Average Energy Dissipation Rate Research Articles

Dynamical analysis of a ferrofluid subjected to oscillatory field and shear rates: Applications to magnetic hyperthermia

The dynamical magnetic response of a small sample of ferrofluid is investigated numerically. A validated in-house research code is used to compute the translational and rotational motion of the particles. This code uses a robust scheme of Ewald summation to compute long-range periodic torques and forces between the particles. The model of the ferrofluid consists in a suspension of magnetic hard spheres replicated in lattices to ensure the convergence of the system’s transport properties. Ensemble averages over several realizations for each simulation are carried out. The suspension is subjected to field and shear time-dependent excitations. The effect of magnetic hyperthermia is evaluated by the average rate of internal energy dissipation due to an oscillatory magnetic field and oscillatory shear rate. Nonlinear dynamical tools such as phase spaces and Poincaré maps are applied to interpret the dynamical behavior of the suspension. Results show that when the suspension reaches its saturation magnetization due to a delayed time-response of the particles the internal energy dissipation decreases with respect to the local applied field. The Poincaré maps reveal that in dilute regimes the system presents quasi-periodic behavior for an alternating magnetic field. Also, the application of an oscillatory shear-rate increases the bulk internal energy of the system due to the magneto-viscous effect, even though it diminishes the internal area of the hysteresis loop. This work brings a better understanding of the dynamical response of ferrofluids that could be useful in magnetic hyperthermia applications.

Deciphering the effect of variation in slope on flow characteristics in a vertical slot fishway

The effects of a vertical slot fishway slope (with slope values from 1.5% to 6%) on a flow field are numerically investigated, using a re-normalization group k – ε model. The distribution of the velocity, turbulence kinetic energy (TKE), average energy dissipation rate per unit volume (E), and vorticity for different slopes are systemically explored. The results indicate that, with an increase in slope, the appearance of downward flow in conjunction with an increase in vertical velocity results in three-dimensional flow characteristics. The recirculation region in Hs, at a 6.0% slope, was 20.9% less than that at a 1.5% slope. Meanwhile, the flow velocity in the vertical slot region grew with increasing slope, which would limit the passage of fish with burst speed lower than the velocity in the vertical slot region. The TKE and E may locally exceed the threshold at larger slopes. Furthermore, vorticity distribution shows little variability with increasing slope, but may interfere with the equilibrium of the fish in the vertical slot region. In addition, the change in water level has little effect on the flow field, which is changed by the increase in slope. These findings can aid vertical slot fishway designs especially in terms of the efficiency of fish passage.

Three-Dimensional Numerical Analysis and Operational Optimization of High-Efficiency Sedimentation Tank

The high-efficiency sedimentation tank has a wide range of application prospects in industrial wastewater treatment due to its small footprint, strong resistance to shock loads, and high efficiency. However, the complex flow field distribution inside significantly affects the treatment performance of the high-efficiency tank. In this study, a three-dimensional geometric model of the high-efficiency sedimentation tank was constructed based on an engineering prototype. The corresponding solid–liquid two-phase, whole-process computational fluid dynamics (CFD) model for the high-efficiency sedimentation tank was established using the realizable k-ε turbulent model and the multiple reference frame (MRF) method. The internal structures of the flocculation zone, plug-flow zone, and clarification zone were optimized, and then the influence of operational process conditions on the flocculation treatment performance was investigated. The results indicate that, for the given engineering model, the average turbulent kinetic energy k in the flocculation zone exhibits a trend that initially increases and then decreases with the increase in the diameter and height of the draft tube. The optimal hydraulic conditions for the flocculation zone are achieved when the diameter of the draft tube is 2.5 m and the height is 3.5 m. The average turbulent kinetic energy dissipation rate in the plug-flow/clarification zone tends to decrease first and then increase as the height of the water tunnel and water-retaining weir increases. The optimal hydraulic conditions for the plug-flow and clarification zones are achieved when the height of the water tunnel is 1.0 m and the height of the water-retaining weir is 1.6 m. Under optimal operating conditions (dosage of dense media particles: 40 mg/L, stirring rate: 30 rpm, and inlet velocity: 0.72 m/s), satisfactory overall hydraulic conditions can be achieved throughout the entire high-efficiency sedimentation tank. Comparisons between a high-efficiency settling tank and a conventional clarifier for the treatment of circulating water sewage in a practical implementation reveals that the ballasted high-efficiency settling tank has advantages in terms of high hydraulic loading, high removal efficiency of hardness, small footprint, and low doses of flocculant. This research will provide reference values for the design and operation optimization of high-efficiency sedimentation tanks.

