Mean Energy Dissipation Rate Research Articles

Open-jet facility for bio-inspired micro-air-vehicle flight experiment at low speed and high turbulence intensity

Bio-inspired micro-air-vehicles (MAVs) usually operate in the atmospheric boundary layer at a low Reynolds number and complex wind conditions including large-scale turbulence, strong shear, and gusts. We develop an open jet facility (OJF) to meet the requirements of MAV flight experiments at very low speed and high turbulence intensity. Powered by a stage-driven fan, the OJF is capable of generating wind speeds covering 0.1 – 16.8 m/s, with a velocity ratio of 100:1. The contraction section of the OJF is designed using an adjoint-driven optimization method, resulting in a contraction ratio of 3:1 and a length-to-diameter ratio of 0.75. A modularized design of the jet nozzle can produce laminar or high-turbulence wind conditions. Flow field calibration results demonstrate that the OJF is capable of producing a high-quality baseline flow with steady airspeed as low as 0.1 m/s, uniform region around 80% of the cross-sectional test area, and turbulence intensity around 0.5%. Equipped with an optimized active grid (AG), the OJF can reproduce controllable, fully-developed turbulent wind conditions with the turbulence intensity up to 24%, energy spectrum satisfying the five-thirds power law, and the uniform region close to 70% of the cross-sectional area of the test section. The turbulence intensity, integral length scale, Kolmogorov length scale, and mean energy dissipation rate of the generated flow can be adjusted by varying the area of the triangular through-hole in the wings of the AG.

Turbulence Transitions in Kelvin–Helmholtz Instability “Tube” and “Knot” Dynamics: Vorticity, Helicity, and Twist Waves

We address the sources and dynamics of vorticity and helicity and their relations in transitions to turbulence arising due to Kelvin–Helmholtz instability (KHI) “Tube” and “Knot” (T&K) events. Such events are common in the atmosphere and oceans, and initial numerical simulations reveal that T&K dynamics significantly accelerate turbulence transitions and enhance KHI peak and mean energy dissipation rates. KHI T&K events arise where emerging KH billows exhibit varying wavelengths, phases, amplitudes, and/or discontinuities along their axes. As the KH billows intensify, these regions evolve roughly orthogonal billow cores and induced vortex tubes in close proximity. Their mutual advection as they intensify induces large-amplitude Kelvin vortex waves, or “twist waves”, that arise where locally uniform vortices are distorted by axial or radial advection. The twist waves propagate along, and fragment, the vortex tubes and billow cores, thus accounting for the emergence of helicity and the down-scale energy, enstrophy, and helicity fluxes within the turbulence inertial range. We describe the results of four direct numerical simulations (DNS) addressing KHI T&K dynamics in large and idealized small domains. The large-domain vorticity fields reveal the character and diversity of KHI T&K dynamics, the emergence of twist waves at larger and smaller scales, and their driving of turbulence transitions. Two small-domain DNS exhibit idealized KHI T&K events arising from KH billows that are mis-aligned and that exhibit phase variability along their axes. A third examines the interactions of two vortex tubes in close proximity. These reveal that twist waves drive the character and evolutions of the vorticity and helicity fields.

Micromixing performance of a miniaturized annular rotating flow mixer (MARFM)

Miniaturization of mixers is becoming an increasingly significant topic in process intensification. In this work, we develop a novel miniaturized annular rotating flow mixer (MARFM) by integrating the rotating flow field and micro-scale effect. The micromixing performance of MARFM is evaluated by the Villermaux/Dushman reaction system. Effects of various structural parameters on the micromixing performance are investigated. Two flow regions named stratification region and entrainment region have been firstly distinguished. Increasing rotational speed can remarkably improve micromixing performance under the stratification region rather than the entrainment region. In addition, the mixing performance at extreme flow conditions including high fluid viscosity and high flow rate ratio can be substantially improved in the MARFM. Segregation index is at least an order of magnitude smaller than that without the rotating flow field. Moreover, the micromixing time could range from 10−5 to 10−3 s in the MARFM, which is 1-3 orders of magnitude smaller than that of conventional mixers. Relationship between micromixing time and mean energy dissipation rate is established, which shows that higher energy utilization efficiency has been reached.

