Details Of Numerical Simulations Research Articles

Cohesive finite element modeling of the delamination of HTPB binder and HMX crystals under tensile loading

Accurately modeling the mechanical behavior of the polymer binders and the degradation of interfaces between binder and crystal is important to science-based understanding of the macro-scale response of polymer bonded explosives. The paper presents a description of relatively a simple bi-crystal HMX-HTPB specimen and associated tensile loading experiment including computed tomography imaging, the pertinent constitutive theory, and details of numerical simulations used to infer the behavior of the material during the delamination process. Within this work, mechanical testing and direct numerical simulation of this relatively simple bi-crystal system enabled reasonable isolation of binder-crystal interface delamination, in which the effects of the complicated thermomechanical response of explosive crystals were minimized. Cohesive finite element modeling of the degradation and delamination of the interface between a modified HTPB binder and HMX crystals was used to reproduce observed results from tensile loading experiments on bi-crystal specimens. Several comparisons are made with experimental measurements in order to identify appropriate constitutive behavior of the binder and appropriate parameters for the cohesive traction-separation behavior of the crystal-binder interface.This research demonstrates the utility of directly modeling the delamination between binder and crystal within crystal-binder-crystal tensile specimen towards characterizing the behavior of these interfaces in a manner amenable to larger scale simulation of polycrystalline PBX materials. One critical aspect of this approach is micro computed tomography imaging conducted during the experiments, which enabled comparison of delamination patterns between the direct numerical simulation and actual specimen. In addition to optimizing the cohesive interface parameters, one important finding from this investigation is that understanding and representing the strain-hardening plasticity of HTPB binder is important within the context of using a cohesive traction-separation model for the delamination of a crystal-binder system.

Mixing of thermally stratified water layer by a free rising wobbling air bubble

The purpose of this research was to provide further insights on bubble-induced agitation of heated bulk liquid. Fundamental studies on the bubble disturbance of a stratified thermal layer were carried out for a 6mm sphere-volume equivalent diameter air bubble suspended in water (Eo=1.2). A video digital image system and thermochromic liquid crystals were used to reproduce the bubble movement as well as the wake drift of the liquid. A three-dimensional interface tracking simulation was used as a numerical tool. The results have revealed a long open wake region that is formed along the fluctuating bubble path. The amplitude of the bubble wake is much larger than that of the bubble path. In addition to longitudinal mixing, strong lateral mixing is also caused by the movement of vortices in the transverse direction. Details of numerical simulations have revealed a wake that tends to form a chain of Omega shaped vortex rings. These “rings” are connected to each other in the near wake region. The coherent effects further downstream lead to more complex vortex patterns in the far wake. The disintegration of the coherent chain of vortices due to bubble surface deformability is highly complex and not clear at this stage. A comparison with liquid crystal temperature response has revealed that the time scale of the mixing is much longer than the ascending bubble residence, approximately 8s as obtained by several experimental runs. A transverse propagation of entrained cold water has given an estimate of the bubble-induced diffusion to be about 170 times larger than the diffusivity of momentum. The bulk liquid agitation cannot be correctly modeled without taking into account the bubble size dependent wake structure.

Influence of application of Hottel’s zonal model and six-flux model of thermal radiation on numerical simulations results of pulverized coal fired furnace

Difference of results of numerical simulation of pulverized coal fired furnace when mathematical models contain various radiation models has been described in paper. Two sets of numerical simulations of pulverized coal fired furnace of 210 MWe power boiler have been performed. One numerical simulation has contained Hottel?s zonal model, whereas the other numerical simulation has contained six-flux model. Other details of numerical simulations have been identical. The influence of radiation models has been examined through comparison of selected variables (gas-phase temperature, oxygen concentration, and absorbed radiative heat rate of surface zones of rear and right furnace walls), selected global parameters of furnace operation (total absorbed heat rate by all furnace walls and furnace exit gas-phase temperature). Computation time has been compared as well. Spatially distributed variables have been compared through maximal local differences and mean differences. Maximal local difference of gas-phase temperature has been 8.44%. Maximal local difference of absorbed radiative heat rate of the surface zones has been almost 80.0%. Difference of global parameters of furnace operation has been expressed in percents of value obtained by mathematical model containing Hottel?s zonal model and has not been bigger than 7.0%. Computation time for calculation of 1000 iterations has been approximately the same. Comparison with other radiation models is necessary for assessment of differences.

