scholarly journals Derivation of Canopy Resistance in Turbulent Flow from First-Order Closure Models

Water ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 1782 ◽  
Author(s):  
Wei-Jie Wang ◽  
Wen-Qi Peng ◽  
Wen-Xin Huai ◽  
Gabriel Katul ◽  
Xiao-Bo Liu ◽  
...  
Keyword(s):  
Friction Factor ◽  
Free Surface Flows ◽  
Hydrodynamic Resistance ◽  
Small Scale ◽  
Length Scale ◽  
Length Scales ◽  
First Order ◽  
Closure Models ◽  
Wide Range ◽  
The Mean

Quantification of roughness effects on free surface flows is unquestionably necessary when describing water and material transport within ecosystems. The conventional hydrodynamic resistance formula empirically shows that the Darcy–Weisbach friction factor f~(r/hw)1/3 describes the energy loss of flowing water caused by small-scale roughness elements characterized by size r (<<hw), where hw is the water depth. When the roughness obstacle size becomes large (but <hw) as may be encountered in flow within canopies covering wetlands or river ecosystem, the f becomes far more complicated. The presence of a canopy introduces additional length scales above and beyond r/hw such as canopy height hv, arrangement density m, frontal element width D, and an adjustment length scale that varies with the canopy drag coefficient Cd. Linking those length scales to the friction factor f frames the scope of this work. By adopting a scaling analysis on the mean momentum equation and closing the turbulent stress with a first-order closure model, the mean velocity profile, its depth-integrated value defining the bulk velocity, as well as f can be determined. The work here showed that f varies with two dimensionless groups that depend on the canopy submergence depth and a canopy length scale. The relation between f and these two length scales was quantified using first-order closure models for a wide range of canopy and depth configurations that span much of the published experiments. Evaluation through experiments suggests that the proposed model can be imminently employed in eco-hydrology or eco-hydraulics when using the De Saint-Venant equations.

scholarly journals Subject-specific multiscale modeling of aortic valve biomechanics

2021 ◽  
Author(s):  
G. Rossini ◽  
A. Caimi ◽  
A. Redaelli ◽  
E. Votta
Keyword(s):  
Aortic Valve ◽  
Boundary Conditions ◽  
Narrow Range ◽  
Radial Strain ◽  
Length Scale ◽  
Length Scales ◽  
Anatomical Features ◽  
Wide Range ◽  
Subject Specific ◽  
Cell Strains

AbstractA Finite Element workflow for the multiscale analysis of the aortic valve biomechanics was developed and applied to three physiological anatomies with the aim of describing the aortic valve interstitial cells biomechanical milieu in physiological conditions, capturing the effect of subject-specific and leaflet-specific anatomical features from the organ down to the cell scale. A mixed approach was used to transfer organ-scale information down to the cell-scale. Displacement data from the organ model were used to impose kinematic boundary conditions to the tissue model, while stress data from the latter were used to impose loading boundary conditions to the cell level. Peak of radial leaflet strains was correlated with leaflet extent variability at the organ scale, while circumferential leaflet strains varied over a narrow range of values regardless of leaflet extent. The dependency of leaflet biomechanics on the leaflet-specific anatomy observed at the organ length-scale is reflected, and to some extent emphasized, into the results obtained at the lower length-scales. At the tissue length-scale, the peak diastolic circumferential and radial stresses computed in the fibrosa correlated with the leaflet surface area. At the cell length-scale, the difference between the strains in two main directions, and between the respective relationships with the specific leaflet anatomy, was even more evident; cell strains in the radial direction varied over a relatively wide range ($$0.36-0.87$$ 0.36 - 0.87 ) with a strong correlation with the organ length-scale radial strain ($$R^{2}= 0.95$$ R 2 = 0.95 ); conversely, circumferential cell strains spanned a very narrow range ($$0.75-0.88$$ 0.75 - 0.88 ) showing no correlation with the circumferential strain at the organ level ($$R^{2}= 0.02$$ R 2 = 0.02 ). Within the proposed simulation framework, being able to account for the actual anatomical features of the aortic valve leaflets allowed to gain insight into their effect on the structural mechanics of the leaflets at all length-scales, down to the cell scale.