Rapid demulsification and phase separation in a miniaturized centrifugal demulsification device

To achieve effective demulsification of stable emulsions, we proposed a miniaturized centrifugal demulsification device (MCDD) based on the centrifugal force and microscale effect. Various parameters were studied to determine the demulsification efficiency, phase separation time, and mean energy dissipation rate per unit volume of the reactor. Detailed investigations of the controlled mechanism of demulsification efficiency and phase separation time are discussed. A demulsification efficiency of up to 99.9% was achieved. The relationship between phase separation time and demulsification efficiency was obtained. In addition, the mean energy dissipation rate per unit volume of the reactor primarily ranged from 0.32 × 104 to 4.76 × 104 W/m3, which is one order of magnitude lower than that of other active demulsification equipment. Furthermore, competitive demulsification for both water-in-oil and oil-in-water emulsions can be achieved with the MCDD. This study is the first to propose an MCDD with high demulsification efficiency, fast separation time, and low energy consumption.

Relationship between the methods of bounding time averages.

The problem of finding bounds of time-averaged characteristics of dynamical systems, such as the bound on the mean energy dissipation rate in a turbulent flow governed by incompressible Navier-Stokes equations, is considered. It is shown that the direct method described by Seis (2015 J. Fluid Mech. 777, 591-603. (doi:10.1017/jfm.2015.384)) and the auxiliary functional method by Chernyshenko et al. (2014 Phil. Trans. R. Soc. B 372, 20130350. (doi:10.1098/rsta.2013.0350)) are related and can lead to the same bound. The well-known background flow method of Doering and Constantin is equivalent to the auxiliary functional method with a quadratic auxiliary functional. The known implementations of the direct method apparently also correspond to quadratic auxiliary functionals. The findings are illustrated by the analysis of the plane Couette flow. Three routes of further progress using non-quadratic auxiliary functionals and at the same time allowing to use the experience accumulated with the background flow method are proposed: making the balance parameter dependent on the energy, making the background flow time-dependent in a specific way and adding helicity to the auxiliary functional. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.

Liquid-liquid flow and mass transfer characteristics in a miniaturized annular centrifugal device

• A MACD with efficient mass transfer, fast phase separation and low energy consumption is proposed. • The dimensionless correlation of maximum throughput is obtained. • Operation region and controlled mechanism of liquid–liquid phase separation are obtained. • the maximum η and k L a are up to 99.8 % and 0.31 s −1 , respectively. • The mean energy dissipation rate is lower than that of similar rotating equipment. Miniaturization of chemical equipment is becoming an important topic in process intensification and microscale flow chemistry. In this context, we developed a miniaturized annular centrifugal device (MACD) based on the microscale effect and centrifugal force. Various parameters were investigated to determine the maximum throughput of the single-phase, operating region of liquid–liquid phase separation, mass transfer performance, and mean energy dissipation rate. Detailed investigations of the controlled mechanism of the liquid–liquid flow process showed that a very fast phase separation can be achieved. The extraction efficiency and volume mass transfer coefficient were up to 99.8 % and 0.31 s −1 , respectively. The mean energy dissipation rate ranged from 0.8 × 10 4 to 3.9 × 10 4 W/m 3 , which is lower than that of the similar rotating equipment. In addition, dimensionless correlations were obtained to predict the maximum throughput of the single-phase, the operating region of liquid–liquid phase separation, and the volume mass transfer coefficient. This study is the first time to propose a MACD with fast phase separation, efficient mass transfer, and low energy consumption, and provides a highly promising liquid–liquid process intensification tool.

