Local Energy Dissipation Rate Research Articles

Bubble size distribution and turbulence characterization in a bubbly flow in the presence of surfactant

This study aimed to quantify the less explored complex multiphase hydrodynamics of a bubble swarm in the presence of surfactant which is the key to flotation process widely used in the resources and environmental engineering applications.Experiments were conducted in a rectangular column (cross-section: 100 mm × 100 mm) in batch mode by varying the gas flux (0.02 to and 0.08 cm/s) in the presence of an anionic surfactant sodium dodecyl sulphate (5 to 15 ppm). High-speed imaging was then used to visualise the unsteady bubble plume dispersion behaviour and estimate the bubble size distribution (BSD) which showed a reduction in the mean bubble size with the increasing gas flux and surfactant concentration.Next, particle image velocimetry (PIV) was utilised to measure the instantaneous velocity field which was used to determine the turbulence characteristics. It was shown that the bubble plume contributes to significant anisotropy in the flow field which increased in the higher surfactant concentration and gas flux cases. The energy containing turbulence length scale was characterized by the integral length scale, which was observed to increase linearly with both the gas flux and surfactant concentration. Also, the local turbulence energy dissipation rate exhibited a strong linear correlation with the bubble surface area flux parameter. In the presence of surfactant, the turbulence energy spectrum of the system exhibited a less steep slope in the inertial subrange regime compared to the Kolmogorov −5/3 slope. The spectrum also showed a leftward shift indicating energy addition to the larger turbulence length scales which was reflected in the formation of large recirculation zones around the bubble plume.

Investigation of the impact of probes and internals on power and flow in stirred tank reactors

This study characterises the power requirements and flow patterns in several commercial stirred tank bioreactors with working volumes ranging from 60 mL to 1 L, and investigates the isolated impact of internals, i.e. baffles and probes, on the power number, P0. Results show that the presence of probes leads to a rise of the turbulent power number, P0, equivalent to the presence of baffles, and as the number of internals increases the variation of P0 gets smaller until it plateaus for large probe quantity and high-volume blockage. Internals have a greater impact on flow with radial flow impellers, causing a significant increase in P0 in comparison to axial flow impellers. An experimental and computational flow dynamics study is also conducted to investigate the interaction between the probe wake and the impeller trailing vortices, and an estimate is provided of the form drag from the pressure distribution acting on the probe, with a good agreement to the corresponding power number increase. A comparison between P0 data obtained from conventional-cylindrical and novel-streamlined probe configurations shows that optimising probe geometry and location with respect to the incoming flow can be an effective approach for reducing power requirements, local values energy dissipation rate and stress levelsinside the tank. This study provides valuable insights into the impact of internal components and flow type on power input per unit volume, P/V, in small-scale bioreactors and supports the development of more robust scaling procedures for the biopharma industry.

A general approach for predicting convective heat transfer coefficients in turbulent systems

A generalized approach for predicting turbulent convective heat transfer coefficients using large eddy simulation is presented. This model is based on semi-empirical transport theory, which links the local convective heat transfer rate to the local energy dissipation rate within the near-wall boundary layer. We apply these approaches to agitated tanks, pipe flow systems, cylinders in crossflow, and tube bundles. We validate the generality and reliability of the theoretical model against expectations from experimentally derived empirical design correlations.

Tethered Balloon-Borne Turbulence Measurements in Winter and Spring during the MOSAiC Expedition

During the Multidisciplinary Drifting Observatory for the Study of Arctic Climate expedition, a tethered balloon system was operated with a turbulence probe attached to study the lower troposphere in the high Arctic. Overall, measurements were conducted on 34 days between December 2019 and May 2020, resulting in 47 quality-assured sampling records consisting of vertical profiles and constant-altitude measurements. The continuous profiles extend from the surface, i.e., the sea ice floe, to a height of several hundred meters typically. The high-resolution wind velocity measurements using a hot-wire anemometer and temperature measurements using a thermocouple provide a comprehensive basis for examining the dynamical processes and thermodynamic stratification in the Arctic atmospheric boundary layer under cloudless and cloudy conditions. This paper provides a detailed technical description of the turbulence payload, including calibration and quality assurance, and a general overview of the data. A particular focus of this work is the estimation of local energy dissipation rates. The data are freely available from the World Data Center PANGAEA.

