Specific Dissipation Research Articles

Bubble sizes in agitated air–alcohol systems with and without particles: Turbulent and transitional flow

In heterogeneous catalytic processes, the relationship between bubble size and various process parameters is important in determining interfacial area, hence mass transfer rate. This paper presents the results of an experimental study of bubble sizes in air–alcohol dispersions with and without the presence of catalyst particles in a batch stirred reactor at different agitation speeds and mean specific energy dissipation rates. Factors investigated include catalyst type, particle size and concentration. It has been found that: • Since there are large differences in the viscosity of the various alcohols used, by dividing them into two groups based on the flow type (turbulent or transitional), a consistent correlation has been found for mean bubble size as a function of Weber number, We, for each region, though neither correlation agrees with the precise relationship suggested by Kolmogoroff's theory of locally, homogeneous, isotropic turbulence. • At the same We number, the size is bigger in transitional flow than in turbulent. The functionality of the correlation of d 32 / D versus We is similar whether particles are present or not. • In fully developed turbulent flow, the bubble size is slightly reduced when catalyst particles are present, independent of catalyst size or type. • In transitional flow, the effect of catalyst particles on bubble size is much stronger, the size being reduced by approximately 30%.

Mesoscale Analysis of Shear Bands in High Strain Rate Deformations of Tungsten/Nickel-Iron Composites

ABSTRACT We analyze the initiation and propagation of adiabatic shear bands in a tungsten heavy alloy by modeling each constituent as a heat-conducting, microporous, isotropic, elastothermoviscoplastic material. The two constituents are assumed to be perfectly bonded to each other so that the temperature, heat flux, displacements, and surface tractions are continuous across an interface between a tungsten particulate and the nickel-iron matrix. Three different modes of deformation, namely plane strain tension/compression, plane strain shear, and axisymmetric tension/compression are analyzed. No other defects are introduced. It is found that contours of the rate of temperature rise and/or velocity and/or the specific energy dissipation rate rather than those of effective plastic strain delineate the shear banded regions. For the same volume fraction of particulates smaller diameter particulates enhance the formation of adiabatic shear bands. The time of initiation of an adiabatic shear band also depends upon the particulate arrangement.

Convective mass transport in cross-corrugated membrane exchangers

Cross-corrugated triangular ducts provide high mass transfer capabilities in membrane related gas separations. The mixing effect would intensify the convective mass transfer coefficients on membrane surfaces. By modeling transport of water vapor in dry air, in this study, periodic fully developed fluid flow and mass transfer in a cross-corrugated triangular duct is numerically studied. To model the transitional flow in the topology, a validated low Reynolds number k– ω (LKW) turbulence model is employed to account for the turbulence in the flow. The vapor mass fractions, velocity, and turbulent kinetic energy and specific dissipation rate contours are obtained in the three-dimensional complex domain. The friction factors and the segment mean Sherwood numbers are calculated and correlated with Reynolds numbers, for uniform mass fraction boundary conditions. It is found that the transitional flow is represented by a turbulence center, which intensifies and migrates from the upper wall corrugation to the lower wall corrugation with increasing Reynolds numbers.

Intensifying micromixing in a semi-batch reactor using a Rushton turbine

The ‘iodide–iodate’ reaction scheme has been used to ascertain the effectiveness of micromixing in a semi-batch reactor when feeding with pipes rotating and discharging continuously into the region of highest local specific energy dissipation rate, ε T . The results are compared with those obtained using a fixed pipe at the equivalent position and at other positions including near the top surface, the most convenient position industrially. The results show significant intensification, i.e., a seven-fold reduction in ‘waste product’, between the most convenient fixed feed pipe position and the rotating pipes, even at the modest specific power input of ∼ 1.0 W / kg . This mode of addition also ensures that feeding is always into a constant value of ε T , whereas with a static pipe close to the impeller the reactants are being fed in a region where ε T varies cyclically. This difference in the ε T values experienced by the two modes of addition poses problems for previous models of micromixing in the literature linking selectivity to local specific energy dissipation rates.

