Relevant bibliographies by topics / Mixing – 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 'Mixing – Mathematical models'

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Published: 4 June 2021
Last updated: 6 February 2022

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Journal articles on the topic "Mixing – Mathematical models"

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Cutler, Alan H. "Mathematical models of temporal mixing in the fossil record." Short Courses in Paleontology 6 (1993): 169–87. http://dx.doi.org/10.1017/s2475263000001100.

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In December 1969 officials from the U.S. Selective Service System conducted a draft lottery to establish the order in which nineteen-year-old men were to be called for military service. Three hundred sixty-six capsules, one for each possible birthday, were placed in a large wooden box. As the capsules for each month were added to the box, the contents of the box were mixed. Once all 366 capsules were in the box, it was shaken several times and emptied into a deep bowl. Capsules were then drawn from the bowl to determine the draft number corresponding to each date. Observers were satisfied that the capsules had been thoroughly mixed, but, as it turned out, the results were anything but random. The Spearman rank correlation between birth date and draft number was significant at the.001 level – men with December birthdays had a significantly higher probability of being called than did those with January birthdays (Fienberg, 1971).
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Moser, A., B. Mayr, W. Jury, W. Steiner, and P. Horvat. "Mathematical models for mixing in deep jet bioreactors: analysis." Bioprocess Engineering 7, no. 4 (December 1991): 171–76. http://dx.doi.org/10.1007/bf00387413.

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Ganser, G. H., I. Christie, and M. A. McCawley. "Two Mathematical Models for Predicting Dispersion of Particles in the Human Lung." Journal of Biomechanical Engineering 129, no. 1 (June 30, 2006): 51–57. http://dx.doi.org/10.1115/1.2401183.

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The dispersion of particles in the human lung is modeled as a series of virtual mixing tanks. Using the experimental results of Scherer et al. (1975, J. Appl. Physiol., 38(4), pp. 719–723) for a five-generation glass lung model, it is shown that each generation of the glass lung behaves like an independent virtual mixing tank. The corresponding resident time distribution is shown to have a variance approximately equal to the square of the average time a particle spends in the generation. By assuming that each generation of the human lung behaves as an independent virtual mixing tank, the realistic lung data provided by Weibel (1963, Morphometry of the Human Lung, Spinger-Verlag, New York) are used to validate this assumption in two ways. First, the half-width of the exhaled particle concentration profile is obtained. Second, a system of differential equations, with the concentration of particles in each mixing tank as its solution, is derived and solved numerically. This gives the exhaled concentration profile. Both techniques yield similar results to each other, and both give excellent agreement with the experimental data. The virtual mixing tank approach allows the complex mixing that occurs in the branching pathways of the lung to be more simply modeled. The model, thereby derived, is simple to change and could lead to enhancements in the understanding of the underlying processes contributing to the ventilation of the lung in health and disease.
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Romanko, D. A., and V. M. Fomichev. "On mathematical models of key mixing for iterative block encryption algorithms." Prikladnaya diskretnaya matematika. Prilozhenie, no. 10 (September 1, 2017): 93–96. http://dx.doi.org/10.17223/2226308x/10/38.

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Moser, A., B. Mayr, W. Jury, W. Steiner, and P. Horvat. "Mathematical models for mixing in deep-jet bioreactors: Calculation of parameters." Bioprocess Engineering 7, no. 4 (December 1991): 177–82. http://dx.doi.org/10.1007/bf00387414.

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Sterpu, Ancaelena Eliza, Nicoleta Teodorescu, Iuliana Marlena Prodea, Eugeniu Popescu, and Irina Nita. "MATHEMATICAL MODELS FOR POWER CONSUMPTION AT THE MIXING OF SOME LUBRICATING GREASES." Environmental Engineering and Management Journal 9, no. 8 (2010): 1063–68. http://dx.doi.org/10.30638/eemj.2010.139.

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Ma, Lian Xiang, Rong Shan Bi, Xin Shun Tan, Zhen Dong Liu, Wen Wu Chen, and Shi Qing Zheng. "Turbulent Mixing and Scale-Up of Ejectors at High Schmidt Number." Advanced Materials Research 233-235 (May 2011): 1340–44. http://dx.doi.org/10.4028/www.scientific.net/amr.233-235.1340.

