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The current maldistribution along the flow path of electrodialysis (ED) units is a well-known phenomenon. However, it has been poorly quantified via experimental tests so far. This work aimed at measuring the current distribution in an ED stack with 40 cm path length, provided with four-segment electrodes. The current-voltage curve (CVC) of each segment was recorded under several operating conditions of inlet concentrations and feed velocity. In the CVC of the first segment, the current increased approaching a saturation, while in that of the remaining segments it passed through a maximum and then settled at near-zero values when high voltage values were applied. The current fraction on the segments decreased from inlet to outlet. In the overall CVC's first region, up to ~50 % of total current flowed through the first quarter of stack. As the voltage increased, the current fraction increased in the first segment, while it decreased in the other ones tending to vanish. At the limiting condition, the relative standard deviation of the current fraction distribution ranged from 40 % to 68 %. This strong non-uniformity in the ED stack, which may represent one stage of an industrial plant, implies that the design of commercial units must be improved.

Aim of this chapter is that of describing in detail the REAPower project from the very beginning up to the testing of the pilot plant built at the end of the project.

Energy extraction from salinity gradients (salinity gradient power, SGP) represents a novel and valuable renewable energy source. Among the existing SGP technologies, reverse electrodialysis (RED) is the oldest and one of the most promising. RED is a membrane-based electrochemical process that directly converts the salinity gradient energy into electric current. More precisely, in a RED unit two solutions at different concentration flow in two series of alternated channels, which are formed by piling two alternated series of cation and anion exchange membranes (CEMs and AEMs, respectively). The chemical potential difference between the two solutions generates an electric potential difference over each membrane along with a selective transport of cations (across CEMs) and anions (across AEMs) from each concentrate channel towards the two contiguous dilute ones. Eventually, the so generated ionic current is converted by redox reactions into an electric current in the two electrode compartments closing the stack. RED is characterized by a number of different physical phenomena, which should be properly modelled in order to drive the process design and optimization. In this regard, this work presents a novel approach for multi-physical modelling of the entire RED process. A single 2-D cell pair (encompassing two membranes and two feed channels) is the identified process repeating unit, coinciding with the computational domain investigated. In order to fully cover the phenomenological complexity of the operation of a RED unit, a number of different physical models were implemented and interconnected each other. In particular: (i) Navier–Stokes and continuity equations were solved for fluid dynamics modelling; (ii) Nernst–Plank equation was used for ion mass transfer; (iii) local electroneutrality condition was assumed everywhere, taking also into account the fixed charges concentration within the membranes. At membrane-solution interfaces: (iv) Donnan exclusion theory was applied to simulate voltage jump; (v) partition coefficients were adopted to simulate concentration jump. Finally, the model is completed by (vi) algebraic equations for the calculation of stack potential, current density and gross / net power density in a stack of any given number of cell pairs, by taking into account also the electrode compartments resistance and the external load variation. As model outputs, the distributions of velocity, pressure, concentrations, fluxes and potential in the overall domain were obtained, and the values of gross and net power density were computed. Different membrane/channel configurations were investigated, including flat membranes, either with or without non-conductive spacers, and profiled membranes. Moreover, the influence of the feeds concentration was evaluated. The model developed appears to be a promising tool for the optimization of RED units design and operation

Reverse electrodialysis (RED) is an electrochemical membrane process that converts the salinity gradient energy between two solutions into electric current, by using ion exchange membranes. A novel multi-physical approach for RED modelling is proposed. 2-D simulations of one cell pair with tertiary current distribution (Nernst–Plank equation and local electroneutrality) were performed. Moreover, the Donnan exclusion theory was implemented for simulating double layer phenomena. Transport phenomena and electrochemical behavior were well described. The influence of membrane/channel configuration, dilute concentration and feeds velocity on the process performance was assessed. For a dilute concentration ≤ 0.01M, stacks with profiled membranes reached lower resistances and higher net powers (up to 4.4 W/m2) with respect to stacks with empty channels, thus suggesting that only in some cases the profiles lead to a performance enhancement.

Reverse electrodialysis (RED) is a promising technology for electric power generation by the chemical potential difference of two salt solutions within a stack equipped by selective ionexchange membranes (salinity gradient energy). Mechanical energy is required for pumping the feed solutions, which can reduce dramatically the net power output. In this work Computational Fluid Dynamics (CFD) simulations of spacer-filled channels for RED were carried out in parallel with an experimental campaign focused on the collection of data for model validation.

