Relevant bibliographies by topics / Stratified flow – Mathematical models

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Stratified flow – Mathematical models'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Stratified flow – Mathematical models"

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Ilyasov, A. M., V. N. Kireev, S. F. Urmancheev, and I. Sh Akhatov. "Mathematical modeling of steady stratified flows." Proceedings of the Mavlyutov Institute of Mechanics 3 (2003): 195–207. http://dx.doi.org/10.21662/uim2003.1.014.

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The work is devoted to the analysis of the flow of immiscible liquid in a flat channel and the creation of calculation schemes for determining the flow parameters. A critical analysis of the well-known Two Fluids Model was carried out and a new scheme for the determination of wall and interfacial friction, called the hydraulic approximation in the theory of stratified flows, was proposed. Verification of the proposed approximate model was carried out on the basis of a direct numerical solution of the Navier–Stokes equations for each fluid by a finite-difference method with phase-boundary track
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Deleersnijder, Eric, Emmanuel Hanert, Hans Burchard, and Henk A. Dijkstra. "On the mathematical stability of stratified flow models with local turbulence closure schemes." Ocean Dynamics 58, no. 3-4 (September 19, 2008): 237–46. http://dx.doi.org/10.1007/s10236-008-0145-6.

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Kang, Qi, Jiapeng Gu, Xueyu Qi, Ting Wu, Shengjie Wang, Sihang Chen, Wei Wang, and Jing Gong. "Hydrodynamic Modeling of Oil–Water Stratified Smooth Two-Phase Turbulent Flow in Horizontal Circular Pipes." Energies 14, no. 16 (August 23, 2021): 5201. http://dx.doi.org/10.3390/en14165201.

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In the petrochemical industry, multiphase flow, including oil–water two-phase stratified laminar flow, is more common and can be easily obtained through mathematical analysis. However, there is limited mathematical analytical model for the simulation of oil–water flow under turbulent flow. This paper introduces a two-dimensional (2D) numerical simulation method to investigate the pressure gradient, flow field, and oil–water interface height of a pipeline cross-section of horizontal tube in an oil–water stratified smooth flow. Three Reynolds average N–S equation models (k−ε, k−ω, SST k−ω) are i
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Iornumbe, SI, T. Tivde, and RA Chia. "A Mathematical Model of Stratified Geophysical Fluid Flows Over Variable Bottom Topography." NIGERIAN ANNALS OF PURE AND APPLIED SCIENCES 3, no. 3b (November 15, 2020): 112–37. http://dx.doi.org/10.46912/napas.202.

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In this paper, a mathematical model of stratified geophysical fluid flow over variable bottom topography was derived for shallow water. The equations are derived from the principles of conservation of mass and conservation of momentum. The force acting on the fluid is gravity, represented by the gravitational constant. A system of six nonlinear partial differential equations was obtained as the model equations. The solutions of these models were obtained using perturbation method. The presence of the coriolis force in the shallow water equations were shown as the causes of the deflection of fl
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Senapati, Santosh Kumar, and Satish Kumar Dewangan. "COMPARISON OF PERFORMANCE OF DIFFERENT MULTIPHASE MODELS IN PREDICTING STRATIFIED FLOW." Computational Thermal Sciences: An International Journal 9, no. 6 (2017): 529–39. http://dx.doi.org/10.1615/computthermalscien.2017017248.

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Regnier, P., P. Jourabchi, and C. P. Slomp. "Reactive-Transport modeling as a technique for understanding coupled biogeochemical processes in surface and subsurface environments." Netherlands Journal of Geosciences - Geologie en Mijnbouw 82, no. 1 (April 2003): 5–18. http://dx.doi.org/10.1017/s0016774600022757.

