Michele Ciofalo

Numerical prediction of flow fields in baffled stirred vessels: A comparison of alternative modelling approaches

Abstract Numerical simulations of the flow field in baffled mixing tanks, based on three alternative methods, are presented and discussed. In the first method, the impeller is not explicitly simulated, and its effects are modelled by imposing suitable, empirically derived, boundary conditions to the external flow. In the second method, the whole vessel volume is divided into two concentric, partially overlapping, regions. In the inner region, containing the impeller, the flow field is simulated in the rotating reference frame of the latter, while in the outer region simulations are conducted in the reference frame of the laboratory. Information is iteratively exchanged between the two regions after azimuthally averaging and transforming for the relative motion. In the third method, the tank volume is divided into two concentric blocks, the inner one rotating with the impeller and the outer one stationary. The two blocks do not overlap and are coupled by a sliding-mesh technique. Predictions are presented here for baffled tanks stirred either by single and dual Rushton turbines (radial impellers) or by a constant-pitch helical impeller (axial impeller), and are compared with experimental data from the literature. Satisfactory results can be obtained by the first method only if reliable empirical data are available for the flow near the impeller, while large errors may arise if this is not known with reasonable accuracy. The other two methods both yield satisfactory results while requiring no empirical information, and thus allow a much greater generality.

Investigation of flow and heat transfer in corrugated passages—II. Numerical simulations

An experimental and numerical study of flow and heat transfer was conducted for a crossed-corrugated geometry, representative of compact heat exchangers under transitional and weakly turbulent conditions. Three-dimensional numerical predictions were obtained by a finite volume method using a variety of approaches ranging from laminar flow assumptions to standard and low-Reynolds number k-e turbulence models, direct simulation, and large-eddy simulation. In this paper, the various computational approaches are presented and their relative performance is discussed for various geometries and Reynolds numbers; results are compared with experimental measurements and literature data. Detailed experimental results are presented in Part I.

Investigation of flow and heat transfer in corrugated passages—I. Experimental results

Abstract An experimental and numerical study of flow and heat transfer was conducted for a crossed-corrugated geometry, representative of compact heat exchangers including air preheaters for fossil-fuelled power plant. In this paper, we describe the method of applying thermochromic liquid crystals and true-colour image processing to give local Nusselt number distribution over the surface, and average Nu, both of quantitative reliability; a careful uncertainty analysis is also presented. Typical experimental results for heat transfer and pressure drop are presented and discussed for various geometries and Reynolds numbers, and are compared with literature data. Numerical predictions are discussed in Part II.

Turbulent flow in closed and free-surface unbaffled tanks stirred by radial impellers

The three-dimensional turbulent flow field in unbaffled tanks stirred by radial impellers was numerically simulated by a finite-volume method on body-fitted, co-located grids. Simulations were run, with no recourse to empirical input, in the rotating reference frame of the impeller. Free-surface problems were also simulated, in which the profile of the central vortex was computed as part of the solution by means of an iterative technique. Predicted velocity and turbulence fields in the whole vessel and power consumptions were assessed against available literature data; free-surface profiles were also compared with original experimental data obtained in a model tank. Both the eddy-viscosity k−e turbulence model and a second-order differential stress (DS) model were used and compared: satisfactory results were obtained only by using the latter model. The need for including source terms arising from fluctuating Coriolis forces in the Reynolds stress transport equations is highlighted.

On the simulation of stirred tank reactors via computational fluid dynamics

Abstract Predictions of flow fields in a stirred tank reactor, obtained by computational fluid dynamics, were used for the simulation of a mixing sensitive process consisting of two parallel reactions competing for a common reagent: A + B → Prod .1 A + C → Prod .2. Experimental data were obtained for A = OH − , B = 1 2 Cu ++ and C=ethyl-chloroacetate. For this reaction scheme the final selectivity of the process, easily measured by a simple colorimetric analysis of the residual Cu++, was found to depend on agitation speed and therefore on the mixing history during the batch process. The flow field-based three-dimensional simulations performed here led to predictions that compared very well with the experimental data, though no adjustable parameters were used. Interestingly, these encouraging results were obtained by modelling only the “macromixing” phenomenon, while “micromixing” phenomena were neglected, i.e. the system was always considered as being locally perfectly micro-mixed. The good agreement found between simulation predictions and experimental data retrospectively confirms the negligibility of micromixing phenomena in the system investigated.