Image‐based measurement of engulfment vortex to quantitatively assess micromixing efficiency in a gas–liquid stirred tank

AbstractMicromixing in reactors is typically characterized by chemical test reactions. A novel image‐based measurement system of engulfment vortex (IMEV system) is developed to assess the micromixing efficiency. Over 2000 vortices were recognized from images captured under various experimental cases, and key frames for their formation, engulfment and dissipation were identified. Inspired by the engulfment model (i.e., E model), this work quantified the micromixing time and local turbulent energy dissipation rate with the vortex lifetimes. The micromixing time obtained through the IMEV method is comparable to its value estimated by the micromixing model and segregation index of the test reaction, with a deviation of less than 20%. In turbulent gas–liquid systems, bubbles play a dual role on the local micromixing due to frequent disturbance and phase interface limitation. To summarize, this work offers an alternative approach for micromixing studies and provides valuable insights into dispersed phase effects on the micromixing efficiency.

Micromixing Performance in a Taylor–Couette Reactor with Ribbed Rotors

The Taylor–Couette reactor (TCR) is becoming an increasingly significant topic in chemical industry. This study investigates the micromixing performance of a ribbed TCR with axial flow in the Villermaux–Dushman reaction system. The local micromixing mechanism of the ribbed TCR was analyzed, and the volume-averaged energy dissipation rate was calculated using CFD. The effects of operating parameters and rib structural parameters on micromixing performance were investigated. The results show that the introduction of ribs eliminates the high shear region between the vortex pairs, resulting in the strong micromixing region being situated on the inner and outer cylinder wall surfaces and the ribbed surface region. Smaller rib spacing, larger rib width, and rib height can strengthen micromixing and result in a smaller segregation index. Micromixing times of ribbed TCRs were calculated using the incorporation model, tm, in the range of 2.0 × 10−5 to 8.0 × 10−3. The results show that ribbed TCRs require a lower energy consumption to achieve a lower tm than other rotating reactors. A correlation equation between tm and five parameters was developed, with a correlation coefficient of 0.951. The accuracy of the volume-averaged energy dissipation rate obtained via CFD was verified through experimental analysis. The correlation between the micromixing time and the volume-averaged energy dissipation rate was established in a form that satisfies Kolmogorov’s turbulence theory for tm. To convert the volume-averaged energy dissipation rate into a local energy dissipation rate, a factor ϕ was introduced and solved using the engulfing diffusion model. This study provides insights into the design and optimization of ribbed TCRs.

A characterization method for equivalent elastic modulus of rock based on elastic strain energy

Energy is an internal variable during rock deformation and failure, and its dissipation and conversion law can reflect the rock’s internal damage and deterioration state. Analysis of rock deformation and failure process from the perspective of energy is helpful to deeply understand the mechanism of rock damage, fracture and instability failure, and has important theoretical and practical significance for the stability evaluation and support control of surrounding rock. In this study, through single cyclic loading and unloading (SCLU) experiments, cyclic triaxial loading and unloading (CTLU) experiments and conventional triaxial compression (CTC) experiments, the equivalent elastic modulus method based on elastic strain energy is proposed to analyze the energy conversion of rock. The results show that the error of the elastic strain energy calculated by the strain energy formula method is generally higher than 10% with the secant and tangent modulus of the loading and unloading curve as input parameters. Taking the equivalent elastic modulus proposed in this study as an input parameter, more accurate elastic strain energy can be obtained by the strain energy formula. During the rock failure process, the equivalent elastic modulus shows a three-stage characteristic of increase, steady and decrease. The equivalent elastic modulus can be estimated by the quadratic function between the equivalent elastic modulus and confining pressure and axial strain. Under the same deformation and deviatoric stress, the elastic strain energy stored in rock increases with increasing confining pressure. The local maximum energy dissipation rate corresponds to stress drop, and the peak energy dissipation rate appears near the peak strength. High energy dissipation mainly occurs in a short time after peak strength, and energy release and dissipation are more sudden and severe under high confining pressure.