The strategy of ecosystem development: specific dissipation as an indicator of ecosystem maturity

The ratio of entropy generation rate to entropy embodied in structures relatively to the surroundings can be considered as an indicator of the ability of a self-organizing dissipative system to maintain itself far from equilibrium by pumping out entropy. The higher the ratio (which may be called the specific entropy production or the specific dissipation of a system), the lower the capacity of a system to convert the incoming low-entropy energy into internal organization. It appears that the ratio attains special significance for interpreting the evolution of biological systems, as the maximum expression of self-organizing systems, from the sub-cellular to the ecosystem scale. This paper proposes specific dissipation, written as the ratio of biological entropy production to exergy stored in the living biomass, as a thermodynamic orientor as well as an indicator of the development state of ecological systems. After having presented a method for estimating the specific dissipation in lakes, the adequacy of the proposed indicator is discussed and also tested by comparing its response to those of some classical ecological attributes (successional sequences of species, biodiversity, individual body size, structural organization and generation time of organisms) throughout the seasonal progression of the plankton community in Lake Trasimeno (Umbria, Italy). The results support the hypothesis that the minimization of specific dissipation is a primary criterion of evolution of ecological systems and also sustain the use of specific dissipation as an indicator of ecological maturity.

Measurement of strain rate sensitivity of aluminium foams for energy dissipation

In this paper the structural performance of aluminium alloy foams have been investigated under both static and dynamic compression loads. Three foam typologies (M-PORE, CYMAT, SCHUNK) in a wide range of density (from 0.14 to 0.75 g/cm 3), made by means of different process-routes (melt gas injection, powder metallurgy, investment casting) have been analysed. Foams microstructural characterization has been carried out through morphometric measurements by means of Scanning Electron Microscopy (SEM) and Computed Tomography (CT) and subsequent digital image processing in order to determine average cells size and cell distributions on different section planes. The experimental study aims to assess the strain rate sensitivity and energy absorption capability of commercially available metal foams and to point out the correlation between the mechanical behaviour and the physical and geometrical properties of the foam. It has been found that the specific energy dissipation of foams with similar density can be quite different: for the same volume of foam, average values of 1770, 1780 and 5590 J/kg at 50% nominal compression have been measured on M-PORE (0.19 g/cm 3), CYMAT (0.28 g/cm 3) and SCHUNK (0.28 g/cm 3) foams, respectively. Impact tests showed that the dependence of the plateau stress on strain rate could be considered negligible for M-PORE and CYMAT foams while it is quite remarkable for SCHUNK foams. Moreover, it was found that the peak stress of CYMAT foams has a quite large sensitivity on the loading rate.

Pellet morphology, culture rheology and lovastatin production in cultures of Aspergillus terreus

Pellet growth of Aspergillus terreus ATCC 20542 in submerged batch fermentations in stirred bioreactors was used to examine the effects of agitation (impeller tip speed u t of 1.01–2.71 m s −1) and aeration regimens (air or an oxygen-enriched mixture containing 80% oxygen and 20% nitrogen by volume) on the fungal pellet morphology, broth rheology and lovastatin production. The agitation speed and aeration methods used did not affect the biomass production profiles, but significantly influenced pellet morphology, broth rheology and the lovastatin titers. Pellets of ∼1200 μm initial diameter were reduced to a final stable size of ∼900 μm when the agitation intensity was ≥600 rpm ( u t ≥ 2.03 m s −1). A stable pellet diameter of ∼2500 μm could be attained in less intensely agitated cultures. These large fluffy pellets produced high lovastatin titers when aerated with oxygen-enriched gas but not with air. Much smaller pellets obtained under highly agitated conditions did not attain high lovastatin productivity even in an oxygen-enriched atmosphere. This suggests that both an upper limit on agitation intensity and a high level of dissolved oxygen are essential for attaining high titers of lovastatin. Pellet size in the bioreactor correlated equally well with the specific energy dissipation rate and the energy dissipation circulation function. The latter took into account the frequency of passage of the pellets through the high shear regions of the impellers. Pellets that gave high lovastatin titers produced highly shear thinning cultivation broths.

Bubble Size Distribution and Void Fraction in the Wake Region Below a Ventilated Gas Cavity in Downward Pipe Flow

The aim of this study was to develop a population balance model to predict the resultant bubble size distribution and gas void fraction in the wake region below a ventilated cavity in down-flowing liquid inside a pipe. The model includes (1) the gas entrainment process from the ventilated cavity; (2) fluid flow and specific energy dissipation rate in the wake region, comprising both wall-jet and recirculation-vortex zones; (3) bubble breakup and coalescence events, determined by a critical Weber number criterion and bubble interaction and film drainage times, respectively; and finally (4) gas void fraction in the wake and recirculation of gas back into the base of the ventilated cavity. The model predictions are compared with experimental measurements for an air–water system. The model successfully predicts the length of the wake region and the gas void fraction within it, and the average and resultant bubble size distributions immediately downstream of the wake. The average bubble diameter was of the order 2–3 mm for each of the cases studied. In applying the model, attention was focused on the specific energy dissipation rate distribution between the wall-jet and recirculating-vortex zones within the wake. As part of the analysis Fluent computational fluid dynamics simulation was carried out and the results from this work are also presented in the paper.