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AbstractReactive-transport models contribute significantly to the field of modern geosciences. A general mathematical approach to solving models of complex biogeochemical systems is introduced. It is argued that even though mathematical models for reactive-transport simulations can be developed at various levels of approximation, the approach for their construction and application to the various compartments of the hydrosphere is fundamentally the same. The workings of coupled transport-reaction systems are described in more detail by means of examples, which demonstrate the similarities in th
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Kwon, Young-Sam. "Singular Limit of the Rotational Compressible Magnetohydrodynamic Flows." Advances in Mathematical Physics 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/9493186.

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We consider the compressible models of magnetohydrodynamic flows giving rise to a variety of mathematical problems in many areas. We derive a rigorous quasi-geostrophic equation governed by magnetic field from the stratified flows of the rotational compressible magnetohydrodynamic flows with the well-prepared initial data and the tool of proof is based on the relative entropy. Furthermore, the convergence rates are obtained.
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SEZAI, I., and A. A. MOHAMAD. "Three-dimensional double-diffusive convection in a porous cubic enclosure due to opposing gradients of temperature and concentration." Journal of Fluid Mechanics 400 (December 10, 1999): 333–53. http://dx.doi.org/10.1017/s0022112099006540.

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A three-dimensional mathematical model based on the Brinkman extended Darcy equation has been used to study double-diffusive natural convection in a fluid-saturated porous cubic enclosure subject to opposing and horizontal gradients of temperature and concentration. The flow is driven by conditions of constant temperature and concentration imposed along the two vertical sidewalls of the cubic enclosure, while the remaining walls are impermeable and adiabatic. The numerical simulations presented here span a wide range of porous thermal Rayleigh number, buoyancy ratio and Lewis number to identif
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Strickland, Christopher, Nadiah P. Kristensen, and Laura Miller. "Inferring stratified parasitoid dispersal mechanisms and parameters from coarse data using mathematical and Bayesian methods." Journal of The Royal Society Interface 14, no. 130 (May 2017): 20170005. http://dx.doi.org/10.1098/rsif.2017.0005.

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Biological invasions have movement at the core of their success. However, due to difficulties in collecting data, medium- and long-distance dispersal of small insects has long been poorly understood and likely to be underestimated. The agricultural release of parasitic hymenoptera, a group of wasps that are critical for biological pest control, represents a rare opportunity to study the spread of insects on multiple spatial scales. As these insects are typically less than 1 mm in size and are challenging to track individually, a first-time biocontrol release will provide a known spatial positi
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Koohbor, B., M. Fahs, B. Belfort, B. Ataie-Ashtiani, and C. T. Simmons. "Fourier series solution for an anisotropic and layered configuration of the dispersive Henry Problem." E3S Web of Conferences 54 (2018): 00014. http://dx.doi.org/10.1051/e3sconf/20185400014.

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Henry Problem (HP) still plays an important role in benchmarking numerical models of seawater intrusion (SWI) as well as being applied to practical and managerial purposes. The popularity of this problem is due to having a closed-form semi-analytical (SA) solution. The early SA solutions obtained for HP were limited to extensive assumptions that restrict its application in practical works. Several further studies expended the generality of the solution by assuming lower diffusion coefficients or including velocity-dependent dispersion in the results. However, all these studies are limited to h
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Dissertations / Theses on the topic "Stratified flow – Mathematical models"

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Yeates, Peter Stafford. "Deep mixing in stratified lakes and reservoirs." University of Western Australia. Centre for Water Research, 2008. http://theses.library.uwa.edu.au/adt-WU2008.0046.

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The onset of summer stratification in temperate lakes and reservoirs forces a decoupling of the hypolimnion from the epilimnion that is sustained by strong density gradients in the metalimnion. These strong gradients act as a barrier to the vertical transport of mass and scalars leading to bottom anoxia and subsequent nutrient release from the sediments. The stratification is intermittently overcome by turbulent mixing events that redistribute mass, heat, dissolved parameters and particulates in the vertical. The redistribution of ecological parameters then exerts some control over the ecologi
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Hnidei, Stephen D. "Selective withdrawal of a linearly stratified fluid in a triangular reservoir." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/28834.