Simultaneous In Situ Characterization of Turbulent Flocculation and Reactor Mixing Using Image Analysis and Particle Image Velocimetry in Unison

Floc characteristics, including their size distribution, mean size, and fractal dimension, are impacted by mixing intensity and duration, coagulant dosing method, dose, type, and pH. Herein, we directly employ flocs inherently generated during treatment to determine instantaneous velocity fields, which were further utilized to estimate local velocity gradients and turbulent kinetic energy dissipation (TKED) rates. This novel non-intrusive methodology, which combines particle image velocimetry (PIV) and an imagery-based sizing scheme, was examined through the characteristics of reactor mixing and flocculation from in situ measurements for conventional FeCl3 chemical coagulation and iron electrocoagulation (EC). Our first-of-its-kind procedure avoids the need to externally add artificial seeding particles for PIV analysis, automatically reducing the number of experiments, and simultaneously improves both accuracy and precision by linking fluid dynamics and particle characteristics with only a single experiment. The TKED rates estimated using flocs were largely similar with conventional artificial seeding at the early stage of flocculation when flocs were smaller. However, the new method is expected to estimate turbulence more accurately in the flocs’ microenvironment during the later stages of tapered flocculation when particle sizes are similar to dissipation eddy dimensions, especially at high particle concentrations (i.e., highly turbid waters). Measured size distributions, mean sizes, and fractal dimensions confirm the robustness of the present imagery-based sizing scheme and showed that EC produced numerous and more compact flocs than conventional coagulation.

Scale-up of an amoeba-based process for the production of the cannabinoid precursor olivetolic acid

BackgroundThe availability of new biological platform organisms to get access to innovative products and processes is fundamental for the progress in biotechnology and bioeconomy. The amoeba Dictyostelium discoideum represents a novel host system that has recently been employed for both the discovery of new natural products and as a cell factory for the production of bioactive compounds such as phytochemicals. However, an essential parameter to evaluate the potential of a new host system is the demonstration of its scalability to allow industrial applicability. Here, we aimed to develop a bioprocess for the production of olivetolic acid, the main precursor of cannabinoids synthesized by a recently engineered D. discoideum strain.ResultsIn this study, a sophisticated approach is described to scale-up an amoeba-based polyketide production process in stirred tank bioreactors. Due to the shear sensitivity of the cell wall lacking amoebae, the maximum local energy dissipation rate (εmax) was selected as a measure for the hydromechanical stress level among different scales. By performing 1.6-L scale batch fermentations with different stress conditions, we determined a maximum tolerable εmax of 3.9 W/kg for D. discoideum. Further, we used this parameter as scale-up criterion to develop a bioprocess for olivetolic acid production starting from a 7-L stirred tank reactor to the industrially relevant 300-L scale with a product concentration of 4.8 µg/L, a productivity of 0.04 µg/L/h and a yield of 0.56 µg/g glucose.ConclusionWe developed a robust and reliable scale-up strategy for amoeba-based bioprocesses and evaluated its applicability for the production of the cannabinoid precursor olivetolic acid. By determining the maximum tolerable hydromechanical stress level for D. discoideum, we were able to scale-up the process from shake flasks to the 300-L stirred tank reactor without any yield reduction from cell shearing. Hence, we showed the scalability and biotechnological exploitation of amoeba-based processes that can provide a reasonable alternative to chemical syntheses or extractions of phytochemicals from plant biomass.

Numerical estimation of critical local energy dissipation rate for particle detachment from a bubble-particle aggregate captured within a confined vortex

In flotation, interactions of bubble-particle aggregates with turbulent flow structures in the liquid medium result in particle detachment. This study aims to simulate this phenomenon involving a bubble-particle aggregate (bubble diameter ∼ 3 mm and particle diameter ∼ 314 µm) interacting with a turbulent flow structure manifested as a confined vortex in a square cavity connected to a square cross-section channel. An interface resolved three dimensional (3D) computational fluid dynamics (CFD) model was developed to quantify the bubble-vortex interaction dynamics over a range of channel Reynolds numbers. The CFD model produced a good agreement with the experimentally measured vorticity magnitude, local energy dissipation rate, and bubble motion. It was shown that a bubble-particle aggregate could be captured within the vortex by suitably varying the channel Reynolds number, eventually leading to particle detachment. A separate force balance analysis was performed to determine a criterion for particle detachment utilising the CFD model predicted vorticity and local energy dissipation rate. It was shown that a critical local energy dissipation rate ∼ 1.59 m2/s3 was required for particle detachment to occur, which was also verified experimentally.

