Breakup Model Research Articles

Conceptual model of coalescence and break-up in the presence of external agitation

Abstract A Markovian probabilistic cellular automaton with the capability to capture the essential phenomenology of coalescence and break-up processes in the presence of external agitation is introduced. The existence of homogeneous stationary states of the model which admit large cluster formation for a range of agitation speeds is analytically predicted by mean field calculations. Through mean field analysis it is possible to obtain formulas that link experimental and model parameters on the base of simple measurable quantities. In this way, the experimental conditions for which a desirable stationary particle size distribution should be expected can be derived.

Use of generalized hyperspherical Sturmian functions for a three-body break-up model problem

A hyperspherical Sturmian approach recently developed for three-body break-up processes is tested through an analytically solvable S-wave model. The scattering process is represented by a non-homogeneous Schrödinger equation in which the driven term is given by a Coulomb-like interaction multiplied by the product of a continuum wavefunction and a bound state in the particles' coordinates. The model contains most of the difficulties encountered in a real three-body scattering problem, e.g., non-separability in the electrons' spherical coordinates and Coulombic asymptotic behaviour, and thus provides an interesting benchmark for numerical methods. Since the Sturmian basis functions are constructed so as to include the correct asymptotic behaviour, a very fast convergence of the scattering wavefunction is observed. Excellent agreement is found with the analytical results for the associated transition amplitude. This holds true down to very low energies, a domain which is usually challenging as it involves huge spatial extensions. Within our method, such calculations can be performed without increasing significantly the computational requirements.

Study on the Kinetic Anti-Missile Fragment Based on NASA Model

The question of the anti-missile fragment produced by the Kinetic Kill Vehicle (KKV) intercepting the Tactical Ballistic Missile (TBM) is studied. It turns out the anti-missile fragment are composite outcome of the impact and explosion. By analysis the National Aeronautics and Space Administration (NASA) impact breakup model is suggested to calculate the fragment charac-teristic. The minimum mass threshold of effective fragment is deduced; the damages probability model that the debris cloud impacts the cooperative target is established based on Poisson distribu-tion. The simulation case indicates that the damage probability can achieve the 10-3 magnitude, and should attach importance to this threat.

Effects of alloy type and heat treatment on ejecta and crater sizes in aluminum alloys subjected to hypervelocity impacts

The effects of alloy type and heat treatment on crater size, ejecta fragment mass, and ejecta fragment size were examined for polycarbonate spheres striking thick aluminum alloy targets at very high velocities. The diameter and depth of the craters were compared with those obtained through an empirical equation. The size and mass of the ejecta fragments collected from the test chamber were also measured. The ejecta fragment mass was proportional to the impact energy of the projectiles, and the ejecta fragment size was proportional to the cubic root of the impact energy. The calculated characteristic lengths, cross-sectional areas, and mass-to-area ratios were compared with those from the NASA breakup model and Hata's model. The ejecta ring diameter obtained from the witness plates decreased with increasing impact velocity.

Two-dimensional modeling of viscous liquid jet breakup

A two-dimensional computational model has been developed to study the evolution and breakup of a viscous laminar liquid jet, using a boundary-fitted curvilinear coordinate system. A system of elliptic partial differential equations for coordinate transformations has been developed to map the moving boundaries’ physical domain of the jet to a simple rectilinear computational domain. The equations developed for the model comprise the transformed two-dimensional unsteady Navier–Stokes equations for the liquid jet, grid velocity equations, kinematic boundary conditions, and the Geometric Conservation Law. The resulting systems of equations are solved using an implicit finite difference scheme. Effects of inflow oscillation magnitude, wave number, Weber number, and Reynolds number on the breakup process of jets have been studied. The model predicts the instantaneous shape of the jet surface, formation of the main and satellite drops, and the breakup length and time. These results are compared with available experimental data. The comparisons show a good agreement between measured and computed values of drop sizes and breakup lengths for different Reynolds and Weber numbers. However, at a relatively high Reynolds number of 1,254, the model slightly overpredicts the main drop sizes and underpredicts the satellite drop sizes at a wave number of 0.4. At a low Reynolds number of 587, the model overpredicts the main drop sizes at a lower wave number of 0.3. Moreover, the model underpredicts the satellite drop sizes at a lower wave number of about 0.4 and overpredicts the satellite drop sizes at a wave number of 0.8.

