Steady, periodic, quasi-periodic and chaotic flow regimes in toroidal pipes

Incompressible flow in a toroidal pipe was investigated by direct numerical simulation. The curvature a/c (radius of the cross section / radius of the torus) was 0.3 or 0.1 and the bulk Reynolds number ranged between 3500 and 14 700. The study revealed a rich scenario of transition to turbulence. For the higher curvature a/c = 0.3, a supercritical transition from stationary to periodic flow (Hopf bifurcation) was observed at Re=4600. The periodic flow was characterized by a travelling wave which, in the whole periodic Re range, took the form of a varicose modulation of the twin Dean vortex rings, included 8 wavelengths along the axis of the torus, and exhibited instantaneous anti-symmetry about the equatorial midplane. A further transition to quasi-periodic flow, characterized by two independent fundamental frequencies and their first few harmonics, occurred at Re=5200. The two frequencies were associated with two travelling wave systems, the first consisting of a varicose modulation of the Dean vortex rings, the second of an array of oblique near-wall vortices produced at the edge of the Dean cells, co-rotating with these latter and travelling from the inner towards the outer side, against the secondary circulation. For the lower curvature a/c=0.1, the results suggested the existence of a subcritical Hopf bifurcation at Re=5200 and of a secondary Hopf bifurcation to quasi-periodic flow at a lower Reynolds number of ~4900. Starting from zero-velocity initial conditions, the steady-state flow remained stable up to a Reynolds number of 5139, while a further increase in Re to 5208 yielded an abrupt transition to quasi-periodic flow which remained stable up to Re=6280 or larger. When a quasi-periodic solution (e.g., that obtained for Re=5658) was used as the initial condition and Re was made to decrease, the quasi-periodic regime remained stable down to values of Re well below the subcritical Hopf bifurcation at ~5200. Only a further, substantial decrease of Re to ~4108 led to the smooth disappearance of mode II and to a stable periodic solution. An abrupt transition to stationary flow was obtained when the Reynolds number decreased well below 4000 (e.g., a test case was computed for Re =3490). All periodic and quasi-periodic solutions for a/c=0.1 exhibited instantaneous symmetry about the equatorial midplane. Also the further transition from quasi-periodic to chaotic flow occurred with different mechanisms for the two curvatures. For a/c=0.3, quasi-periodic flow was obtained in the whole Reynolds number range 5270-7850. As Re increased slightly beyond this value (Re=8160), strong fluctuations, associated with random streamwise vortices, arose in the outer region. The ensuing chaotic flow regime was characterized by a broadband, almost continuous, frequency spectrum. A further increase of Re to 13180 did not modify to any appreciable extent the flow regime and the distribution of the velocity fluctuation intensity. For a/c=0.1, the convergence of the results to quasi-periodic flow became impossible to achieve as Re increased beyond ~6280, and was replaced by long and erratic transients. For Re=8160, the solution, albeit stationary in a statistical sense, was chaotic and exhibited a large number of frequencies, but the outer region remained basically stationary. Only when Re increased further, the outer region became unsteady and was characterized by the production of streamwise vortices which were then transported by the secondary flow destroying all remains of regular oscillations

Experimental Analysis via Thermochromic Liquid Crystals of the Temperature Local Distribution in Membrane Distillation Modules

A reliable and optimized design of channels for Membrane Distillation (MD) requires knowledge of local temperature distributions within the module. This information is essential to measure the temperature polarization, choice the module configuration (net spacer features, channel size, etc) providing the best process performance. Notwithstanding such crucial aspects, only few studies have been devoted to the experimental characterization of MD channels and none of them includes data on the local temperature distribution. In the present work, an experimental technique based on the use of Thermochromic Liquid Crystals (TLCs) and digital image processing, previously proposed by the authors (Pitò et al., 2011), was further developed and employed in order to measure the temperature and local heat transfer coefficient distribution on the membrane surface in a MD spacer-filled channel. The performance of different types of commercial net spacers were tested. The channel provided with the symmetric net spacer was found to be the configuration leading to the best heat transfer and to the lowest temperature polarization

Friction and Heat Transfer in Membrane Distillation Channels: An Experimental Study on Conventional and Novel Spacers

The results of an experimental investigation on pressure drop and heat transfer in spacer- filled plane channels, which are representative of Membrane Distillation units, are presented and discussed. Local and mean heat transfer coefficients were obtained by using Thermochromic Liquid Crystals and Digital Image Processing. The performances of a novel spacer geometry, consisting of spheres that are connected by cylindrical rods, and are hereafter named spheres spacers, were compared with those of more conventional woven and overlapped spacers at equal values of the Reynolds number Re (in the range ~150 to ~2500), the pitch-to-channel height ratio, the flow attack angle and the thermal boundary conditions (two-side heat transfer). For any flow rate, the novel spacer geometry provided the least friction coefficient and a mean Nusselt number intermediate between those of the overlapped and the woven spacers. For any pressure drop and for any pumping power, the novel spacer provided the highest mean Nusselt number over the whole Reynolds number range that was investigated. The influence of buoyancy was also assessed for the case of the horizontal channels. Under the experimental conditions (channel height H ≈ 1 cm, ∆T ≈ 10 ◦C), it was found to be large in empty (spacer-less) channels that were up to Re ≈ 1200 (corresponding to a Richardson number Ri of ~0.1), but it was much smaller and limited to the range Re < ~500 (Ri < ~0.5) in the spacer-filled channels

CFD prediction of concentration polarization phenomena in spacer-filled channels for Reverse Electrodialysis

