Error estimates of a linear decoupled Euler–FEM scheme for a mass diffusion model

We present error estimates of a linear fully discrete scheme for a threedimensional mass diffusion model for incompressible fluids (also called Kazhikhov– Smagulov model). All unknowns of the model (velocity, pressure and density) are approximated in space by C0-finite elements and in time an Euler type scheme is used decoupling the density from the velocity–pressure pair. If we assume that the velocity and pressure finite-element spaces satisfy the inf–sup condition and the density finite-element space contains the products of any two discrete veloci-ties, we first obtain point-wise stability estimates for the density, under the constraint lim(h,k)→0 h/k = 0 (h and k being the space and time discrete parameters, respectively), and error estimates for the velocity and density in energy type norms, at the same time. Afterwards, error estimates for the density in stronger norms are deduced. All these error estimates will be optimal (of order O(h + k)) for regular enough solu-tions without imposing nonlocal compatibility conditions at the initial time. Finally, we also study two convergent iterative methods for the two problems to solve at each time step, which hold constant matrices (independent of iterations).Ministerio de Educación y Ciencia MTM2006-07932Junta de Andalucía P06-FQM-0237

Analysis of the thermomechanical inconsistency of some extended hydrodynamic models at high Knudsen number

There are some hydrodynamic equations that, while their parent kinetic equation satisfies fundamental mechanical properties, appear themselves to violate mechanical or thermodynamic properties. This article aims to shed some light on the source of this problem. Starting with diffusive volume hydrodynamic models, the microscopic temporal and spatial scales are first separated at the kinetic level from the macroscopic scales at the hydrodynamic level. Then we consider Klimontovich’s spatial stochastic version of the Boltzmann kinetic equation, and show that, for small local Knudsen numbers, the stochastic term vanishes and the kinetic equation becomes the Boltzmann equation. The collision integral dominates in the small local Knudsen number regime, which is associated with the exact traditional continuum limit. We find a sub-domain of the continuum range which the conventional Knudsen number classification does not account for appropriately. In this sub-domain, it is possible to obtain a fully mechanically-consistent volume (or mass) diffusion model that satisfies the second law of thermodynamics on the grounds of extended non-local-equilibrium thermodynamics

Evaluating a Measure-Calculate Method for Determining Sediment Oxygen Demand in Lakes

A steady-state mass diffusion model used with simple measurable and calculable inputs for determining sediment oxygen demand (SOD) is compared to an intact core incubation (ICI) SOD method using samples from three lakes. The mass diffusion model coupled with inputs is known as the measure-calculate method (M-C) and is a potential alternative to existing methods for measuring SOD which are more complex, time-consuming, and costly. The M-C method requires inputs for volumetric sediment oxygen uptake (Ṅsed), sediment density and porosity, and water properties. Ṅsed was determined by suspending sediment in oxygen-saturated water with a DO probe and determining the steady state rate of oxygen decline for the volume of sediment suspended. The SOD values determined using the M-C method were not significantly different from SOD determined using the ICI method using water property inputs representative of lake conditions. Thus, the study confirms the method’s efficacy under test conditions and encourages further research. A separate comparison using water property inputs representative of conditions within incubated cores showed that M-C SOD correlated negatively against ICI SOD despite having similar mean values. This appears to be a result of different boundary conditions for flow velocity and DO within the core, and may discourage the ICI method’s use, as tested, for determining actual in-situ lake SOD

A fast, low-memory, and stable algorithm for implementing multicomponent transport in direct numerical simulations

Implementing multicomponent diffusion models in reacting-flow simulations is computationally expensive due to the challenges involved in calculating diffusion coefficients. Instead, mixture-averaged diffusion treatments are typically used to avoid these costs. However, to our knowledge, the accuracy and appropriateness of the mixture-averaged diffusion models has not been verified for three-dimensional turbulent premixed flames. In this study we propose a fast,efficient, low-memory algorithm and use that to evaluate the role of multicomponent mass diffusion in reacting-flow simulations. Direct numerical simulation of these flames is performed by implementing the Stefan-Maxwell equations in NGA. A semi-implicit algorithm decreases the computational expense of inverting the full multicomponent ordinary diffusion array while maintaining accuracy and fidelity. We first verify the method by performing one-dimensional simulations of premixed hydrogen flames and compare with matching cases in Cantera. We demonstrate the algorithm to be stable, and its performance scales approximately with the number of species squared. Then, as an initial study of multicomponent diffusion, we simulate premixed, three-dimensional turbulent hydrogen flames, neglecting secondary Soret and Dufour effects. Simulation conditions are carefully selected to match previously published results and ensure valid comparison. Our results show that using the mixture-averaged diffusion assumption leads to a 15% under-prediction of the normalized turbulent flame speed for a premixed hydrogen-air flame. This difference in the turbulent flame speed motivates further study into using the mixture-averaged diffusion assumption for DNS of moderate-to-high Karlovitz number flames.Comment: 36 pages, 14 figure

Simulation of Oxygen Transport Membranes for CPO Reactors in Small-scale Hydrogen or Syngas Production Applications

The proposed work aims at presenting a 1D finite volume steady state simulation model of an Oxygen Transport Membrane for Catalytic Partial Oxidation (OTM-CPO) reactor developed at the Group of Energy COnversion Systems (GECOS) at Politecnico di Milano. The model is able to simulate supported and unsupported perovskite-based reactive membranes by means of a lumped mass and energy transport method; the active ceramic layer is modelled throughout a generalised O2permeation equation, which depends on the micro-structure characteristics and mixed-ion conduction properties of the material. The supporting porous structure is represented by a mass diffusion model dominated by gas-gas, porous and surface exchange transport processes. The model also includes a global chemical reaction kinetic mechanism of CPO on Rh-based catalysts. The model is applied to simulate the behaviour of a membrane reactor operated upstream the Hydrogen Transport Membrane for Methane Steam Reforming (HTM-MSR) installed at the Laboratory of Micro-Cogeneration (LMC) at Politecnico di Milano. The test bench is focused on testing fuel pre-processing systems for low temperature fuel cells (PEM) applications. The simulation object of this work would allow obtaining a feasibility assessment of the system and a preliminary design of the OTM-CPO reactor

Application of a Multiscale Particle Scheme to High Altitude Rocket Exhaust Flows

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76663/1/AIAA-2009-1567-355.pd