2 Dimensional finite stochastic breakup model of biomass particle breakup

Due to the high content of cellulose, hemicellulose and lignin, the anisotropy of biomass particle in spatial structure induces the difference of mechanical properties in different directions. In this paper, based on the finite stochastic breakup model and anisotropy of biomass particles, 2-dimensional finite stochastic breakup model (2D-FSBM) of biomass particle was proposed, and the breakup process of biomass particle was investigated. In this model, the strength difference in different directions and the minimum mass ratio of a sub-particle to the parent particle were both considered. The simulation results agreed well with the experimental results in particle shapes, which indicated that 2D-FSBM could predict the breakup process of biomass particles.

CFD Modeling of Spray Atomization for a Nasal Spray Device

The purpose of this work is to evaluate numerical modeling techniques for simulation of spray atomization from a nasal spray device to complement experimental measurements previously. In the past, spray breakup models have not been applied to nasal spray applications, but rather for high-pressure applications such as combustion, and industry and agricultural spraying. The parameters in breakup model were not optimized for this kind of low-pressure injection with small-scale atomizer. Thus, there is a need to tune the spray model constants of the linear instability sheet atomization (LISA) model and evaluate its performance for low-pressure applications such as those found in nasal spray devices. Some parameters that were evaluated include the dispersion angle and the liquid sheet constant that influences the droplet size distribution and dispersion. The simulation results were evaluated against experimental data that has been previously performed. It was found that the LISA model provided good comparisons...

Evolution of cake batter bubble structure and rheology during planetary mixing

The incorporation of air into a high ratio cake batter by planetary mixing was studied using two bench mixers, a Kenwood KM250 and a Hobart-N50. Power draw (expressed as specific mechanical power input) and air volume fraction, ϕ, were monitored over time for batters prepared in each mixer for heat-treated and un-treated cake flours. The two flour types gave very similar results, indicating that the benefit of heat treatment for cake manufacture is manifested during the baking step. Both mixers gave a rapid initial increase in ϕ up to ∼0.50 followed by a gradual decay. Bubble size distributions of batters prepared in the Hobart showed the initial aeration stage to be accompanied by the formation of a large number of small bubbles, with diameters around 5μm: the average bubble size increased and number of bubbles decreased with extended mixing. Batters prepared without emulsifier exhibited a steady increase in ϕ to a plateau at ∼0.2 and contained larger bubbles which did not change in average size significantly over time. All batters exhibited power-law shear-thinning behaviour with power law indices and consistency strongly dependent on ϕ. At low shear rates, the apparent viscosity showed the non-linear dependency on ϕ expected for dense suspensions. At higher shear rates, elastic forces generated by the bubble phase became significant. The non-Newtonian nature of the liquid phase and the elasticity generated by the bubbles meant that shear-thinning and bubble break-up could not be predicted by analyses based on the capillary number. The results support a qualitative model of bubble formation and break-up caused by extensional deformation generated by shearing these bubbly liquids: the bubbles cream out slowly owing to the high viscosity of the continuous phase at rest.

Uplift prior to continental breakup: Indication for removal of mantle lithosphere?

Uplift or reduced subsidence prior to continental breakup is a key component of the rift-drift transition. This uplift causes lateral variations in the lithospheric potential energy, which can increase intraplate deviatoric tension, thereby facilitating continental rupture. There is a growing body of evidence that pre-breakup uplift is a global phenomenon characteristic of magmatic and magma-poor rifted margins. Evidence is provided by the subaerial extrusion of lava interpreted from drill logs, stratigraphic records, the presence of breakup unconformities, and the spatial extent of uplift associated with Afar (the Ethiopian-Somali plateau), which may be at the stage of rupture. Previously discussed mechanisms contributing to this uplift include phase transitions, dynamic uplift from mantle plumes, and magmatic underplated bodies. We show in this study that dynamic uplift resulting from passive upwelling asthenosphere below the rift is limited (∼200 m). Isostatic arguments suggest that removal of mantle lithosphere is a necessary and effective mechanism for uplift coincident with rupture. The combination of mantle phase transitions and a very thin mantle lid produces an excess potential energy state (as evidenced by a positive geoid anomaly) and leads to tensional forces favorable for rupture. These results underpin our proposed model for continental breakup where removal of mantle lithosphere by either detachment or formation of gravitational instabilities is a characteristic process. Observations of depth-dependent thinning and geochemical data support this model.