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The water in most reservoirs is density stratified with depth. This stratification leads to the inhibition of vertical movement, consequently, when water is withdrawn from the reservoir it tends to move in a jet-like layer called a withdrawal layer, towards the sink. By placing the sink at a certain depth, one is able to selectively withdrawal water from a limited range of depths and thus obtain water of a desired quality. Much work has been done in this field by considering a simplified boundary geometry, usually rectangular. However little attention has been given to the effects of accurate
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Marti, Clelia Luisa. "Exchange processes between littoral and pelagic waters in a stratified lake." University of Western Australia. Centre for Water Research, 2004. http://theses.library.uwa.edu.au/adt-WU2005.0005.

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[Truncated abstract] The lake boundaries are an important source of sediment, nutrients and chemicals. For life inside the lake, the exchange between the lake boundaries (littoral) and lake interior (pelagic) is of central importance to Limnology as the net flux of nutrients into the water column is both the driving force and limiting factor for most algae blooms found during the stratification period. Consequently, the understanding of the relevant processes defining such an exchange is a further step toward a sound basis for future decisions by lake managers in order to ensure high water qua
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Dunbar, Donald Stanley 1953. "A numerical model of stratified circulation in a shallow-silled inlet." Thesis, University of British Columbia, 1985. http://hdl.handle.net/2429/25571.

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A numerical model has been developed for the study of stratified tidal circulation in Indian Arm - a representative inlet on the southern coast of British Columbia. Equations for horizontal velocity, salt conservation, continuity, density (calculated as a linear function of salinity), and the hydrostatic approximation govern the dynamics. All equations have been laterally integrated under the assumption of negligible cross-inlet variability. The model is time dependent and includes nonlinear advective terms, horizontal and vertical turbulent diffusion of salt and momentum, and variations in wi
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Shimizu, Kenji. "Application of modal analysis to strongly stratified lakes." University of Western Australia. Faculty of Engineering, Computing and Mathematics, 2009. http://theses.library.uwa.edu.au/adt-WU2009.0079.

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Modal analysis for strongly stratified lakes was extended to obtain a better understanding of the dynamics of the basin-scale motions. By viewing the basin-scale motions as a superposition of modes, that have distinct periods and three-dimensional structures, the method provides a conceptual understanding for the excitation, evolution, and damping of the basin-scale motions. Once the motion has been decomposed into modes, their evolution and energetics may be extracted from hydrodynamic simulation results and field data. The method was applied to Lake Biwa, Japan, and Lake Kinneret, Israel, an
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Zhang, Xizheng. "Mathematical modelling of nonlinear ring waves in a stratified fluid." Thesis, Loughborough University, 2015. https://dspace.lboro.ac.uk/2134/18587.

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Oceanic waves registered by satellite observations often have curvilinear fronts and propagate over various currents. In this thesis, we study long linear and weakly-nonlinear ring waves in a stratified fluid in the presence of a depth-dependent horizontal shear flow. It is shown that despite the clashing geometries of the waves and the shear flow, there exists a linear modal decomposition, which can be used to describe distortion of the wavefronts of surface and internal waves, and systematically derive a 2+1-dimensional cylindrical Korteweg-de Vries (cKdV)-type equation for the amplitudes of
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Jung, Kyung Tae. "On three-dimensional hydrodynamic numerical modelling of wind induced flows in stably stratified waters : a Galerkin-finite difference approach." Title page, contents and summary only, 1989. http://web4.library.adelaide.edu.au/theses/09PH/09phj95.pdf.

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Eaves, Thomas Scott. "Generalised nonlinear stability of stratified shear flows : adjoint-based optimisation, Koopman modes, and reduced models." Thesis, University of Cambridge, 2016. https://www.repository.cam.ac.uk/handle/1810/260824.