Suspension of Microcarriers for Cell Culture with Axial Flow Impellers

The suspension characteristics, the agitator speed, Njs, and the mean specific energy dissipation rate, ( e ¯ T )js, required to just fully suspend ∼20% wet weight Cytodex 3® microcarrier beads have been studied using a range of different diameter Chemineer HE-3 hydrofoils, a pair of Ekato InterMIG impellers and a six-blade mixed-flow impeller in a baffled vessel of 19.2 l operating volume containing phosphate buffer saline solution. Flat and modified tank bases were used. Njs values were observed to be in the range of 50 to 90 rev min−1. The use of Zwietering's correlation using existing literature geometric suspension parameters, S, to predict Njs would give values up to 50% higher. The low Njs values obtained in the experiments are attributed to the very small particle–liquid density difference (40 kg m−3), which eased the lifting of the particles from the tank bottom, compared to those studied previously. Also, it was found that at Njs, it took up to about 40 min to suspend all particles as the upper surface of the initially settled bed was scoured away. Previous work has not reported such a long-term phenomenon. With the liquid/particle properties used in this study, the three-blade hydrofoil HE-3 impeller of D/T = 0.39 in a cone-and-fillet based tank was marginally the most efficient; that is, it had the lowest ( e ¯ T )js of ∼0.5 x 10−3 W kg−1. However, ( e ¯ T )js was less than 1 x 10−3 Wkg−1 in most cases with the different size HE-3 hydrofoils, which implies that these geometries would probably be suitable for application in shear-sensitive animal cell culture systems using such microcarriers.

Sediment trapping, turbidity maxima, and bathymetric stability in macrotidal estuaries

This paper examines how fine marine sediments are trapped in macrotidal estuaries and what processes coexist to maintain bathymetric stability. An analytical emulator is constructed integrating explicit formulations for tidal and residual current structures together with sediment erosion, suspension, and deposition. The emulator estimates suspended concentrations and net sediment fluxes and indicates the nature of their functional dependencies and corresponding sensitivities to tidal elevation amplitude (or tidal current ), channel depth D, bed friction coefficient f, sediment size (specifically, settling velocity Ws), and river flow velocity UR. Associated scaling analyses reveal the relative impacts of terms representing tidal nonlinearities, gravitational circulation, and “delayed” settling. Using the emulator to determine conditions consistent with zero net flux of sediments or bathymetric stability, we deduce Ws ≈ f. Overall, finer sediments are imported and coarser ones are exported, with more imports (extending to a coarser fraction) on spring tides than on neaps. The emulator indicates that the spring‐neap shifting of this coarse‐fine boundary corresponds to particle diameters between 30 and 50 μm. This constitutes selective sorting, maintaining a widely distributed source of continuously resuspended material in a size range commonly observed. By illustrating the acute sensitivity of sediment fluxes to the bed friction coefficient, we anticipate feedback adjustments between suspended and surficial sediments. Factors governing the generation, location, and characteristics of turbidity maxima are indicated, including dependence on /D. A direct link is shown between parameters that control sediment flux at a specific cross section and net upstream tidal energy dissipation.

PROPERTIES of CROSS‐LINKED STARCH PRODUCED IN A SINGLE SCREW EXTRUDER WITH and WITHOUT A MIXING ELEMENT

ABSTRACTStarch was extruded with sodium hydroxide and sodium trimetaphosphate in order to cross‐link it in a single‐screw extruder with and without a mixing element at constant screw speed of 90 rpm in the first set of experiments and at similar mean residence time controlled by screw speed in the second set of experiments. For the screw without mixing element in the second set of experiments, screw speed was adjusted to give the similar residence time as the single‐screw extruder with mixing element at 220 rpm. Phosphorus content and pasting curves of extrudates showed that starch was cross‐linked during extrusion. Replacing the screw without mixing element by the screw with mixing

Mixing Studies Related to the Cleaning of Molten Aluminium

AbstractMolten aluminium is traditionally “cleaned” by a chlorine‐based fluxing gas. This gas also has to provide the motive power for mixing. Recently, mechanical agitation with solid fluxes has been considered as a replacement for environmental reasons. Here, these two methods of mixing are compared using particle image velocimetry (PIV), decolourisation for homogenisation and power measurement for comparison of efficiencies. A geometrically scaled‐down vessel was used, with air to mimic “chlorine” fluxing and with water as the working fluid. At equivalent mean specific energy dissipation rates, $ \bar \varepsilon $T, maximum velocities are higher and mixing times are shorter with an impeller. This improved performance is achieved with the impeller without causing surface gas entrainment, the latter being detrimental to fluxing.

