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'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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

1

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 tracking by the VOF (Volume of Fluid) method. The graphical dependencies illustrating the change in the interfase boundaries of liquids and the averaged over the occupied area of the phase velocities along the flat channel are presented. The results of comparative calculations for two-fluid models are also given, according to the developed model in the hydraulic approximation and direct modeling. It is shown that the calculations in accordance with the hydraulic approximation are more consistent with the simulation results. Thus, the model of hydraulic approximation is the most preferred method for calculating stratified flows, especially in cases of variable volumetric content of liquids.
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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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3

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 involved to simulate oil–water stratified smooth flow according to the finite volume method. The pressure gradient and oil–water interface height can be computed according to the given volume flow rate using the iteration method. The predicted result of oil–water interface height and velocity profile by the model fit well with several published experimental data, except that there is a large error in pressure gradient. The SST k−ω turbulence model appears higher accuracy for simulating oil–water two-phase stratified flow in a horizontal pipe.
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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 fluid parcels in the direction of wave motion and causes gravity waves to disperse. As water depth decreases due to varied bottom topography, the wave amplitude were shown to increase while the wavelength and wave speed decreases resulting in overturning of the wave. The results are presented graphically.
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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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6

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 the approach. Three models of the carbon dynamics in redox-stratified environments are compared: porous media flow problems in a coastal sediment and in a contaminated groundwater system; and a surface flow problem in a eutrophic estuary. Considering the interdisciplinary nature of such models, a Knowledge Base System for biogeochemical processes is proposed. Incorporation of the proposed knowledge base in an appropriate modeling framework, such as the Biogeochemical Reaction Network Simulator, proves an effective approach to the modeling of complex natural systems. This methodology allows for construction of multi-component reactive-transport models applicable to a wide range of problems of interest to the geoscientist.
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7

