scholarly journals Entrainment at multi-scales across the turbulent/non-turbulent interface in an axisymmetric jet

2016 ◽  
Vol 802 ◽  
pp. 690-725 ◽  
Author(s):  
Dhiren Mistry ◽  
Jimmy Philip ◽  
James R. Dawson ◽  
Ivan Marusic
Keyword(s):  
Surface Area ◽  
Power Law ◽  
Mass Flux ◽  
Time Resolved ◽  
Axisymmetric Jet ◽  
Entrainment Velocity ◽  
Multi Scale ◽  
Planar Laser ◽  
The Mean ◽  
High Reynolds

We consider the scaling of the mass flux and entrainment velocity across the turbulent/non-turbulent interface (TNTI) in the far field of an axisymmetric jet at high Reynolds number. Time-resolved, simultaneous multi-scale particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) are used to identify and track the TNTI, and directly measure the local entrainment velocity along it. Application of box-counting and spatial-filtering methods, with filter sizes $\unicode[STIX]{x1D6E5}$ spanning over two decades in length, show that the mean length of the TNTI exhibits a power-law behaviour with a fractal dimension $D\approx 0.31{-}0.33$. More importantly, we invoke a multi-scale methodology to confirm that the mean mass flux, which is equal to the product of the entrainment velocity and the surface area, remains constant across the range of filter sizes. The results, within experimental uncertainty, also show that the entrainment velocity along the TNTI exhibits a power-law behaviour with $\unicode[STIX]{x1D6E5}$, such that the entrainment velocity increases with increasing $\unicode[STIX]{x1D6E5}$. In fact, the mean entrainment velocity scales at a rate that balances the scaling of the TNTI length such that the mass flux remains independent of the coarse-grain filter size, as first suggested by Meneveau & Sreenivasan (Phys. Rev. A, vol. 41, no. 4, 1990, pp. 2246–2248). Hence, at the smallest scales the entrainment velocity is small but is balanced by the presence of a very large surface area, whilst at the largest scales the entrainment velocity is large but is balanced by a smaller (smoother) surface area.

Entrainment in a compressible turbulent shear layer

2016 ◽  
Vol 797 ◽  
pp. 564-603 ◽  
Author(s):  
Reza Jahanbakhshi ◽  
Cyrus K. Madnia
Keyword(s):  
Mach Number ◽  
Shear Layer ◽  
Surface Area ◽  
Mass Flux ◽  
Geometrical Shape ◽  
Turbulent Region ◽  
Irrotational Flow ◽  
Entrainment Velocity ◽  
Mass Fluxes ◽  
Convective Mach Number

Direct numerical simulations (DNS) of temporally evolving shear layers have been performed to study the entrainment of irrotational flow into the turbulent region across the turbulent/non-turbulent interface (TNTI). Four cases with convective Mach number from 0.2 to 1.8 are used. Entrainment is studied via two mechanisms; nibbling, considered as vorticity diffusion across the TNTI, and engulfment, the drawing of the pockets of the outside irrotational fluid into the turbulent region. The mass flow rate due to nibbling is calculated as the product of the entrained mass flux with the surface area of the TNTI. It is found that increasing the convective Mach number results in a decrease of the average entrained mass flux and the surface area of the TNTI. For the incompressible shear layer the local entrained mass flux is shown to be highly correlated with the viscous terms. However, as the convective Mach number increases, the mass fluxes due to the baroclinic and the dilatation terms play a more important role in the local entrainment process. It is observed that the entrained mass flux is dependent on the local dilatation and geometrical shape of the TNTI. For a compressible shear layer, most of the entrainment of the irrotational flow into the turbulent region due to nibbling is associated with the compressed regions on the TNTI. As the convective Mach number increases, the percentage of the compressed regions on the TNTI decreases, resulting in a reduction of the average entrained mass flux. It is also shown that the local shape of the interface, looking from the turbulent region, is dominated by concave shaped surfaces with radii of curvature of the order of the Taylor length scale. The average entrained mass flux is found to be larger on highly curved concave shaped surfaces regardless of the level of dilatation. The mass fluxes due to vortex stretching, baroclinic torque and the shear stress/density gradient terms are weak functions of the local curvatures on the TNTI, whereas the mass fluxes due to dilatation and viscous diffusion plus the viscous dissipation terms have a stronger dependency on the local curvatures. As the convective Mach number increases, the probability of finding highly curved concave shaped surfaces on the TNTI decreases, whereas the probability of finding flatter concave and convex shaped surfaces increases. This results in a decrease of the average entrained mass flux across the TNTI. Similar to the previous works on jets, the results show that the contribution of the engulfment to the total entrainment is small for both incompressible and compressible mixing layers. It is also shown that increasing the convective Mach number decreases the velocities associated with the entrainment, i.e. induced velocity, boundary entrainment velocity and local entrainment velocity.