Local Energy Dissipation Rate Preserving Approximations to Driven Gradient Flows with Applications to Graphene Growth

Local Energy Dissipation Rate Preserving Approximations to Driven Gradient Flows with Applications to Graphene Growth

Statistics of local Reynolds number in box turbulence: ratio of inertial to viscous forces

In high-Reynolds-number turbulence the spatial distribution of velocity fluctuation at small scales is strongly non-uniform. In accordance with the non-uniformity, the distributions of the inertial and viscous forces are also non-uniform. According to direct numerical simulation (DNS) of forced turbulence of an incompressible fluid obeying the Navier–Stokes equation in a periodic box at the Taylor microscale Reynolds number $R_\lambda \approx 1100$ , the average $\langle R_{loc}\rangle$ over the space of the ‘local Reynolds number’ $R_ {loc}$ , which is defined as the ratio of inertial to viscous forces at each point in the flow, is much smaller than the conventional ‘Reynolds number’ given by $Re \equiv UL/\nu$ , where $U$ and $L$ are the characteristic velocity and length of the energy-containing eddies, and $\nu$ is the kinematic viscosity. While both conditional averages of the inertial and viscous forces for a given squared vorticity $\omega ^{2}$ increase with $\omega ^{2}$ at large $\omega ^{2}$ , the conditional average of $R_ {loc}$ is almost independent of $\omega ^{2}$ . A comparison of the DNS field with a random structureless velocity field suggests that the increase in the conditional average of $R_ {loc}$ with $\omega ^{2}$ at large $\omega ^{2}$ is suppressed by the Navier–Stokes dynamics. Something similar is also true for the conditional averages for a given local energy dissipation rate per unit mass. Certain features of intermittency effects such as that on the $Re$ dependence of $\langle R_{loc}\rangle$ are explained by a multi-fractal model by Dubrulle (J. Fluid Mech., vol. 867, 2019, P1).

Velocity gradient statistics in turbulent shear flow: an extension of Kolmogorov's local equilibrium theory

This paper presents an extension of Kolmogorov's local similarity hypotheses of turbulence to include the influence of mean shear on the statistics of the fluctuating velocity in the dissipation range of turbulent shear flow. According to the extension, the moments of the fluctuating velocity gradients are determined by the local mean rate of the turbulent energy dissipation$\left \langle \epsilon \right \rangle$per unit mass, kinematic viscosity$\nu$and parameter$\gamma \equiv S (\nu /\left \langle \epsilon \right \rangle )^{1/2}$, provided that$\gamma$is small in an appropriate sense, where$S$is an appropriate norm of the local gradients of the mean flow. The statistics of the moments are nearly isotropic for sufficiently small$\gamma$, and the anisotropy of moments decreases approximately in proportion to$\gamma$. This paper also presents a report on the second-order moments of the fluctuating velocity gradients in direct numerical simulations (DNSs) of turbulent channel flow (TCF) with the friction Reynolds number$Re_\tau$up to$\approx 8000$. In the TCF, there is a range$y$where$\gamma$scales approximately$\propto y^ {-1/2}$, and the anisotropy of the moments of the gradients decreases with$y$nearly in proportion to$y^ {-1/2}$, where$y$is the distance from the wall. The theoretical conjectures proposed in the first part are in good agreement with the DNS results.

Clausius-Duhem inequality for quasi-1D transient flows in variable cross-section area deformable pipes

This paper presents the derivation of the Clausius-Duhem inequality for quasi-1D transient flows of compressible fluids in radially deformable pipes of varying cross-section area. To do so, a decomposition of the normal stress in spherical and deviatoric components was considered, so that the power expended to radially deform the fluid could be properly accounted for in the first law of thermodynamics, generating a coherent Clausius-Duhem inequality. Based on the derived inequality for Newtonian-Fourier fluids, we focus on their implications and applications. As implications we show that the restrictions imposed on the dynamic and bulk viscosities are different from those retrieved from the 1D and 3D contexts. As applications, we present two distinct studies concerning pipe flows. The first shows by appealing to numerical simulations that the weighting-function and local-balance unsteady friction models violate the second law of thermodynamics since they present negative local rate of energy dissipation. The second presents an analysis to estimate upper bounds of the local rate of energy dissipation associated with shear, and volumetric and axial deformations for laminar and turbulent transient regimes, under flow conditions characterized by the Ghidaoui's dimensionless parameter P^, for liquids with different bulk to shear viscosity ratios. Although the dissipation is dominated by shear, that one due to volumetric deformation may become more relevant for laminar flows, when small numbers P^ and high bulk viscosities liquids are considered.

