Distribution Of Length Scales Research Articles

Automated Shape and Process Parameter Optimization for Scaling Up Geometrically Non-Similar Bioreactors

Scaling bioprocesses remains a major challenge. Since it is physically impossible to increase all process parameters equally, a suitable scale-up strategy must be selected for a successful bioprocess. One of the most widely used criteria when scaling up bioprocesses is the specific power input. However, this represents only an average value. This study aims to determine the Kolmogorov length scale distribution by means of computational fluid dynamics (CFD) and to use it as an alternative scale-up criterion for geometrically non-similar bioreactors for the first time. In order to obtain a comparable Kolmogorov length scale distribution, an automated geometry and process parameter optimization was carried out using the open-source tools OpenFOAM and DAKOTA. The Kolmogorov–Smirnov test statistic was used for optimization. A HEK293-F cell expansion (batch mode) from benchtop (Infors Minifors 2 with 4 L working volume) to pilot scale (D-DCU from Sartorius with 30 L working volume) was carried out. As a reference cultivation, the classical scale-up approach with constant specific power input (233 W m−3) was used, where a maximum viable cell density (VCDmax) of 5.02·106 cells mL−1 was achieved (VCDmax at laboratory scale 5.77·106 cells mL−1). Through the automated optimization of the stirrer geometry (three parameters), position and speed, comparable cultivation results were achieved as in the small scale with a maximum VCD of 5.60·106 cells mL−1. In addition, even on the pilot scale, cell aggregate size distribution was seen to strictly follow a geometric distribution and can be predicted with the help of CFD with the previously published correlation.

Change of Spectral Properties of Magnetic Field Fluctuations across Different Types of Interplanetary Shocks

The interaction between interplanetary (IP) shocks and the solar wind has been studied in the past for the understanding of energy dissipation mechanisms within collisionless plasmas. Compared to the study of fast shocks, other types of IP shocks, including slow mode shocks (i.e., fast forward, fast reverse, slow forward, and slow reverse shocks) remained largely unnoticed. We analyze magnetic field fluctuations observed by the Wind spacecraft from 1995 to 2021 upstream and downstream of the IP shocks using a continuous wavelet transform. The evolution of spectral indices in the ion inertial and transition ranges and the changes in distributions of characteristic ion length scales with respect to the spectral break and proton beta are presented. We found that spectral indices in both inertial and transition ranges and the characteristic length scale distributions are statistically conserved across three types of IP shocks, suggesting that mechanisms associated with the energy dissipation are unaffected by the shocks. The results obtained for the transition range of fast reverse shocks show a larger difference between upstream and downstream plasmas and this will be further studied.

Connecting the early afterglow to the prompt GRB and the central engine in the striped jet model

ABSTRACT Despite a generally accepted framework for describing the gamma-ray burst (GRB) afterglows, the nature of the compact object at the central engine and the mechanism behind the prompt emission remain debated. The striped jet model is a promising venue to connect the various GRB stages since it gives a robust prediction for the relation of jet bulk acceleration, magnetization, and dissipation profile as a function of distance. Here, we use the constraints of the magnetization and bulk Lorentz of the jet flow at the large scales, where the jet starts interacting with the ambient gas in a large sample of bursts to (i) test the striped jet model for the GRB flow and (ii) study its predictions for the prompt emission and the constraints on the nature of the central engine. We find that the peak of the photospheric component of the emission predicted by the model is in agreement with the observed prompt emission spectra in the majority of the bursts in our sample, with a radiative efficiency of about 10 per cent. Furthermore, we adopt two different approaches to correlate the peak energies of the bursts with the type of central engine to find that more bursts are compatible with a neutron star central engine compared to a black hole one. Lastly, we conclude that the model favours broader distribution of stripe length-scales which results in a more gradual dissipation profile in comparison to the case, where the jet stripes are characterized by a single length-scale.