Salinity Gradient Power generation through Reverse Electrodialysis (SGP-RE) is a promising technology to convert the chemical potential difference of a salinity gradient into electric energy. In SGP-RE systems, as in most membrane processes, concentration polarization phenomena may affect the theoretical driving force and thus the performance of the process. Operating conditions, including the feed solution flow rate and concentration and the channels’ geometrical configuration, may greatly influence both the polarization effect and the pumping energy consumption. The present work uses CFD to investigate the dependence of concentration polarization and pressure drop on flow rate, feeds concentration, current density and spacer features. Concentration polarization effects were found to be significant at low feed solution concentration (river water), but only secondary at higher concentrations (seawater and brine), thus suggesting that different optimization strategies should be employed depending on the feeds concentration. The features that a spacer-filled channel should possess for high efficiency and high current density SGP-RE applications were identified

CFD analysis of concentration polarization phenomena in spacer-filled channels for Reverse Electro-Dialysis

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

Dense Solid-Liquid Off-Bottom Suspension Dynamics: Simulation and Experiment

Dense solid-liquid off-bottom suspension inside a baffled mechanically agitated stirred tank equipped with a standard Rushton turbine is investigated. Dynamic evolution of the suspension from start up to steady state conditions has been inspected by both visual experiments and computational fluid dynamics. A classical Eulerian-Eulerian Multi Fluid Model along with the “homogeneous” k-epsilon turbulence model is adopted to simulate suspension dynamics. In these systems the drag inter-phase force affects both solids suspension and distribution. Therefore, different computational approaches are tested in order to compute this term. Simulation results are compared with images acquired on the real system and a good agreement is found

Influence of drag and turbulence modelling on CFD predictions of solid liquid suspensions in stirred vessels

Suspensions of solid particles into liquids within industrial stirred tanks are frequently carried out at an impeller speed lower than the minimum required for complete suspension conditions. This choice allows power savings which usually overcome the drawback of a smaller particle-liquid interfacial area. Despite this attractive economical perspective, only limited attention has been paid so far to the modelling of the partial suspension regime. In the present work two different baffled tanks stirred by Rushton turbines were simulated by employing the Eulerian-Eulerian Multi Fluid Model (MFM) along with either the Sliding Grid algorithm (transient simulations) or the Multiple Reference Frame technique (steady state simulations). In particular, a comparison of alternative modelling approaches for inter-phase drag force and turbulence closure is presented. The results are evaluated against a number of experimental data concerning sediment features (amount and shape) and local axial profiles of solids concentration, with emphasis on the partial suspension regime. Results show that some of the approaches commonly adopted to account for dense particle effects or turbulent fluctuations of the volumetric fractions may actually lead to substantial discrepancies from the experimental data. Conversely simpler models which do not include such additional effects give the best overall predictions in the whole range of partial to complete suspension conditions

A Thermochromic Liquid Crystals Image Analysis technique to investigate temperature polarization in spacer-filled channels for Membrane Distillation

The analysis of flow fields and temperature distributions is of paramount importance in the development and optimization of new spacer-filled channel geometries for Membrane Distillation modules. The literature reports only few studies on the experimental characterization of such channels and, to the authors’ knowledge, none of them presents local information concerning the temperature distribution on the membrane surface. In the present work, a non-intrusive experimental technique named TLC-IA-TP is presented: it is based on the use of Thermochromic Liquid Crystals (TLCs) and digital Image Analysis (IA) and it is applied here for the first time to the analysis of Temperature Polarization (TP) in spacer-filled channels typically adopted in thermally-driven membrane separation processes. In particular, this technique allows the local distribution of convective heat transfer coefficients to be determined, thus providing (i) useful indications on strengths and weaknesses of some spacer arrangements and (ii) valuable benchmark data for Computational Fluid Dynamics (CFD) studies. For the purpose of the present work, the technique’s fundamentals are presented, along with a comprehensive assessment of the technique’s accuracy. Results of some preliminary measurements on commercial spacers are also reported

Heat-transfer performance comparison between overlapped and woven spacers for membrane distillation

Sustainable production of fresh water from seawater desalination is a problem of crucial importance nowadays. Recently, some desalination technologies are taking advantage from the coupling with renewable resources. Among emerging technologies, Membrane Distillation (MD) is considered as one of the most promising as it can be easily powered by solar thermal energy or waste-heat. As an emerging technology, efforts are required to optimize MD unit geometry and operating conditions in order to reduce fresh water production specific cost. Temperature polarization phenomenon is a well-known detrimental effect for the MD process. Spacers are traditionally used to enhance mixing and shrink temperature boundary layers yet yielding higher pressure-losses. The present work is devoted to testing the performance of two different two-layer net-spacers: overlapped and woven. Investigations were carried out by both experiments and Computational Fluid Dynamics (CFD) simulations at different Reynolds numbers ranging from creeping to turbulent flow regime. Experiments (intermediate to high Re) were performed via a novel experimental technique making use of thermochromic liquid crystals and digital image analysis. Computational data (low to intermediate Re) were obtained via steady state (low Re) and Direct Numerical Simulations (intermediate Re), adopting the Unit Cell approach. A good agreement between experiments and CFD data was found in the range of superposition. Results showed that woven spacers guarantee a better mixing than overlapped ones especially in the low-intermediate range of Re thus resulting into a higher Nusselt number. On the other hand, the less disturbed flow field induced by the overlapped wires was found to give raise to lower pumping losses

CFD prediction of solid particle distribution in baffled stirred vessels under partial to complete suspension conditions

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)