Re-Examination of A1 → L10 Ordering: Generalized Bragg-Williams Model with Elastic Relaxation

2011 ◽  
Vol 172-174 ◽  
pp. 608-617 ◽  
Author(s):  
William A. Soffa ◽  
David E. Laughlin ◽  
Nitin Singh
Keyword(s):  
Nearest Neighbor ◽  
Binary Solution ◽  
Mean Field ◽  
Lattice Relaxation ◽  
Two Phase ◽  
First Order ◽  
Tetragonal Lattice ◽  
Wide Range ◽  
Third Law Of Thermodynamics ◽  
The Mean

The tetragonal lattice relaxation has been included in the thermodynamics of the fcc→L10ordering to produce a first-order character of the transition within the mean field description of the binary solution energetics. In view of growing interest in such systems e.g. Fe-Pd and Co-Pt alloys, which display a wide range of applications relevant to current and futuristic technologies, the fcc→L10two-phase field is re-examined utilizing a generalized Bragg-Williams approach including first and second nearest neighbor interactions. The thermodynamic behavior is examined in the limit of T→0K and discussed in terms of the implications of the Third Law of Thermodynamics.

Experiments on turbulence in a rotating fluid

1975 ◽  
Vol 68 (4) ◽  
pp. 639-672 ◽  
Author(s):  
A. Ibbetson ◽  
D. J. Tritton
Keyword(s):  
Rotation Rate ◽  
Rotation Axis ◽  
Turbulence Energy ◽  
Length Scale ◽  
Grid Turbulence ◽  
Rotating Fluid ◽  
Mean Flow ◽  
Length Scales ◽  
Wide Range ◽  
Energy Sink

Experiments have been carried out to investigate the effect of rotation of the whole system on decaying turbulence, generally similar to grid turbulence, generated in air in an annular container on a rotating table. Measurements to determine the structure of the turbulence were made during its decay, mean quantities being determined by a mixture of time and ensemble averaging. Quantities measured (as functions of time after the turbulence generation) were turbulence intensities perpendicular to and parallel to the rotation axis, spectra of these two components with respect to a wavenumber perpendicular to the rotation axis, and some correlation coefficients, selected to detect differences in length scales perpendicular and parallel to the rotation axis. The intensity measurements were made for a wide range of rotation rates; the other measurements were made at a single rotation rate (selected to give a Rossby number varying during the decay from about 1 to small values) and, for comparison, at zero rotation. Subsidiary experiments were carried out to measure the spin-up time of the system, and to determine whether the turbulence produced any mean flow relative to the container.A principal result is that increasing the rotation rate produces faster decay of the turbulence; the nature of the additional energy sink is an important part of the interpretation. Other features of the results are as follows: the measurements with-outrotation can be satisfactorily related to wind-tunnel measurements; even with rotation, the ratio of the intensities in the two directions remains substantially constant; the normalized spectra for the rotating and the non-rotating cases show surprising similarity but do contain slight systematic differences, consistent with the length scales indicated by the correlations; rotation produces a large increase in the length scale parallel to the rotation axis and a smaller increase in that perpendicular to it; the turbulence produces no measurable mean flow.A model for the interpretation of the results is developed in terms of the action of inertial waves in carrying energy to the boundaries of the enclosure, where it is dissipated in viscous boundary layers. The model provides satisfactory explanations of the overall decay of the turbulence and of the decay of individual spectral components. Transfer of energy between wavenumbers plays a much less significant role in the dynamics of decay than in a non-rotating fluid. The relationship of the model to the interpretation of the length-scale difference in terms of the Taylor-Proudman theorem is discussed.The model implies that the overall dimensions of the system enter in an important way into the dynamics. This imposes a serious limitation on the application of the results to the geophysical situations at which experiments of this type are aimed.The paper includes some discussion of the possibility of energy transfer from the turbulence to a mean motion (the ‘vorticity expulsion’ hypothesis). It is possible, on the basis of the observations, to exclude this process as the additional turbulence energy sink. But this does not provide any evidence either for or against the hypothesis in the conditions for which it has been postulated.

scholarly journals Pressure–strain terms in Langmuir turbulence

2019 ◽  
Vol 880 ◽  
pp. 5-31
Author(s):  
Brodie C. Pearson ◽  
Alan L. M. Grant ◽  
Jeff A. Polton
Keyword(s):  
Slow Component ◽  
Strain Tensor ◽  
Large Eddy Simulations ◽  
Langmuir Turbulence ◽  
Closure Model ◽  
First Order ◽  
Closure Models ◽  
Large Eddy ◽  
The Mean ◽  
Mean Current