Experimental and modeling study on meso- and micromixing in the rotor–stator spinning disk reactor

The micromixing efficiency in the rotor–stator spinning disk reactor is studied for increasing injection flow rates of limiting reagent. Using both the Villermaux–Dushman method and second Bourne reaction, an increase in segregation index was found with increasing injection flow rate. Mechanistic models describing micro- and mesomixing were reviewed and implemented to describe the effects of increasing segregation index with increasing injection flow rate. A simplified turbulent-dispersion model was found to describe this trend effectively. A new parameter, based on a logistic function, was proposed to couple mesomixing by turbulent-dispersion and micromixing by engulfment on basis of the ratio of the characteristic times for turbulent-dispersion and engulfment. For injection flow rates where micromixing was calculated to be dominant, the engulfment model was implemented. An experimental relation was fitted to describe the dependency of the local energy dissipation rate on the turbulent diffusion coefficient in the rotor–stator spinning disk reactor. For the Villermaux–Dushman test reaction and the second Bourne reaction, discrepancies were found in the local energy dissipation rates experienced by the reaction zone. These discrepancies were analyzed on basis of the reaction times of both test reactions. The effect of the reaction time was accounted for by introducing a time-dependent local energy dissipation rate, which could be used to study the energy dissipation rate profile in the rotor–stator spinning disk reactor.

RESEARCH OF EXTERNAL MASS TRANSFER PROCESSES FOR ADSORPTION FROM SOLUTIONS IN A APPARATUS WITH STIRRING

A study has been mode of transport-controlled mass transfer-controlled to particles suspended in a stirred vessel. The motion of particle in a fluid was examined and a method of predicting relative velocities in terms of Kolmogoroff’s theory of local isotropic turbulence for mass transfer was outlined.
 To provide a more concrete visualization of complex wave form of turbulence, the concepts of eddies, of eddy velocity, scale (or wave number) and energy spectrum, have proved convenient.
 Large scale motions of scale contain almost all of the energy and they are directly responsible for energy diffusion throughout the stirring vessel by kinetic and pressure energies. However, almost no energy is dissipated by the large-scale energy-containing eddies. A scale of motion less than is responsible for convective energy transfer to even smaller eddy sires. At still smaller eddy scales, close to a characteristic microscale, both viscous energy dissipation and convection are the rule. The last range of eddies has been termed the universal equilibrium range. It has been further divided into a low eddy size region, the viscous dissipation subrange, and a larger eddy size region, the inertial convection subrange.
 Measurements of energy spectrum in mixing vessel are shown that there is a range, where the so called -(5/3) power law is effective. Accordingly, the theory of local isotropy of Kolmogoroff can be applied because existence of the internal subrange. As the integrated value of local energy dissipation rate agrees with the power per unit mass of liquid from the impeller, almost all energy from the impeller is viscous dissipated in eddies of microscale.
 The correlation for mass transfer to particles suspended in a stirred vessel is recommended. The results of experimental study are approximately 12 % above the predicted values.

Optimization of liquid jet ejector geometry and its impact on flow fields

Liquid jet liquid (LJL) ejectors have wide industrial application and the improvement in their efficiency is sought to increase the viability of their use. This study performs the optimization of the entire geometry of an LJL ejector with multiple parameters to maximize energy efficiency. The approach with multiple parameters allows to identify key geometrical features and interdependent parameters, like nozzle position and mixing chamber length, with respect to performance. Computational fluid dynamics (CFD) and optimization simulations were performed to optimize the parameters of Bézier curves that characterize the device's geometry. The optimization results showed that the ejector efficiency curve is sensitive to the nozzle and the suction chamber geometries. Simulations that consider the nozzle diameter and the nozzle position along ejector axis (NXP) as parameters of the optimization process resulted in higher efficiency values than those that kept these parameters fixed. The optimization of the diffuser curve, including the diameter of the diffuser and the length of the mixing chamber, also contributed to increase the efficiency of the device. It was observed that the increase in the length of the mixing chamber and the spacing of the nozzle imply similar effects in the efficiency and in the pressure, velocity and energy dissipation rate profiles confirming some correlation of these parameters on the performance. One may observe the effect of geometry modification through optimization on the flow profiles in key sections of the ejector: the flow profiles in the optimized geometry tend to be more homogenous, hence less dissipative, and it is also confirmed by local energy dissipation rate.