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In this thesis I investigate a number of problems in the nonlinear stability of density stratified plane Couette flow. I begin by describing the history of transient growth phenomena, and in particular the recent application of adjoint based optimisation to find nonlinear optimal perturbations and associated minimal seeds for turbulence, the smallest amplitude perturbations that are able to trigger transition to turbulence. I extend the work of Rabin et al. (2012) in unstratified plane Couette flow to find minimal seeds in both vertically and horizontally sheared stratified plane Couette flow.
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Ben, Cheikh Samir. "Etude numerique comparative des solutions exactes et approchees de la convection naturelle instationnaire en milieu confine stratifie." Poitiers, 1987. http://www.theses.fr/1987POIT2257.

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Darbyshire, Oliver Richard. "Modelling of turbulent stratified flames." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/247473.

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Due to concerns about pollutant emission combustion systems are increasingly being designed to operate in a lean premixed mode. However, the reduction in emissions offered by lean premixed combustion can be offset by its susceptibility to instabilities and ignition and extinction problems. These instabilities, caused by the coupling of unsteady heat release and pressure fluctuations can cause significant damage to combustion devices. One method of avoiding these problems whilst still operating a globally lean system is to employ a stratified premixed mode where areas of richer mixture are used
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Books on the topic "Stratified flow – Mathematical models"

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Koba, Hajime. Nonlinear stability of Ekman boundary layers in rotation stratified fluids. Providence, Rhode Island: American Mathematical Society, 2013.

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2

P, Castro I., Rockliff N. J, and Institute of Mathematics and Its Applications., eds. Stably stratified flows: Flow and dispersion over topography : based on the proceedings of the Fourth Conference on Stably Stratified Flows, organized by the Institute of Mathematics and Its Applications and held at the University of Surrey in September, 1992. Oxford: Clarendon Press, 1994.

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Mazzaferro, David L. Estimation of the recharge area of a pumped, stratified-drift aquifer in Connecticut by simulation modeling. Hartford, Conn: Dept. of the Interior, U.S. Geological Survey, 1989.

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Mazzaferro, David L. Estimation of the recharge area of a pumped, stratified-drift aquifer in Connecticut by simulation modeling. Hartford, Conn: Dept. of the Interior, U.S. Geological Survey, 1989.

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Mazzaferro, David L. Estimation of the recharge area of a pumped, stratified-drift aquifer in Connecticut by simulation modeling. Hartford, Conn: Dept. of the Interior, U.S. Geological Survey, 1989.

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Introduction to PDEs and waves for the atmosphere and ocean. New York: Courant Institute of Mathematical Sciences, 2003.

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Miyazaki, Takeshi. Vortices, waves and turbulence in a rotating stratified fluid. Tsukuba, Ibaraki, Japan: Center for Global Environmental Research, National Institute for Environmental Studies, Japan, 2004.

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Kulkarni, A. K. Vertical wall fire in a stratified atmosphere. University Park, PA: Pennsylvania State University, Department of Mechanical Engineering, 1987.

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Multicomponent flow modeling. Boston: Birkhäuser, 1999.

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As, S. C. van. Traffic flow theory. 3rd ed. [Pretoria]: SARB Chair in Transportation Engineering, Dept. of Civil Engineering, University of Pretoria, 1990.

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Book chapters on the topic "Stratified flow – Mathematical models"

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Centeno-Reyes, C., and O. Cazarez-Candia. "Mathematical Model for “Bubble Gas-Stratified Oil” Flow in Horizontal Pipes." In Fluid Dynamics in Physics, Engineering and Environmental Applications, 209–16. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-27723-8_14.

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Centeno-Reyes, C., and O. Cazarez-Candia. "Mathematical Model for Heavy Oil–Water–Gas Stratified Flow in Horizontal Pipes." In Experimental and Theoretical Advances in Fluid Dynamics, 277–86. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-17958-7_22.

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Elefteriadou, Lily. "Mathematical and Empirical Models." In An Introduction to Traffic Flow Theory, 129–35. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8435-6_6.

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Kovarik, Karel. "Mathematical Models of Groundwater Flow." In Numerical Models in Groundwater Pollution, 61–108. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-56982-1_5.