Break-up, coalescence and catastrophic phase inversion in turbulent contactors

When a low concentration of immiscible phase is dispersed, break-up in the impeller region controls the drop size. The traditional application of Kolmogoroff's theory of local isotropic turbulence has been moderately successful in relating equilibrium drop sizes to the physical properties and the turbulent flow, with low power number impellers giving smaller drops at equal mean specific energy dissipation rates, ε ̄ T. However, to explain the reduction in drop size at equal ε ̄ T on scale-up, the concept of intermittency must be introduced leading to a scale-up rule close to constant tip speed. With increasing concentration, coalescence generally becomes important and drop sizes increase. Modelling of coalescence involves collision frequency and coalescence efficiency. The latter is dependent on the type of drop interface, the establishment of which type for a particular system being difficult. The difficulty is compounded since in clean systems, at concentrations of the aqueous phase >∼20% by volume, droplets of oil appear in the aqueous drops whilst the converse is not found. At sufficiently high concentrations, where the concept of collision frequency is questionable, catastrophic phase inversion (CPI) occurs because coalescence becomes so high. Anything that enhances coalescence, e.g. surfactants, particles that bridge interfaces, wettable surfaces, bulk flow patterns, encourages CPI to occur at lower concentrations of dispersed phase. Satisfactory models for CPI are not available.

Design of Optimum Plate-Fin Natural Convective Heat Sinks

The effort described herein extends the use of least-material single rectangular plate-fin analysis to multiple fin arrays, using a composite Nusselt number correlation. The optimally spaced least-material array was also found to be the globally best thermal design. Comparisons of the thermal capability of these optimum arrays, on the basis of total heat dissipation, heat dissipation per unit mass, and space claim specific heat dissipation, are provided for several potential heat sink materials. The impact of manufacturability constraints on the design and performance of these heat sinks is briefly discussed.

Numerical Solution of Fully Developed Flow with Vegetative Resistance

This paper presents a numerical solution of the Reynolds averaged Navier-Stokes and the near-wall \ik- (turbulent kinetic energy) and \Iω\N- (specific dissipation or dissipation per unit kinetic energy) transport equations, which are modified to include vegetative drag terms. For similar treatment of the model coefficients, the use of the near-wall \Ik-ω\N model produces similar results to previous models that employed the standard \Ik-e\N models with wall functions. The study shows that reasonable predictions of streamwise velocity and Reynolds stress profiles can be achieved by adopting universal values for all model coefficients, but the calculated energy gradient can have significant error. The study also indicates that predictions of streamwise turbulence intensity are significantly improved by adopting the universal values of \IC\Dfk\N\N = 0.05 and \IC\Dfω\N\N = 0.16 rather than the theoretically based values, \IC\Dfk\N\N = 1.0 and \IC\Dfω\N\N = \Iβ/αβ*C\Dfk\N\N.

The Impact of Fluid Mechanical Stress on Saccharomyces Cerevisiae Cells During Continuous Cultivation in an Agitated, Aerated Bioreactor; its Implication for Mixing in the Brewing Process and Aerobic Fermentations

The introduction of mechanical agitation or re-circulation of CO 2 from the headspace to facilitate the natural CO 2 -driven mixing in anaerobic brewing fermentations has the potential to cause damage to yeast cells through increased hydrodynamic stress. In addition, such damage has been reported in aerobic yeast fermentations. Here, a reproducible, duplicate series of aerobic, carbon-limited, continuous culture yeast fermentations have been carried out up to approximately 340 h. In the first series, mean specific energy dissipation rates, e ¯ T from ∼4.5 × 10 –2 to ∼6.0 W kg −1 were used, the former mimicking for approximately 20 h the maximum level found in anaerobic fermentations at the large scale and the latter a higher value than that usually found in aerobic fermentations. In the second, e ¯ T was held at ∼4.5 x 10 −2 W kg −1 and two aeration rates (1 and 3 vvm) were used. Both values are very high for brewing, even if headspace CO 2 recirculation is used. The latter value is also high for aerobic fermentations. In all cases, the dissolved oxygen level was held constant by gas blending at 40% of saturation. At e ¯ T > ∼4.5 W kg −1 , a transient effect on the cells as measured by multi-parameter flow cytometry was found, but all other measured parameters, including mass spectrometry and classical microbiological data, showed that, statistically, there was no effect on cellular morphology or physiology. For all other conditions of agitation and aeration, all measured parameters remained constant. This study indicates that the potentially deleterious effects of agitation or CO 2 gas recirculation can be largely discounted with respect to brewing fermentations and for more intense aerobic fermentations up to ∼6 W kg −1 and 3 vvm.