New Insights from Locally Resolved Hydrodynamics in Stirred Cell Culture Reactors

The link between hydrodynamics and biological process behavior of antibody-producing mammalian cell cultures is still not fully understood. Common methods to describe dependencies refer mostly to averaged hydrodynamic parameters obtained for individual cultivation systems. In this study, cellular effects and locally resolved hydrodynamics were investigated for impellers with different spatial hydrodynamics. Therefore, the hydrodynamics, mainly flow velocity, shear rate and power input, in a single- and a three-impeller bioreactor setup were analyzed by means of CFD simulations, and cultivation experiments with antibody-producing Chinese hamster ovary (CHO) cells were performed at various agitation rates in both reactor setups. Within the three-impeller bioreactor setup, cells could be cultivated successfully at much higher agitation rates as in the single-impeller bioreactor, probably due to a more uniform flow pattern. It could be shown that this different behavior cannot be linked to parameters commonly used to describe shear effects on cells such as the mean energy dissipation rate or the Kolmogorov length scale, even if this concept is extended by locally resolved hydrodynamic parameters. Alternatively, the hydrodynamic heterogeneity was statistically quantified by means of variance coefficients of the hydrodynamic parameters fluid velocity, shear rate, and energy dissipation rate. The calculated variance coefficients of all hydrodynamic parameters were higher in the setup with three impellers than in the single impeller setup, which might explain the rather stable process behavior in multiple impeller systems due to the reduced hydrodynamic heterogeneity. Such comprehensive insights lead to a deeper understanding of the bioprocess.

Intraband dynamics of mid-infrared HgTe quantum dots

Femtosecond pump-probe spectroscopy reveals ultrafast carrier dynamics in mid-infrared (MIR) colloidal HgTe nanoparticles with a bandgap of 2.5 μm. We observe intraband relaxation processes after photoexcitation ranging from resonant excitation up to the multi-exciton generation (MEG) regime by identifying initially excited states from atomic effective pseudopotential calculations. Our study elucidates the earliest dynamics below 10 ps in this technologically relevant material. With increasing photon energy, we find carrier relaxation times as long as 2.1 ps in the MEG regime close to the ionization threshold of the particles. For all photon energies, we extract a constant mean carrier energy dissipation rate of 0.36 eV ps-1 from which we infer negligible impact of the density of states on carrier cooling.

Theoretical and experimental investigations on swirling steam-water mixture flow in a circular channel with modified surface walls

The influence of surface roughness as well as protrusion geometry laid over the inner wall of the horizontal channel, on mean velocity and turbulent quantities along with thermal quantities of the swirling steam-water flow are determined experimentally. These were compared with the measurements for those obtained for smooth inner surface of the channel. The test facility has comprised of a Perspex pipe having inner diameter of 15 cm and length 30 cm. It contains three sections; one has smooth inner surface, second has rough inner surface with mild sand blasting and the third has square circular protruded collars along with mild treatment with the sand blasting. Mean velocity profile within the region close to the vicinity of the surface roughness has been lower than the values of the mean velocity profile in case of smooth inner surface of the pipe. And mean velocity values with protruded collar along with roughened surface are even lower than those in case of inner rough surface. However, the mean velocity values at distance away from the rough surface match among the three cases. Similar profiles representative of the three surfaces are obtained in case of velocity deficit. Whereas different turbulent characteristics are observed among smooth, rough, and protruded surfaces. Significant influences on the normal and Reynolds stresses occur over the whole of the layer due to the rough and protruded surfaces than those of the stresses generated in case of smooth surface. Although velocity spectra exhibit differences between the three surfaces, the mean energy dissipation rate does not appear to be significantly affected by the roughness and protruded surface. Nusselt number with passage of time following initiation of steam into the pipe, drops to an equilibrium value after passage of about 50–70 s. And the heat transfer characterized by normalized Stanton number ratio of rough surface to smooth surface, increases with increase in size of the sand grain for all the three surfaces. The increase in Stanton number ratio representing the rough surfaces is higher than the values of ratio in case of smooth surface. However, the major outcome of this study has been owed to the vorticities shed through the roughness, which is comparable to the roughness scale, k and this was found substantial than the turbulence scale of the outer layer.

How close are shell models to the 3D Navier–Stokes equations?

