Simulations of the kettle reboiler shell side thermal-hydraulics with different two-phase flow models

A computational fluid dynamics approach is presented for the simulation and analyses of the kettle reboiler shell side thermal-hydraulics with two different models of two-phase flow – the mixture and two fluid model. The mixture model is based on solving one momentum equation for two-phase mixture flow and a closure law for the calculation of the slip between gas and liquid phase velocities. In the two fluid modeling approach the momentum balance is formed for each phase, while the gas-liquid interaction due to momentum exchange at the interface surface is predicted with an empirical correlation for the interface friction coefficient. In both approaches the two-phase flow is observed as two inter-penetrating continua. The models are solved for the two-dimensional geometry of the kettle reboiler shell side vertical cross section. The computational fluid dynamics numerical method based on the SIMPLE type algorithm is applied. The results of both liquid and vapor velocity fields and void fraction are presented for each modeling approach. The calculated void fraction distributions are compared with available experimental data. The differences in the modeling approaches and obtained results are discussed. The main finding is that the void fraction distribution and two-phase flow field strongly depends on the modeling of the slip between liquid and gas phase velocity in mixture model or on the interface friction model in two fluid model. The better agreement of the numerically predicted void fraction with the experimental data is obtained with the two fluid model and an interfacial friction model developed for the conditions of two-phase flows in large volumes of kettle reboilers or different designs of steam generators

Simulations of the kettle reboiler shell side thermal-hydraulics with different two-phase flow models

A computational fluid dynamics approach is presented for the simulation and analyses of the kettle reboiler shell side thermal-hydraulics with two different models of two-phase flow – the mixture and two fluid model. The mixture model is based on solving one momentum equation for two-phase mixture flow and a closure law for the calculation of the slip between gas and liquid phase velocities. In the two fluid modeling approach the momentum balance is formed for each phase, while the gas-liquid interaction due to momentum exchange at the interface surface is predicted with an empirical correlation for the interface friction coefficient. In both approaches the two-phase flow is observed as two inter-penetrating continua. The models are solved for the two-dimensional geometry of the kettle reboiler shell side vertical cross section. The computational fluid dynamics numerical method based on the SIMPLE type algorithm is applied. The results of both liquid and vapor velocity fields and void fraction are presented for each modeling approach. The calculated void fraction distributions are compared with available experimental data. The differences in the modeling approaches and obtained results are discussed. The main finding is that the void fraction distribution and two-phase flow field strongly depends on the modeling of the slip between liquid and gas phase velocity in mixture model or on the interface friction model in two fluid model. The better agreement of the numerically predicted void fraction with the experimental data is obtained with the two fluid model and an interfacial friction model developed for the conditions of two-phase flows in large volumes of kettle reboilers or different designs of steam generators

Strongly Regular Graphs with Parameters (4m4, 2m4 + m2, m4 + m2, m4 + m2) Exist for All m>1

Using results on Hadamard difference sets, we construct regular graphical Hadamard matrices of negative type of order 4m4 for every positive integer m. If m > 1, such a Hadamard matrix is equivalent to a strongly regular graph with parameters (4m4, 2m4 +m2,m4 +m2,m4 +m2). Strongly regular graphs with these parameters have been called max energy graphs, because they have maximal energy (as defined by Gutman) among all graphs on 4m4 vertices. For odd m>3 the strongly regular graphs seem to be new.Cayley graph;difference set;energy of a graph;Hadamard matrix;regular Hadamard matrix;strongly regular graph;Seidel switching.

Strong-coupling scales and the graph structure of multi-gravity theories

In this paper we consider how the strong-coupling scale, or perturbative cutoff, in a multi-gravity theory depends upon the presence and structure of interactions between the different fields. This can elegantly be rephrased in terms of the size and structure of the `theory graph' which depicts the interactions in a given theory. We show that the question can be answered in terms of the properties of various graph-theoretical matrices, affording an efficient way to estimate and place bounds on the strong-coupling scale of a given theory. In light of this we also consider the problem of relating a given theory graph to a discretised higher dimensional theory, a la dimensional deconstruction.Comment: 23 pages, 7 figures; v2: additional references included, and minor typos corrected; version published in JHE

Comparing the Zagreb Indices

Let G = (V, E) be a simple graph with n = |V | vertices and m = |E | edges; let d1, d2, …, dn denote the degrees of the vertices of G. If Δ= maxdi ≤ 4, G is a chemical graph. The first and second Zagreb indices are defined as M1 = Σdi ²and M2 = Σd i d j We show that for all chemical graphs M 1/n ≤ M2/m. This does not hold for all general graphs, connected or not