On the impact of waves and turbulence on the power fluctuations and wake structure of a tidal-stream turbine

Anticipating the power output of tidal-stream turbines (TSTs) is relevant for its technological advance and success. Therefore, it is important to clarify the behavior of TSTs under tidal-stream environments, which include both waves and currents. In this study, a scale-model horizontal-axis TST was examined in turbulent conditions and in the presence of waves. The impact of waves on the wake structure and output power fluctuations were analyzed in terms of integral length scales, the turbine's power statistics, and spectral density. Due to wave–current interactions, the distribution of integral length scales is asymmetric at downstream positions behind the rotor's lateral tips. The fluctuations of the wave speed in the wake lead to a homogenized but reduced length scale. In the spectral domain, waves mix with the turbulent cascade, effectively reducing the energy decay from f 0 to f−1 in the low-frequency region and from f−5/3 to f−11/3 in the intermediate-decay region. The bandwidth of the mechanical noise in the high-frequency range, along with the periodic components, intensifies with increasing wave height and length. Although they are preliminary, these findings will prove useful for understanding the disruption of turbine flow and power output in wave–current flows. This is a first step toward assessing the damage caused to ecology and the structural parts of TSTs in real-world conditions.

The deflection platform phenomenon of functionally graded flexoelectric simply supported nanobeam

Direct flexoelectricity appears in dielectrics as a kind of coupling effect of electric field and elastic strain gradient. Its strong size dependence makes it effective in nanostructures. In this paper, based on the flexoelectric theory and mixed finite element method (FEM), the mechanical properties of the two-dimensional functionally graded (FG) flexoelectric nanobeam are studied, and the phenomenon of the deflection platform is found. By applying various types of loads to FG nanobeams, the influence of geometric parameters, length scale, and material distribution on the phenomenon of the deflection platform is discussed. According to the simulation results, it is found that the aspect ratio and the length scale of the beam will change the shape of the deflection platform, making it change regularly among various shapes. The geometric size will greatly increase the height of the platform, but it has little effect on the dimensionless deflection. Reasonable material distribution can enhance the internal coupling effect, increase the height of the platform and reduce the required load. Our results suggest that when studying nano-scale flexoelectric models, the deflection platforms or similar phenomena should be considered.

Connection between the time distribution and length scale of dynamic heterogeneity explored by probe reorientations of different sizes.

The rotational dynamics of fluorescent probes of different sizes in glass-forming materials were examined to correlate the time distribution and length scale of the dynamic heterogeneity (ξhet). As the size of the probe increased, the temperature dependence of the rotation correlation time (τc) shifted to longer times, and from this shift, the length scale associated with the glass transition (ξα) was estimated through the Debye-Stokes-Einstein (DSE) relationship and the length scale of the probe (ξsDFT) estimated from quantum mechanical calculations. The estimated ξα values roughly matched with ξhet obtained from calorimetric analysis but were considerably smaller than those deduced from 4D NMR, boson peak, and four-point dynamic susceptibility measurements but with a similar trend of decrease in the length scale upon the increase in the stretching exponent (β) of the system. Because β of the glass formers represents the time distribution of the system, and τc is related to the weighted average of the distribution, the length-scale distribution of the glass transition can be deduced by adopting the DSE relationship and assuming ξα is the weighted average of this distribution at the glass transition temperature. In such a case, the upper bound of the length scale and trend matches the experimentally obtained ξhet from 4D NMR, boson peak, and four-point dynamic susceptibility measurements. Furthermore, at a given temperature, as the probe size increased, the β value reported by the probe increased, whereas the temperature dependence of β, which strongly correlates with the fragility of the system, was independent of the probe size.