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 identify the different steady-state flow patterns and bifurcations. The effect of the governing parameters on the domain of existence of the three-dimensional flow patterns is studied for opposing flows (N < 0). Comprehensive Nusselt and Sherwood number data are presented as functions of the governing parameters. The present results indicate that the double-diffusive flow in enclosures with opposing buoyancy forces is strictly three-dimensional for a certain range of parameters. At high Lewis numbers multiple dipole vortices form in the transverse planes near the horizontal top and bottom surfaces, which the two-dimensional models fail to detect. The dipolar vortex structures obtained are similar to those created in laboratory experiments by the injection of fluid into a stratified medium.
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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 position and time of initial release for all individuals that are subsequently collected. In this paper, we develop and validate a new mathematical model for parasitoid wasp dispersal from point release, as in the case of biocontrol. The model is derived from underlying stochastic processes but is fully deterministic and admits an analytical solution. Using a Bayesian framework, we then fit the model to an Australian dataset describing the multi-scale wind-borne dispersal pattern of Eretmocerus hayati Zolnerowich & Rose (Hymenoptera: Aphelinidae). Our results confirm that both local movements and long-distance wind dispersal are significant to the movement of parasitoids. The model results also suggest that low velocity winds are the primary indicator of dispersal direction on the field scale shortly after release, and that average wind data may be insufficient to resolve long-distance movement given inherent nonlinearities and heterogeneities in atmospheric flows. The results highlight the importance of collecting wind data when developing models to predict the spread of parasitoids and other tiny organisms.
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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 homogeneous and isotropic domains. The present work made an attempt to improve the reality of the SA solution obtained for dispersive HP by considering anisotropic and stratified heterogeneous coastal aquifers. The solution is obtained by defining Fourier series for both stream function and salt concentration, applying a Galerkin treatment using the Fourier modes as trial functions and solving the flow and the salt transport equations simultaneously in the spectral space. In order to include stratified heterogeneity, a special depth-hydraulic conductivity model is applied that can be solved analytically without significant mathematical complexity. Several examples are proposed and studied. The results show excellent agreement between the SA and numerical solutions obtained with an in-house advanced finite element code.
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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 ecological response of the lake. This dissertation is focused on the physics of deep vertical mixing that occurs beneath the well-mixed surface layer in stratified lakes and reservoirs. The overall aim is to improve the ability of numerical models to reproduce deep vertical mixing, thus providing better tools for water quality prediction and management. In the first part of this research the framework of a one-dimensional mixed-layer hydrodynamic model was used to construct a pseudo two-dimensional model that computes vertical fluxes generated by deep mixing processes. The parameterisations developed for the model were based on the relationship found between lake-wide vertical buoyancy flux and the first-order internal wave response of the lake to surface wind forcing. The ability of the model to reproduce the observed thermal structure in a range of lakes and reservoirs was greatly improved by incorporating an explicit turbulent benthic boundary layer routine. Although laterally-integrated models reproduce the net effect of turbulent mixing in a vertical sense, they fail to resolve the transient distribution of turbulent mixing events triggered by local flow properties defined at far smaller scales. Importantly, the distribution of events may promote tertiary motions and ecological niches. In the second part of the study a large body of microstructure data collected in Lake Kinneret, Israel, was used to show that the nature of turbulent mixing events varied considerably between the epilimnion, metalimnion, hypolimnion and benthic boundary layer, yet the turbulent scales of the events and the buoyancy flux they produced collapsed into functions of the local gradient Richardson number. It was found that the most intense events in the metalimnion were triggered by high-frequency waves generated near the surface that grew and imparted a strain on the metalimnion density field, which led to secondary instabilities with low gradient Richardson numbers. The microstructure observations suggest that the local gradient Richardson number could be used to parameterise vertical mixing in coarse-grid numerical models of lakes and reservoirs. However, any effort to incorporate such parameterisations becomes meaningless without measures to reduce numerical diffusion, which often dominates over parameterised physical mixing. As a third part of the research, an explicit filtering tool was developed to negate numerical diffusion in a threedimensional hydrodynamic model. The adaptive filter ensured that temperature gradients in the metalimnion remained within bounds of the measured values and so the computation preserved the spectrum of internal wave motions that trigger diapycnal mixing events in the deeper reaches of a lake. The results showed that the ratio of physical to numerical diffusion is dictated by the character of the dominant internal wave motions.
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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 boundary geometry. For this thesis, five numerical experiments were conducted for the problem of a two-dimensional, viscous, incompressible, slightly-stratified flow towards a sink in a triangular reservoir.
Science, Faculty of
Mathematics, Department of
Graduate
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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 quality. The objective of this research was to investigate the physical processes responsible for the exchange of water and particles between the lake boundaries and the lake interior. An integrated approach using field experiments and 3D modelling as applied to Lake Kinneret (Israel) is presented. The field data revealed large-scale metalimnion oscillations with amplitudes up to 10 m in response to westerly diurnal winds, the existence of a well-defined suspended particle intrusion into the metalimnion of the lake, characterized by high concentrations of organic matter, and a well-mixed benthic boundary layer (BBL). The changes in the thermal structure explained the observed vertical and horizontal movements of the suspended particle intrusion. The horizontal advective transport via the metalimnion, associated with the velocities induced by the basin-scale mode-two Poincare wave, controlled the exchange between the lake boundaries and lake interior on daily time scales. The observed BBL over the lake slope varied markedly with time and space. Detailed comparison of simulation results with field data revealed that the model captured the lake hydrodynamics for time scales from hours to days. The model could then be used to extract the residual motions in the various regions of the lake. The residual motions below the surface layer were predominantly forced by the basin-scale internal wave motions, but the residual motion in the surface layer was found to be very sensitive to the curl of the wind field. The residual circulation was responsible for redistributing mass throughout the lake basin on time scales from days to weeks. A clear connection of dynamics of the BBL with the large-scale features of the flow was addressed. The time history of the mixing in the BBL and the resulting cross-shore flux was shown to vary with the phase of the basin-scale internal waves.
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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 width and depth. Provisions for surface wind stress and a flux of fresh water are also included, although neither was utilized in this study. An explicit finite difference scheme centred in both time and space was used to solve for the horizontal and vertical velocity components, salinity, and surface elevation on a staggered rectangular grid. A backward Euler scheme was used to suppress the computational mode. Tests using a semi-implicit scheme to solve the finite difference equations over realistic topography led to numerical instabilities at modest values of the time step - in spite of the unconditional stability criteria - suggesting that linear stability analysis may give misleading results for strongly nonlinear systems. Surface elevations calculated from tidal harmonic analysis and salinity timeseries derived from linearly interpolated CTD casts were prescribed at the open boundary. Initial and boundary conditions based on observations in Burrard Inlet and Indian Arm during the winter of 1974-75 were used to study the inlet's response to tidal forcing and to simulate the deep-water renewal that occurred during this period. Coefficients for the horizontal turbulent diffusion of momentum and salt were set equal to 10⁶ cm² s⁻¹. Reducing this value by a factor of two was found to have little impact on the solution. A further reduction to 10³ cm² s⁻¹ led to numerical instabilities under conditions of dense water inflow. The side friction term in the momentum balance was tuned to match calculated and observed dissipation rates in Burrard Inlet; leading to good agreement between the observed and calculated barotropic tide. Contour plots of tidal amplitudes and phases for model currents and salinities revealed a standing wave pattern for the K₁ and M₂ internal tides in Indian Arm; thus allowing for the possibility of resonance. A comparison of model results with vertical amplitude and phase profiles from harmonic analysis of Cyclesonde current meter timeseries at two locations in Indian Arm was consistent with this result. A least-squares fit was made of the vertical modal structure in the model to the complex tidal amplitudes. This led to calculations of the kinetic energy contained in each of the modes along the model inlet for the M₂ and K₁ constituents. Most of the energy was found to be contained in the barotropic and first baroclinic modes, with the latter dominating in the deep basin, and the former dominating near the sill. Second mode energy was significant for the K₁ constituent at some locations in Indian Arm. There are clear indications in the model of barotropic tidal energy being radiated into the inlet basin via the internal tide. Simulations of the influx of dense water into Indian Arm yielded exchange rates that are consistent with observed values and suggest the possibility of fine-tuning the model coefficients to allow prediction of future overturning events.
Science, Faculty of
Earth, Ocean and Atmospheric Sciences, Department of
Graduate
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5