Shell models have found wide application in the study of hydrodynamic turbulence because they are easily solved numerically even at very large Reynolds numbers. Although bereft of spatial variation, they accurately reproduce the main statistical properties of fully-developed homogeneous and isotropic turbulence. Moreover, they enjoy regularity properties which still remain open for the three-dimensional (3D) Navier–Stokes equations (NSEs). The goal of this study is to make a rigorous comparison between shell models and the NSEs. It turns out that only the estimate of the mean energy dissipation rate is the same in both systems. The estimates of the velocity and its higher-order derivatives display a weaker Reynolds number dependence for shell models than for the 3D NSEs. Indeed, the velocity-derivative estimates for shell models are found to be equivalent to those corresponding to a velocity gradient averaged version of the 3D Navier–Stokes equations (VGA-NSEs), while the velocity estimates are even milder. Numerical simulations over a wide range of Reynolds numbers confirm the estimates for shell models.

Gravity Wave Breaking and Vortex Ring Formation Observed by PMC Turbo

AbstractPolar mesospheric cloud (PMC) imaging and lidar profiling performed aboard the 5.9‐day PMC Turbo balloon flight from Sweden to northern Canada in July 2018 revealed a wide variety of gravity wave (GW) and instability events occurring nearly continuously at approximately 82 km. We describe one event exhibiting GW breaking and associated vortex rings driven by apparent convective instability. Using PMC Turbo imaging with spatial and temporal resolution of 20 m and 2 s, respectively, we quantify the GW horizontal wavelength, propagation direction, and apparent phase speed. We identify vortex rings with diameters of 2–5 km and horizontal spacing comparable to their size. Lidar data show GW vertical displacements of ±0.3 km. From the data, we find a GW intrinsic frequency and vertical wavelength of 0.009 ± 0.003 rad s−1 and 9 ± 4 km, respectively. We show that these values are consistent with the predictions of numerical simulations of idealized GW breaking. We estimate the momentum deposition rate per unit mass during this event to be 0.04 ± 0.02 m s−2 and show that this value is consistent with the observed GW. Comparison to simulation gives a mean energy dissipation rate for this event of 0.05–0.4 W kg−1, which is consistent with other reported in situ measurements at the Arctic summer mesopause.

A spectral approach of suspending solid particles in a turbulent stirred vessel

AbstractThe 2015 Grenville‐Mak‐Brown (GMB) correlation for predicting the just suspended condition assumes that the length scale of the suspending eddy is equivalent to the particle diameter. This article investigates the role of the time scale of the relevant eddies with respect to the particle response time. The local turbulence just above the tank bottom is gauged by means of single‐phase LESs at the just suspended conditions determined in new experiments in dilute suspensions. By means of a novel nondimensional Suspension number we found that the relevant suspending eddies in the inertial subrange are 1.2–1.5 times larger than the particle size while the required eddy time scale is of the order of two times the particle response time. Further, we concluded that the mean energy dissipation rate is a suitable approximation of the local energy responsible for suspension. These results do not impact the effectiveness of the GMB correlation.

Computational fluid dynamics analysis of mixing and gas-liquid mass transfer in wave bag bioreactor.

Single use bioreactors provide an attractive alternative to traditional deep-tank stainless steel bioreactors in process development and more recently manufacturing process. Wave bag bioreactors, in particular, have shown potential applications for cultivation of shear sensitive human and animal cells. However, the lack of knowledge about the complex fluid flow environment prevailing in wave bag bioreactors has so far hampered the development of a scientific rationale for their scale up. In this study, we use computational fluid dynamics (CFD) to investigate the details of the flow field in a 20-L wave bag bioreactor as a function of rocking angle and rocking speed. The results are presented in terms of local and mean velocities, mixing, and energy dissipation rates, which are used to create a process engineering framework for the scale-up of wave bag bioreactors. Proof-of-concept analysis of mixing and fluid flow in the 20-L wave bag bioreactor demonstrates the applicability of the CFD methodology and the temporal and spatial energy dissipation rates integrated and averaged over the liquid volume in the bag provide the means to correlate experimental volumetric oxygen transfer rates (kL a) data with power per unit volume. This correlation could be used as a rule of thumb for scaling up and down the wave bag bioreactors.