CFD modelling of a wave-mixed bioreactor with complex geometry and two degrees of freedom motion

Optimizing bioprocesses requires an in-depth understanding, from a bioengineering perspective, of the cultivation systems used. A bioengineering characterization is typically performedviaexperimental or numerical methods, which are particularly well-established for stirred bioreactors. For unstirred, non-rigid systems such as wave-mixed bioreactors, numerical methods prove to be problematic, as often only simplified geometries and motions can be assumed. In this work, a general approach for the numerical characterization of non-stirred cultivation systems is demonstrated using the CELL-tainer bioreactor with two degree of freedom motion as an example. In a first step, the motion is recordedviamotion capturing, and a 3D model of the culture bag geometry is generatedvia3D-scanning. Subsequently, the bioreactor is characterized with respect to mixing time, and oxygen transfer rate, as well as specific power input and temporal Kolmogorov length scale distribution. The results demonstrate that the CELL-tainer with two degrees of freedom outperforms classic wave-mixed bioreactors in terms of oxygen transport. In addition, it was shown that in the cell culture version of the CELL-tainer, the critical Kolmogorov length is not surpassed in any simulation.

On the interaction of turbulence with nucleation and growth in reaction crystallisation

The objective of this work is to investigate the interaction of turbulence with the nonlinear processes of particle nucleation and growth that occur in reaction crystallisation, also known as precipitation. A validated methodology for coupling the population balance equation with direct numerical simulation of turbulent flows is employed for simulating an experiment conducted by Schwarzeret al.(Chem. Engng Sci., vol. 61, no. 1, 2006, pp. 167–181), where barium sulphate nanoparticles are formed by mixing and reaction of barium chloride and sulphate acid in a T-mixer, with the spatial resolution resolved down to the Kolmogorov scale. A unity Schmidt number is assumed, since at present it is not possible to resolve the Batchelor scale for realistic Schmidt numbers (order of 1000 or more). The probability density function, filtered averages and spatial distribution of time and length scales are all examined in order to shed light on the interplay of turbulence and precipitation. Separate Damköhler numbers are defined for nucleation and growth and both are found to be close to unity, indicating that the process is neither mixing nor kinetics controlled. The nucleation length scales are also evaluated and compared with the Kolmogorov scale to show the importance of resolving nucleation bursts. In addition, zones of different rate-determining mechanisms are identified. The ultimate aim of precipitation is to obtain control over the product particle size distribution, and the present study elucidates the synergistic or competing roles of mixing, nucleation and growth on the process outcome and discusses the implications for modelling.

The study on the broadband thrust spectrum of propeller in anisotropic and inhomogeneous turbulence

Considering the effects of stretching of turbulent eddies and inhomogeneous distribution of turbulence parameters, such as turbulence length scale, a new analytical approach to calculating the unsteady broadband thrust of propeller in anisotropic and inhomogeneous turbulence was introduced based on the correlation methods conducted in isotropic turbulence. Stephens's experiment was used to verify the theoretical approach to modeling in anisotropic and inhomogeneous turbulence. The effects of turbulence parameters on propeller broadband thrust in anisotropic and inhomogeneous turbulent field were discussed. The results showed that the haystack amplitudes at blade passage frequencies increase with the nonuniform level of the turbulent intensity and stretching parameters of turbulence eddy, while the effects of nonuniform distribution of inflow velocity and turbulence length scale can be neglected. Additionally, the haystack frequencies of propeller thrust spectrum are only dependent on blade passage frequency.

Numerical study of heat transfer, flow fields, turbulent length scales, and anisotropy in corrugated heat exchanger channels

In this study, we report on large eddy simulation (LES) of convectively dominated heat transfer in a corrugated heat exchanger channel using the computational fluid dynamics toolbox, OpenFOAM. A chevron pattern domain with 63 contact points is used to represent the conditions in a real plate heat exchanger (PHE). The unsteady nature of the flow is elucidated using visualization techniques based on volume rendering of temperature and iso surfaces of vorticity defined using the λ2-criterion and contours of wall shear stress and wall heat flux to illustrate the heat transfer process. Global surface averaged temperature and pressure drop are extracted from the LES on successively finer grids, approaching direct numerical simulation resolution, to increase the understanding of grid resolution requirements for LES in PHEs. Industry standard Reynolds-averaged Navier–Stokes simulations are compared to the LES results along selected profiles to demonstrate similarities and differences between the two techniques. The differences detected are further investigated using anisotropy invariant mapping, energy spectra, and turbulence length scale distributions. Significant differences between the model classes are detected and detailed. Moreover, the LES resolution requirements for the flow and the heat transfer processes are found to be different with the latter being more severe.