Studies on the Impact of Mixing in Brewing Fermentation: Comparison of Methods of Effecting Enhanced Liquid Circulation

Mixing during beer production by natural CO2 evolution has been enhanced at the bench scale by headspace gas recirculation to the base of a 3.5l cylindroconical fermenter or by mechanical agitation in a 4l fermenter. Standardized lager fermentations were used to compare the two methods at a range of mean specific energy dissipation rates ( e ¯ T , W kg−1), including ∼5 × 10−2W kg−1. The latter corresponds approximately to the maximum e ¯ T found at the production scale (∼400m3) due to natural CO2 evolution. The work has shown that gas recirculation is a viable technique that avoids the loss of volatiles found if mixing is enhanced by sparging a separate gas such as nitrogen. For both types of mixing, it was found that e ¯ T resulted in increased yeast growth and fermentation rates and an alteration in the balance of key volatile compounds, with, in general, an enhanced formation of higher alcohols and a suppression of the formation of esters. However, with gas recirculation this enhanced performance was limited to an e ¯ T of ∼5 × 10−2Wkg−1 because of the tendency for excessive foaming at higher recirculation rates, whilst values up to ∼2.5 × 10−1W kg−1 proved effective under agitated conditions. On comparison, at an e ¯ T of ∼5× 10−2W kg−1, the two modes of operation gave similar results, although gas recirculation produced a slightly increased fermentation rate. The possible reasons for this are briefiy discussed. Both methods seem to have the potential for reducing fermentation time and enhancing reproducibility, especially at the small scale.

Dynamic response and energy dissipation characteristics of balsa wood: experiment and analysis

Dynamic response of a cellular sandwich core material, balsa wood, is investigated over its entire density spectrum ranging from 55 to 380 kg/m 3. Specimens were compression loaded along the grain direction at a nominal strain rate of 3 × 10 3 s −1 using a modified Kolsky (split Hopkinson) bar. The dynamic data are discussed and compared to those of quasi-static experiments reported in a previous study (Mech. Mater. 35 (2003) 523). Results show that while the initial failure stress is very sensitive to the rate of loading, plateau (crushing) stress remains unaffected by the strain rate. As in quasi-static loading, buckling and kink band formation were identified to be two major failure modes in dynamic loading as well. However, the degree of dynamic strength enhancement was observed to be different for these two distinct modes. Kinematics of deformation of the observed failure modes and associated micro-inertial effects are modeled to explain this different behavior. Specific energy dissipation capacity of balsa wood was computed and is found to be comparable with those of fiber-reinforced polymer composites.

Optimising activated sludge growth rate by intensifying hydrodynamic forces

AbstractIn this study a Couette device was used to examine the influence of hydrodynamic forces on the overall behaviour of activated sludge. The specific growth rate of activated sludge increased with increasing specific energy dissipation rate, reaching a maximum rate at an energy input of approximately 40 m2 s−3, beyond which any further increases resulted in a reduction in the overall growth. At levels above about 250 m2 s−3 the specific growth rate was negligible. Experimental growth rates in the range 0.04–0.20 h−1 were obtained, depending on the energy input levels and substrate (glucose) concentration. A theoretical model successfully predicted both the decrease in the floc radius and microbial activity with increasing energy input into the system, and when combined was able to provide a reasonable prediction for the optimum specific energy dissipation rate to maximise the specific growth rate.© 2003 Society of Chemical Industry

An investigation of wall-anisotropy expressions and length-scale equations for non-linear eddy-viscosity models

New closure approximations are proposed, within the framework of non-linear eddy-viscosity modeling, which aim specifically at an improved representation of near-wall anisotropy in both shear and stagnation flows. The main novel element is the introduction of tensorial terms, alongside strain and vorticity, which depend on wall-direction indicators and which procure the correct asymptotic near-wall behavior of the Reynolds stresses. The newly formulated non-linear constitutive equation for the Reynolds stresses is combined with low-Reynolds-number forms of equations for the rate of dissipation ε or the specific dissipation ω, the latter incorporating a number of new features into the established form of the equation. The predictive performance of three model variants is investigated by reference to three test flows: a plane channel flow, a separated flow in a channel with periodic hill-shaped obstacles on one wall and a plane impinging jet. It is shown that the new model elements result in a substantially improved representation of the Reynolds-stress field at the wall, especially in the wall-normal Reynolds stress. One of the variants includes the use of the modified ω-equation, and it is shown that this model performs especially well in the presence of separation.