Abstract

Freezing is an important step in the manufacturing process of ice-cream and sorbet, since the operating conditions have a strong influence on the micro-structure, and consequently on the sensorial attributes of the final product. This steep of freezing is carried out by a scraped surface heat exchanger (SSHE) where the product quality is conditioned by process conditions as the evaporation temperature of a refrigerant fluid, the mix flow rate, the dasher speed and the cylinder pressure due to the air introduction. In order to study the relevance of a control system based on the influence of process variables on product quality, this paper presents a model for a continuous crystallization of a sorbet using the method of moments, which is validated by experimental data.The model created by this methodology has been able to represent the influence of the process conditions during the crystallization of the sorbet on the final product characteristics such as crystal size and the draw temperature in the outlet of the SSHE in absence of air. The model based in moments is studied as a reduced model of the population balance equation and includes the phenomena of heterogeneous nucleation and growth. This model developed represents minimal computational requirements and is highly adapted for optimization and/or process control tasks.

Abstract

c-congestion period of an m/m/ ∞-queue is a period during which the number of customers in the system is continuously above level c. Interesting quantities related to a c-congestion period are, besides its duration Dc, the total area Ac above c, and the number of arrived customers Nc. In the literature Laplace transforms for these quantities have been derived, as well as explicit formulae for their means. Explicit expressions for higher moments and covariances (between Dc, Nc and Ac), however, have not been found so far. This paper presents recursive relations through which all moments and covariances can be obtained. Up to a starting condition, we explicitly solve these equations; for instance, we write E Dc2 explicitly in terms of E D02. We then find formulae for these starting conditions (which directly relate to the busy period in the m/m/ ∞ queue). Finally, a c-intercongestion period is defined as the period during which the number of customers is continuously below level c. Also for this situation a recursive scheme allows us to explicitly compute higher moments and covariances. Additionally we present the Laplace transform of a so-called intercongestion triple of the three performance quantities. It is also shown that expressions for the quantities of a c-intercongestion period can be used in an approximation for the c-congestion period. This is especially useful as the expressions for the c-intercongestion period are numerically more stable than those for the c-congestion period. © 2007 Elsevier Ltd. All rights reserved.

Abstract

The purpose of this paper is to present a method to model earthing systems subjected to lightning strikes with a one-dimensional moment method. This paper was conducted because an accurate method to model earthing systems subjected to lightning strikes, was deemed necessary. To name a few examples of relevant situations: supply stations of railway systems, from which also critical signalling infrastructure is fed, earthing systems of cellular phone basestations, located in the vicinity of high-antenna towers, prone to lightning strikes, and gas and oil pipelines. There exist already methods to solve this problem, based on circuit theory, but the electromagnetic method of this work is based directly on Maxwell’s equations and therefore more accurate. The earthing electrodes and meshes are represented as wire scatterers. First, the method is outlined for scatterers in a single medium. Next, the method is extended to model to presence of the soil-air interface layer. An approximate technique, known as the modified image theory, is used to account for the vicinity of the soil. Finally, a second extension is given so that cables without metal sheets which are in the vicinity of the earthing systems, can be included in the model. Thereafter, it is described how the method can be used to calculate the effects of lightning strikes on earthing structures, and finally a validation of the method is presented. The method is validated by applying it to simple situations which can also analytically be calculated, and by applying it to earthing structures for which the transient voltage was measured or calculated with circuit methods. A good agreement is seen. However, the method is computationally very expensive. ispartof: COMPEL vol:28 issue:4 pages:989-1004 ispartof: location:Graz, AUSTRIA status: published