A numerical method for junctions in networks of shallow-water channels

There is growing interest in developing mathematical models and appropriate numerical methods for problems involving networks formed by, essentially, one-dimensional (1D) domains joined by junctions. Examples include hyperbolic equations in networks of gas tubes, water channels and vessel networks for blood and lymph in the human circulatory system. A key point in designing numerical methods for such applications is the treatment of junctions, i.e. points at which two or more 1D domains converge and where the flow exhibits multidimensional behaviour. This paper focuses on the design of methods for networks of water channels. Our methods adopt the finite volume approach to make full use of the two-dimensional shallow water equations on the true physical domain, locally at junctions, while solving the usual one-dimensional shallow water equations away from the junctions. In addition to mass conservation, our methods enforce conservation of momentum at junctions; the latter seems to be the missing element in methods currently available. Apart from simplicity and robustness, the salient feature of the proposed methods is their ability to successfully deal with transcritical and supercritical flows at junctions, a property not enjoyed by existing published methodologies. Systematic assessment of the proposed methods for a variety of flow configurations is carried out. The methods are directly applicable to other systems, provided the multidimensional versions of the 1D equations are available

A novel 1D-2D coupled model for hydrodynamic simulation of flows in drainage networks

Drainage network modelling is often an essential component in urban flood prediction and risk assessment. Drainage network models most commonly use different numerical procedures to handle flows in pipes and junctions. Numerous numerical schemes and models of different levels of complexity have been developed and reported to predict flows in pipes. However, calculation of the flow conditions in junctions has received much less attention and has been traditionally achieved by solving only the continuity equation. This method is easy to implement but it neglects the momentum exchange in the junctions and cannot provide sufficient boundary conditions for the pipe calculation. In this work, a novel numerical scheme based on the finite volume solution to the two-dimensional (2D) shallow water equations (SWEs) is proposed to calculate flow dynamics in junctions, which directly takes into account both mass and momentum conservation and removes the necessity of implementing complicated boundary settings for pipe calculations. This new junction simulation method is then coupled with the widely used two-component pressure approach (TPA) for the pipe flow calculation, leading to a new integrated drainage network model. The new 1D-2D coupled drainage network model is validated against an experimental and several idealised test cases to demonstrate its potential for efficient and stable simulation of flow dynamics in drainage networks.<br

Rheological Study of Transient Networks with Junctions of Limited Multiplicity

Viscoelastic and thermodynamic properties of transient gels comprised of telechelic polymers are theoretically studied. We extend classical theories of transient networks so that correlations among polymer chains through the network junctions are taken into account. This extension enables us to investigate how rheological quantities, such as viscosity and elastic modulus, are affected by the association equilibrium conditions, and how these quantities are related to the aggregation number of junctions. We present a theoretical model of transient networks with junctions comprised of variable number of hydrophobic groups on the chain ends. Elastically effective chains are defined as the chains whose both ends are associated with end groups on other chains. It is shown that the dynamic shear moduli are well described in terms of the Maxwell model characterized by a single relaxation time and the high-frequency plateau modulus as in the classical theories, but the reduced dynamic shear moduli depend on the polymer concentration and temperature through the reduced concentration c given as a combination of the association constant and the volume fraction of end groups. The plateau modulus and the zero-shear viscosity rise nonlinearly with increasing c when c is small, but they are proportional to c for higher c. The relaxation time also increases as c increases due to the presence of pairwise junctions at small c.Comment: 24 pages, 17 figure

A co-operating solver approach to building simulation

This paper describes the co-operating solver approach to building simulation as encapsulated within the ESP-r system. Possible adaptations are then considered to accommodate new functional requirements

Multi-component gas flow non-linear hyperbolic systems with sources segregated scheme finite volume method well-balanced scheme

This is the accepted manuscript of the following article: Finite volume methods for multi-component Euler equations with source terms A Bermúdez, X López, ME Vázquez-Cendón Computers & Fluids 156, 113-134. https://doi.org/10.1016/j.compfluid.2017.07.004A first-order well-balanced finite volume scheme for the solution of a multi-component gas flow model in a pipe on non-flat topography is introduced. The mathematical model consists of Euler equations with source terms which arise from heat exchange, and gravity and viscosity forces, coupled with the mass conservation equations of species. We propose a segregated scheme in which the Euler and species equations are solved separately. This methodology leads to a flux vector in the Euler equations which depends not only on the conservative variables but also on time and space variables through the gas composition. This fact makes necessary to add some artificial viscosity to the usual numerical flux which is done by introducing an additional source term. Besides, in order to preserve the positivity of the species concentrations, we discretize the flux in the mass conservation equations for species, in accordance with the upwind discretization of the total mass conservation equation in the Euler system. Moreover, as proposed in a previous reference by the authors, \cite{BLV}, the discretizations of the flux and source terms are made so as to ensure that the full scheme is well-balanced. Numerical tests including both academic and real gas network problems are solved, showing the performance of the proposed methodology.The authors wish to thank the referees for their useful remarks. This work was supported by the Reganosa company, by FEDER and the Spanish Ministry of Science and Innovation under research projects ENE2013-47867-C2-1-R and MTM2013-43745-R, and by FEDER and Xunta de Galicia under research project GRC2013/014S