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, and used for a theoretical study. The real lake applications showed that winds excited basin-scale motions that had a surface layer velocity structure similar to the wind stress pattern. Three-dimensional hydrodynamics simulations of Lake Biwa indicated that most of the energy input from winds was partitioned into the internal waves that decayed within a few days. The gyres, on the other hand, received much less energy but dominated the dynamics during calm periods due to their slow damping. Analyses of field data from Lake Kinneret suggested that the internal waves, excited by the strong winds every afternoon, were damped over a few days primarily due to bottom friction. Theoretical investigations of damping mechanisms of internal waves revealed that bottom friction induced a velocity anomaly at the top of the boundary layer that drained energy from the nearly inviscid interior by a combination of internal wave cancelling and spin-down. These results indicate that gyres induce long-term horizontal transport near the surface and internal waves transfer energy from winds to near-bottom mixing. Modal structure of dominant basin-scale internal waves can induce large heterogeneity of nearbottom mass transfer processes. The method presented here provides a tool to determine how basin-scale motions impact on biogeochemical processes in stratified lakes.
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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 the waves. The general theory is applied to the case of the waves in a two-layer fluid with a piecewise-constant shear flow, with an emphasis on the effect of the shear flow on the geometry of the wavefronts. The distortion of the wavefronts is described by the singular solution (envelope of the general solution) of the nonlinear first order differential equation, constituting generalisation of the dispersion relation in this curvilinear geometry. There exists a striking difference in the shape of the wavefronts: the wavefront of the surface wave is elongated in the shear flow direction while the wavefront of the interfacial wave is squeezed in this direction. We solve the derived 2+1-dimensional cKdV-type equation numerically using a finite-difference scheme. The effects of nonlinearity and dispersion are studied by considering numerical results for surface and interfacial ring waves generated from a localised source with and without shear flow and the 2D dam break problem. In these examples, the linear and nonlinear surface waves are faster than interfacial waves, the wave height decreases faster at the surface, the shear flow leads to the wave height decreasing slower downstream and faster upstream, and the effect becomes more prominent as the shear flow strengthens.
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7