Finding Extremal Periodic Orbits with Polynomial Optimization, with Application to a Nine-Mode Model of Shear Flow

Tobasco et al. [Physics Letters A, 382:382-386, 2018; see https://doi.org/10.1016/j.physleta.2017.12.023] recently suggested that trajectories of ODE systems that optimize the infinite-time average of a certain observable can be localized using sublevel sets of a function that arise when bounding such averages using so-called auxiliary functions. In this paper we demonstrate that this idea is viable and allows for the computation of extremal unstable periodic orbits (UPOs) for polynomial ODE systems. First, we prove that polynomial optimization is guaranteed to produce auxiliary functions that yield near-sharp bounds on time averages, which is required in order to localize the extremal orbit accurately. Second, we show that points inside the relevant sublevel sets can be computed efficiently through direct nonlinear optimization. Such points provide good initial conditions for UPO computations. As a proof of concept, we then combine these methods with a single-shooting Newton-Raphson algorithm to study extremal UPOs for a nine-dimensional model of sinusoidally forced shear flow. We discover three previously unknown families of UPOs, one of which simultaneously minimizes the mean energy dissipation rate and maximizes the mean perturbation energy relative to the laminar state for Reynolds numbers approximately between 81.24 and 125.

Condensational and Collisional Growth of Cloud Droplets in a Turbulent Environment

AbstractWe investigate the effect of turbulence on the combined condensational and collisional growth of cloud droplets by means of high-resolution direct numerical simulations of turbulence and a superparticle approximation for droplet dynamics and collisions. The droplets are subject to turbulence as well as gravity, and their collision and coalescence efficiencies are taken to be unity. We solve the thermodynamic equations governing temperature, water vapor mixing ratio, and the resulting supersaturation fields together with the Navier–Stokes equation. We find that the droplet size distribution broadens with increasing Reynolds number and/or mean energy dissipation rate. Turbulence affects the condensational growth directly through supersaturation fluctuations, and it influences collisional growth indirectly through condensation. Our simulations show for the first time that, in the absence of the mean updraft cooling, supersaturation-fluctuation-induced broadening of droplet size distributions enhances the collisional growth. This is contrary to classical (nonturbulent) condensational growth, which leads to a growing mean droplet size, but a narrower droplet size distribution. Our findings, instead, show that condensational growth facilitates collisional growth by broadening the size distribution in the tails at an early stage of rain formation. With increasing Reynolds numbers, evaporation becomes stronger. This counteracts the broadening effect due to condensation at late stages of rain formation. Our conclusions are consistent with results of laboratory experiments and field observations, and show that supersaturation fluctuations are important for precipitation.

Effects of active fluctuations on energetics of a colloidal particle: Superdiffusion, dissipation and entropy production

We consider a colloidal particle immersed in an active bath and derive a Smoluchowski equation that governs the dynamics of the colloidal particle. We address this as active Smoluchowski equation. Our analysis based on this active Smoluchowski equation shows a short time superdiffusive behavior that strongly depends on the activity. Our model also predicts a non-monotonic dependence of the mean energy dissipation against time, a signature of activity-induced dynamics. By introducing a frequency-dependent effective temperature, we show that the mean rate of entropy production is time-dependent, unlike in a thermal system. The main reason for these anomalies is the absence of any fluctuation–dissipation theorem for the active noise. We also comment on how microscopic details of activity can reverse the trends for the mean energy dissipation and mean rate of entropy production.