The multi-scale geometry of the near field in an axisymmetric jet

2018 ◽  
Vol 838 ◽  
pp. 501-515 ◽  
Author(s):  
Dhiren Mistry ◽  
James R. Dawson ◽  
Alan R. Kerstein
Keyword(s):  
Surface Area ◽  
Scale Invariance ◽  
Near Field ◽  
Coarse Grain ◽  
Far Field ◽  
Scale Separation ◽  
Potential Core ◽  
Axisymmetric Jet ◽  
Multi Scale ◽  
Axisymmetric Jets

A characteristic feature of axisymmetric jets, and turbulent shear flows in general, is the entrainment of mass across the turbulent/non-turbulent interface (TNTI). The multi-scale nature of the TNTI surface area was recently observed to exhibit power-law scaling with a fractal dimension, $D_{f}$, between $D_{f}=2.3{-}2.4$, inferred from two-dimensional data, in both high Reynolds number boundary layers and the far field of axisymmetric jets. In this paper, we show that the fractal scaling previously observed in the far field of an axisymmetric jet is established at the end of the potential core. Simultaneous measurements of the velocity and scalar fields were obtained and coarse grain filtering was applied over two decades of scale separation, showing that $D_{f}$ evolves to ${\approx}2.35$ at $x/d=4.6$, which is similar to $D_{f}$ found in the far field between $x/d=40{-}60$. This is evidence that scale separation becomes sufficiently developed to achieve scale invariance of the TNTI surface area in the near field of the jet well before self-similarity is established. We also observe that the onset of this geometric scale invariance coincides with the onset of radial homogeneity shown by two-point velocity correlations. Finally, we present a simple theoretical basis for these results using an exact fractal construction based on the Koch curve and applying a coarse-grain filtering analysis.

Stochastic homogenization and macroscopic modelling of composites and flow through porous media

2002 ◽  
pp. 337-378 ◽  
Author(s):  
Jozef Telega ◽  
Wlodzimierz Bielski
Keyword(s):  
Porous Medium ◽  
Random Distribution ◽  
Flow Through Porous Media ◽  
Macroscopic Models ◽  
Linear Elastic ◽  
Multi Scale ◽  
Convergence Method ◽  
Flow Through ◽  
The Mean ◽  
Random Porous Medium

The aim of this contribution is mainly twofold. First, the stochastic two-scale convergence in the mean developed by Bourgeat et al. [13] is used to derive the macroscopic models of: (i) diffusion in random porous medium, (ii) nonstationary flow of Stokesian fluid through random linear elastic porous medium. Second, the multi-scale convergence method developed by Allaire and Briane [7] for the case of several microperiodic scales is extended to random distribution of heterogeneities characterized by separated scales (stochastic reiterated homogenization). .

scholarly journals Multi-Scale Aggregation Graph Neural Networks Based on Feature Similarity for Semi-Supervised Learning

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 403
Author(s):  
Xun Zhang ◽  
Lanyan Yang ◽  
Bin Zhang ◽  
Ying Liu ◽  
Dong Jiang ◽  
...  
Keyword(s):  
Neural Network ◽  
Supervised Learning ◽  
Structured Data ◽  
Similarity Matrix ◽  
Scale Feature ◽  
Multi Scale ◽  
Adjacent Node ◽  
Feature Similarity ◽  
The Mean ◽  
Graph Neural Networks

The problem of extracting meaningful data through graph analysis spans a range of different fields, such as social networks, knowledge graphs, citation networks, the World Wide Web, and so on. As increasingly structured data become available, the importance of being able to effectively mine and learn from such data continues to grow. In this paper, we propose the multi-scale aggregation graph neural network based on feature similarity (MAGN), a novel graph neural network defined in the vertex domain. Our model provides a simple and general semi-supervised learning method for graph-structured data, in which only a very small part of the data is labeled as the training set. We first construct a similarity matrix by calculating the similarity of original features between all adjacent node pairs, and then generate a set of feature extractors utilizing the similarity matrix to perform multi-scale feature propagation on graphs. The output of multi-scale feature propagation is finally aggregated by using the mean-pooling operation. Our method aims to improve the model representation ability via multi-scale neighborhood aggregation based on feature similarity. Extensive experimental evaluation on various open benchmarks shows the competitive performance of our method compared to a variety of popular architectures.

scholarly journals Aerodynamics of smooth and rough square-section prisms at incidence in very high Reynolds-number cross-flows

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
Nils Paul van Hinsberg
Keyword(s):  
Reynolds Number ◽  
Cross Sections ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Surface Boundary ◽  
Experimental Proof ◽  
Surface Boundary Layer ◽  
Pitch Moment ◽  
The Mean ◽  
High Reynolds