This study investigates the pressure–strain tensor ($\unicode[STIX]{x1D72B}$) in Langmuir turbulence. The pressure–strain tensor is determined from large-eddy simulations (LES), and is partitioned into components associated with the mean current shear (rapid), the Stokes shear and the turbulent–turbulent (slow) interactions. The rapid component can be parameterized using existing closure models, although the coefficients in the closure models are particular to Langmuir turbulence. A closure model for the Stokes component is proposed, and it is shown to agree with results from the LES. The slow component of $\unicode[STIX]{x1D72B}$ does not agree with existing ‘return-to-isotropy’ closure models for five of the six components of the Reynolds stress tensor, and a new closure model is proposed that accounts for these deviations which vary systematically with Langmuir number, $La_{t}$, and depth. The implications of these results for second- and first-order closures of Langmuir turbulence are discussed.

On the scaling of air entrainment from a ventilated partial cavity

2013 ◽  
Vol 732 ◽  
pp. 47-76 ◽  
Author(s):  
Simo A. Mäkiharju ◽  
Brian R. Elbing ◽  
Andrew Wiggins ◽  
Sarah Schinasi ◽  
Jean-Marc Vanden-Broeck ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Weber Number ◽  
Large Scale ◽  
Air Entrainment ◽  
Small Scale ◽  
Length Scale ◽  
Entrainment Rate ◽  
Two Dimensional ◽  
Wide Range ◽  
Stable Cavity

AbstractThe behaviour of a nominally two-dimensional ventilated partial cavity was examined over a wide range of size scales and flow speeds to determine the influence of Froude, Reynolds, and Weber number on the cavity shape, dynamics, and gas entrainment rate. Two geometrically similar experiments were conducted with a 14:1 length scale ratio. The results were compared to a two-dimensional semi-analytical model of the cavity flow, and Froude scaling was found to be sufficient to match basic cavity shapes. However, the air flux required to maintain a stable cavity did not scale with Froude number alone, as the dynamics of the cavity closure changed with increasing Reynolds number. The required air flux differed over one order of magnitude between the lowest and highest Reynolds number flows. But, for sufficiently high Reynolds numbers, the rate of scaled entrainment appeared to approach Reynolds number independence. Modest changes in surface tension of the small-scale experiment suggested that the Weber number was important only at the lowest speeds and smaller length scale. Otherwise, the Weber numbers of the flows were sufficiently high to make the effects of interfacial tension negligible. We also observed that modest unsteadiness in the inflow to the large-scale cavity led to a significant increase in the required air flux needed to maintain a stable cavity, with the required excess gas flux nominally proportional to the flow’s perturbation amplitude. Finally, discussion is provided on how these results relate to model testing of partial cavity drag reduction (PCDR) systems for surface ships.

scholarly journals A Workflow for Rapid Unbiased Quantification of Fibrillar Feature Alignment in Biological Images

2021 ◽  
Vol 3 ◽  
Author(s):  
Stefania Marcotti ◽  
Deandra Belo de Freitas ◽  
Lee D Troughton ◽  
Fiona N Kenny ◽  
Tanya J Shaw ◽  
...  
Keyword(s):  
Fourier Transforms ◽  
Image Feature ◽  
Global Alignment ◽  
Length Scale ◽  
Desktop Computer ◽  
Length Scales ◽  
Advantages And Disadvantages ◽  
Segmentation Methods ◽  
Wide Range ◽  
Feature Alignment

Measuring the organization of the cellular cytoskeleton and the surrounding extracellular matrix (ECM) is currently of wide interest as changes in both local and global alignment can highlight alterations in cellular functions and material properties of the extracellular environment. Different approaches have been developed to quantify these structures, typically based on fiber segmentation or on matrix representation and transformation of the image, each with its own advantages and disadvantages. Here we present AFT − Alignment by Fourier Transform, a workflow to quantify the alignment of fibrillar features in microscopy images exploiting 2D Fast Fourier Transforms (FFT). Using pre-existing datasets of cell and ECM images, we demonstrate our approach and compare and contrast this workflow with two other well-known ImageJ algorithms to quantify image feature alignment. These comparisons reveal that AFT has a number of advantages due to its grid-based FFT approach. 1) Flexibility in defining the window and neighborhood sizes allows for performing a parameter search to determine an optimal length scale to carry out alignment metrics. This approach can thus easily accommodate different image resolutions and biological systems. 2) The length scale of decay in alignment can be extracted by comparing neighborhood sizes, revealing the overall distance that features remain anisotropic. 3) The approach is ambivalent to the signal source, thus making it applicable for a wide range of imaging modalities and is dependent on fewer input parameters than segmentation methods. 4) Finally, compared to segmentation methods, this algorithm is computationally inexpensive, as high-resolution images can be evaluated in less than a second on a standard desktop computer. This makes it feasible to screen numerous experimental perturbations or examine large images over long length scales. Implementation is made available in both MATLAB and Python for wider accessibility, with example datasets for single images and batch processing. Additionally, we include an approach to automatically search parameters for optimum window and neighborhood sizes, as well as to measure the decay in alignment over progressively increasing length scales.