An analytically solvable three-body break-up model problem in hyperspherical coordinates

An analytically solvable S-wave model for three particles break-up processes is presented. The scattering process is represented by a non-homogeneous Coulombic Schrodinger equation where the driven term is given by a Coulomb-like interaction multiplied by the product of a continuum wave function and a bound state in the particles coordinates. The closed form solution is derived in hyperspherical coordinates leading to an analytic expression for the associated scattering transition amplitude. The proposed scattering model contains most of the difficulties encountered in real three-body scattering problem, e.g., non-separability in the electrons’ spherical coordinates and Coulombic asymptotic behavior. Since the coordinates’ coupling is completely different, the model provides an alternative test to that given by the Temkin-Poet model. The knowledge of the analytic solution provides an interesting benchmark to test numerical methods dealing with the double continuum, in particular in the asymptotic regions. An hyperspherical Sturmian approach recently developed for three-body collisional problems is used to reproduce to high accuracy the analytical results. In addition to this, we generalized the model generating an approximate wave function possessing the correct radial asymptotic behavior corresponding to an S-wave three-body Coulomb problem. The model allows us to explore the typical structure of the solution of a three-body driven equation, to identify three regions (the driven, the Coulombic and the asymptotic), and to analyze how far one has to go to extract the transition amplitude.

Finite element reconstruction approach for on-orbit spacecraft breakup dynamics simulation and fragment analysis

Breakup model is the key area of space debris environment modeling. NASA standard breakup model is currently the most widely used for general-purpose. It is a statistical model found based on space surveillance data and a few ground-based test data. NASA model takes the mass, impact velocity magnitude for input and provides the fragment size, area-to-mass ratio, velocity magnitude distributions for output. A more precise approach for spacecraft disintegration fragment analysis is presented in this paper. This approach is based on hypervelocity impact dynamics and takes the shape, material, internal structure and impact location etc. of spacecraft and impactor, which might greatly affect the fragment distribution, into consideration. The approach is a combination of finite element and particle methods, entitled finite element reconstruction (FER). By reconstructing elements from the particle debris cloud, reliable individual fragments are identified. Fragment distribution is generated with undirected graph conversion and connected component analysis. Ground-based test from literature is introduced for verification. In the simulation satellite targets and impactors are modeled in detail including the shape, material, internal structure and so on. FER output includes the total number of fragments and the mass, size and velocity vector of each fragment. The reported fragment distribution of FER shows good agreement with the test, and has good accuracy for small fragments.

Heteroflocculation of a Cationic Oil-in-Water Emulsion Resulting from Fontainebleau’s Sandstone Powder Addition as a Model for Asphalt Emulsion Breakup

The use of asphalt emulsions for road fabrication is rapidly gaining in importance mainly due to energy savings, less environmental impact, and better properties of the final product. However, the formulation of these emulsions still requires a better understanding, particularly concerning their breaking phenomena. When a cationic model emulsion is contacted with a solid having a negative-charged surface, physicochemical driving forces result in the emulsion destabilization. As a consequence, a viscosity reduction of the remaining emulsion is observed, as well as the emulsion breakup through a heteroflocculation mechanism provided the solid surface is large enough. Emulsion systems at equilibrium, containing cetylpyridinium chloride (CPC), paraffin oil, and Fontainebleau’s sandstone powder and having different droplet sizes, are studied. The results show that the dispersed oil fraction decreases after each addition of sandstone aliquots, and this depends on the concentration of CPC in the continuous phase of the emulsion. As the droplet size and distribution remain constant during the process, it is assumed that the emulsion heteroflocculation is the result of direct oil droplets adhesion on the sand surface, followed by their coalescence around the sand particles.