Predicting the hydrodynamic properties of a bioreactor: Conditional density estimation as a surrogate model for CFD simulations

The rising quantity and quality demands in biopharmaceutical manufacturing require a deep understanding of the underlying bioprocesses. For this purpose, computational fluid dynamics (CFD) simulations are typically used to predict the hydrodynamics properties of a bioreactor, offering a toolset for process design. However, CFD approaches are computationally demanding and therefore often restricted to a small set of input parameters. Basic regression techniques can be used to predict the hydrodynamic properties for new input parameter values, but these surrogate models are only capable of interpolating simple statistics such as the mean or maximum of the CFD simulation results. We propose a novel approach that allows to interpolate the volume-averaged distributions of a hydrodynamic property instead of only a simple statistic. In doing so, we: (i) obtain a computationally tractable model (ii) that is less expressive than a CFD simulation but more expressive than a basic regression model. The proposed approach has been applied to model the hydrodynamic stress and Kolmogorov length scale distributions using a CFD model of a sparged and stirred bioreactor. However, the methodology is generic and can be applied to further geometries and parameters.

Striation Thickness Distribution in Split-and-Recombine Mixers in the Stokes Regime

Slipt-and-recombine (SR) mixers typically operate in the Stokes flow regimes. Numerical and experimental studies have shown that a non-homogeneous distribution of the mixing scales is observed due to the difficulty of ensuring plug flow with viscous liquids. The parabolic velocity profile generated in the duct promotes the formation of larger mixing scales next to the walls and smaller scales in the centre of the duct. The mixing efficiency controlled by diffusion at the molecular scale depends on the non-ideal striation thickness decay. In this work, a simple model to estimate the distribution of mixing length scales in a SR mixer is proposed and compared to Computational Fluid Dynamics simulations. It is shown that the striation thickness of the largest scales in the flow decays at half the rate of an idealised baker's transformation, and that an SR mixer must be 1.81 times longer than an ideal one to achieve complete mixedness. The intensity of segregation is calculated for the largest mixing scales and set as an industrial design criterion for SR mixers. The main novelty of this work is the introduction of a new model to describe the non-homogeneous distribution of mixing scales in SR mixers.

Impact of horizontal spatial clustering in two-dimensional fracture networks on solute transport

This study explores the prevalence of fracture clustering in natural networks and its influence on fluid flow and advective transport. Fracture networks from a compilation of previously published maps that encompass igneous, metamorphic and sedimentary rock types, various geological and tectonic settings, and a broad distribution of length scales are analyzed using a two-point correlation technique to characterize the spatial scaling between fracture barycenters. The correlation dimension (Dc) ranges from 1.47 to 1.89 with a median of 1.8. These results suggest that fracture networks often exhibit spatial clustering and are rarely Poissonian as commonly assumed. Synthetic Discrete Fracture Networks (DFNs) with constant and variable transmissivity applied to all fractures are generated for three clustering (Dc = 1.6, Dc = 1.8, and Poissonian) and power law length exponent (α = 1.4, α = 1.8, and α = 2.2) scenarios. Median particle breakthrough times are shown to increase by 10–70% as spatial clustering transitions from Poissonian to highly clustered (Dc = 1.6). Median particle breakthrough times also increase, by a factor of 1.2–3.4 (20–240%), when the power law length exponent increases from α = 1.4 to α = 2.2. As clustering increases (i.e., Dc reduces), breakthrough curves become highly variable and exhibit features indicative of enhanced solute retention. The increase in median breakthrough times with clustering persists with different network size and transmissivity distribution. These results indicate that spatial clustering and length exponent both significantly influence transport. The use of power-law length distributions in generating fracture networks is relatively common, whereas the spatial organization of fractures is rarely included in transport studies of fractured rock. Structural heterogeneity introduced by spatially clustered organization of fractures leads to substantial complexity in flow paths which is not captured by Poissonian DFNs.

