A Case Study in Rapid Prototyping

Since the first quarter of 1988, Pratt & Whitney (P&W), a Division of United Technologies Corporation (UTC), has been involved in the development for the use of rapid prototyping technologies that use a "layer-by-Iayer" building approach. Based on over 4 1/2 years experience with Stereolithography, this paper will address three aspects of our experience including: Implementation, Current Operations, and Future PlansMechanical Engineerin

AGRICULTURAL TRADE LIBERALIZATION UNDER NAFTA: REPORTING ON THE REPORT CARD

International Relations/Trade,

Modeling Turbulent Flow in Stirred Tanks with CFD: The Influence of the Modeling Approach, Turbulence Model and Numerical Scheme

Single phase turbulent flow in a tank stirred by a down- and an up-pumping pitched blade turbine has been simulated using CFD. The effect of the modeling approach, discretization scheme and turbulence model on mean velocities, turbulent kinetic energy and global quantities, such as the power and circulation numbers, has been investigated. The results have been validated by LDV data. The stationary and time-dependent modeling approaches were found to have little effect on the turbulent flow, however the choice of the numerical scheme was found to be important, especially for the predicted turbulent kinetic energy. A first order method was found to highly underestimate LDV data compared with higher order methods. The type of the turbulence model was limited to the k-e and RNG models due to convergence difficulties encountered with a Reynolds Stress Model (RSM) and there was found to be little effect of these models on the mean flow and turbulent kinetic energy. This latter quantity was found to be largely under predicted in the discharge region of the down-pumping impeller in comparison with LDV data. Better agreement was found for the up-pumping pitched blade turbine. Estimated power numbers were found generally to be in good agreement for the down- and up-pumping data. However, the circulation number tended to be over predicted by about 30% and 40% for the down- and uppumping agitators, respectively

K to pi and K to 0 in 2+1 Flavor Partially Quenched Chiral Perturbation Theory

We calculate results for K to pi and K to 0 matrix elements to next-to-leading order in 2+1 flavor partially quenched chiral perturbation theory. Results are presented for both the Delta I=1/2 and 3/2 channels, for chiral operators corresponding to current-current, gluonic penguin, and electroweak penguin 4-quark operators. These formulas are useful for studying the chiral behavior of currently available 2+1 flavor lattice QCD results, from which the low energy constants of the chiral effective theory can be determined. The low energy constants of these matrix elements are necessary for an understanding of the Delta I=1/2 rule, and for calculations of epsilon'/epsilon using current lattice QCD simulations.Comment: 43 pages, 2 figures, uses RevTeX, added and updated reference

Alternate operating methods for improving the performance of a continuous stirred tank reactor

The effect of the pumping direction of an axial flow impeller, the feeding rate and the number of feed inlets on the operation of a continuously-fed stirred tank has been studied using CFD. The flow patterns generated by the up-pumping and down-pumping impeller, under both ‘typical’ and ‘intensified’ operating conditions, are compared. The effect of various tank configurations on the performance of the vessel is assessed by analysing the flow and power numbers, as well as the concentration field of a non-reactive tracer. Furthermore, the inlet feed jets are reduced using traditional jet similarity analysis and are compared with that of a typical round jet. The results show that up-pumping impellers improve circulation in the upper part of the tank and reduce shortcircuiting of the feed stream with only a small increase in power consumption. Furthermore, by using multiple feed inlets to increase the total throughput capacity, the amplitude of torque fluctuations is decreased and impeller bypassing is also decreased. The ensemble of conclusions suggest that the throughput capacity and mixing quality of a CSTR can be improved, without problems of short-circuiting, by employing up-pumping impellers coupled with multiple surface feed points

PIV measurements in an aerated tank stirred by a down- and up-pumping axial flow impeller

Liquid phase hydrodynamics in an aerated tank stirred by a down- and an up-pumping pitched blade turbine have been investigated using Particle Image Velocimetry. The effect of agitator configuration and the gas phase on the mean velocity fields and turbulent quantities in the vessel have been investigated. The global mean gas holdup has also been evaluated for the two pumping conditions. For the gas flow rate used, the presence of gas only slightly alters the liquid flow patterns produced by both the down- and up-pumping configurations and causes a general decrease in the mean liquid velocities. The turbulent kinetic energy in the impeller discharge region was not affected by the presence of gas, but in the bulk of the tank, aeration caused a decrease in this value. Global gas holdup was found to be ~36% greater for the up-pumping impeller and a large amount of gas was found to be entrained by the primary circulation loop

Local lipschitzness of reachability maps for hybrid systems with applications to safety

Motivated by the safety problem, several definitions of reachability maps, for hybrid dynamical systems, are introduced. It is well established that, under certain conditions, the solutions to continuous-time systems depend continuously with respect to initial conditions. In such setting, the reachability maps considered in this paper are locally Lipschitz (in the Lipschitz sense for set-valued maps) when the right-hand side of the continuous-time system is locally Lipschitz. However, guaranteeing similar properties for reachability maps for hybrid systems is much more challenging. Examples of hybrid systems for which the reachability maps do not depend nicely with respect to their arguments, in the Lipschitz sense, are introduced. With such pathological cases properly identified, sufficient conditions involving the data defining a hybrid system assuring Lipschitzness of the reachability maps are formulated. As an application, the proposed conditions are shown to be useful to significantly improve an existing converse theorem for safety given in terms of barrier functions. Namely, for a class of safe hybrid systems, we show that safety is equivalent to the existence of a locally Lipschitz barrier function. Examples throughout the paper illustrate the results

Approach of a class of discontinuous dynamical systems of fractional order: existence of the solutions

In this letter we are concerned with the possibility to approach the existence of solutions to a class of discontinuous dynamical systems of fractional order. In this purpose, the underlying initial value problem is transformed into a fractional set-valued problem. Next, the Cellina's Theorem is applied leading to a single-valued continuous initial value problem of fractional order. The existence of solutions is assured by a P\'{e}ano like theorem for ordinary differential equations of fractional order.Comment: accepted IJBC, 5 pages, 1 figur