scholarly journals Relating force balances and flow length scales in geodynamo simulations

2020 ◽  
Vol 224 (3) ◽  
pp. 1890-1904
Author(s):  
T Schwaiger ◽  
T Gastine ◽  
J Aubert
Keyword(s):  
Kinetic Energy ◽  
Large Scale ◽  
Magnetic Energy ◽  
Force Balance ◽  
Small Scale ◽  
Scaling Analysis ◽  
Length Scale ◽  
Crossover Point ◽  
Length Scales ◽  
Flow Length

SUMMARY In fluid dynamics, the scaling behaviour of flow length scales is commonly used to infer the governing force balance of a system. The key to a successful approach is to measure length scales that are simultaneously representative of the energy contained in the solution (energetically relevant) and also indicative of the established force balance (dynamically relevant). In the case of numerical simulations of rotating convection and magnetohydrodynamic dynamos in spherical shells, it has remained difficult to measure length scales that are both energetically and dynamically relevant, a situation that has led to conflicting interpretations, and sometimes misrepresentations of the underlying force balance. By analysing an extensive set of magnetic and non-magnetic models, we focus on two length scales that achieve both energetic and dynamical relevance. The first one is the peak of the poloidal kinetic energy spectrum, which we successfully compare to crossover points on spectral representations of the force balance. In most dynamo models, this result confirms that the dominant length scale of the system is controlled by a previously proposed quasi-geostrophic (QG-) MAC (Magneto-Archimedean-Coriolis) balance. In non-magnetic convection models, the analysis generally favours a QG-CIA (Coriolis-Inertia-Archimedean) balance. Viscosity, which is typically a minor contributor to the force balance, does not control the dominant length scale at high convective supercriticalities in the non-magnetic case, and in the dynamo case, once the generated magnetic energy largely exceeds the kinetic energy. In dynamo models, we introduce a second energetically relevant length scale associated with the loss of axial invariance in the flow. We again relate this length scale to another crossover point in scale-dependent force balance diagrams, which marks the transition between large-scale geostrophy (the equilibrium of Coriolis and pressure forces) and small-scale magnetostrophy, where the Lorentz force overtakes the Coriolis force. Scaling analysis of these two energetically and dynamically relevant length scales suggests that the Earth’s dynamo is controlled by a QG-MAC balance at a dominant scale of about $200 \, \mathrm{km}$, while magnetostrophic effects are deferred to scales smaller than $50 \, \mathrm{km}$.

Performance of the k-kL model for aerodynamics applications

2019 ◽  
Vol 30 (8) ◽  
pp. 3985-4011
Author(s):  
Nikhil Kalkote ◽  
Ashutosh Kumar ◽  
Ashwani Assam ◽  
Vinayak Eswaran
Keyword(s):  
Unstructured Grid ◽  
Model Performance ◽  
Length Scale ◽  
Mean Flow ◽  
Complex Flow ◽  
High Lift ◽  
Content Type ◽  
Aerodynamic Flows ◽  
Wide Range ◽  
The Mean

Purpose The purpose of this paper is to study the predictability of the recently proposed length scale-based two-equation k-kL model for external aerodynamic flows such as those also encountered in the high-lift devices. Design/methodology/approach The two-equation k-kL model solves the transport equations of turbulent kinetic energy (TKE) and the product of TKE and the integral length scale to obtain the effect of turbulence on the mean flow field. In theory, the use of governing equation for length scale (kL) along with the TKE promises applicability in a wide range of applications in both free-shear and wall-bounded flows with eddy-resolving capability. Findings The model is implemented in the in-house unstructured grid computational fluid dynamics solver to investigate its performance for airfoils in difficult-to-predict situations, including stalling and separation. The numerical findings show the good capability of the model in handling the complex flow physics in the external aerodynamic computations. Originality/value The model performance is studied for stationary turbulent external aerodynamic flows, using five different airfoils, including two multi-element airfoils in high-lift configurations which, in the knowledge of the authors, have not been simulated with k-kL model until now.