Experimental investigation on the frequency-spectrum characteristic of stress wave propagation through thermally treated granite

The propagation properties of stress waves in rock masses are significantly affected by high temperature. This paper presents an experimental investigation on the frequency-spectrum characteristics of stress waves in high-temperature granites. The pendulum impact test was performed on high-temperature granite bars to generate stress waves. The frequency-spectrum variation of stress waves in high-temperature granites was investigated by adopting the discrete Fourier transform. The effects of temperature on both the spectral attenuation ratio and the average energy dissipation rate of the harmonic wave were discussed. The results show that frequency spectra of stress waves occur attenuation when stress waves propagate in high-temperature granites. The frequency-spectrum attenuation is more obvious in the granite with higher temperature. Moreover, the spectral attenuation ratio and the average energy dissipation rate of the harmonic wave are significantly affected by the high temperature. The spectral attenuation ratio and the average energy dissipation rate of the harmonic wave increase as temperature increases.

Nucleation enhancement by energy dissipation with the collision of a supercooled water droplet

Lack of knowledge on nucleation with mechanical disturbances hinders researchers in understanding the anti-icing properties of superhydrophobic surfaces. In this research, experiments are designed to observe the freezing process of a supercooled water droplet at −14 °C with different levels of external disturbances by changing the impact velocity, and the nucleation rates are statistically analyzed. It is found that compared with the static state, the nucleation rates of droplets during the collision increase by three and five orders of magnitude on the hydrophilic epoxy resin and superhydrophobic polytetrafluoroethylene (PTFE) surfaces, respectively, which leads to a much higher instantaneous nucleation rate on the superhydrophobic surface than on the hydrophilic surface. Then, the mechanical energy dissipation during the impact is analyzed. The logarithm of the nucleation rate is approximately linear in relation to the logarithm of the average energy dissipation rate, while the nucleation rate of the rough PTFE surface increases more rapidly than that of the other smooth surface. Finally, the effect of the energy dissipation on the nucleation energy barrier is discussed theoretically and an impact-nucleation model is proposed, which drives the reconsideration of the design of a superhydrophobic anti-icing coating.

Hydrodynamic Characteristics of Diagonal Brush Fish Pass: Prototype Measurements

The present study investigates the hydrodynamic characteristics of the diagonal brush upstream fishway at the Incirli run-of-river hydropower plant on Iyidere River in Turkey. Three-dimensional velocity measurements were conducted in the fish pass using a Micro acoustic Doppler velocimeter under real-time operation conditions. The diagonal arrangement of brush blocks creates favorable hydrodynamic conditions (i.e., lateral momentum exchange) that allow fish to minimize swimming energy. We found that the spatially averaged lateral component of Reynolds shear stress is 2.2 times higher than spatially averaged vertical component of Reynolds shear stress, which could be due to the lateral velocity gradient in the vicinity of brush blocks. It is shown that the low-velocity zones behind the brush blocks constitute important resting sites for fish. The monitoring data showed that inlet water levels have considerable effects on the turbulence quantities. The brushes become submerged with the increased reservoir water level from 102 m to 102.05 m above sea level. The maximum turbulent kinetic energy was increased by a factor of three compared to unsubmerged conditions. We found a strong relationship between the average energy dissipation rate per unit mass and the Reynolds number. On the other hand, the prototype data reveal the inverse relationship between the Darcy-Weissbach friction factor and the relative submergence of bristles. The present results allow the efficient design of diagonal fish passes.

Intensification of Liquid–Liquid Emulsification Process in a Rotating Solid Foam Stirrer Tank: Experiments and Modeling

Process intensification equipment is playing an increasingly role in the emulsion process. A novel rotating solid foam stirrer tank (RSFST) is developed in this work to try to intensify the liquid–liquid emulsification process. The effects of operating parameters and physical parameters, such as emulsification time, rotational speed, packing size, dispersed phase volume fraction, and continuous-phase viscosity, on the droplet size distribution and Sauter mean diameter d32 of oil-in-water emulsions produced in RSFST were investigated using a kerosene–water system. To benchmark the emulsion performance of the RSFST, a Rushton stirrer is used a reference stirrer and the generated droplet size and average energy dissipation rate as the evaluation metrics. Based on the experimental data of emulsification under different operating conditions and physical parameters, models are applied to describe the bimodal distribution of oil-in-water emulsion droplet sizes, and correlation is proposed to predict the Sauter mean diameter d32 of RSFST. This work provides fundamental data for practical applications of RSFST used in emulsion process intensification.