Small-angle X-ray and neutron scattering

Small-angle scattering (SAS) is a technique that is able to probe the structural organization of matter and quantify its response to changes in external conditions. X-ray and neutron scattering profiles measured from bulk materials or materials deposited at surfaces arise from nanostructural inhomogeneities of electron or nuclear density. The analysis of SAS data from coherent scattering events provides information about the length scale distributions of material components. Samples for SAS studies may be prepared in situ or under near-native conditions and the measurements performed at various temperatures, pressures, flows, shears or stresses, and in a time-resolved fashion. In this Primer, we provide an overview of SAS, summarizing the types of instrument used, approaches for data collection and calibration, available data analysis methods, structural information that can be obtained using the method, and data depositories, standards and formats. Recent applications of SAS in structural biology and the soft-matter and hard-matter sciences are also discussed.

Experimental investigation of turbulent characteristics in pore-scale regions of porous media

The study of flow dynamics in porous media or randomly packed beds is essential because these systems are commonly applied in a wide array of engineering applications, such as thermal energy storage, catalytic reactors for processing and distillation, oil recovery, fuel cells, and pebble bed nuclear reactor cores. The flow mixing and turbulence characteristics in pore-scale regions of an experimental facility composed of randomly packed spheres with an aspect ratio of 4.4 were experimentally investigated in this study. Velocity measurements at several pores in the test facility were conducted by combining the matched-index-of-refraction and time-resolved particle image velocimetry techniques, and these measurements were performed at Reynolds numbers of 490, 1023, and 1555. The results obtained from the velocity measurements in the pore regions revealed different and complex flow patterns depending on the pore geometries. In pore region 1, it was found that a strong axial flow entered the pore and impinged into the sphere’s surface when it encountered another flow entering laterally. These dynamic interactions created a high level of turbulent mixing, a recirculation flow region, and a shear layer, as observed in the computed statistical results for $$u^{\prime }_\mathrm{{rms}}$$ , $$v^{\prime }_\mathrm{{rms}}$$ , and $$u^{\prime }v^{\prime }$$ . In other pore regions, the flow field results exhibited complex interactions among jet flows discharging into the pores from various flow gaps created by neighboring spheres. These mutual interactions between the entering jet flows were found to create highly turbulent mixing regions at the pore’ centers and low-velocity or stagnation-flow regions in the vicinity of the sphere surfaces. Flapping shear layers were also observed when two jet flows with unequal strengths entered the pores. The characteristics of turbulent flow mixing in different pore regions were investigated via the spatiotemporal two-point correlation of fluctuating velocities along the velocity streamlines. This approach mitigated the constraints of the random geometries of pore regions on the extent of spatial separation lengths in the two-point velocity correlations. Using this approach, spatial distributions of integral length scales and convection velocities were estimated along the streamlines within the random geometries of pore regions. It was found that the estimated values of the integral length scales and convection velocities were spatially dependent on the localized flow characteristics within the pores. The integral length scales were found to be less than $$0.4D_\mathrm{{sp}}$$ , experimentally confirming the pore-scale prevalence hypothesis that turbulent structures in porous media are restricted by the pore sizes. In addition, the ratio of the convection velocity to the interstitial velocity (or local velocity magnitude) decreased as the Reynolds number increased.

Designing of Dynamic Spectrum Shifting in Terms of Non-Local Space-Fractional Mechanics

In this paper, the applicability of the space-fractional non-local formulation (sFCM) to design 1D material bodies with a specific dynamic eigenvalue spectrum is discussed. Such a formulated problem is based on the proper spatial distribution of material length scale, which maps the information about the underlying microstructure (it is important that the material length scale is one of two additional material parameters of sFCM compared to the classical local continuum mechanics—the second one, the order of fractional continua—is treated herein as a scaling parameter only). Technically, the design process for finding adequate length scale distribution is not trivial and requires the use of an inverse optimization procedure. In the analysis, the objective function considers a subset of eigenvalues reduced to a single value based on Kreisselmeier–Steinhauser formula. It is crucial that the total number of eigenvalues considered must be smaller than the limit which comes from the ratio of the sFCM length scale to the length of the material body.