Issues of terminology, gradient dynamics and the ease of sympatric speciation in Adaptive Dynamics

It has been plainly stated that Adaptive Dynamics is ‘not a scientific theory, but a mathematical framework’ (Metz, 2005); it is a ‘method but not a model’ (Kisdi & Gyllenberg, 2005). From a completely pragmatic point of view, there is, then, only one question that evolutionary biologists need to ask: Is Adaptive Dynamics a useful way of approaching problems? The 14 Commentaries present a variety of different views, indicating that there is no consensus in the answer to this question. Indeed, we view the previous pages, consisting of the Target Review and the 14 Commentaries, as a part of a much larger public discussion on Adaptive Dynamics, and we thank the other authors for their contributions to the discussion. We feel it necessary to acknowledge that the wording of our comment in Question 6 of our Target Review (Waxman & Gavrilets, 2005) concerning ‘hidden limitations and unconscious or implicit assumptions’ was not optimal. It was not our intention to imply that limitations and assumptions of Adaptive Dynamics are hidden or unconsciously made by practitioners of Adaptive Dynamics. Rather, the statement was intended for biologists who use Adaptive Dynamics, or who wish to understand the biological implications of its mathematical results, and may not be aware of the underlying limitations and assumptions. These limitations and assumptions are not, in our opinion, sufficiently emphasised in the literature and, equally importantly, the consequences of their violation are not made clear. The Commentary of Geritz & Gyllenberg (2005) makes it admirably clear what these limitations are but not the consequences of their violation. The Commentaries of Abrams (2005), Barton & Polechova (2005), Kokko (2005), Spencer & Feldman (2005), Butlin & Tregenza (2005), and Van Dooren (2005) provide additional discussion of the issue. We also feel it necessary to clarify our wording about the treatment of genetic drift in Adaptive Dynamics. In the second paragraph of Question 4.3, we said an implicit assumption of Adaptive Dynamics is that all beneficial mutations will always initially increase in frequency. However in the first paragraph, we noted that in the work of Dieckmann & Law (1996), fixation of new alleles occurs at a rate proportional to the probability of fixation of a mutant. Since the probability of fixation of all mutants is not unity, the two paragraphs are clearly inconsistent. Our reading of the Adaptive Dynamics literature, however, leads us to believe that it is common to make the assumption that beneficial mutations always initially increase in frequency (see Meszena, 2005). We are also of the opinion that the treatment of genetic drift, when included in Adaptive Dynamics, has not been particularly realistic. As an example, the probability of invasion of a deleterious mutation is invariably taken as zero in Adaptive Dynamics (Geritz & Gyllenberg, 2005; Meszena, 2005). However, if a mutation is deleterious, but only very slightly so, and the population is finite, then such near neutral mutants can invade and become fixed in the population (Kimura, 1957). At the end of our Review, we stated our earnest and legitimate wish to see more details of numerical simulations, but this was somehow interpreted, in some Commentaries, as an attempt to denigrate Adaptive Dynamics, because of the lack of analytical results, or to attach specific significance to simulations in Adaptive Dynamics. This was not our intention. Although we appreciate all of the Commentaries made, we will not answer them directly. Rather we discuss three controversial points raised in more than one Commentary. A separate response is, however, also necessary for a number of peripheral points raised by Dieckmann & Doebeli (2005). Our response to these points is contained in Appendix B.