Intermittency of turbulent velocity and scalar fields using three-dimensional local averaging

An efficient approach for extracting 3D local averages in spherical subdomains is proposed and applied to study the intermittency of small-scale velocity and scalar fields in direct numerical simulations of isotropic turbulence. We focus on the inertial-range scaling exponents of locally averaged energy dissipation rate, enstrophy and scalar dissipation rate corresponding to the mixing of a passive scalar $\theta$ in the presence of a uniform mean gradient. The Taylor-scale Reynolds number $R_\lambda$ goes up to $1300$, and the Schmidt number $Sc$ up to $512$ (albeit at smaller $R_\lambda$). The intermittency exponent of the energy dissipation rate is $\mu \approx 0.23$, whereas that of enstrophy is slightly larger; trends with $R_\lambda$ suggest that this will be the case even at extremely large $R_\lambda$. The intermittency exponent of the scalar dissipation rate is $\mu_\theta \approx 0.35$ for $Sc=1$. These findings are in essential agreement with previously reported results in the literature. We further show that $\mu_\theta$ decreases monotonically with increasing $Sc$, either as $1/\log Sc$ or a weak power law, suggesting that $\mu_\theta \to 0$ as $Sc \to \infty$, reaffirming recent results on the breakdown of scalar dissipation anomaly in this limit.

CFD-Based and Experimental Hydrodynamic Characterization of the Single-Use Bioreactor XcellerexTM XDR-10.

Understanding the hydrodynamic conditions in bioreactors is of utmost importance for the selection of operating conditions during cell culture process development. In the present study, the two-phase flow in the lab-scale single-use bioreactor Xcellerex XDR-10 is characterized for working volumes from 4.5 L to 10 L, impeller speeds from 40 rpm to 360 rpm, and sparging with two different microporous spargers at rates from 0.02 L min to 0.5 L min. The numerical simulations are performed with the one-way coupled Euler–Lagrange and the Euler–Euler models. The results of the agitated liquid height, the mixing time, and the volumetric oxygen mass transfer coefficient are compared to experiments. For the unbaffled XDR-10, strong surface vortex formation is found for the maximum impeller speed. To support the selection of suitable impeller speeds for cell cultivation, the surface vortex formation, the average turbulence energy dissipation rate, the hydrodynamic stress, and the mixing time are analyzed and discussed. Surface vortex formation is observed for the maximum impeller speed. Mixing times are below 30 s across all conditions, and volumetric oxygen mass transfer coefficients of up to 22.1 h are found. The XDR-10 provides hydrodynamic conditions which are well suited for the cultivation of animal cells, despite the unusual design of a single bottom-mounted impeller and an unbaffled cultivation bioreactor.

On the Equality of Modal Damping Power and the Average Rate of Transient Energy Dissipation in a Multimachine Power System

This letter establishes a relationship between the concepts of damping torque and the dissipation of transient energy in a multimachine power system with constant power loads. To that end, we present a mathematical proof showing that, for a poorly-damped mode, the total damping power stemming from the interaction of electromagnetic torques and rotor speeds is approximately equal to the average rate of transient energy dissipation in the system corresponding to the modal oscillation. This is verified with numerical studies on the IEEE 2-area 4-machine and 5-area 16-machine test systems.

Determination of hydraulic resistance of channels using spectral geometry methods

In this paper, we propose a new method for calculation of hydraulic resistance of channels with constant cross-section. The method is based on the obtained estimates for the average energy dissipation rate in a turbulent flow. The first part of the paper is devoted to theoretical justification of the method. The second part is devoted to calculation of hydraulic resistance of various channels using the above-mentioned method and comparison of these values with the known results. The proposed method allows for calculation of hydraulic resistance of various channels with sufficiently high accuracy and is based only on the information about the channel geometry.

Computational fluid dynamic characterization of vertical‐wheel bioreactors used for effective scale‐up of human induced pluripotent stem cell aggregate culture

AbstractBioreactor‐based processes are the method of choice for efficient expansion of cells in a controlled setting. However, induced pluripotent stem cells (iPSCs) have proven to be extremely sensitive to the bioreactor hydrodynamic environment, making the use of suspension bioreactors to produce quality‐assured cells at clinical and commercial scales very challenging. The PBS vertical‐wheel (VW) bioreactor combines radial and axial flow components to produce uniform hydrodynamic force distributions, making it a promising platform to overcome the scale‐up challenges associated with iPSCs. In this study, hydrodynamic characterization through computational fluid dynamics modelling of VW bioreactors was performed. Analysis of these models proved that important volume average hydrodynamic variables could be maintained throughout scale‐up from the 0.1 L to the 15 L VW bioreactor scale. Each bioreactor scale (0.1, 0.5, 3, and 15 L) was modelled at a variety of agitation rates, leading to the generation of scale‐up correlation equations. These equations allow operators to define a working range of hydrodynamic variables at one scale and calculate the corresponding agitation rates at other modelled scales. A suggested operating range of agitation rates was determined for the successful culture of iPSCs in the VW bioreactor at each scale, corresponding to constant volume average energy dissipation rate. Agitation rates from the 0.1 and 0.5 L VW bioreactor scale were experimentally tested to biologically validate the suggested range. High cell‐fold expansion, healthy aggregate morphology, growth, and uniformity were demonstrated for all conditions tested within the suggested working range.