Hydraulic Analysis of Surcharged Storm Sewer Systems

Surcharge in a storm sewer system is the condition in which an entire sewer section is submerged and the pipe is flowing full under pressure. Flow in a surcharged storm sewer is essentially slowly varying unsteady pipe flow and methods for analyzing this type of flow are investigated. In this report the governing equations for unsteady fluid flow in pressurized storm sewers are presented. From these governing equations three numerical models are developed using various assumptions and simplifications. These flow models are applied to several example storm sewer systems under surcharge conditions. Plots of hydraulic grade and flow throughout the sewer network are presented in order to evaluate the ability of each model to accurately analyze surcharged storm sewer systems. Computer programs are developed for each of the models considered and these programs are presented and documented in the Appendix of this report

Early structure formation from cosmic string loops

We examine the effects of cosmic strings on structure formation and on the ionization history of the universe. While Gaussian perturbations from inflation are known to provide the dominant contribution to the large scale structure of the universe, density perturbations due to strings are highly non-Gaussian and can produce nonlinear structures at very early times. This could lead to early star formation and reionization of the universe. We improve on earlier studies of these effects by accounting for high loop velocities and for the filamentary shape of the resulting halos. We find that for string energy scales G\mu > 10^{-7} the effect of strings on the CMB temperature and polarization power spectra can be significant and is likely to be detectable by the Planck satellite. We mention shortcomings of the standard cosmological model of galaxy formation which may be remedied with the addition of cosmic strings, and comment on other possible observational implications of early structure formation by strings.Comment: 22 pages, 10 figures. References adde

NASA Contributions to Development of Special-Purpose Thermocouples. A Survey

The thermocouple has been used for measuring temperatures for more than a century, but new materials, probe designs, and techniques are continually being developed. Numerous contributions have been made by the National Aeronautics and Space Administration and its contractors in the aerospace program. These contributions have been collected by Midwest Research Institute and reported in this publication to enable American industrial engineers to study them and adapt them to their own problem areas. Potential applications are suggested to stimulate ideas on how these contributions can be used

Mathematical modelling of gas flow networks in pellet induratlon systems

The objective of this research is to develop a simulation software tool, GASFLO, which should evaluate pressure, flow and temperature distributions of process gas in pellet induration system networks. Pellet induration systems are complex industrial systems composed of heterogenous components. The magnitude of gas through leaks i.e. the air entering or leaving the system from the points other than the known exits, is substantial and it adversely effects the performance of induration process. These leaks are very difficult to measure because of the hostile environment in the plant. The modelling of such industrial systems requires a notable amount of experimentation so the tool has been designed to enable the user modeller to change the component models and solution algorithms easily. The conventional methods for flow network simulation are based on process centred approach, mostly composed of homogeneous components. For ease of computation, the non-pipe elements are modelled with an approximate linear or non-linear generic equation, whose coefficients can simulate different states of the element. The resulting set of non-linear equations is linearised and solved simultaneously using some iterative method. By contrast, GASFLO is based on device centred or unit based approach, and uses a two level hierarchical solution algorithm. The pellet induration system network is first idealised into a connected graph of streams (sets of serially connected components) and nodes. At the top or coordination level the flow and pressure distributions satisfying the Kirchhoff's laws are evaluated for the connected graph. At the lower or component level the exact mathematical models of components ale computed, in order of their occurrence in respective streams, using coordination variables as parameters. The converged flows are used for the temperature computation. The solution algorithm requires partitioning of the connected graph into forest and coforest structures, for which secondary algorithms have been developed using specific heuristics relevant to the pellet induration systems. The rigorous application of software engineering techniques for the design and implementation of software, enabled the resolution of the complexity of the modelled system, embedded the characteristics of 'quality software' into the resulting code and benefits from object orientation, even though it is implemented in standard FORTRAN 77. GASFLO predicted results are in a good agreement with the measured results, it has been validated for a real life pellet induration system. It has been applied to simulate several practical scenarios, like addition of extra wind boxes to the zones and to determine how the plant production can be increased by certain ratio, such simulations were not feasible otherwise. GASFLO takes less than a minute to simulate a real-life pellet induration system on a 486 PC. The combined simulation with an other software tool, INDSYS, which evaluates the heat distribution in the solids, is also feasible