Volume 41, Issue 4 -

The rate-controlled constrained-equilibrium (RCCE) method is employed to study the interactions between mixing and chemical reaction. Considering that mixing can influence the RCCE state, the key objective is to assess the accuracy and numerical performance of the method in simulations involving both reaction and mixing. The RCCE formulation includes rate equations for constraint potentials, density and temperature, which allows taking account of mixing alongside chemical reaction without splitting. The RCCE is a dimension reduction method for chemical kinetics based on thermodynamics laws. It describes the time evolution of reacting systems using a series of constrained-equilibrium states determined by RCCE constraints. The full chemical composition at each state is obtained by maximizing the entropy subject to the instantaneous values of the constraints. The RCCE is applied to a spatially homogeneous constant pressure partially stirred reactor (PaSR) involving methane combustion in oxygen. Simulations are carried out over a wide range of initial temperatures and equivalence ratios. The chemical kinetics, comprised of 29 species and 133 reaction steps, is represented by 12 RCCE constraints. The RCCE predictions are compared with those obtained by direct integration of the same kinetics, termed detailed kinetics model (DKM). The RCCE shows accurate prediction of combustion in PaSR with different mixing intensities. The method also demonstrates reduced numerical stiffness and overall computational cost compared to DKM.

We examine the linear stability analysis of the equations governing Rayleigh–Bénard convection flows when the basic temperature profile is unstably stratified solely over a thin horizontal slice of the fluid region. We conduct both asymptotic and numerical analyses on three distinct shapes of the basic temperature: (i) a hyperbolic tangent profile, (ii) a piecewise linear profile and (iii) a step-function profile. In the first two cases, the thin unstably stratified layer is centrally located. The presence of stably stratified regions below and above the central layer diminishes the effect of the velocity and thermal boundary layers that form at the plates. This in turn allows for the analysis of the convection process without the constraints of the horizontal boundaries to be simulated in a finite domain. We obtain expressions for the threshold parameters for convection onset as well as flow features as function of the thickness of the unstably stratified layer. In the limit of a vanishingly small thickness, the hyperbolic tangent profile tends to a step-function profile with a heavy top layer overlying a lighter bottom layer. These two layers are separated by an interface where a jump in density occurs. This situation resembles the Rayleigh–Taylor instability of a horizontal interface except that neither is the interface free nor is the buoyancy diffusion absent. The exploration of this case uncovers new instability threshold values and flow patterns. Finally, we discuss some relevant applications.

We develop a phase-field model for the liquid–vapor phase transition. The model aims to describe in a thermodynamically consistent way the phase change phenomenon coupled with the macroscopic motion of the fluid. The phase field φ∈[0,1]$\varphi \in [0, \,1]$ describes the liquid fraction at any point and the overall water density is a function of the phase field and the pressure. An extra gaseous substance (e.g. air) is allowed in the system and contributes to the mechanical pressure. The phase transition is described by a Ginzburg–Landau equation. The parameter that drives the transition is the partial vapor pressure, which is the relevant quantity for condensation and evaporation phenomena. Moreover, a velocity-dependent term contributes to the phase change in the transition layers where a vapor pressure gradient exists.

A consecutive chemical reaction A⇔B⇔C$$A \Leftrightarrow B \Leftrightarrow C$$ is studied in this paper. The optimal concentration configuration of the reaction for minimum entropy generation with fixed yield of aimed product B$$B$$ is derived. The optimal concentration configuration with different initial conditions and the optimal initial concentration CC0,opt$${C_{C0}}_{{\rm{, opt}}}$$ of the by-product C$$C$$ are obtained numerically. Compared with the control method that the concentration of A$$A$$ increases linearly, the entropy production is reduced by more than 90 %. The minimum entropy generation and optimal configuration of elementary reaction A⇔B$$A \Leftrightarrow B$$ are studied by using variational method and nonlinear programming method. The validity of the nonlinear programming method is verified. The reaction rate of elementary reaction A⇔B$$A \Leftrightarrow B$$ is in proportion to the square root of the concentration of A$$A$$ when entropy generation of the reaction process is minimum. The results obtained can help one to find the realizable regimes for a chemical reactor.

One promising sustainable energy source is the chemical potential difference between salt and freshwater. The membrane process of pressure-retarded osmosis (PRO) has been the most widely investigated means to harvest salinity gradient energy. In this report, we analyse the thermodynamic efficiency of multistage PRO systems to optimize energy recovery from a salinity gradient. We establish a unified description of the efficiencies of the component pumps ( P ), turbines ( T ), pressure exchangers (PX), and membrane modules ( M ) and exploit this model to determine the maximum available work with respect to the volume of the brine produced, the volume of the sea water consumed, or the volume of the freshwater that permeates the membrane. In an idealized series configuration of 1–20 modules ( P – M – T ), the three optimization conditions have significantly different intermediate operating pressures in the modules, but demonstrate that multistage systems can recover a significantly larger fraction of the available work compared to single-stage PRO. The biggest proportional advantage occurs for one to three modules in series. The available work depends upon the component efficiencies, but the proportional advantage of multistage PRO is retained. We also optimize one- and two-stage PX– M – T and P – M – T configurations with respect to the three volume parameters, and again significantly different optimal operating conditions are found. PX– M – T systems are more efficient than P – M – T systems, and two-stage systems have efficiency advantages that transcend assumed component efficiencies. The results indicate that overall system design with a clear focus on critical optimization parameters has the potential to significantly improve the near-term practical feasibility of PRO.