Turbulent flow and heat transfer in helically coiled pipes at Retau=400 was investigated by DNS using finite volume grids with up to 2.36×10E7 nodes. Two curvatures (0.1 and 0.3) and two torsions (0 and 0.3) were considered. The flow was fully developed hydrodynamically and thermally. The central discretization scheme was adopted for diffusion and advection terms, and the second order backward Euler scheme for time advancement. The grid spacing in wall units was ~3 radially, 7.5 circumferentially and 20 axially. The time step was equal to one viscous wall unit and simulations were typically protracted for 8000 time steps, the last 4000 of which were used to compute statistics. The results showed that curvature affects the flow significantly. As it increases from 0.1 to 0.3 the friction coefficient and the Nusselt number increase and the secondary flow becomes stronger; axial velocity fluctuations decrease, but the main Reynolds shear stress increases. Torsion, at least at the moderate level tested (0.3), has only a minor effect on mean and turbulence quantities, yielding only a slight reduction of peak turbulence levels while leaving pressure drop and heat transfer almost unaffected.

In the present work, a recently presented experimental technique, based on the use of thermochromic liquid crystals (TLCs) and digital image processing, has been employed in order to measure the temperature and local heat transfer coefficient distribution on the membrane surface in a MD spacer-filler channel

Reverse electrodialysis (RE) is a promising technology for electric power generation by converting the chemical potential difference of a salinity gradient, within a stack equipped by selective ion-exchange membranes. Concentration polarization phenomena and pressure drop affect strongly the power output obtainable; therefore the channel geometry is a fundamental operating parameter for the optimization of the system. In this work, Computational Fluid Dynamic simulations were performed to predict fluid flow and mass transfer in spacer-filled channels for RE applications. A parametric analysis for different spacer geometries was carried out; in particular, woven and non woven spacers were simulated, with different pitch to height ratios, at various Reynolds numbers typical of RE channels, and with two different orientation. From the rigorous Stefan–Maxwell equation along with the assumptions of binary electrolyte and local electroneutrality, the transport equation was obtained. Periodic boundary conditions were adopted to simulate a fully developed flow. Simulation results show how the parameters investigated influence pressure drop and concentration polarization, thus suggesting the features that a spacer should have in order to obtain high process performance.

Reverse electrodialysis (RE) is a promising technology for electric power generation from controlled mixing of two differently concentrated salt solutions, where ion-exchange membranes are adopted for the generation of ionic currents within the system. Channel geometry strongly influences fluid flow and thus crucial phenomena such as pressure drop and concentration polarization. Profiled membranes are an alternative to the more commonly adopted net spacers and offer a number of advantages: avoiding the use of non-conductive and relatively expensive materials, reducing hydraulic losses and increasing the active membrane area. In this work, Computational Fluid Dynamic simulations were performed to predict the fluid flow and mass transfer behaviour in channels with profiled membranes for RE applications. In particular, channels equipped with pillars were simulated. The influence of channel geometry on fluid flow and concentration polarization was assessed by means of a parametric analysis for different profile geometries. The unit cell approach along with periodic boundary conditions was adopted to simulate fully developed boundary conditions. Transport equations, valid also for concentrated solutions, were obtained from the rigorous Stefan–Maxwell equation along with the assumptions of binary electrolyte and local electroneutrality. Simulation results show that, in the geometries investigated here, the pumping power consumption is much lower than in a conventional net spacer and very close to that of the empty channel, while calm zones are generated by the profiles, which may accentuate polarization phenomena.

Solid-liquid mixing within tanks agitated by stirrers can be easily encountered in many industrial processes. It is common to find an industrial tank operating at an impeller speed N lower than the minimum agitation speed for the suspension of solid particles: under such conditions the distribution of solid-particles is very far from being homogeneous and very significant concentration gradients exist. The present work evaluates the capability of a Computational Fluid Dynamics (CFD) model to reliably predict the particle distribution throughout the tank under either partial or complete suspension conditions. A flat bottomed baffled tank stirred by a Rushton turbine was investigated. Both transient and steady state RANS simulations of the stirred tank were performed with the commercial code CFX4.4. The Eulerian-Eulerian Multi Fluid Model along with the k-ε turbulence model was adopted. Either the Sliding Grid or the Multiple Reference Frame technique was employed to simulate the impeller to baffle relative rotation. Inter-phase momentum exchange terms were approximated only by the inter-phase drag forces. Literature experimental data were used for the model validation. Results show that the model along with the Sliding Grid technique can reliably predict the experimental particle distribution at all investigated impeller speeds. Radial gradients of solids concentration, usually neglected in the literature, where found to be significant in the presence of unsuspended solid particles (partial suspension conditions).