Abstract The aerodynamics of smooth and slightly rough prisms with square cross-sections and sharp edges is investigated through wind tunnel experiments. Mean and fluctuating forces, the mean pitch moment, Strouhal numbers, the mean surface pressures and the mean wake profiles in the mid-span cross-section of the prism are recorded simultaneously for Reynolds numbers between 1$$\times$$ × 10$$^{5}$$ 5 $$\le$$ ≤ Re$$_{D}$$ D $$\le$$ ≤ 1$$\times$$ × 10$$^{7}$$ 7 . For the smooth prism with $$k_s$$ k s /D = 4$$\times$$ × 10$$^{-5}$$ - 5 , tests were performed at three angles of incidence, i.e. $$\alpha$$ α = 0$$^{\circ }$$ ∘ , −22.5$$^{\circ }$$ ∘ and −45$$^{\circ }$$ ∘ , whereas only both “symmetric” angles were studied for its slightly rough counterpart with $$k_s$$ k s /D = 1$$\times$$ × 10$$^{-3}$$ - 3 . First-time experimental proof is given that, within the accuracy of the data, no significant variation with Reynolds number occurs for all mean and fluctuating aerodynamic coefficients of smooth square prisms up to Reynolds numbers as high as $$\mathcal {O}$$ O (10$$^{7}$$ 7 ). This Reynolds-number independent behaviour applies to the Strouhal number and the wake profile as well. In contrast to what is known from square prisms with rounded edges and circular cylinders, an increase in surface roughness height by a factor 25 on the current sharp-edged square prism does not lead to any notable effects on the surface boundary layer and thus on the prism’s aerodynamics. For both prisms, distinct changes in the aerostatics between the various angles of incidence are seen to take place though. Graphic abstract

scholarly journals Extended power-law scaling of air permeabilities measured on a block of tuff

2012 ◽  
Vol 16 (1) ◽  
pp. 29-42 ◽  
Author(s):  
M. Siena ◽  
A. Guadagnini ◽  
M. Riva ◽  
S. P. Neuman
Keyword(s):  
Power Law ◽  
Structure Functions ◽  
Self Similarity ◽  
Scaling Exponents ◽  
Multi Scale ◽  
Sample Structure ◽  
Heavy Tailed ◽  
Non Gaussian ◽  
Nonlinear Fashion ◽  
Extended Power

Abstract. We use three methods to identify power-law scaling of multi-scale log air permeability data collected by Tidwell and Wilson on the faces of a laboratory-scale block of Topopah Spring tuff: method of moments (M), Extended Self-Similarity (ESS) and a generalized version thereof (G-ESS). All three methods focus on q-th-order sample structure functions of absolute increments. Most such functions exhibit power-law scaling at best over a limited midrange of experimental separation scales, or lags, which are sometimes difficult to identify unambiguously by means of M. ESS and G-ESS extend this range in a way that renders power-law scaling easier to characterize. Our analysis confirms the superiority of ESS and G-ESS over M in identifying the scaling exponents, ξ(q), of corresponding structure functions of orders q, suggesting further that ESS is more reliable than G-ESS. The exponents vary in a nonlinear fashion with q as is typical of real or apparent multifractals. Our estimates of the Hurst scaling coefficient increase with support scale, implying a reduction in roughness (anti-persistence) of the log permeability field with measurement volume. The finding by Tidwell and Wilson that log permeabilities associated with all tip sizes can be characterized by stationary variogram models, coupled with our findings that log permeability increments associated with the smallest tip size are approximately Gaussian and those associated with all tip sizes scale show nonlinear variations in ξ(q) with q, are consistent with a view of these data as a sample from a truncated version (tfBm) of self-affine fractional Brownian motion (fBm). Since in theory the scaling exponents, ξ(q), of tfBm vary linearly with q we conclude that nonlinear scaling in our case is not an indication of multifractality but an artifact of sampling from tfBm. This allows us to explain theoretically how power-law scaling of our data, as well as of non-Gaussian heavy-tailed signals subordinated to tfBm, are extended by ESS. It further allows us to identify the functional form and estimate all parameters of the corresponding tfBm based on sample structure functions of first and second orders.

scholarly journals Temperature Resistance of Mo3Si: Phase Stability, Microhardness, and Creep Properties

Metals ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 564 ◽  
Author(s):  
Olha Kauss ◽  
Susanne Obert ◽  
Iurii Bogomol ◽  
Thomas Wablat ◽  
Nils Siemensmeyer ◽  
...  
Keyword(s):  
Power Law ◽  
Phase Stability ◽  
Gas Turbines ◽  
Constitutive Models ◽  
Creep Properties ◽  
Multi Scale ◽  
Scale Modeling ◽  
Significant Difference ◽  
Before And After ◽  
Multi Phase