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Communar, G. "Mathematical Models of Contaminant Transport in Stratified Media." In Advances in Groundwater Pollution Control and Remediation, 233–47. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-009-0205-3_12.

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Bedrikovetsky, Pavel, and Gren Rowan. "Analytical Models of Water-Flooding of Stratified Reservoirs." In Mathematical Theory of Oil and Gas Recovery, 40–59. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-2205-6_3.

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de Andrés, Belen, Ana R. Sánchez-Archidona, Isabel Cortegano, Natalia Serrano, Sharmili Jagtap, María-Luisa Gaspar, and Miguel-Angel Rodríguez Marcos. "B Cell Strategies of Ag Recognition in a Stratified Immune System." In Mathematical Models and Immune Cell Biology, 259–74. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-7725-0_13.

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Kaltenbacher, Manfred, and Stefan Schoder. "Physical Models for Flow: Acoustic Interaction." In Advances in Mathematical Fluid Mechanics, 265–353. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-67845-6_6.

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Szymkiewicz, Adam. "Mathematical Models of Flow in Porous Media." In GeoPlanet: Earth and Planetary Sciences, 9–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-23559-7_2.

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Kłos, Andrzej. "Current-Based Method of Load Flow Solution." In Mathematical Models of Electrical Network Systems, 97–105. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-52178-7_15.

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Conference papers on the topic "Stratified flow – Mathematical models"

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Calay, Rajnish K., and Ahmad Awad. "A Model to Predict Stratification in Two Phase Flow in Horizontal Pipes." In ASME/JSME 2004 Pressure Vessels and Piping Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/pvp2004-2848.

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Stratified flow is encountered in many situations. The flow of hydrocarbons transported in horizontal pipes often gets stratified. The prediction of pressure drop and liquid hold-up is essential for reservoir and pipe management and optimizing the cost of transportation of constituents. The present paper presents a simple mathematical model to predict the pressure drop, water and oil hold up and stratified layer. A good agreement with the experimental data was found. The model will be further developed and incorporated within a numerical model in order to investigate the flow field characteris
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Vaidheeswaran, Avinash, William D. Fullmer, Krishna Chetty, Raul G. Marino, and Martin Lopez de Bertodano. "Stability Analysis of Chaotic Wavy Stratified Fluid-Fluid Flow With the 1D Fixed-Flux Two-Fluid Model." In ASME 2016 Fluids Engineering Division Summer Meeting collocated with the ASME 2016 Heat Transfer Summer Conference and the ASME 2016 14th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/fedsm2016-1058.

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The one-dimensional fixed-flux two-fluid model (TFM) is used to analyze the stability of the wavy interface in a slightly inclined pipe geometry. The model is reduced from the complete 1-D TFM, assuming a constant total volumetric flux, which resembles the equations of shallow water theory (SWT). From the point of view of two-phase flow physics, the Kelvin-Helmholtz instability, resulting from the relative motion between the phases, is still preserved after the simplification. Hence, the numerical fixed-flux TFM proves to be an effective tool to analyze local features of two-phase flow, in par
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Sondermann, Carina N., Rodrigo A. C. Patricio, Aline B. Figueiredo, Renan M. Baptista, Felipe B. F. Rachid, and Gustavo C. R. Bodstein. "Numerical Simulation of Non-Isothermal Two-Phase Flow in a Pipeline Using the Flux-Corrected Transport Method." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-66827.

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Two phase flows occur in many engineering problems, especially in the nuclear, gas and petroleum industries. In oil and gas applications, specifically, a mixture of oil and natural gas is transported in pipelines from offshore platforms to the continent. The prediction of how the flow behaves in time as it moves along the pipe is extremely important, mainly during the pipeline design stage or regular operation. This paper presents simulations for stratified gas-liquid two-phase flow in a horizontal pipeline that is subject to the temperature gradients that exist in the bottom of the ocean, and
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de Freitas, Raphael V. N., Carina N. Sondermann, Rodrigo A. C. Patricio, Aline B. Figueiredo, Gustavo C. R. Bodstein, Felipe B. F. Rachid, and Renan M. Baptista. "Numerical Study of Two-Phase Flow in a Horizontal Pipeline Using an Unconditionally Hyperbolic Two-Fluid Model." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-87571.