Reactor design for continuous monoclonal antibody precipitation based upon micro‐mixing

AbstractBACKGROUNDPrecipitation has been applied for the processing of important therapeutics, including monoclonal antibodies (mAbs). The scale‐up has proven to be a challenging task due to the complexity of the reactions and transport processes involved. This requires a good understanding of the molecular processes underpinning precipitate formation. The aim of this study was to build a micro‐mixing model for the precipitation of a mAb in continuous tubular reactors using ammonium sulphate. The effect of micro‐mixing on precipitate formation (with respect to size, strength, and nature) was evaluated. An ultra scale‐down (USD) centrifugation methodology was applied to determine the ease of precipitate clarification.RESULTSThe results demonstrated that the final mean particle size decreased with increased micro‐mixing, and was obtained with short residence times. Antibody yields in the tubular reactors were consistently above 90% and were shown to be independent of the mixing. Similar particle sizes between a lab and pilot‐scale reactor were correlated with the average energy dissipation rate. The smaller particles obtained from improved micro‐mixing had higher fractal dimensions that correlated with minimal breakage upon exposure to turbulent shear. Precipitates were easily clarified at the USD scale (> 95% clarification), but less so at pilot‐scale (< 80% clarification).CONCLUSIONPrecipitation is a rapid process where the final precipitate properties are controlled by the flow conditions. Therefore, the process can be manipulated to acquire a certain particle size range. A high‐throughput precipitation process is also possible. However, further investigation into large‐scale precipitate recovery is required. © 2020 Society of Chemical Industry

Advancing understanding of turbulence through extreme-scale computation: Intermittency and simulations at large problem sizes

Advanced GPU-optimized algorithms coupled with a multiresolution short-time sampling paradigm can make extreme-scale turbulence simulations focused on small-scale physics much more accessible. One example is in the study of scaling exponents of the locally averaged energy dissipation rate at high Reynolds number.

A mesh adaptation strategy for complex wall-modeled turbomachinery LES

A mesh adaptation methodology for wall-modeled turbomachinery Large Eddy Simulation (LES) is proposed, simultaneously taking into account two quantities of interest: the average kinetic energy dissipation rate and the normalized wall distance y+. This strategy is first tested on a highly loaded transonic blade with separated flow, and is compared to wall-resolved LES results, as well as experimental data. The adaptation methodology allows to predict fairly well the boundary layer transition on the suction side and the recirculation bubble of the pressure side. The method is then tested on a real turbofan stage for which it is shown that the general operating point of the computation converges toward the experimental one. Furthermore, comparison of turbulence predictions with hot-wire anemometry show good agreement as soon as a first adaptation is performed, which confirms the efficiency of the proposed adaptation method.

Turbulent Drift of Finely Dispersed Particles in Emulsions and Suspensions in Pressure Hydrocyclones

Consideration has been given to a mathematical model of turbulent drift of fi nely dispersed particles in the liquid phase of a hydrocyclone. With the two-layer model of a turbulent boundary layer and the coefficient of turbulent diffusion of the particles, the authors have obtained an expression for calculating the coefficient of the rate of particle transport from the flow core to the boundary of a viscous sublayer on the apparatus wall. On the basis of the expression for shear stress on the wall, which was written with a momentum-transfer coefficient, an expression has been obtained for calculating the average circular velocity in the hydrocyclone. The basic parameter of these expressions is the dynamic velocity, which is determined from the average rate of energy dissipation. Results of calculations of the coeffi cient of transport of particles, the average circular velocity, and the efficiency of separation of particles of diameter 6 μm (sand particles in oil) have been presented; a comparison of the results with experimental data has been made.