Role of cellular wavelengths in self-acceleration of lean hydrogen-air expanding flames under turbulent conditions

An investigation is done upon the lean H2-air flame under turbulent conditions to clarify the role of inherent instabilities and turbulence in self-acceleration of expanding flames. The result shows that, in weak turbulent flow fields, the two-stage self-acceleration feature still exists. As the turbulent intensity increases, the originally evident two-stage “transition-saturation” feature is weakened. When the Karlovitz number becomes greater than 1, the self-acceleration process no longer experiences the transition stage and performs a single-stage feature. These observations are correlated with the distribution and evolution of length scales in the cellular structure of the flamefront. A theoretical analysis is conducted to compare growth rates of disturbances induced by instability and turbulence, with consideration of their wavelength dependence. On this basis, interpretations are proposed on afore-mentioned phenomenal observations and response of quantitative parameters such as fractal excess and average cell wavelength.

Glassy Behavior of Sticky Spheres: What Lies beyond Experimental Timescales?

We use the swap MonteCarlo algorithm to analyze the glassy behavior of sticky spheres in equilibrium conditions at densities where conventional simulations and experiments fail to reach equilibrium, beyond predicted phase transitions and dynamic singularities. We demonstrate the existence of a unique ergodic region comprising all the distinct phases previously reported, except for a phase-separated region at strong adhesion. All structural and dynamic observables evolve gradually within this ergodic region, the physics evolving smoothly from well-known hard sphere glassy behavior at small adhesions and large densities, to a more complex glassy regime characterized by unusually broad distributions of relaxation timescales and length scales at large adhesions.

Superconducting Cu/Nb nanolaminate by coded accumulative roll bonding and its helium damage characteristics

A very broad distribution of microstructural length scales spanning few nm- to the μm-scale has proven effective to achieve exceptional materials properties. Here, we fabricate a Cu/Nb two-phase composite made of a hierarchically layered structure by modifying the conventional accumulative roll bonding (ARB) technique, where fresh Nb sheets are inserted and bonded during a repeated stacking and rolling process. This barcode-like multilayer with a designed hierarchical length scale distribution possesses densely distributed phase boundaries and rich interfacial structures. The composite demonstrates similar superconductivity characteristics as pure Nb, but is 3 × stronger, has theoretically better oxidation resistance, and retains considerable ductility. Under the helium irradiation environment, the unique interfacial structures featuring chemical intermixing zones (3-dimensional) are more immune to the formation of large helium clusters than atomically sharp interfaces (2-dimensional), screening them from radiation damage and improving their long-term mechanical integrity. This work signifies an effective strategy of constructing hierarchical laminates to achieve high-performance materials, which holds promise in fusion and fission energy applications.

Numerical characterization of downburst wind field at WindEEE dome

Downbursts are acknowledged for being a major loading hazard for horizontally-extending structures like transmission line systems. With these structures being inherently flexible, it is important to characterize the turbulence associated with the wind flow of downburst events being essential to quantify dynamic excitations on structures. Accordingly, the current study numerically characterizes the downburst wind field of open terrain simulated at the Wind Engineering, Energy and Environment (WindEEE) dome testing facility at The University of Western Ontario in Canada through a high-resolution large eddy simulation (LES). The study validates the numerical simulation considering both the mean and the turbulent components of the flow. It then provides a detailed visual description of the flow at WindEEE through the capabilities enabled by LES to identify the key factors affecting the flow. The study also presents the spatial distribution of turbulence intensities and length scales computed from the numerical model and compares them with previous values reported in the literature. The comparison shows the ability of the downburst simulated at WindEEE to reproduce turbulence characteristics similar to those reported from field measurements. The study also indicates that downburst turbulence is well-correlated circumferentially which imposes high correlated loads on horizontally-distributed structures such as transmission lines.