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Numerical simulation is a very useful tool for the prediction of physical quantities in two-phase flows. One important application is the study of oil-gas flows in pipelines, which is necessary for the proper selection of the equipment connected to the line during the pipeline design stage and also during the pipeline operation stage. The understanding of the phenomena present in this type of flow is more crucial under the occurrence of undesired effects in the duct, such as hydrate formation, fluid leakage, PIG passage, and valve shutdown. An efficient manner to model two-phase flows in long
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Rahman, Aowabin, Nelson Fumo, and Amanda D. Smith. "Simplified Modeling of Thermal Storage Tank for Distributed Energy Heat Recovery Applications." In ASME 2015 9th International Conference on Energy Sustainability collocated with the ASME 2015 Power Conference, the ASME 2015 13th International Conference on Fuel Cell Science, Engineering and Technology, and the ASME 2015 Nuclear Forum. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/es2015-49170.

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A simplified mathematical model was developed to analyze a storage tank containing a stationary fluid with hot and cold heat exchanger coils. The model is to be used as a screening tool for determining tank size and configurations for operation with a given power generation unit in a combined cooling, heating and power (CCHP) system. As such, the model was formulated so that it requires minimal information about the thermo-physical properties of the fluids and design parameters in order to determine the temperature profiles of the stored fluid and the heat transfer fluid for turbulent flow ins
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Abegunde, Mobolaji, Tobinson Briggs, Fidelis Abam, and Tayo Awolola. "Evaluation of Interfacial Friction Models in Stratified Flow: Gas-Liquid Two-Phase Flow." In SPE Nigeria Annual International Conference and Exhibition. Society of Petroleum Engineers, 2019. http://dx.doi.org/10.2118/198840-ms.

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Chen, Yuanyuan, Jing Gong, Xiaoping Li, Nan Zhang, Shaojun He, Jianfeng Liu, Yuwei Liu, and Jiawen Wu. "Simulation of Liquid-Gas Replacement in Commissioning Process for Large-Slope Crude Oil Pipeline." In 2012 9th International Pipeline Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/ipc2012-90349.

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Pipeline commissioning, which is a key link from engineering construction to production operation, is aim to fill an empty pipe by injecting water or oil to push air out of it. For a large-slope crude oil pipeline with great elevation differences, air is fairly easy to entrap at downward inclined parts. The entrapped air, which is also called air pocket, will cause considerable damage on pumps and pipes. The presence of it may also bring difficulties in tracking the location of the liquid head or the interface between oil and water. It is the accumulated air that needed to be exhausted in time
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Ishak, Anuar, Roslinda Nazar, and Ioan Pop. "Mixed convection boundary layer flow over a stretching vertical sheet in a thermally stratified fluid." In PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4882523.

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Bonilla, Javier, Luis Jose Yebra, Eduardo Zarza, and Sebastian Dormido. "Chattering in dynamic mathematical two-phase flow models." In 2009 European Control Conference (ECC). IEEE, 2009. http://dx.doi.org/10.23919/ecc.2009.7075015.

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Lopez de Bertodano, Martin A., and William D. Fullmer. "Two Equation Two-Fluid Model Analysis for Stratified Flow Under Kinematic and Dynamic Instabilities." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-66743.

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The unstable one-dimensional incompressible two-fluid model including a hydrostatic force is reduced to a two equation model in terms of the liquid volume fraction and the liquid velocity. For small density ratios the model may be simplified to a formulation that is equivalent tothe Shallow Water Theory (SWT) equations [Whitham, 1975] with a source term corresponding to the two-fluid model constitutive relations for wall and interfacial shear and to a void gradient term that contains the Kelvin-Helmholtz mechanism. Linear stability of the SWT equations shows that the model is made well-posed s
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