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Micro- and Macro-mixing models were built and numerical investigation of turbulent mixing in ejectors was carried out. Mixture fraction and its variance presented by Fox were remodeled to demonstrate micro- and macro-mixing performance. The length needed to reach 98% micro- and macro-mixing were founded is functions of uj/umand D/d. The mathematical scale-up models were presented based on the simulation results using least square method for micro- and macro-mixing and five different cases were used to validate the models. The results showed that macro-mixing scale-up model agreed well with CFD simulations but the micro-mixing scale-up model had a less precision compared with that of macro-mixing model. This because that the mechanism of micro-mixing process is very complexity but the CFD models we used in this work are fairy simple.
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Jelenčiaková, Nina, Bojan Petrović, Sanja Kojić, Jovana Jevremov, and Stevan Hinić. "Application of Mathematical Models and Microfluidics in the Analysis of Saliva Mixing with Antiseptic Solutions." Balkan Journal of Dental Medicine 24, no. 2 (July 1, 2020): 84–90. http://dx.doi.org/10.2478/bjdm-2020-0014.

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SummaryBackground/Aim: Human saliva offers many advantages over blood-based biochemical assays, therefore, becomes the biological fluid of interest. Once antiseptic solutions react with saliva, both fluids undergo significant changes of their biophysical properties, consequently, those changes have an impact on their principal function.Material and Methods: In this study, saliva was collected and mixed with 0,1% chlorhexidine digluconate solution, fluoride mouthwash, zinc-hydroxyapatite solution and CPP-ACP paste. Microfluidic PVC/Green tape chips within the experimental setup were used to simulate solution mixing. The chip had 2 inlets and 1 outlet, and channel was designed in Y shape without any obstacles. The inlet channels were set at a 60° angle. The channel width was 600 µm and the diameter of inlets and outlet was 2 mm. For better visualization, blue food coloring was added to the saliva. The procedure was recorded with digital USB microscope camera and afterwards the percentage of mixing was obtained by MATLAB programming language.Results: Obtained results show incomplete mixing of all the solutions with saliva. The value of mixed liquid, when mixing 0,1% chlorhexidine digluconate solution with saliva was 51,11%. In case of medium concentration fluoride mouthwash, result was 84,37%. Zinc hydroxyapatite solution obtained result of 85,24%, and the fourth tested solution, CPP-ACP paste, 83,89%.Conclusions: Analyzed mouthwashes exhibit specific, non uniform behavior during mixing with saliva. Microfluidic setups could be efficiently used in simulating real clinical conditions in laboratory settings. Image processing mathematical models are applicable, accurate and useful in determination of the interaction of saliva with commonly used antiseptic solutions.
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Khvostov, Anatoly, Anatoly Khvostov, Viktor Ryazhskikh, Viktor Ryazhskikh, Gazibeg Magomedov, Gazibeg Magomedov, Aleksey Zhuravlev, and Aleksey Zhuravlev. "Matrix dynamic models of elements of technological systems with perfect mixing and plug-flow hydrodynamics in Simulink." Foods and Raw Materials 6, no. 2 (December 20, 2018): 483–92. http://dx.doi.org/10.21603/2308-4057-2018-2-483-492.

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The dynamic models of elements of technological systems with perfect mixing and plug-flow hydrodynamics are based on the systems of algebraic and differential equations that describe a change in the basic technological parameters. The main difficulty in using such models in MathWorks Simulink™ computer simulation systems is the representation of ordinary differential equations (ODE) and partial differential equations (PDE) that describe the dynamics of a process as a MathWorks Simulink™ block set. The study was aimed at developing an approach to the synthesis of matrix dynamic models of elements of technological systems with perfect mixing and plug-flow hydrodynamics that allows for transition from PDE to an ODE system on the basis of matrix representation of discretization of coordinate derivatives. A sugar syrup cooler was chosen as an object of modeling. The mathematical model of the cooler is formalized by a set of perfect reactors. The simulation results showed that the mathematical model adequately describes the main regularities of the process, the deviation of the calculated data from the regulations did not exceed 10%. The proposed approach significantly simplifies the study and modernization of the current and the development of new technological equipment, as well as the synthesis of algorithms for controlling the processes therein.
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Bose, S. K., P. Ray, and B. K. Dutta. "Mathematical Models for Mixing and Dispersion in Forecasting and Management of Estuarine Water Quality." Water Science and Technology 19, no. 9 (September 1, 1987): 183–93. http://dx.doi.org/10.2166/wst.1987.0079.

