Chaotic Mixing in Time-Periodic 3-D Flows

2002 ◽  
Author(s):  
A. J. S. Rodrigo ◽  
J. P. B. Mota ◽  
E. Saatdjian
Keyword(s):  
Residence Time ◽  
Mean Residence Time ◽  
Modulation Frequency ◽  
Outer Cylinder ◽  
Three Dimensional ◽  
Axial Flow ◽  
Cross Sectional ◽  
The Cross ◽  
Two Parameters ◽  
Time Periodic

Mixing in a special class of three-dimensional, non-inertial time-periodic flows is studied quantitatively. In the type of flow considered here, the cross-sectional velocity components are independent of the axial flow which is assumed to be fully developed. Using the eccentric helical annular mixer as a prototype, the time-periodic flow field is induced by adding a sinusoidal component to the rotation speed of the inner cylinder. For a given 3-D mixer geometry, the degree of mixing achieved is a function of two parameters that measure the strength of the cross-sectional stirring protocol relative to the mean residence time of the fluid in the mixer: the average number of turns of the outer cylinder, and the average number of modulation periods. We find that for a given mixer geometry and mean residence time, there is an optimum modulation frequency for which the standard deviation of the temperature field at the exit is a minimum.

scholarly journals Petiole-Lamina Transition Zone: A Functionally Crucial but Often Overlooked Leaf Trait

Plants ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 774
Author(s):  
Max Langer ◽  
Thomas Speck ◽  
Olga Speck
Keyword(s):  
Transition Zone ◽  
Three Dimensional ◽  
Spatial Arrangement ◽  
Body Plan ◽  
The Body ◽  
Vascular Bundles ◽  
Cross Sectional ◽  
Thin Sections ◽  
Transition Zones ◽  
The Cross

Although both the petiole and lamina of foliage leaves have been thoroughly studied, the transition zone between them has often been overlooked. We aimed to identify objectively measurable morphological and anatomical criteria for a generally valid definition of the petiole–lamina transition zone by comparing foliage leaves with various body plans (monocotyledons vs. dicotyledons) and spatial arrangements of petiole and lamina (two-dimensional vs. three-dimensional configurations). Cross-sectional geometry and tissue arrangement of petioles and transition zones were investigated via serial thin-sections and µCT. The changes in the cross-sectional geometries from the petiole to the transition zone and the course of the vascular bundles in the transition zone apparently depend on the spatial arrangement, while the arrangement of the vascular bundles in the petioles depends on the body plan. We found an exponential acropetal increase in the cross-sectional area and axial and polar second moments of area to be the defining characteristic of all transition zones studied, regardless of body plan or spatial arrangement. In conclusion, a variety of terms is used in the literature for describing the region between petiole and lamina. We prefer the term “petiole–lamina transition zone” to underline its three-dimensional nature and the integration of multiple gradients of geometry, shape, and size.

Long waves in a straight channel with non-uniform cross-section

2015 ◽  
Vol 770 ◽  
pp. 156-188 ◽  
Author(s):  
Patricio Winckler ◽  
Philip L.-F. Liu
Keyword(s):  
Boundary Layer ◽  
Wave Propagation ◽  
Cross Section ◽  
Three Dimensional ◽  
Channel Cross Section ◽  
Cross Sectional ◽  
New Model ◽  
One Dimensional ◽  
Uniform Channel ◽  
The Cross

A cross-sectionally averaged one-dimensional long-wave model is developed. Three-dimensional equations of motion for inviscid and incompressible fluid are first integrated over a channel cross-section. To express the resulting one-dimensional equations in terms of the cross-sectional-averaged longitudinal velocity and spanwise-averaged free-surface elevation, the characteristic depth and width of the channel cross-section are assumed to be smaller than the typical wavelength, resulting in Boussinesq-type equations. Viscous effects are also considered. The new model is, therefore, adequate for describing weakly nonlinear and weakly dispersive wave propagation along a non-uniform channel with arbitrary cross-section. More specifically, the new model has the following new properties: (i) the arbitrary channel cross-section can be asymmetric with respect to the direction of wave propagation, (ii) the channel cross-section can change appreciably within a wavelength, (iii) the effects of viscosity inside the bottom boundary layer can be considered, and (iv) the three-dimensional flow features can be recovered from the perturbation solutions. Analytical and numerical examples for uniform channels, channels where the cross-sectional geometry changes slowly and channels where the depth and width variation is appreciable within the wavelength scale are discussed to illustrate the validity and capability of the present model. With the consideration of viscous boundary layer effects, the present theory agrees reasonably well with experimental results presented by Chang et al. (J. Fluid Mech., vol. 95, 1979, pp. 401–414) for converging/diverging channels and those of Liu et al. (Coast. Engng, vol. 53, 2006, pp. 181–190) for a uniform channel with a sloping beach. The numerical results for a solitary wave propagating in a channel where the width variation is appreciable within a wavelength are discussed.

