scholarly journals The Balanced-Force Volume Tracking Algorithm and Global Embedded Interface Formulation for Droplet Dynamics With Mass Transfer

2010 ◽  
Author(s):  
Marianne M. Francois ◽  
Neil N. Carlson
Keyword(s):  
Mass Transfer ◽  
Three Dimensional ◽  
Surface Tension Force ◽  
Two Dimensions ◽  
Tracking Algorithm ◽  
Droplet Dynamics ◽  
Flow Equations ◽  
Interfacial Conditions ◽  
Pure Diffusion ◽  
Force Volume

Understanding the complex interaction of droplet dynamics with mass transfer and chemical reactions is of fundamental importance in liquid-liquid extraction. High-fidelity numerical simulation of droplet dynamics with interfacial mass transfer is particularly challenging because the position of the interface between the fluids and the interface physics need to be predicted as part of the solution of the flow equations. In addition, the discontinuity in fluid density, viscosity and species concentration at the interface present additional numerical challenges. In this work, we extend our balanced-force volume-tracking algorithm for modeling surface tension force (Francois et al., 2006) and we propose a global embedded interface formulation to model the interfacial conditions of an interface in thermodynamic equilibrium. To validate our formulation, we perform simulations of pure diffusion problems in one- and two-dimensions. Then we present two and three-dimensional simulations of a single droplet dynamics rising by buoyancy with mass transfer.

Linearized Unsteady Viscous Turbomachinery Flows Using Hybrid Grids

2001 ◽  
Vol 123 (3) ◽  
pp. 568-582 ◽  
Author(s):  
L. Sbardella ◽  
M. Imregun
Keyword(s):  
Unsteady Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Laplacian Operator ◽  
Finite Volume Scheme ◽  
Test Case ◽  
Flow Equations ◽  
Mixed Element

The paper describes the theory and the numerical implementation of a three-dimensional finite volume scheme for the solution of the linearized, unsteady Favre-averaged Navier–Stokes equations for turbomachinery applications. A further feature is the use of mixed element grids, consisting of triangles and quadrilaterals in two dimensions, and of tetrahedra, triangular prisms, and hexahedra in three dimensions. The linearized unsteady viscous flow equations are derived by assuming small harmonic perturbations from a steady-state flow and the resulting equations are solved using a pseudo-time marching technique. Such an approach enables the same numerical algorithm to be used for both the nonlinear steady and the linearized unsteady flow computations. The important features of the work are the discretization of the flow domain via a single, unified edge-data structure for mixed element meshes, the use of a Laplacian operator, which results in a nearest neighbor stencil, and the full linearization of the Spalart–Allmaras turbulence model. Four different test cases are presented for the validation of the proposed method. The first one is a comparison against the classical subsonic flat plate cascade theory, the so-called LINSUB benchmark. The aim of the second test case is to check the computational results against the asymptotic analytical solution derived by Lighthill for an unsteady laminar flow. The third test case examines the implications of using inviscid, frozen-turbulence, and fully turbulent models when linearizing the unsteady flow over a transonic turbine blade, the so-called 11th International Standard Configuration. The final test case is a rotor/stator interaction, which not only checks the validity of the formulation for a three-dimensional example, but also highlights other issues, such as the need to linearize the wall functions. Detailed comparisons were carried out against measured steady and unsteady flow data for the last two cases and good overall agreement was obtained.

Laser Scanning Confocal Microscopy and Three-Dimesnsional Reconstruction of the Mitotic Spindles of Unequally Dividing Embryonic Cells

1990 ◽  
Vol 48 (3) ◽  
pp. 166-167
Author(s):  
J. Holy ◽  
G. Schatten
Keyword(s):  
Confocal Microscopy ◽  
Mitotic Spindle ◽  
Laser Scanning ◽  
Three Dimensional ◽  
Laser Scanning Confocal Microscopy ◽  
Two Dimensions ◽  
Embryonic Cells ◽  
Mitotic Spindles ◽  
Cleavage Division ◽  
Scanning Confocal Microscopy

One of the classic limitations of light microscopy has been the fact that three dimensional biological events could only be visualized in two dimensions. Recently, this shortcoming has been overcome by combining the technologies of laser scanning confocal microscopy (LSCM) and computer processing of microscopical data by volume rendering methods. We have employed these techniques to examine morphogenetic events characterizing early development of sea urchin embryos. Specifically, the fourth cleavage division was examined because it is at this point that the first morphological signs of cell differentiation appear, manifested in the production of macromeres and micromeres by unequally dividing vegetal blastomeres.The mitotic spindle within vegetal blastomeres undergoing unequal cleavage are highly polarized and develop specialized, flattened asters toward the micromere pole. In order to reconstruct the three-dimensional features of these spindles, both isolated spindles and intact, extracted embryos were fluorescently labeled with antibodies directed against either centrosomes or tubulin.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

Simulation of small-angle scattering curves by numerical Fourier transformation

2007 ◽  
Vol 40 (1) ◽  
pp. 16-25 ◽  
Author(s):  
Klaus Schmidt-Rohr
Keyword(s):  
Form Factor ◽  
Small Angle ◽  
Fourier Transformation ◽  
Three Dimensional ◽  
Power Laws ◽  
Numerical Approach ◽  
Peak Position ◽  
Two Dimensions ◽  
Correlation Peak ◽  
Scattering Intensity

A simple numerical approach for calculating theq-dependence of the scattering intensity in small-angle X-ray or neutron scattering (SAXS/SANS) is discussed. For a user-defined scattering density on a lattice, the scattering intensityI(q) (qis the modulus of the scattering vector) is calculated by three-dimensional (or two-dimensional) numerical Fourier transformation and spherical summation inqspace, with a simple smoothing algorithm. An exact and simple correction for continuous rather than discrete (lattice-point) scattering density is described. Applications to relatively densely packed particles in solids (e.g.nanocomposites) are shown, where correlation effects make single-particle (pure form-factor) calculations invalid. The algorithm can be applied to particles of any shape that can be defined on the chosen cubic lattice and with any size distribution, while those features pose difficulties to a traditional treatment in terms of form and structure factors. For particles of identical but potentially complex shapes, numerical calculation of the form factor is described. Long parallel rods and platelets of various cross-section shapes are particularly convenient to treat, since the calculation is reduced to two dimensions. The method is used to demonstrate that the scattering intensity from `randomly' parallel-packed long cylinders is not described by simple 1/qand 1/q4power laws, but at cylinder volume fractions of more than ∼25% includes a correlation peak. The simulations highlight that the traditional evaluation of the peak position overestimates the cylinder thickness by a factor of ∼1.5. It is also shown that a mix of various relatively densely packed long boards can produceI(q) ≃ 1/q, usually observed for rod-shaped particles, without a correlation peak.

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