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The dispersion or spread of a dissolved or suspended substance in an estuarine system occurs mainly due to the non-uniformity of velocity distribution, including turbulent fluctuations, shear stress at the boundary and surface stress caused by winds. The mixing and dispersion phenomena in rivers and estuaries are extremely important in water quality management and control. The development of a dispersion model in harmony with the nature of the flow field in a river or estuary is necessary in the estimation and correlation of dispersion parameters, called dispersion coefficients, which may, in general, be anisotropic in a multidimensional transport process. The earlier one-dimensional models have gradually given way to higher dimensional models for better description of the phenomena as well as for more accurate estimation of parameters. Field studies of dispersion of tracers have been the most important method of generating data for parameter estimation. A number of correlations for mixing and dispersion coefficients in terms of flow rates and other fundamental system parameters are available. The present study incorporates the analysis, assessment and applications of various dispersion and mixing models available. Also, a critical appraisal of the validity, inherent degree of uncertainty and the range of applications of different correlations has been incorporated.
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Dissertations / Theses on the topic "Mixing – 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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Lee, Wing-yan, and 李永仁. "Mixing of horizontal sediment laden jets." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B46078022.

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Chan, Shu-ning, and 陳樹寧. "Mixing and deposition of sediment-laden buoyant jets." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hub.hku.hk/bib/B50605720.

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Sediment-laden turbulent buoyant jets are commonly encountered in the natural and man-made environments. Examples of sediment-laden buoyant jets include volcanic eruptions, deep ocean hydrothermal vents (“black smokers”), ocean dumping of dredged spoils and sludge, and submarine discharge of wastewater effluent. It is important to understand the fluid mechanics of sediment jets for environmental impact assessment, and yet there is currently no general model for predicting the mixing of sediment-laden jets. This study reports a theoretical and experimental investigation the sediment mixing, fall-out and deposition from sediment-laden buoyant jets. It is well known that turbulence generates fluctuations to the particle motion, modulating the particle settling velocity. A general three-dimensional (3D) stochastic particle tracking model is developed to predict the particle settling out and deposition from a sediment-laden jet. Particle velocity fluctuations are modelled by a Lagrangian velocity autocorrelation function that accounts for the loitering and trapping of sediment particles in turbulent eddies which results in the reduction of settling velocity. The model is validated against results of independent experimental studies. Consistent with basic experiments using grid-generated turbulence, the model predicts that the apparent settling velocity can be reduced by as much as 30% of the stillwater settling velocity. The mixing and deposition of sediment-laden horizontal momentum jets are studied using laboratory experiments and 3D computational fluid dynamics (CFD) modelling. It is shown that there is a significant settling velocity reduction up to about 25-35%, dependent on jet turbulent fluctuations and particle properties. The CFD approach necessitates an ad hoc adjustment/reduction on settling velocity and lacks generality. Using classical solutions of mean velocity, and turbulent fluctuation and dissipation rate profiles derived from CFD solutions, 3D particle tracking model predictions of sediment deposition and concentration profiles are in excellent agreement with measured data over a wide range of jet flow and particle properties. Unlike CFD calculations, the present method does not require any a priori adjustment of particle settling velocity. A general particle tracking model for predicting sediment fall-out and deposition from an arbitrarily inclined buoyant jets in stagnant ambient is successfully developed. The model incorporates the three flow regimes affecting the sediment dynamics in a buoyant jet, namely turbulent jet flow, jet entrainment-induced external flow and surface spreading current. The jet mean flow velocity is determined using a well-validated jet integral model. The external jet-induced irrotational flow field is computed by a distribution of point sinks along the jet trajectory. The surface spreading current is predicted using an integral model accounting for the interfacial shear. The model is validated against experimental data of sediment deposition from vertical and horizontal sediment-laden buoyant jets.
published_or_final_version
Civil Engineering
Doctoral
Doctor of Philosophy
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Sreedhar, Madhu K. "Large eddy simulation of turbulent vortices and mixing layers." Diss., This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-06062008-163324/.

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Del, Valle Sara Yemimah. "Effects of behavioral changes and mixing patterns in mathematical models for smallpox epidemics." Diss., University of Iowa, 2005. https://ir.uiowa.edu/etd/105.