Mo-Si-B alloys are one of the most promising candidates to substitute Ni based superalloys in gas turbines. The optimization of their composition can be achieved more effectively using multi-scale modeling of materials behavior and structural analysis of components for understanding, predicting, and screening properties of new alloys. Nevertheless, this approach is dependent on data on the properties of the single phases in these alloys. The focus of this investigation is Mo3Si, one of the phases in typical Mo-Si-B alloys. The effect of 100 h annealing at 1600 °C on phase stability and microhardness of its three near-stoichiometric compositions—Mo-23Si, Mo-24Si and Mo-25Si (at %)—is reported. While Mo-23Si specimen consist only of Mo3Si before and after annealing, Mo-24Si and Mo-25Si comprise Mo5Si3 and Mo3Si before annealing. The latter is then increased by the annealing. No significant difference in microhardness was detected between the different compositions as well as after annealing. The creep properties of Mo3Si are described at 1093 °C and 1300 °C at varying stress levels as well as at 300 MPa and temperatures between 1050 °C and 1350 °C. Three constitutive models were used for regression of experimental results—(i) power law with a constant creep exponent, (ii) stress range dependent law, and (iii) power law with a temperature-dependent creep exponent. It is confirmed that Mo3Si has a higher creep resistance than Moss and multi-phase Mo-Si-B alloys, but a lower creep strength as compared to Mo5SiB2.

scholarly journals Free Convective MHD Flow Past a Vertical Cone with Variable Heat and Mass Flux

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
J. Prakash ◽  
S. Gouse Mohiddin ◽  
S. Vijaya Kumar Varma
Keyword(s):  
Boundary Layer ◽  
Power Law ◽  
Mass Flux ◽  
Numerical Study ◽  
Convection Boundary Layer ◽  
Vertical Cone ◽  
Local Skin ◽  
Surface Mass ◽  
Flow Past ◽  
Power Law Exponent

A numerical study of buoyancy-driven unsteady natural convection boundary layer flow past a vertical cone embedded in a non-Darcian isotropic porous regime with transverse magnetic field applied normal to the surface is considered. The heat and mass flux at the surface of the cone is modeled as a power law according to qwx=xm and qw*(x)=xm, respectively, where x denotes the coordinate along the slant face of the cone. Both Darcian drag and Forchheimer quadratic porous impedance are incorporated into the two-dimensional viscous flow model. The transient boundary layer equations are then nondimensionalized and solved by the Crank-Nicolson implicit difference method. The velocity, temperature, and concentration fields have been studied for the effect of Grashof number, Darcy number, Forchheimer number, Prandtl number, surface heat flux power-law exponent (m), surface mass flux power-law exponent (n), Schmidt number, buoyancy ratio parameter, and semivertical angle of the cone. Present results for selected variables for the purely fluid regime are compared with the published results and are found to be in excellent agreement. The local skin friction, Nusselt number, and Sherwood number are also analyzed graphically. The study finds important applications in geophysical heat transfer, industrial manufacturing processes, and hybrid solar energy systems.

scholarly journals Time-Resolved Reflectance Spectroscopy Applied to the Nondestructive Monitoring of the Internal Optical Properties in Apples

2001 ◽  
Vol 55 (10) ◽  
pp. 1368-1374 ◽  
Author(s):  
Rinaldo Cubeddu ◽  
Cosimo D'Andrea ◽  
Antonio Pifferi ◽  
Paola Taroni ◽  
Alessandro Torricelli ◽  
...  
Keyword(s):  
Optical Properties ◽  
Industrial Applications ◽  
Nondestructive Monitoring ◽  
Nondestructive Measurement ◽  
Time Resolved ◽  
Mean Values ◽  
Scattering Coefficients ◽  
Scattering Spectra ◽  
The Mean ◽  
Temporal Dispersion

Time-resolved reflectance has been used for the nondestructive measurement of optical properties in apples. The technique is based on the detection of the temporal dispersion of a short laser pulse injected into the probed medium. The time distribution of re-emitted photons interpreted with a solution of the diffusion equation yields the mean values of the absorption and reduced scattering coefficients of the medium. The proposed technique proved useful for the measurement of the absorption and scattering spectra of different varieties of apples, revealing the spectral shape of chlorophyll. No major variations were observed in the experimental data when the fruit was peeled, showing that the optical properties measured were those of the pulp. With this technique the change in chlorophyll absorption during storage and ripening could be followed. Finally, a compact prototype working at few selected wavelengths was designed and constructed, demonstrating potentialities of the technique for industrial applications.

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