Gerhart Eigenberger

Applicability of the standard k–ε turbulence model to the dynamic simulation of bubble columns: Part I. Detailed numerical simulations

Abstract Detailed simulation results for the test case of a locally aerated flat bubble column for laminar and turbulent models of Euler–Euler type in two and three dimensions are presented for different space resolutions. The flow structure observed in the experiment has an instationary turbulent character. If the 2D laminar model is applied for calculations the dynamic character of the flow field can be resolved, but the simulation results depend strongly on the space resolution used. If the 2D k–e turbulence model is used instead, the grid independent solution can be achieved on a relatively coarse grid, but the dynamic nature of the flow is not reproduced in the simulation. Only if the 3D turbulent model is used, the simulation results show a good agreement with experiments. This means, that the three-dimensional effects which are neglected in the 2D simulation have a strong influence on the numerical solution. Further, the influence of the discretization on the accuracy of the solution is discussed, and a comparison between results obtained with 2D Euler–Euler and Euler–Lagrange models is presented.

Gas—liquid flow in bubble columns and loop reactors: Part II. Comparison of detailed experiments and flow simulations

Gas-liquid bubble flow was studied in a flat bubble column with rectangular cross-section and essentially two-dimensional flow structure. Both a bubble column and an airlift loop reactor arrangement have been considered. The experimental techniques used comprise visual observation of the flow structure and photographic documentation of the bubble distribution as well as detailed measurements of the two-phase flow characteristics at distinct levels over the column width. The experimental results are compared with numerical simulations based upon the dynamic laminar two-dimensional two-phase Euler—Euler model presented in Part I. The steady state as well as the transient behaviour was well reproduced in the simulations. Good quantitative agreement could be obtained if the value of the laminar viscosity used was increased by a factor 100 to account for the influence of turbulent viscosity. The standardk—ɛ model results in a much higher increase in the viscosity which does not give satisfactory agreement in the range of the bubble flow regime considered.

Limiting current density and water dissociation in bipolar membranes

The behaviour of bipolar membranes in NaCl and Na2SO4 solutions is discussed. The membranes are characterized in terms of their limiting current densities. Below the limiting current density the electric current is carried by salt ions migrating from the transition region between the anion and the cation exchange layer of the bipolar membrane. In steady state these ions are replaced by salt ions transported from the bulk solutions into the transition region by diffusion and migration due to the fact that the ion-exchange layers are not strictly permselective. When the limiting current density is exceeded, the salt transport from the transition region can no longer be compensated by the transport into the region and a drastic increase in the membrane resistance and enhanced water dissociation is observed. This water dissociation is described as being a combination of the second Wien effect and the protonation and deprotonation of functional groups in the membrane. The limiting current density is calculated from a mass balance that includes all components involved in the transport. The parameters used in the mathematical treatment are the diffusion coefficients of salt ions and water, the ion mobilities in the membrane, the fixed charge densitiy of the membrane, the pKb values of the functional groups and the solution bulk concentrations.

Fluid flow through catalyst filled tubes

A detailed knowledge of the fluid flow profile is essential for a proper design of fixed-bed processes. For different sphere, ring and cylinder sizes, radial velocity profiles were measured below the bed at empty tube velocities of air of 0.5 m/s <v0 < 1.5 m/s and the tube-to-particle diameter ratios 3.3 <dtdP < 11. The profiles show a velocity maximum in the vicinity of the wall. As a consequence of the statistical behaviour of packings, it was necessary to average velocity measurements after repacking in order to obtain representative flow profiles. These averaged profiles were the basis for a model through which the flow profile inside the packing can be calculated for spheres, cylinders and rings. The model is based upon the extended Brinkman equation and the independently determined radial void fraction profiles. It considers an ‘effective viscosity’ for which correlations have been derived. Comparison of simulated velocity profiles with exemplary liquid flow measurements inside the packed bed of Vortmeyer and co-workers shows reasonable agreement.

Autothermal fixed-bed reactor concepts

The principles, properties and applications of autothermal fixed-bed reactor concepts are presented. First we focus on different reactor types for weakly exothermic reactions and discuss their basic behavior, their stability and nonlinear dynamic features. The second part is devoted to the autothermal coupling of endothermic and exothermic reactions. A systematic classification is proposed for the process alternatives developed so far and a simplified model is developed from which basic features of an optimal design can be deduced.

Dynamic Modelling and Simulation of a Polymer Membrane Fuel Cell Including Mass Transport Limitation.

Abstract The direct conversion of hydrogen into electricity by polymer membrane fuel cells (PEFC) is a promising option for future transportation and stationary energy supply systems. A model for heat and water transport in a polymer membrane fuel cell has been developed for evaluation with regard to structure and material. Moreover the dynamic simulation allows simulation of the transient state after changes of electrical load or gas flow rate and humidification. The polymer membrane fuel cell is subdivided into different components: gas distributor, gas diffusion layer, catalytic layer and membrane. Each of these components is described by a mathematical model which accounts for the physical phenomena arising in this structure: i.e. energy and mass transfer and electrochemical kinetics. In the simulation program each component is represented by a separate module. Coupling these modules results in a model describing a single electrode membrane unit or a complete fuel cell stack. Results are presented by current-voltage curves or temperature plots. The influence of model parameters such as thickness and porosity of the diffusion layer, or the structure of the catalytic layer, are shown. Furthermore, results of the dynamic behaviour of a polymer membrane fuel cell are presented.