Mathematical modeling and analysis of the flocculation process in chambers in series

In this study, the flocculation process in continuous systems with chambers in series was analyzed using the classical kinetic model of aggregation and break-up proposed by Argaman and Kaufman, which incorporates two main parameters: K a and K b. Typical values for these parameters were used, i. e., K a=3.68×10(-5)-1.83×10(-4) and K b=1.83×10(-7)-2.30×10(-7)s(-1). The analysis consisted of performing simulations of system behavior under different operating conditions, including variations in the number of chambers used and the utilization of fixed or scaled velocity gradients in the units. The response variable analyzed in all simulations was the total retention time necessary to achieve a given flocculation efficiency, which was determined by means of conventional solution methods of nonlinear algebraic equations, corresponding to the material balances on the system. Values for the number of chambers ranging from 1 to 5, velocity gradients of 20-60s(-1) and flocculation efficiencies of 50-90% were adopted.

Inverse methods for modeling non-rigid plate kinematics: Application to mesozoic plate reconstructions of the Central Atlantic

Published plate reconstructions commonly show significant differences in initial plate configuration and syn-extensional opening directions. The variability of published models is primarily due to the difficulty associated with restoring crustal stretching history. Here we present an inverse non-rigid kinematic method that inverts plate motion and present day crustal thickness to approximate the history of bulk lateral strain and crustal thinning associated with lithospheric stretching. The kinematic link between plate motion and bulk crustal thickness that is used with this method is based on insights obtained from geodynamic models. We implement this approach in open source kinematic modeling software and apply it to test new Early Mesozoic plate kinematic models of the Central Atlantic. This application shows that the patterns of stretching inferred from the syn-rift basins of the Newark Supergroup can be explained if (1) syn-rift Euler pole flow lines were parallel to the Grand Banks transform margin and (2) initial formation of the East Coast Margin Igneous Province was coincident with the formation of the Central Atlantic Magmatic Province. These syn-rift to breakup models of the Central Atlantic lead to better constrained models of early seafloor spreading that show full spreading velocities in the ultraslow regime and within the transition from ultraslow to slow spreading regimes.

An Analytical Approach for Calculation of Critical Weber Number of Droplet Breakup in Turbulent Gaseous Flows

An analytical approach for prediction of the ambient turbulence effects on critical Weber number of droplet breakup is suggested and validated against available experimental data. Critical Weber number is an appropriate criterion for prediction of droplet breakup initiation in inertially dominated flow fields. Experiments indicate that the breakup of droplets in turbulent flows requires a lower ratio of mean aerodynamic to surface forces (Weber number) compared with that in laminar flows. Until now no analytical or theoretical model for calculation of critical Weber number for droplet breakup considering ambient turbulence effects has been reported. The mathematical method suggested and developed in this research is partly based on Taylor analogy breakup model. In the present model the concept of hybrid time scale is used to consider the ambient turbulence effects on droplet breakup criterion. Comprehensive and simple analytical expression for prediction of critical Weber number derived in this paper gives accurate and close predictions compared with experimental data. Results indicate that the value of critical Weber number of droplet breakup decreases with increasing turbulence intensity. Furthermore, the effect of carrier-phase turbulence on droplet breakup is apparent even at high ambient pressures.

Numerical Investigation on Primary Atomization of the Fuel Spray in Diesel Engines

In addition to the aerodynamic effects, turbulence and cavitation play an important role on the primary atomization. Different spray breakup models were analysized and evaluated though simulation of spray with them and then a new model of coupling the nozzle cavitating and turbulence flow to the spray primary breakup was put forward. The numerical simulation results with all these different spray primary breakup models were comparied with the experimental data and then the new model were proved to be much better. The study may effectively help establish the accurate spray breakup model.