MHD free convection in a liquid-metal filled cubic enclosure. II. Internal heating

The buoyancy-driven magnetohydrodynamic flow in a liquid-metal filled cubic enclosure was investigated by three-dimensional numerical simulation. The enclosure was differentially heated at two opposite vertical walls, all other walls being adiabatic, and a uniform magnetic field was applied orthogonal to the temperature gradient and to the gravity vector. The Rayleigh number was 105 and the Prandtl number was 0.0321 (characteristic of Pb–17Li at 573 K). The Hartmann number was made to vary between 102 and 103 and the electrical conductance of the walls between 0 and ∞. The continuity, momentum and enthalpy transport equations, in conjunction with a Poisson equation for the electric potential, were solved by a finite volume method using the general-purpose CFX-4 package with some necessary adaptations. Steady-state conditions were assumed. With respect to the case of parallel flow in an infinitely tall enclosure, studied in previous work, the suppression of convective motions due to magnetohydrodynamic interactions was stronger in the core, and a complex three-dimensional flow (with secondary motions) and current pattern was established in the fluid domain. Increasing the Hartmann number suppressed convective motions and exalted the square-shape of the circulation cells. Increasing the wall conductance ratio from perfectly insulating to perfectly conducting walls also resulted in an increasing suppression of convection. The related case of an internally heated enclosure is discussed in a companion paper.

Investigation of the cooling of hot walls by liquid water sprays

Abstract An experimental study was conducted for the heat transfer from hot walls to liquid water sprays. Four full cone, swirl spray nozzles were used at different upstream pressures, giving mass fluxes impinging on the wall, G, from 8 to 80 kg m−2 s−1, mean droplet velocities, U, from 13 to 28 m s−1 and mean droplet diameters, D, from 0.4 to 2.2 mm. A target consisting of two slabs of beryllium–copper alloy, each 4×5 cm in size and 1.1 mm thick, was electrically heated to about 300°C and then rapidly and symmetrically cooled by water sprays issuing from two identical nozzles. The midplane temperature was measured by a fast response, thin-foil thermocouple and the experimental data were regularized by Gaussian filtering. The inverse heat conduction problem was then solved by an approximation of the exact Stefan solution to yield the wall temperature Tw and the heat flux qw transferred to the spray at temperature Tf. As a result, cooling curves expressing the heat flux qw as a function of Tw−Tf were obtained. The single-phase heat transfer coefficient h and the maximum heat flux qc were found to depend upon the mass flux G and the droplet velocity U, while the droplet size D had a negligible independent influence. Simple correlations for h and qc were proposed.

Low-Prandtl number natural convection in volumetrically heated rectangular enclosures III. Shallow cavity, AR=0.25

Abstract Natural convection in a volumetrically heated rectangular enclosure filled with a low-Prandtl number (Pr=0.0321) fluid was studied by direct numerical two-dimensional simulation. The enclosure had isothermal side walls and adiabatic top/bottom walls. The aspect ratio was 4 and the Grashof number Gr, based on conductive maximum temperature and cavity width, ranged from 3.79 × 104 to 1.26 × 109. According to the value of Gr, different flow regimes were obtained: steady-state, periodic, and chaotic. The first instability of the steady-state solution occurred at Gr≈3×105; the resulting time-periodic flow field consisted of a central rising plume and of convection rolls, periodically generated in the upper corners of the cavity and descending regularly along the vertical isothermal walls. Transition from periodic to chaotic motion occurred at Gr≈1×106; up to the highest Grashof numbers studied, the fluid motion exhibited a recognizable dominating frequency, associated with the process of roll renewal and scaling as Gr1/2. The flow field still consisted of a meandering rising plume and of downcoming convection rolls, but these coherent structures were now irregular in shape, size and velocity. For Grashof numbers larger than ∼106 (chaotic flow), the friction coefficient averaged along the vertical walls was found to scale as Gr−1/3 and the Nusselt number (overall/conductive heat transfer) as Gr1/6.

Natural convection heat transfer in a partially-or completely-partitioned vertical rectangular enclosure

Abstract The effect of symmetric partitions protruding centrally from the end walls of a rectangular vertical enclosure on heat transfer rates is investigated numerically. The enclosure has opposite isothermal walls at different temperatures. The Rayleigh number is varied from 10 4 to 10 7 and the aspect ratio from 0.5 to 10. The thickness of the partitions is fixed and equal to one tenth of the width of the enclosure. Their non-dimensional length ( L / H ) is varied from 0 (non-partitioned enclosure) to 0.5 (two separate enclosures). The effect of different thermal boundary conditions at the end walls and at the partitions is included in the investigation.

CFD simulation of channels for direct and reverse electrodialysis

Abstract Flows within very thin channels, typically filled with spacers, can be often encountered in many processes such as electrodialysis (ED) and reverse electrodialysis (RED). Although the ED and the RED processes have been studied for a long time, the optimization of the fluid dynamics within the channels is still an open problem. In the present work, realized within the EU-FP7 funded REAPower project, computational fluid dynamics simulations were carried out in order to predict the fluid flow field inside a single ED/RED channel. Some different configurations were tested which includes: an empty channel, a channel provided with a spacer, and a channel filled with a purposely manufactured fiber porous medium. Two types of spacers were investigated: (1) a commercial type made of woven perpendicular filaments and (2) an overlapped perpendicular filament spacer. A sensitivity analysis concerning computational grid size and topology was performed. For the cases investigated, adopting the hybrid grids mai...