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. I find that the coherent states visited by such minimal seed trajectories are significantly altered by the stratification, and so proceed to investigate these states both with generalised Koopman mode analysis and by stratifying the self-sustaining process described by Waleffe (1997). I conclude with an introductory problem I considered that investigates the linear Taylor instability of layered stratified plane Couette flow, and show that the nonlinear evolution of the primary Taylor instability is not coupled to the form of the linearly unstable mode, in contrast to the Kelvin-Helmholtz instability, for example. I also include an appendix in which I describe joint work conducted with Professor Neil Balmforth of UBC during the 2015 WHOI Geophysical Fluid Dynamics summer programme, investigating stochastic homoclinic bifurcations.
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9

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 to enhance the stability of the flame. In this thesis a computational modelling methodology for the simulation of stratified premixed flames is developed. Firstly, several sub-models for the dissipation rate of a reacting scalar are evaluated by the simulation of two laboratory scale flames, a turbulent stratified V-flame and a dump combustor fed by two streams of different mixture strength. This work highlights the importance of this quantity and its influence on the simulation results. Any model for stratified combustion requires at least two variables to describe the thermochemical state of the gas: one to represent the mixing field and another to capture the progress of reaction. In turbulent stratified flames the joint probability density function (pdf) of these variables can be used to recover the mean reaction rates. A new formulation for this pdf based on copula methods is presented and evaluated alongside two alternative forms. The new method gives improved results in the simulation of the two test cases above. As it is likely that practical stratified combustion devices will have some unsteadiness to the flow the final part of this work applies the modelling methodology to an unsteady test case. The influence of the unsteady velocity forcing on the pollutant emissions is investigated. Finally the methodology is used to simulate a developmental, liquid fuelled, lean burn aero-engine combustor. Here the model gives reasonable predictions of the measured pollutant emissions for a relatively small computational cost. As such it is hoped that the modelling methodology presented can be useful in the iterative industrial design process of stratified combustion systems.
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Books on the topic "Stratified flow – Mathematical models"