Experimental investigation of the effects of mean shear and scalar initial length scale on three-scalar mixing in turbulent coaxial jets

2017 ◽  
Vol 817 ◽  
pp. 183-216 ◽  
Author(s):  
W. Li ◽  
M. Yuan ◽  
C. D. Carter ◽  
C. Tong
Keyword(s):  
Annular Flow ◽  
Molecular Diffusion ◽  
Turbulent Transport ◽  
Velocity Ratio ◽  
Scalar Fields ◽  
Small Scale ◽  
Length Scale ◽  
Scalar Mixing ◽  
Mean Flow ◽  
The Mean

In a previous study we investigated three-scalar mixing in a turbulent coaxial jet (Caiet al.J. Fluid Mech., vol. 685, 2011, pp. 495–531). In this flow a centre jet and a co-flow are separated by an annular flow; therefore, the resulting mixing process approximates that in a turbulent non-premixed flame. In the present study, we investigate the effects of the velocity and length scale ratios of the annular flow to the centre jet, which determine the relative mean shear rates between the streams and the degree of separation between the centre jet and the co-flow, respectively. Simultaneous planar laser-induced fluorescence and Rayleigh scattering are employed to obtain the mass fractions of the centre jet scalar (acetone-doped air) and the annular flow scalar (ethylene). The results show that varying the velocity ratio and the annulus width modifies the scalar fields through mean-flow advection, turbulent transport and small-scale mixing. While the evolution of the mean scalar profiles is dominated by the mean-flow advection, the shape of the joint probability density function (JPDF) was found to be largely determined by the turbulent transport and molecular diffusion. Increasing the velocity ratio results in stronger turbulent transport, making the initial scalar evolution faster. However, further downstream the evolution is delayed due to slower small-scale mixing. The JPDF for the higher velocity ratio cases is bimodal at some locations while it is always unimodal for the lower velocity ratio cases. Increasing the annulus width delays the progression of mixing, and makes the effects of the velocity ratio more pronounced. For all cases the diffusion velocity streamlines in the scalar space representing the effects of molecular diffusion generally converge quickly to a curved manifold, whose curvature is reduced as mixing progresses. The curvature of the manifold increases significantly with the velocity and length scale ratios. Predicting the observed mixing path along the manifold as well as its dependence on the velocity and length scale ratios presents a challenge for mixing models. The results in the present study have implications for understanding and modelling multiscalar mixing in turbulent reactive flows.

scholarly journals Two-level, two-phase model for intense, turbulent sediment transport

2018 ◽  
Vol 839 ◽  
pp. 198-238 ◽  
Author(s):  
Jose M. Gonzalez-Ondina ◽  
Luigi Fraccarollo ◽  
Philip L.-F. Liu
Keyword(s):  
Sediment Transport ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
High Concentration ◽  
Two Phase ◽  
Theoretical Derivation ◽  
Length Scales ◽  
Fluid Turbulence ◽  
Wide Range

The study of sediment transport requires in-depth investigation of the complex effects of sediment particles in fluid turbulence. In this paper we focus on intense sediment transport flows. None of the existing two-phase models in the literature properly replicates the liquid and solid stresses in the near bed region of high concentration of sediment. The reason for this shortcoming is that the physical processes occurring at the length scale of the particle collisions are different from those occurring at larger length scales and therefore, they must be modelled independently. We present here a two-level theoretical derivation of two-phase, Favre averaged Navier–Stokes equations (FANS). This approach treats two levels of energy fluctuations independently, those associated with a granular spatial scale (granular temperature and small-scale fluid turbulence) and those associated with the ensemble average (turbulent kinetic energy for the two phases). Although similar attempts have been made by other researchers, the two level approach ensures that the two relevant length scales are included independently in a more consistent manner. The model is endowed with a semi-empirical formulation for the granular scale fluid turbulence, which is important even in the dense collisional shear layer, as has been recently recognized. As a result of the large and small scale modelling of the liquid and solid fluctuations, predictions are promising to be reliable in a wide range of flow conditions, from collisional to turbulent suspensions. This model has been validated for steady state flows with intense, collisional or mixed collisional–turbulent sediment transport, using various sources of detailed experimental data. It compares well with the experimental results in the whole experimental range of Shields parameters, better than previous models, although at the cost of increased complexity in the equations. Further experiments on turbulent suspensions would be necessary to definitely assess the model capabilities.

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