Condensation in ducts

Phase changing flows are being considered for thermal management in space platforms. The resulting flow patterns are very complicated and extremely sensitive to gravity action. Concerning fluid flow in ducts, the available evidence indicates that although the pressure loss does not depend too much on the fluid flow pattern,the heat transfer (and resulting phase change) does. A simple exercise to illustrate this point is presented in this paper. It deals with condensing flow in straight circular cross-sectional ducts. Two extreme configurations are considered here, one corresponds to a stratified flow and the other to an annular flow. Both types of flow patterns have been extensively considered in the past and from this point of view almost nothing is new in the paper, but past results look conflictive and this could be due to the limitations and computational intricacies of the models used. Thus the problem has been reformulated from the onset and the results are presented as the evolution of the vapor quality (vapor to total mass flow rate) along the duct, in typical cases. The results presented here indicate that within the validity of the present models and the assumed ranges of mass flow rate, duct diameter, thermal conditions and fluid characteristics,the length of the ducts required to achieve complete condensation under zero gravity are an order of magnitude larger than in horizontal tubes under normal terrestrial conditions.

Cálculo de pilas con aparatos de apoyo tipo POT y tablero con punto fijo

In recent years a great number of high speed railway bridges have been constructed within the Spanish borders. Due to the demanding high speed trains route's geometrical requirements, bridges frequently show remarkable lengths. This fact is the main reason why railway bridges are overall longer than roadway bridges. In the same line, it is also worth highlighting the importance of high speed trains braking forces compared to vehicles. While vehicles braking forces can be tackled easily, the railway braking forces demand the existence of a fixed-point. It is generally located at abutments where the no-displacements requirement can be more easily achieved. In some other cases the fixed-point is placed in one of the interior columns. As a consequence of these bridges' length and the need of a fixed-point, temperature, creep and shrinkage strains lead to fairly significant deck displacements, which become greater with the distance to the fixed-point. These displacements need to be accommodated by the piers and bearings deformation. Regular elastomeric bearings are not able to allow such displacements and therefore are not suitable for this task. For this reason, the use of sliding PTFE POT bearings has been an extensive practice mainly because they permit sliding with low friction. This is not the only reason of the extensive use of these bearings to high-speed railways bridges. The value of the vertical loads at each bent is significantly higher than in roadway bridges. This is so mainly because the live loads due to trains traffic are much greater than vehicles. Thus, gravel rails foundation represents a non-negligible permanent load at all. All this together increases the value of vertical loads to be withstood. This high vertical load demand discards the use of conventional bearings for excessive compressions. The PTFE POT bearings' higher technology allows to accommodate this level of compression thanks to their design. The previously explained high-speed railway bridge configuration leads to a key fact regarding longitudinal horizontal loads (such as breaking forces) which is the transmission of these loads entirely to the fixed-point alone. Piers do not receive these longitudinal horizontal loads since PTFE POT bearings displayed are longitudinally free-sliding. This means that longitudinal horizontal actions on top of piers will not be forces but imposed displacements. This feature leads to the need to approach these piers design in a different manner that when piers are elastically linked to superstructure, which is the case of elastomeric bearings. In response to the previous, the main goal of this Thesis is to present a Design Method for columns displaying either longitudinally fixed POT bearings or longitudinally free PTFE POT bearings within bridges with fixed-point deck configuration, applicable to railway and road vehicles bridges. The method was developed with the intention to account for all major parameters that play a role in these columns behavior. The long process that has finally led to the method's formulation is rooted in the understanding of these column's behavior. All the assumptions made to elaborate the formulations contained in this method have been made in benefit of conservatives results. The singularity of the analysis of columns with this configuration is due to a combination of different aspects. One of the first steps of this work was to study they of these design aspects and understand the role each plays in the column's response. Among these aspects, special attention was dedicated to the column's own creep due to permanent actions such us rheological deck displacements, and also to the longitudinally guided PTFE POT bearings implications in the design of the column. The result of this study is the Design Method presented in this Thesis, that allows to work out a compliant vertical reinforcement distribution along the column. The design of horizontal reinforcement due to shear forces is not addressed in this Thesis. The method's formulations are meant to be applicable to the greatest number of cases, leaving to the engineer judgement many of the different parameters values. In this regard, this method is a helpful tool for a wide range of cases. The widespread use of European standards in the more recent years, in particular the so-called Eurocodes, has been one of the reasons why this Thesis has been developed in accordance with Eurocodes. Same trend has been followed for the bearings design implications, which are covered by the rather recent European code EN-1337. One of the most relevant aspects that this work has taken from the Eurocodes is the non-linear calculations security format. The biaxial bending simplified approach that shows the Design Method presented in this work also lies on Eurocodes recommendations. The columns under analysis are governed by a set of dimensionless parameters that are presented in this work. The identification of these parameters is a helpful for design purposes for two columns with identical dimensionless parameters may be designed together. The first group of these parameters have to do with the cross-sectional behavior, represented in the bending-curvature diagrams. A second group of parameters define the columns response. Thanks to this identification of the governing dimensionless parameters, it has been possible what has been named as Dimensionless Design Curves, which basically allows to obtain in a reduced time a preliminary vertical reinforcement column distribution. These curves are of little use nowadays, firstly because each family of curves refer to specific values of many different parameters and secondly because the use of computers allows for extremely quick and accurate calculations.