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In Chapter 1, we study the effects of behavioral changes in a smallpox attack model. Response strategies to a smallpox bioterrorist attack have focused on interventions such as isolation, contact tracing, quarantine, ring vaccination, and mass vaccination. We formulate and analyze a mathematical model in which some individuals lower their daily contact activity rates once an epidemic has been identified in a community. We use computer simulations to analyze the effects of behavior change alone and in combination with other control measures. We demonstrate that the spread of the disease is highly sensitive to how rapidly people reduce their contact activity. In Chapter 2, we study mixing patterns between age groups using social networks. The course of an epidemic through a population is determined by the interactions among individuals. To capture these elements of reality, we use the contact network simulations for the city of Portland, Oregon that were developed as part of the TRANSIMS/EpiSims project to study and identify mixing patterns. We analyze contact patterns between different age groups and identify those groups who are at higher risk of infection. We describe a new method for estimating transmission matrices that describe the mixing and the probability of transmission between the age groups. We use this matrix in a simple differential equation model for the spread of smallpox. Our differential equation model shows that the epidemic size of a smallpox outbreak could be greatly affected by the level of residual immunity in the population. In Chapter 3, we study the effects of mixing patterns in the presence of population heterogeneity. We investigate the impact that different mixing assumptions have on the spread of a disease in an age-structured differential equation model. We use realistic, semi-bias and bias mixing matrices and investigate the impact that these mixing patterns have on epidemic outcomes when compared to random mixing. Furthermore, we investigate the impact of population heterogeneity such as differences in susceptibility and infectivity within the population for a smallpox epidemic outbreak. We find that different mixing assumptions lead to differences in disease prevalence and final epidemic size.
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Zipp, Robert Philip. "Turbulent mixing of unpremixed reactants in stirred tanks." Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184832.

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The turbulent mixing process between two liquid streams in a standard tank stirred by a Rushton turbine has been studied. Experimental measurements of concentration and segregation (fluctuating concentration) have been made for both reacting and non-reacting flows. For the non-reacting case, one stream was marked with a fluorescent dye; the local concentration was measured using a fluorescence technique and a bifurcated fiber optic probe of custom design. Measurements were taken at two axial-radial planes within the tank. In the reacting case, the second-order reaction between sodium hydroxide and hydrochloric acid was studied, and urinine acted as a fluorescent indicator which became non-fluorescent as the reaction proceeded. Numerical studies of the mixing in the laboratory-scale vessel were made. FLUENT, a general-purpose fluid flow modelling program, was used to simulate the flow within the tank. This program uses a k-epsilon closure of the turbulent momentum equations. The program was modified to allow the inclusion of a segregation balance equation. Using this segregation balance technique, the turbulent species balance equations were solved. The results of these simulations agreed with the experimental measurements in all regions except the region near the entrance jets, where the model could not adequately predict the fluid behavior. This study has successfully predicted the behavior of reacting fluids in a bench-scale turbulently mixed stirred tank by the implementation of a segregation balance throughout the entire domain.
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Wells, Judith R. (Judith Roberta). "A laboratory study of localized boundary mixing in a rotating stratified fluid." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/58062.

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Thesis (Ph. D.)--Joint Program in Physical Oceanography (Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, and the Woods Hole Oceanographic Institution), 2003.
Includes bibliographical references (p. 145-148).
Oceanic observations indicate that abyssal mixing is localized in regions of rough topography. How locally mixed fluid interacts with the ambient fluid is an open question. Laboratory experiments explore the interaction of mechanically induced boundary mixing and an interior body of linearly stratified rotating fluid. Turbulence is generated by a vertically oscillating horizontal bar, located at middepth along the tank wall. The turbulence forms a region of mixed fluid which quickly reaches a steady state height and collapses into the interior. The mixed layer thickness ... is independent of the Coriolis frequency f. N is the buoyancy frequency, co is the bar frequency, and the constant, Y=1 cm, is empirically determined by bar mechanics. In initial experiments, the bar is exposed on three sides. Mixed fluid intrudes directly into the interior as a radial front of uniform height, rather than as a boundary current. Mixed fluid volume grows linearly with time ... The circulation patterns suggest a model of unmixed fluid being laterally entrained with velocity, e Nhm, into the sides of a turbulent zone with height hm and width Lf ... where Lf is an equilibrium scale associated with rotational control of bar-generated turbulence. In accord with the model, outflux is constant, independent of stratification and restricted by rotation ... Later experiments investigate the role of lateral entrainment by confining the sides of the mixing bar between two walls, forming a channel open to the basin at one end. A small percentage of exported fluid enters a boundary current, but the bulk forms a cyclonic circulation in front of the bar. As the recirculation region expands to fill the channel, it restricts horizontal entrainment into the turbulent zone. The flux of mixed fluid decays with time.
(cont.) ... The production of mixed fluid depends on the size of the mixing zone as well as on the balance between turbulence, rotation and stratification. As horizontal entrainment is shut down, longterm production of mixed fluid may be determined through much weaker vertical entrainment. Ultimately, the export of mixed fluid from the channel is restricted to the weak boundary current.
by Judith R. Wells.
Ph.D.
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Havard, Stephen Paul. "Numerical simulation of non-Newtonian fluid flow in mixing geometries." Thesis, University of South Wales, 1989. https://pure.southwales.ac.uk/en/studentthesis/numerical-simulation-of-nonnewtonian-fluid-flow-in-mixing-geometries(eaee66ae-2e3d-44ba-9a5f-41d438749534).html.