Residence time distribution in coil and plate micro-reactors

Micro-reactors, enabling continuous processes at small scales, have been of growing interest due to their advantages over batch. These advantages include better scaling, as well as improved mass and heat transfer, though many new challenges arise due to the small scales involved such as non-negligible entrance effects and significant pressure losses. The flow in coils, rectangular channel serpentine plates, mix-and-reside plates, and liquid–liquid (LL) mixing plates was investigated and characterized using residence time distribution (RTD) tests. A pulse test was used to determine the RTD curve of these reactors at flowrates ranging from 15 to 100 g/min of water. A semi-empirical, multi-parameter model was used to describe the asymmetrical curves, while the axial dispersion model was used to describe the symmetrical ones. The Peclet number is given in function of the Reynolds number for the LL plates that were found to be near-plug flow (Pe > 100). In a plate with continuous LL micro-mixers, the Pe ranged from 193 to 467 with Pe increasing as Re increased. Importantly, the effect of straight channel segments interspaced between mixers is also evaluated as a method of volume gain for scale-up of micro-reactors. For a given average energy dissipation rate, the Pe number was maintained for the shorter channel segments between LL micro-mixers whereas longer spacing lengths likely lead to the development of unidirectional laminar flow and resulting in the observed increased axial dispersion and tailing in the RTD.

Micromixing efficiency in a rotating foam stirrer reactor with various reactor configurations and liquid viscosities

AbstractBACKGROUNDThe rotating foam stirrer reactor (RFSR) has shown its high mass transfer efficiency. Nevertheless, its micromixing efficiency, which is one of the significant parameters, still needs more comprehensive study for its better application and optimization. This work therefore employed the iodide–iodate reaction system to analyze the micromixing efficiency in an RFSR, and the effects of reactor configuration and liquid viscosity on micromixing efficiency were investigated.RESULTSThe results show that high micromixing efficiency can be achieved when the feed location is at the outer edge of the rotor. Solid foam with low pores per linear inch (ppi) and equipping baffles on the reactor wall can also considerably improve the micromixing efficiency. The results further reveal that the micromixing efficiency decreased with increasing liquid viscosity. Micromixing times in an RFSR with various configurations, estimated based on the incorporation model, ranged from 2.1 × 10−4 to 2.0 × 10−2 s. The minimum value is smaller than that of many conventional reactors and is competitive with that of some novel reactors. In addition, a correlation to predict the micromixing time based on the average energy dissipation rate was developed, which agreed well with experimental values.CONCLUSIONThis study indicates that the RFSR has excellent micromixing efficiency and also provides fundamental information for optimization of the RFSR and its application in process industries. © 2019 Society of Chemical Industry

Effect of parameters of pool geometry on flow characteristics in low slope vertical slot fishways

A 3D numerical model using the re-normalized group (RNG) k-ϵ turbulent closure was applied to study the hydraulic characteristics of a fishway and their dependence on the shape of the baffles, bed slope and water level difference between two adjacent pools. The results show the hydraulic conditions of a fishway with Type H baffles are better than that of a fishway with Type L baffles based on the analysis of turbulent kinetic energy, energy dissipation rate and vorticity. The flow velocity, turbulent kinetic energy and average energy dissipation rates per unit volume are all positively correlated with bed slopes. Water level difference between two adjacent pools is the main influencing factor for the velocity in the vertical slot. When the water level differences between two adjacent pools are the same, the flow velocities in the vertical slot are almost equal even if the fishways have totally different slopes. These findings enable the design of economic fishways with steep slopes but slower water flow.

Changes in milk fat globules and membrane lipids under the shear fields of microfiltration and centrifugation

This study compared the efficiency of centrifugal and microfiltration separation of milk fat globules (MFG) from bovine cream and the changes that take place in the corresponding lipid membranes (MFGM). Creams were washed with water (1:10) and subjected to either centrifugation or microfiltration to fractionate proteins and other non-fat milk components. Protein analyses of the obtained fractions were carried out by gel electrophoresis. Lipid extraction and thin layer chromatography were also employed to separate lipid types and the amount of polar lipids were determined by gas chromatography. The effect of flow conditions on MFG's colloidal properties and MFGM components was evaluated based on estimates of the average rate of energy dissipation in microfiltration and centrifugation processes. Both were equally effective in removing the protein fraction (93% yield) as well as non-fat dry matter (~100% removal). Microfiltration reduced the mean particle size by 0.3 µm, whereas the opposite was observed for centrifugal separation (average size increase by 0.8 µm). The latter process also induced a more significant reduction in the electrostatic charges (zeta potential) of the colloids in the cream, which relates to the changes in the milk fat globule surface composition and the release of MFGM components. The dissociated polar lipids amounted to 24% and 20% upon centrifugation and microfiltration, respectively. Overall, the results suggest that MFG and MFGM are partially damaged under the shear forces typical of centrifugal and microfiltration separation. A high separation efficiency, with minimal fat globule damage and high MFGM yield is possible by adopting microfiltration under carefully optimized conditions.