Analysis of the turbulent flow patterns generated in isotropic porous media composed of aligned or centered cylinders

The analysis of the turbulent flow inside porous media composed of infinite arrangements of cylinders with square and circular cross sections disposed in aligned or centered configuration is presented. The porosity (ϕ) was varied from 0.3 to 0.8, at a pore Reynolds number Rep=105, representing fully turbulent flow conditions. The flow cases were solved numerically by using the low-Reynolds Abe-Kondoh-Nagano version of the k-ε model. New correlations are provided for the domains composed of aligned particles in terms of ϕ for the volume averaged turbulence kinetic energy (k), its dissipation rate (ε), and macroscopic pressure gradient (MPG). These correlations are especially useful when it is not possible to model the local details of the porous media in macroscopic turbulence modeling. The highest energetic losses in terms of volume averaged k, ε, and MPG was found for the centered square arrangement. In all cases, these parameters increased abruptly as ϕ decreased, as the pore-scale local pressure gradients and turbulent kinetic energy dissipation rate levels increased. Depending on the case, they were triggered by a combination of sudden expansion-contraction of the flow channels, flow impingement, and the decrease of the effective flow area by flow recirculation. In all cases, the pore-scale local pressure gradients and turbulent kinetic energy dissipation rate levels increased abruptly as ϕ decreased, and consequently the energy losses increased. The tracer dispersion presented similar low homogeneity times for the centered cylinder arrangements. At each porous media, the variations of turbulence intensity, effective flow area, and tortuosity levels in terms of ϕ were not as significant as those observed for the local pressure gradient and dissipation rate. This effect may be considered to improve mixing and reduce pressure drops in devices such as static mixers, heat exchangers, cooling fins arrays, and other devices composed of slender tubes.

Aerodynamic wall shear fluctuation in sand-laden flow in a turbulent boundary layer.

To improve our understanding on the aerodynamic wall shear fluctuation in particle-laden flow, we perform statistical and spectral analyses of aerodynamic wall shear fluctuation in sand-free and sand-laden flows in a turbulent boundary layer based on the results of a wind tunnel experiment. An increase in the skewness of the probability density function of aerodynamic wall shear fluctuation is found in the sand-laden flow. The turbulent intensity of aerodynamic wall shear stress increases rapidly with the sand mass flux. The decreased convective velocity indicates blocking effects of sand particles in the near-wall region. The power of aerodynamic wall shear fluctuation in the sand-laden flow increases at low frequencies corresponding to the duration of sand streamers. The results of a superstatistical analysis of skin friction velocity show that spatio-temporal fluctuation in the local energy dissipation rate is enhanced in the sand-laden flow. Finally, the local and spatio-drifting force acting on the stochastic system of wall shear fluctuation in sand-laden flow are different, providing a proof for the significant variation in flow condition caused by sand streamers near the wall.

A mechanistic approach for predicting mass transfer in bioreactors

The biomanufacturing processes that produce biologic drugs has become an extremely important area of study within the pharmaceutical industry. Within such processes, the drug substance is typically produced by living organisms within stirred tank bioreactors that require a continuous supply of sparged oxygen. The overall oxygen transfer rate to the fluid is a nonlinear convolution of the gas bubble size distribution, fluid properties, local fluid energy dissipation rates, and local dissolved oxygen concentrations. The complexity of this process presents challenges to process scale-up and intensification. In this work, we propose, implement, and validate a mechanistic transport model for predicting oxygen transfer rates within stirred tank bioreactors. To begin, we describe the relevant conservation laws and key principles from turbulence theory that govern mass transfer. Next, we present a physics-based modeling approach for solving these equations in tandem and in real-time. We then systematically validate the model against experimental data at operating scales ranging from 5 L to 2000 L. By running the algorithm on graphics processing units (GPUs), the approach is shown to solve at timescales practical for industrial application.