Three-Dimensional Solutions for Rotor Blades Using High-Order Geometrical Nonlinear Beam Finite Elements

2019 ◽  
Vol 64 (3) ◽  
pp. 1-10
Author(s):  
Matteo Filippi ◽  
Alfonso Pagani ◽  
Erasmo Carrera
Keyword(s):  
Finite Elements ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
High Order ◽  
Rotor Blades ◽  
Constitutive Law ◽  
Displacement Fields ◽  
Cross Sectional ◽  
The Cross

This paper proposes a geometrically nonlinear three-dimensional formalism for the static and dynamic study of rotor blades. The structures are modeled using high-order beam finite elements whose kinematics are input parameters of the analysis. The displacement fields are written using two-dimensional Taylor- and Lagrange-like expansions of the cross-sectional coordinates. As far as the Taylor-like polynomials are concerned, the linear case is similar to the first-order shear deformation theory, whereas the higher-order expansions include additional contributions that describe the warping of the cross section. The Lagrange-type kinematics instead utilizes the displacements of certain physical points as degrees of freedom. The inherent three-dimensional nature of the Carrera unified formulation enables one to include all Green–Lagrange strain components as well as all coupling effects due to the geometrical features and the three-dimensional constitutive law. A number of test cases are considered to compare the current solutions with experimental and theoretical results reported in terms of large deflections/rotations and frequencies related to small amplitude vibrations.

Interference in a three-dimensional array of jets

2015 ◽  
Vol 26 (5) ◽  
pp. 795-819
Author(s):  
P. E. WESTWOOD ◽  
F. T. SMITH
Keyword(s):  
Cross Sections ◽  
Flow Direction ◽  
Three Dimensional ◽  
Cross Flow ◽  
Longitudinal Vortex ◽  
Cross Sectional ◽  
Dimensional Array ◽  
Unsteady Jets ◽  
The Cross ◽  
Jet Cross Sections

The theoretical investigation here of a three-dimensional array of jets of fluid (air guns) and their interference is motivated by applications to the food sorting industry especially. Three-dimensional motion without symmetry is addressed for arbitrary jet cross-sections and incident velocity profiles. Asymptotic analysis based on the comparatively long axial length scale of the configuration leads to a reduced longitudinal vortex system providing a slender flow model for the complete array response. Analytical and numerical studies, along with comparisons and asymptotic limits or checks, are presented for various cross-sectional shapes of nozzle and velocity inputs. The influences of swirl and of unsteady jets are examined. Substantial cross-flows are found to occur due to the interference. The flow solution is non-periodic in the cross-plane even if the nozzle array itself is periodic. The analysis shows that in general the bulk of the three-dimensional motion can be described simply in a cross-plane problem but the induced flow in the cross-plane is sensitively controlled by edge effects and incident conditions, a feature which applies to any of the array configurations examined. Interference readily alters the cross-flow direction and misdirects the jets. Design considerations centre on target positioning and jet swirling.

Modeling of Solids and Gas Mixing Effects in Large-Scale CFB Combustors

2003 ◽  
Author(s):  
Karsten Luecke ◽  
Ernst-Ulrich Hartge ◽  
Joachim Werther
Keyword(s):  
Combustion Chamber ◽  
Residence Time ◽  
Large Scale ◽  
Control Volume ◽  
Combustion Process ◽  
Three Dimensional ◽  
Three Dimensional Model ◽  
Cross Sectional ◽  
Fuel Feed ◽  
Cross Section Area

