Axisymmetric model

In Chapter 4 the development of axisymmetric models in which the radial and axial components of flow field variables remain constant in the circumferential direction is discussed. In situations where deviation from such a perfect symmetry is small it may still be possible to decouple components of the equation of motion and analyse the flow regime as a combination of one- and two-dimensional systems. To provide an illustrative example for this type of approximation, in this section we consider the modelling of the flow field inside a cone-and-plate viscometer. 

Figure 10. Comparison of cup average conversion predicted by horizontally lumped model (natural convection included) and axisymmetric model (natural convection neglected) for a = 0, 5 and 10.

Based on the results of these researchers the tubular reactor in this study has been described by the axisymmetric model using effective diffusivities given by Equation 20. 

Figure 12. Comparison between cup average conversion predicted by axisymmetric model with effective transport properties and experimentally measured values for styrene [5] and vinyl acetate [2],...

The present axisymmetric model of the individual photon becomes associated with a number of important questions discussed in the current literature. 

These questions appear to be understandable in terms of both photon models. The wavepacket axisymmetric model has, however, an advantage of being more reconcilable with the dot-shaped marks finally formed by an individual photon impact on the screen of an interference experiment. If the photon would have been a plane wave just before the impact, it would then have to convert itself during the flight into a wavepacket of small radial dimensions, and this becomes a less understandable behavior from a simple physical point of view. Then it is also difficult to conceive how a single photon with angular momentum (spin) could be a plane wave, without spin and with the energy hv spread over an infinite volume. Moreover, with the plane-wave concept, each individual photon would be expected to create a continuous but weak interference pattern that is spread all over the screen, and not a pattern of dot-shaped impacts. 

In parallel with the experimental investigation of flow of LiBr/HjO solutions over horizontal mbe banks, Killion and Garimella [80] also conducted 3-D computational simulations of the same problem, where the experimental results served to validate the results of these computational analyses. The results from this 3-D model were compared with 2-D, axisymmetric models, and it was shown that to adequately address all the features of these... 

A two-dimensional axisymmetric model of a column 0.23 m in diameter and 0.25 m high is used. At rest, the bed is 0.12 m high, and contains sand particles impregnated with iron oxide, 117 pm in diameter with a density of 2.65 g/cm. Two gas phase species (ozone and oxygen) are specified. Ozone enters from inlets at the base of the bed at speeds that range from 4 to 14 cm/sec. The gas lifts and separates the particles in the bed, allowing for better interaction between the ozone and iron oxide at the particle surfaces. The decomposition rate is expressed as... 

The aforementioned analyses were essentially elastic in nature. However, Huang and Kinloch (7,8) developed a two-dimensional, plane-strain model to analyze the stress fields around the dispersed rubbery particles in multiphase, rubber-modified epoxy polymers. The epoxy matrix was modeled as either an elastic or elastic-plastic material. Their work revealed that the plane-strain model predicted higher stress concentrations within the glassy polymeric matrix than the axisymmetric model. Furthermore, they successfully applied their... 

H. Ramamurthy, S. Ramadhyani, and R. Viskanta, A Two-Dimensional Axisymmetric Model for Combusting, Reacting, and Radiating Flows in Radiant Tubes, J. Inst. Energy, 67, pp. 90-100,1994. 

THE CALIBRATION OF THE T-H-M IN-SITU EXPERIMENT USING A SIMPLIFIED AXISYMMETRIC MODEL... 

A simplified axisymmetric model of the in situ THM test at the Kamaishi mine was simulated by five different numerical models. Although the model geometry is much simplified compared to the field test conditions, improved simulation of the general THM responses were obtained as compared to previous blind predictions performed within the DECOVALEX II project. The measures taken for improvement were ... 

As a results of the above measures, the results from the simplified axisymmetric model used in... 

The maximum temperature is reached at the contact with the over-pack, after about 30 years of heating. Three-dimensional models predict a value within the range of 75 to SOX, whereas the axisymmetric model (JNC) leads to about 90°C. The evolution of temperature at point B4 is summarized on Figure 2. On this figure, the ISEG curve relates to a purely TM calculation. 

Jean, R.P., Chen, C.S., and Spector, A.A. Finite element analysis of the adhesion — cytoskeleton-nucleus mechano transduction pathway during endothelial cell rounding, axisymmetric model, J. Biomech. Eng., 127,594,2005. 

Fig. 4.20a shows a variety of deformation mechanisms at the equator of the spherulite, due to differing orientations of the lamellar stacks relative to the tensile stress axis. Computer models are needed to consider the variety of lamellar stack orientations, and calculate the macroscopic stresses. Using an axisymmetric model of a spherulite (in a regular array), the tensile yield stress was predicted to be a nearly linear function of the crystallinity (Fig. 4.20b), and in the same range as experimental data. 

In what follows the magnetoviscosity phenomenon is analyzed by formulating the local ferrohydrodynamic model, the upscaled volume-average model in porous media with the closure problem, and solution and discussion of a simplified zero-order steady-state isothermal incompressible axisymmetric model for non-Darcy-Forchheimer flow of a Newtonian ferrofluid in a porous medium of the... 

Dynamic load applied using JWL equation of state for 2D axisymmetric models having 100 mm blasthole diameter in elasto-plastic rock obeying metal plasticity rules. Volumetric strain (scalar quantity) apportioned by statistical fracture mech principals used for fractures representation. 

The indentation process has been analyzed by the finite element method. It has been used the implicit methodology. The studied models have been analyzed under axisymmetric conditions. It has been demonstrated that apparently the forces do not depend on the friction between the contact surfaces of the punch and workpiece. The forces in axisymmetric models are influenced by the width of the workpiece while the height is not so relevant. 

A similar axisymmetric model to that described above, assuming the jet to be slender such that the longwave approximation holds (Ro < L, in which Rq is the initial meniscus height and L the characteristic length scale of... 

It may be possible to study the critical details identified in the global analysis further by using a more accurate two-dimensional or axisymmetric model of the area of interest. The model should follow the guidelines given in the EUROCOMP Handbook. 

Based on the global analysis, a more accurate model may be employed on details that require further investigation. For this purpose, a two dimensional or axisymmetric model of the joint area is often an optimum choice. Typically, the following requirements should be set for a reliable model of a connection ... 

Nuclear power plants can be modelled in many different ways according to their structural characteristics (e.g. lumped mass models, one dimensional models, axisymmetric models, two or three dimensional finite element models). The most suitable and reliable numerical technique should be used in order to minimize the contribution of the modelling techniques used to the uncertainties in the results. The continuing increase in the speed of computation and the progress in the graphical display of results have enabled the use of greatly refined structural and material models. 

The cylinder/cylinder geometry (for nozzles in cylindrical vessels) is much more difficult to analyze than the nozzle sphere, which can be treated as an axisymmetric structure. To obtain a suitable stress concentration factor for a nozzle in a cylindrical vessel, an approximate axisymmetric model is sometimes used. A popular approximation used is where the equivalent sphere has twice the diameter of the shell. The general trend of the experimental results is shown in Figure 7.8, which is for a flush nozzle in a cylindrical shell. 

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