Numerical and Experimental Study on the Combustion and Emission Characteristics of a Dimethyl Ether (DME) Fueled Compression Ignition Engine

A numerical investigation was carried out to study on the combustion and emission characteristics of dimethyl ether (DME) with wide ranges of injection timings in compression ignition engines. In order to simulate DME combustion processes, a KIVA-3V code coupled with a chemistry solver was used to solve the detailed chemical kinetics model of DME oxidation. In addition, the Kelvin-Helmholtz-Rayleigh-Taylor (KH-RT) hybrid breakup model and Renormalization Group (RNG) k-e models were applied to analyze the spray characteristics and turbulent flow, respectively. To predict the NOx formation during DME combustion, a reduced Gas Research Institute (GRI) NO mechanism was used. From these results on the combustion and emission, the calculated results were compared with experimental ones for the same operating conditions. In the combustion characteristics, the calculated combustion pressure and heat release rates agreed well with experimental results. The levels of experimental NOx emissions was reduced as the start of the injection timing retarded, and also these trends appeared in calculated emission characteristics. Additionally, the calculated CO and HC emissions show an increasing trend as the start of the injection is retarded.

Coherent ρ and [formula omitted] photoproduction in ultraperipheral processes with electromagnetic dissociation of heavy ions at RHIC and LHC

We present predictions for the J/ψ and ρ meson production in the heavy ion ultraperipheral collisions (UPC) for the current energy 2.76 TeV at the LHC. Both total cross sections and cross sections with the neutron emission from one or both nuclei are presented. We also perform analysis of the RHIC ρ meson photoproduction data and emphasize importance of these data for testing the current model for nucleus breakup in the UPC.

Simulation of depth–dose distributions for various ions in polyethylene medium

Study of depth–dose distributions for intermediate energy ion beams in tissue-like media such as polyethylene (CH2)n provides a good platform for further improvements in the fields of hadrontherapy and space radiation shielding. The depth–dose distributions for 12C ions at various energies and for light and intermediate ion beams (3He, 16O, 20Ne and 28Si) as well as for heavy ions 56Fe in polyethylene were estimated by using simulation toolkit: Geant4. Calculations were performed mainly by considering two different combinations of standard electromagnetic (EM), binary cascade (BIC), statistical multifragmentation (SMF) and Fermi breakup (FB) models. The energies of the ion beams were selected to achieve the Bragg peaks at predefined position (∼60mm) and as per their availability. Variations of peak-to-entrance ratio (from 7.44±0.05 to 8.87±0.05), entrance dose (from 2.89±0.01 to 203.71±0.63MeV/mm) and entrance stopping power (from 3.608 to 208.858MeV/mm, calculated by SRIM) with atomic number (Z) were presented in a systematic manner. The better peak-to-entrance ratio and less entrance dose in the region Z=2 to 8 (i.e. 3He to 16O) may provide the suitability of the ion beams for hadrontherapy.

RESEARCH FOR THE TURBULENT TWO-PHASE FLOW GOVERNING EQUATIONS IN DIRECT-INJECTION ENGINE

To calculate the governing equations for the turbulent two-phase flow an Extended TAB-model (TP) model is presented to fit for the gas phase and the liquid phase. In the gas phase, Favre-averaging is used for continuity equation, momentum equation. As a result of the averaging, unclosed terms appear which require modeling. In order to close the turbulent Reynolds stress tensor in the momentum equation, the so-called Boussinesque-approximation, which is based on an analogy between molecular diffusion and diffusion turbulent eddies, has been employed. Turbulent kinetic energy k equation and turbulent dissipation ε equation are added to close the Navier-Stokes equations. The temporal differencing scheme in CFD(computational fluid dynamics) code (KIVA-3V) is largely implicit. In the Lagragian phase, implicit differencing is used for all diffusion terms and terms associated with pressure wave propagation. A method similar to the Semi-Implicit Method for Pressure Linked Equations (SIMPLE)-algorithm is used to solve the couple implicit set of equations. In the liquid phase, probability density function (PDF) method is used for solving droplet spray equation. Taylor Analogy Breakup (TAB) model used in the standard KIVA-code is extended with a deformation velocity such that their lifetime is extended to match experimentally observed jet breakup lengths. Furthermore, other models such as Rayleigh-Taylor (R-T) model, Discrete Droplet Models (DDM) etc are discussed. Finally, cylinder pressure and corresponding heat release rates in a directed-injection diesel engine are calculated and compared with the experiments. It gives the theory and method about calculating turbulence exactly in directed-injection diesel engine.DOI: http://dx.doi.org/10.5755/j01.mech.18.1.1283