In a CFB combustor the reacting solids are locally fed into the combustion chamber. These reactants have to be dispersed across the reactor’s cross-sectional area. Since the rate of mixing is limited this leads to a mal-distribution of the reactants and to locally varying reaction conditions. In order to describe the influence of mixing a three-dimensional model of the combustion chamber is suggested here. The model is divided into three sub-topics. First, the flow structure in terms of local gas and solids velocities and solids volume concentrations is described. Second, mixing of the solids and the gas phase has to be quantified by defining dispersion coefficients, and finally the combustion process itself, i.e. the reaction kinetics, has to be modeled. Employing the information of the three sub-models mass balances for the reactants at each finite control volume inside the CFB combustion chamber can be formulated. The model was validated against data from measurements in the large-scale combustor of Chalmers University of Technology in Go¨teborg/Sweden. Concentration gradients concerning the char phase are only moderate. However, the spatial distribution of the oxygen shows strong non-uniformities, especially under conditions of staged combustion. In further predictive calculations, the influence of the fuel supply arrangement on the emissions of industrial sized CFB boilers was studied. Furthermore, the influence of the fuel composition on the feeding technique has been examined. High volatile fuels tend to form plumes of unburned hydrocarbons near the fuel feed point, and might therefore need more feed points per square meter cross-section area. Since the average gas residence time in the primary cyclone of a CFB plant is about 30–40% of the total gas residence time, a considerable burn-off of not completely oxidized gas species may occur here. An effectively used cyclone may remedy to a certain extent the negative impacts of incomplete mixing in the combustion chamber.

Juice Irradiation with Taylor-Couette Flow: UV Inactivation of Escherichia coli

2004 ◽  
Vol 67 (11) ◽  
pp. 2410-2415 ◽  
Author(s):  
L. J. FORNEY ◽  
J. A. PIERSON ◽  
Z. YE
Keyword(s):  
Escherichia Coli ◽  
Boundary Layer ◽  
Couette Flow ◽  
Residence Time ◽  
Outer Cylinder ◽  
Plug Flow ◽  
Axial Flow ◽  
Grape Juice ◽  
Taylor Couette ◽  
Taylor Couette Flow

A novel reactor is described with flow characteristics that approach that of ideal plug flow but with a residence time that is uncoupled from the hydrodynamics or boundary layer characteristics. The design described consists of an inner cylinder that rotates within a stationary but larger outer cylinder. At low rotation rates, a laminar, hydrodynamic configuration called Taylor-Couette flow is established, which consists of a system of circumferential vortices within the annular fluid gap. The latter constitutes a spatially periodic flow that is the hydrodynamic equivalent to cross flow over a tube bank or lamp array. These vortices provide radial mixing, reduce the boundary layer thickness, and are independent of the axial flow rate and thus the fluid residence time. An additional feature of the rotating design is the repetitive exposure of the fluid parcels to a minimum number of lamps, which substantially reduces the maintenance requirements. Inactivation data for Escherichia coli (ATCC 15597) were recorded in commercial apple and grape juice that are relatively opaque to UV radiation. With initial E. coli concentrations of approximately 106 CFU/ml, Taylor-Couette flow was found to provide a 3- to 5-log improvement in the inactivation efficiency compared with simple channel flow between concentric cylinders.

Formation and decay of coherent structures in pipe flow

2010 ◽  
Vol 655 ◽  
pp. 258-279 ◽  
Author(s):  
JIMMY PHILIP ◽  
JACOB COHEN
Keyword(s):  
Coherent Structures ◽  
Pipe Flow ◽  
Three Dimensional ◽  
Vortex Pair ◽  
Hairpin Vortices ◽  
Cross Sectional ◽  
Instability Waves ◽  
Sectional Plane ◽  
The Cross ◽  
Three Dimensional Coordinate

Experimental investigation of the generation and decay of coherent structures, namely, streaks (accompanied by a counter-rotating vortex pair) and hairpin vortices in pipe flow, is carried out by artificial injection of continuous disturbances. Flow visualization and velocity measurements show that for small amplitudes of disturbances (v0) streaks are produced, and increasing v0 produces instability waves on the streaks, which further break down into an array of hairpin vortices. However, the streaks and hairpins decay along the downstream direction (X). In fact, the critical value of v0 required for the initiation of hairpins at a given Re (Reynolds number) varies with the streamwise distance (in contrast to the previously found scaling of v0 ~ Re−1, valid only close to the location of injection, i.e. smaller X). This is a consequence of the decay of the coherent structures in the pipe. Moreover, the hairpins have been found to decay more slowly with increasing Re. Measurements of energy in the cross-sectional plane of the pipe, and maps of disturbance velocity at various X-locations show the transient growth and decay of energy for relatively low v0. For higher v0 and Re the energy has been seen to increase continuously along the length of the pipe under observation. Owing to the increase in the cross-sectional area occupied by the disturbance along the X-direction, it is observed that energy can transiently increase even when the total disturbance magnitude is decreasing. Observing the similarity of the present work and other investigations wherein decay of turbulence in pipe flow is found, a schematic illustration of the transition surface for pipe flow on a v0−Re−X, three-dimensional coordinate system is presented.