Examining and extending the concept of machine acceleration used in modelling the bubble-particle detachment in flotation

The bubble-particle (BP) detachment is a significant factor in controlling the recovery of coarse particles in mechanical flotation cells. It has been quantified by balancing the restoring force of surface tension and the centrifugal force exerted on the particle-bubble aggregate by the turbulent flow field using a “machine acceleration”. The concept of machine acceleration is useful because it links the mean energy dissipation rate of turbulence with the condition of the BP detachment. Here we further examine the concept of machine acceleration by applying the theory of isotropic turbulence. We confirm the known results of the first approximation for the inertial subrange. We also show that the turbulence acceleration has two principal components, i.e., the longitudinal and transverse components measured relatively to the BP centre-line. Significantly, the longitudinal component corresponds to the centrifugal force of turbulence against the restoring force of surface tension. The transverse component can be significant to quantifying the BP detachment if the turbulence shear is strong. We also extend the theory to cover the full range of isotropic turbulence, from the viscous to inertial subranges. Our estimation of the transition from the viscous to inertial subrange shows that the viscous effect can critically affect the BP detachment. Finally, our assessment of the contributions of the longitudinal and transverse components to the machine acceleration reveals the importance of the transverse component which can lead to a rather poor approximation for the machine acceleration as currently used. This paper shows that the effect of turbulence on the BP detachment should be better quantified using both the longitudinal and transverse components of turbulence acceleration rather than their modulus as the first approximation being termed the machine acceleration.

Cloud-droplet growth due to supersaturation fluctuations in stratiform clouds

Abstract. Condensational growth of cloud droplets due to supersaturation fluctuations is investigated by solving the hydrodynamic and thermodynamic equations using direct numerical simulations (DNS) with droplets being modeled as Lagrangian particles. The supersaturation field is calculated directly by simulating the temperature and water vapor fields instead of being treated as a passive scalar. Thermodynamic feedbacks to the fields due to condensation are also included for completeness. We find that the width of droplet size distributions increases with time, which is contrary to the classical theory without supersaturation fluctuations, where condensational growth leads to progressively narrower size distributions. Nevertheless, in agreement with earlier Lagrangian stochastic models of the condensational growth, the standard deviation of the surface area of droplets increases as t1∕2. Also, for the first time, we explicitly demonstrate that the time evolution of the size distribution is sensitive to the Reynolds number, but insensitive to the mean energy dissipation rate. This is shown to be due to the fact that temperature fluctuations and water vapor mixing ratio fluctuations increase with increasing Reynolds number; therefore the resulting supersaturation fluctuations are enhanced with increasing Reynolds number. Our simulations may explain the broadening of the size distribution in stratiform clouds qualitatively, where the mean updraft velocity is almost zero.

Visual study on the characteristics of liquid and droplet in a novel rotor-stator reactor

Abstract Rotor–stator reactor (RSR), an efficient mass transfer enhancer, has been applied in many fields. However, the hydrodynamic characteristics of liquid flow in RSR are still a mystery despite they are fundamental for the mass transfer performance and processing capacity. In view of the above, this paper studies the liquid–liquid flow and liquid holdup in RSR under various conditions with a high-speed camera. The paper firstly demonstrates two flow patterns and liquid holdup patterns that we obtained from our experiment and then presents in succession a flow pattern and a liquid holdup criterion for the transition of film flow to filament flow and complete filling to incomplete filling. It is found that experimental parameters, including rotor–stator distance, rotational speed and volume flow rate exert great influence on the average droplet diameter and size distribution. Besides, by comparison and contrast, we also find that the experimental values match well with our previous predicted calculations of the average diameter, and the relation between the average diameter and the mean energy dissipation rate.

Influence of Impeller Geometry on Hydromechanical Stress in Stirred Liquid/Liquid Dispersions

Hydromechanical stress is a crucial parameter for a broad range of multiphase processes in the field of (bio)chemical engineering. The effect of impeller type and geometry on hydromechanical stress in stirred tanks is important. The present study aims at characterizing conventional and new impeller types in terms of particle stress. A two-phase liquid/liquid noncoalescing dispersion system is employed, and the drop breakage is monitored in-line in a stirred tank. The published effects of agitation on drop deformation are confirmed and expanded significantly for five modified new impeller types. Radial impellers are advantageous for applications where low shear conditions are desired. A modified propeller with a peripheral ring and the developed wave-ribbon impellers present remarkable results by producing significantly low and high hydromechanical stress, respectively. The results obtained are correlated in terms of mean and maximum energy dissipation rate, as well as circulation frequency in the impeller...