Dynamic numerical simulation of gas-liquid two-phase flows Euler/Euler versus Euler/Lagrange

A dynamical, two-phase flow model in two- and three-space coordinates is presented. The gas-liquid flow is modeled by a Navier-Stokes system of equations in an Eulerian representation. The motion of gas is modeled by a separate continuity equation. The Eulerian approach with UPWIND or TVD discretization and the Lagrangian approach for solving the gas-phase equation are compared with each other on two two-dimensional test problems: the dynamical simulation of a locally aerated bubble column and of a uniformly aerated bubble column. The comparison shows that the results obtained with the TVD-version of the Euler/Euler method and the Euler/Lagrange technique agree quantitatively. On the other hand, it has not been possible to obtain similar agreement even qualitatively with the UPWIND technique, due to the influence of the numerical diffusion effects, which are inherent in the case of UPWIND discretization.

Development and characterization of ion-exchange polymer blend membranes

In the presented paper, the preparation and characterization of new ionomer blend membranes containing sulfonated poly(etheretherketone) PEEK Victrex® is described. The second blend components were Polysulfone Udel®-ortho-sulfone-diamine, polymide PA Trogamid P (producer: Huls) and poly(etherimide) PEI Ultem (producer: General Electric). In the blend membranes swelling was reduced by specific interaction, in the case of the blend components PA and PEI hydrogen bonds, and in the case of the blend component PSU–NH2 (partial) polysalt formation, leading to electrostatic interaction between the blend component macromolecules, and hydrogen bonds. The acid–base interactions also led to decrease of ionic conductivity by partial blocking of SO−3 groups for cation transport, compared with the ionic conductivity of the hydrogen bond blends. The acid–base blends showed better ion permselectivities than the hydrogen bond blends, even at high electrolyte concentrations, and thus better performance in electrodialysis. The thermal stability of the investigated blends was very good and in the case of the acid–base blends even better than the thermal stability of pure PEEK–SO3H. DSC traces of the blend membranes showed only one Tg. In addition, the membranes are transparent to visible light. But therefrom it cannot be concluded that the blend components are miscible to the molecular level: at the acid–base blend blends, the Tg of PEEK–SO3H is very similar to the Tg of PSU–NH2, and in the investigated hydrogen bond blends, the portion of PA or PEI, respectively, might be too low to be detected by DSC. The investigated blend membranes showed similar performance as the commercial cation-exchange membrane CMX in electrodialysis (ED) application. The performance of the acid–base blend membrane is better than the performance of the hydrogen bonded PEEK–PA blend, especially in the ED experiment applying the higher NaCl concentration. This is mainly due to the lower swelling and thus better ion permselectivity of the acid–base blend membrane, compared with the PEEK–PA blend. To get a deeper insight into the microphase structure of the investigated blends, dynamic mechanical analyses and TEM investigations of the prepared blend membranes are planned. In addition, due to their promising properties, the preparation of arylene main-chain acid–base blends with other polymeric acidic and basic components is planned. Furthermore, the acid–base blend membranes will be tested in H2 polymer electrolyte fuel cells and direct methanol fuel cells, because preliminary tests have shown that they have a good perspective in this application.

CATALYTIC COMBUSTION WITH PERIODIC FLOW REVERSAL

Operation of fixed-bed reactors with periodic flow reversal as proposed and demonstrated by Matros and co-workers is a novel mode of operation for weakly exothermic or equilibrium limited reactions. In the present paper catalytic combustion in monolith type catalysts is considered. The influence of the operating parameters upon the shape of the temperature profiles in the stationary state als well as the stability of the ignited state are studied by model calculations. The advantages of inert front- and end sections and of hot gas withdrawal from the centre of the reactor are discussed. Experimental results for the catalytic combustion of traces of methane and propene in air show general agreement with the simulations.

Applicability of the standard k–ε turbulence model to the dynamic simulation of bubble columns. Part II:: Comparison of detailed experiments and flow simulations

Gas–liquid bubble-flow was studied in a flat bubble column with rectangular cross-section. The bubble column was locally aerated through a frit sparger, located in the central part of the bottom plate. The experimental techniques used comprise photographic documentation of the bubble distribution as well as LDA measurements of the liquid velocity. The influence of the liquid level (aspect ratio) in the bubble column and of the gas through-put on the hydrodynamic behaviour of the column has been investigated. At aspect ratio of 1 steady state flow was observed with one circulation cell spread over the full width of the column. This differs from the flow behaviour in a uniformly aerated flat bubble column, reported by Chen, Jamialahmadi and Li (Chemical Engineering Research and Development 67 (1989) 203–207), who observed an essentially symmetric flow field with two stationary circulation cells. At aspect ratios of 2 and 3 the two-phase flow has a transient character with two staggered rows of vortices moving downwards in a periodic way. The long-time averaged liquid velocities obtained from the LDA measurements showed a symmetrical flow field, which is referred to in the literature as the “Gulf-stream” or “cooling-tower” pattern. The experimental results were compared with numerical simulations based upon the dynamic turbulent three-dimensional two-phase Euler–Euler model presented in Part I (Sokolichin and Eigenberger, Chemical Engineering Science (1999) in press). Good qualitative and quantitative agreement was found for the steady state as well as for the transient case.