealed removal levels to below the detection limits of the contaminants and removal efficiencies of 99.7% for HCH and 97.2% for mercury. Subsequently, a one-dimensional nonequilibrium model is proposed which describes the unsteady mass transfer between vapors, condensate and solid phases in a column. A perturbation method is employed to obtain an approximate solution of the governing equations for small Merkel number Me (this dimensionless number constitutes the column length times the mass transfer coefficient, divided by the flushing velocity). Application of the model to the experiments performed results in values for the overall mass transfer coefficients, which can be used for future engineering computations. Furthermore, the model enables the prediction of the initial contaminant level in the soil solely from the measured exit contaminant concentrations in the flushing fluid. A thorough comparison of this prediction with the measured soil concentration (prior to the experiment) yields excellent agreement. The presented model is applicable to any other soil flushing experiment for which Me ⪡ 1.

Modelling boiling delay and transient level swell during emergency pressure relief of liquefied gases

A one-dimensional non-equilibrium model is presented for transient level swell during emergency pressure relief of liquefied gases. The model results are compared to small-scale pressure relief experiments. The effects of thermal non-equilibrium on level swell are summarized and it is shown that non-equilibrium effects are particularly important in small-scale vessels.

First-order phase transition in a one-dimensional nonequilibrium model.

We present an example of a single-component, one-dimensional interacting particle system with a discontinuous transition into an absorbing state. The basic processes in the model are spontaneous annihilation (X\ensuremath{\rightarrow}0), autocatalytic creation by trimers (3X\ensuremath{\rightarrow}4X), and hopping. The transition is continuous, and in the directed percolation class, for low diffusion rates, and first order for sufficiently high diffusion rates. The transition in a similar model with creation by pairs (2X\ensuremath{\rightarrow}3X) remains continuous even at high diffusion rates.

Description of a flowing cascade arc plasma

The plasma in a cascaded arc in argon with flow is studied both experimentally and theoretically. The plasma pressure has been measured as a function of axial position in the are channel with a Baratron pressure transducer. The electron density and the electron temperature have been determined as a function of axial position using Hβ-Stark broadening and line-continuum emissivity ratio, respectively. Comparison of the gas pressure measurements with an equilibrium model suggests that the /low is laminar. A one-dimensional nonequilibrium model based on the electron- and heavy-particle number balances and the heavy-particle energy balance is presented. The measured axial profiles of the electron density agree well with the model predictions, especially in the most upstream part of the arc channel. The plasma is strongly ionizing. Temperature equilibration takes about 20 mm of arc length, depending on the argon flow.