scholarly journals X-ray CT Analysis of the Cross-Section of a 3D-Printed Deformed Layer

Materials ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 7764
Author(s):  
Ho-Jae Lee ◽  
Eun-A Seo ◽  
Won-Woo Kim ◽  
Jun-Mo Yang ◽  
Jae-Heum Moon
Keyword(s):  
Three Dimensional ◽  
Travel Speed ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
X Ray ◽  
Deformed Layer ◽  
Ct Analysis ◽  
3D Printed ◽  
The Cross

In this study, we experimentally analyzed the deformation shape of stacked layers developed using three-dimensional (3D) printing technology. The nozzle traveling speed was changed to 80, 90, 100, and 110 mm/s when printing the layers to analyze its effect on layer deformation. Furthermore, the cross-sectional area and the number of layers were analyzed by printing five layers with overall dimensions of 1000 (w) × 2200 (l) × 50 (h) mm (each layer was 10 mm high) using Vernier calipers. Moreover, we analyzed the interface and cross-sectional area of layers that are difficult to confirm visually using X-ray computed tomography (X-ray CT) analysis. As a result of measuring the deformation at the center of the layer, it was confirmed that the deformation was greater for lower nozzle traveling speeds. Consequently, the X-ray CT analysis verified that the layer had the same cross-sectional area irrespective of the layer printing order at the same nozzle travel speed, even if the layer was deformed.

A super-convergent thin-walled 3D beam element for analysis of laminated composite structures with arbitrary cross-section

2021 ◽  
pp. 1-23
Author(s):  
M. Talele ◽  
M. van Tooren ◽  
A. Elham
Keyword(s):  
Cross Sections ◽  
Composite Structures ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Beam Element ◽  
Arbitrary Cross Section ◽  
Beam Model ◽  
Cross Sectional ◽  
Thin Walled ◽  
The Cross

Abstract An efficient, fully coupled beam model is developed to analyse laminated composite thin-walled structures with arbitrary cross-sections. The Euler–Lagrangian equations are derived from the kinematic relationships for a One-Dimensional (1D) beam representing Three-Dimensional (3D) deformations that take into account the cross-sectional stiffness of the composite structure. The formulation of the cross-sectional stiffness includes all the deformation effects and related elastic couplings. To circumvent the problem of shear locking, exact solutions to the approximating Partial Differential Equations (PDEs) are obtained symbolically instead of by numerical integration. The developed locking-free composite beam element results in an exact stiffness matrix and has super-convergent characteristics. The beam model is tested for different types of layup, and the results are validated by comparison with experimental results from literature.

Evaluation of body geometry and symmetry for adolescent idiopathic scoliosis with 3D body scanning system

2017 ◽  
Vol 21 (4) ◽  
pp. 276-292
Author(s):  
Lu Lu ◽  
Kit-Lun Yick ◽  
Sun Pui Ng ◽  
Joanne Yip ◽  
Chi Yung Tse
Keyword(s):  
Adolescent Idiopathic Scoliosis ◽  
Idiopathic Scoliosis ◽  
Three Dimensional ◽  
The Body ◽  
Scanning System ◽  
X Rays ◽  
Cross Sectional ◽  
Content Type ◽  
Body Scanning ◽  
The Cross

Purpose The purpose of this paper is to quantitatively assess the three-dimensional (3D) geometry and symmetry of the torso for spinal deformity and the use of orthotic bracewear by using non-invasive 3D body scanning technology. Design/methodology/approach In pursuing greater accuracy of body anthropometric measurements to improve the fit and design of apparel, 3D body scanning technology and image analysis provide many more advantages over the traditional manual methods that use contact measurements. To measure the changes in the torso geometry and profile symmetry of patients with adolescent idiopathic scoliosis, five individuals are recruited to undergo body scanning both with and without wearing a rigid brace during a period of six months. The cross-sectional areas and profiles of the reconstructed 3D torso models are examined to evaluate the level of body symmetry. Findings Significant changes in the cross-sectional profile are found amongst four of the patients over the different visits for measurements (p < 0.05), which are consistent with the X-rays results. The 3D body scanning system can reliably evaluate changes in the body geometry of patients with scoliosis. Nevertheless, improvements in the symmetry of the torso are found to be somewhat inconsistent among the patients and across different visits. Originality/value This pilot study demonstrates a practical and safe means to measure and analyse the torso geometry and symmetry so as to allow for more frequent evaluations, which would result in effective and optimal treatment of spinal deformation.

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