Turbulent two-phase flow in a helical pipe was simulated by means of CFD using the ANSYS-CFX code, based on a finite-volume multi-fluid approach. The focus was on flow patterns and frictional pressure drops; inter-phase heat and mass transfer and heat exchange with the pipe walls were not included and physical properties were assumed constant for each phase. The computational domain included a single, vertical axis, coil turn; the flow was assumed to be fully developed. Geometry and physical conditions were representative of the IRIS nuclear reactor steam generators (saturated water at 58 bar, pressure gradient of 0.1 bar/m). Void fraction and computational options (homogeneous vs. inhomogeneous two-phase model, homogeneous vs. phase-specific k- and k- turbulence models, interphase drag model parameters, grid, steady-state vs. transient approach) were made to vary in a sensitivity analysis. Literature correlations were used as reference. Using the inhomogeneous two-phase model, results exhibited a sharp liquid-gas interface; the light (gas) and heavy (liquid) phases stratified diagonally in the cross section under the combined action of gravity and centrifugal forces. Inter-phase drag parameters had only a minor influence on the results. The homogeneous model yielded a uniform mixture at all values of . With all options, the simulations overestimated the mass flow rate for imposed pressure drop and quality. Only minor differences in the results were obtained by changing the turbulence model. Even less was the influence of grid size and other computational details. The influence of gravity was small but not negligible under the conditions investigated.

Fully developed turbulent convective heat transfer in curved pipes was investigated by Direct Numerical Simulation for a friction velocity Reynolds number of 500, yielding bulk Reynolds numbers between 12 630 and ~17 350 according to the curvature (pipe radius/curvature radius). Three different curvatures were compared, i.e. 0 (straight pipe), 0.1 and 0.3. The Prandtl number was 0.86. The computational domain was a tract of pipe 5 diameters in length. A finite volume method was used, with multiblock structured grids of ~5.3x10E6 hexahedral volumes. Simulations were typically protracted for 20 LETOT’s starting from coarse-grid results. Results were post-processed to compute first and second order time statistics, including rms fluctuating temperature and turbulent heat fluxes, on a cross section of the pipe. In curved pipes, time-mean results exhibited Dean circulation and a strong velocity and temperature stratification in the radial direction. Turbulence and heat transfer were strongly asymmetric, with higher values near the outer pipe bend. Overall turbulence levels were lower than in a straight pipe

In this work, carried out within the EU-FP7 funded REAPower project, CFD simulations were carried out in order to study the fluid flow behaviour and mass transport phenomena within spacer-filled channels.

L’attività di ricerca svolta nell’ambito della linea progettuale LP2-B.2 del programma PAR 2008-09 (CERSE III) ha visto una prima fase in cui è stato ulteriormente sviluppato il lavoro svolto nel corso dei precedenti programmi CERSE [1, 2], riguardante la validazione del codice termoidraulico avanzato Relap5/Mod3.2.b, modificato per il calcolo delle cadute di pressione in tubi elicoidali interessati da deflussi monofase e bifase, ed una seconda fase che ha comportato l’implementazione di nuove procedure valide per lo studio dello scambio termico bifase in condotti elicoidali, in aggiunta a quelle relative al solo scambio termico monofase, in precedenza implementate. Per quanto riguarda quest’ultima attività, si pensa, infatti, di affrontare in futuro il lavoro di validazione del codice modificato, facendo ricorso ai dati sperimentali disponibili, che sono ancora in fase di raccolta e sviluppo, per cui in questa relazione ci si limiterà a mostrare i risultati ottenuti nella simulazione, effettuata con il codice modificato e non modificato, delle perdite di carico lungo un condotto elicoidale interessato da deflusso bifase in diverse condizioni operative di portata, temperatura e pressione. Per tale lavoro si è fatto ricorso ad una estesa campagna sperimentale condotta dal Dipartimento dell’Energia del Politecnico di Milano presso i laboratori della SIET di Piacenza per l’indagine teoricosperimentale di vari aspetti inerenti la termoidraulica dei generatori di vapore previsti nel reattore nucleare IRIS. Inoltre, il codice modificato è stato impiegato per la simulazione di dati sperimentali, reperiti in letteratura, riguardanti lo scambio termico monofase in scambiatori di calore elicoidali a tubi concentrici con lo scopo di testare la sua capacità nel trattare anche geometrie diverse da quelle già esaminate. I risultati ottenuti, che sembrano essere confortanti ai fini di un’estensione dell’uso del codice così modificato, vengono riportati in Appendice A.

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