1

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

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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 characteristics and establish correlations for a wide range of parameters.
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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 particular the chaotic behavior of the interface. Experiments on smooth- and wavy-stratified flows with water and gasoline were performed to understand the interface dynamics. The mathematical behavior concerning the well-posedness and stability of the fixed-flux TFM is first addressed using linear stability theory. The findings from the linear stability analysis are also important in developing the eigenvalue based donoring flux-limiter scheme used in the numerical simulations. The stability analysis is extended past the linear theory using nonlinear simulations to estimate the Largest Lyapunov Exponent which confirms the non-linear boundedness of the fixed-flux TFM. Furthermore, the numerical model is shown to be convergent using the power spectra in Fourier space. The nonlinear results are validated with the experimental data. The chaotic behavior of the interface from the numerical predictions is similar to the results from the experiments.
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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 the resulting heat transfer process that may lead to wax formation and deposition. A one-dimensional two-fluid mathematical model was employed that includes conservation equations of mass and momentum for each fluid and one energy equation for the mixture of liquid and gas. The problem was formulated as an initial-boundary value problem of the hyperbolic type and it was solved using the Flux Corrected Transport (FCT) numerical method, which is second-order accurate in space, coupled with an explicit discretization in time that is first-order accurate. The FCT method is appropriate to solve problems characterized by hyperbolic equations that may contain discontinuities and shock waves, and it presents small dispersive effects. The results showed excellent accuracy results when compared to commercial software widely used in the oil and gas industry.
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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 pipelines regarding a compromise between numerical accuracy and cost is the use of a one-dimensional two-fluid model, discretized with an appropriate numerical method. A two-fluid model consists of a system of non-linear partial differential equations that represent the mass, momentum and energy conservation principles, written for each phase. Depending on the two-fluid model employed, the system of equations may lose hyperbolicity and render the initial-boundary-value problem illposed. This paper uses an unconditionally hyperbolic two-fluid model for solving two-phase flows in pipelines in order to guarantee that the solution presents physical consistency. The mathematical model here referred to as the 5E2P (five equations and two pressures) comprises two equations of continuity and two momentum conservation equations, one for each phase, and one equation for the transport of the volume fraction. A priori this model considers two distinct pressures, one for each phase, and correlates them through a pressure relaxation procedure. This paper presents simulation cases for stratified two-phase flows in horizontal pipelines solved with the 5E2P coupled with the flux corrected transport method. The objective is to evaluate the numerical model capacity to adequately describe the velocities, pressures and volume fraction distributions along the duct.
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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 inside the heat exchangers. The presented model is implemented computationally with varying number of nodes, before comparing it with a more detailed model that take into account the variation of thermo-physical properties, as well as the effects of thermal de-stratification and heat loss to the ambient. The simplified model provided accurate temperature predictions that could subsequently be used to design a stratified tank system for a given CCHP application.
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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 during commissioning. This paper focuses on the simulation of liquid-gas replacement in commissioning process that only liquid flow rate exists while gas stays stagnant in the pipe and is demanded to be replaced by liquid. Few previous researches have been found yet in this area. Consequently, the flow in a V-section pipeline consisted of a downhill segment and a subsequent uphill one is used here for studying both the formation and exhaustion behaviors of the intake air. The existing two-fluid model and simplified non-pressure wave model for gas-liquid stratified flow are applied to performance the gas formation and accumulation. The exhausting process is deemed to be a period in which the elongated bubble (Taylor bubble) is fragmented into dispersed small bubbles. A mathematical model to account for gas entrainment into liquid slug is proposed, implemented and incorporated in a computational procedure. By taking into account the comprehensive effects of liquid flow rate, fluid properties, surface tension, and inclination angle, the characteristics of the air section such as the length, pressure and mass can be calculated accurately. The model was found to show satisfactory predictions when tested in a pipeline. The simulation studies can provide theoretical support and guidance for field engineering application, which are meanwhile capable of helping detect changes in parameters of gas section. Thus corresponding control measures can be adopted timely and appropriately in commissioning process.
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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 stable by the hydrostatic force. However, unlike the SWT equations, the two equation two-fluid model is only conditionally stable. As the gas velocity increases the model becomes unstable once the kinematic instability occurs, i.e., the Viscous Kelvin-Helmholtz (VKH) instability. When the gas velocity is increased further the model becomes dynamically unstable, i.e., it reaches the Inviscid Kelvin-Helmholtz (IKH) instability limit. Beyond the IKH limit the model becomes ill-posed and requires higher order modelling, e.g. surface tension. Simple analytic expressions for the two instabilities are obtained because of the simplified mathematics of the two equation model. Furthermore, the wave “sheltering” effect, which allows more accurate predictions of the flow regime transition, may be easily incorporated into the analysis. The theory is validated with the new HAWAC flow regime map [Vallee et al., 2010]. The two equation two-fluid model is consistent with all previous results of two-fluid model linear stability for stratified flow and, since it is a special case of SWT, it is amenable to non-linear stability analysis and a very broad body of mathematics literature on non-linear kinematic waves, e.g., Whitham (1974) is now directly applicable when the model is not IKH unstable.
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