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In this thesis, a theoretical investigation is undertaken into fluid and mixing flows generated by various geometries for Newtonian and non-Newtonian fluids, on both sequential and parallel computer systems. The thesis begins by giving the necessary background to the mixing process and a summary of the fundamental characteristics of parallel architecture machines. This is followed by a literature review which covers accomplished work in mixing flows, numerical methods employed to simulate fluid mechanics problems and also a review of relevant parallel algorithms. Next, an overview is given of the numerical methods that have been reviewed, discussing the advantages and disadvantages of the different methods. In the first section of the work the implementation of the primitive variable finite element method to solve a simple two dimensional fluid flow problem is studied. For the same geometry colour band mixing is also investigated. Further investigational work is undertaken into the flows generated by various rotors for both Newtonian and non-Newtonian fluids. An extended version of the primitive variable formulation is employed, colour band mixing is also carried out on two of these geometries. The latter work is carried out on a parallel architecture machine. The design specifications of a parallel algorithm for a MIMD system are discussed, with particular emphasis placed on frontal and multifrontal methods. This is followed by an explanation of the implementation of the proposed parallel algorithm, applied to the same fluid flow problems as considered earlier and a discussion of the efficiency of the system is given. Finally, a discussion of the conclusions of the entire accomplished work is presented. A number of suggestions for future work are also given. Three published papers relating to the work carried out on the transputer networks are included in the appendices.
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PRUETT, CHARLES DAVID. "NUMERICAL SIMULATION OF NONLINEAR WAVES IN FREE SHEAR LAYERS (MIXING, COMPUTATIONAL, FLUID DYNAMICS, HYDRODYNAMIC STABILITY, SPATIAL, FLUID FLOW MODEL)." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/183869.

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A numerical model has been developed which simulates the three-dimensional stability and transition of a periodically forced free shear layer in an incompressible fluid. Unlike previous simulations of temporally evolving shear layers, the current simulations examine spatial stability. The spatial model accommodates features of free shear flow, observed in experiments, which in the temporal model are precluded by the assumption of streamwise periodicity; e.g., divergence of the mean flow and wave dispersion. The Navier-Stokes equations in vorticity-velocity form are integrated using a combination of numerical methods tailored to the physical problem. A spectral method is adopted in the spanwise dimension in which the flow variables, assumed to be periodic, are approximated by finite Fourier series. In complex Fourier space, the governing equations are spatially two-dimensional. Standard central finite differences are exploited in the remaining two spatial dimensions. For computational efficiency, time evolution is accomplished by a combination of implicit and explicit methods. Linear diffusion terms are advanced by an Alternating Direction Implicit/Crank-Nicolson scheme whereas the Adams-Bashforth method is applied to convection terms. Nonlinear terms are evaluated at each new time level by the pseudospectral (collocation) method. Solutions to the velocity equations, which are elliptic, are obtained iteratively by approximate factorization. The spatial model requires that inflow-outflow boundary conditions be prescribed. Inflow conditions are derived from a similarity solution for the mean inflow profile onto which periodic forcing is superimposed. Forcing functions are derived from inviscid linear stability theory. A numerical test case is selected which closely parallels a well-known physical experiment. Many of the aspects of forced shear layer behavior observed in the physical experiment are captured by the spatial simulation. These include initial linear growth of the fundamental, vorticity roll-up, fundamental saturation, eventual domination of the subharmonic, vortex pairing, emergence of streamwise vorticity, and temporary stabilization of the secondary instability. Moreover, the spatial simulation predicts the experimentally observed superlinear growth of harmonics at rates 1.5 times that of the fundamental. Superlinear growth rates suggest nonlinear resonances between fundamental and harmonic modes which are not captured by temporal simulations.
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Sone, Kazuo. "Unsteady simulations of mixing and combustion in internal combustion engines." Thesis, Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/12171.

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Books on the topic "Mixing – Mathematical models"

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B, Weiss J., and Provenzale A, eds. Transport and mixing in geophysical flows. Berlin: Springer, 2008.

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Tsanis, Ioannis K. Mixing zone models for submerged discharges. Southampton: Computational Mechanics Publications, 1994.

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Langerak, A. Predictive ability of two-dimensional models for mixing in estuaries. Santa Monica, CA: Rand, 1987.

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Falkus, Jan. Fizyczne i matematyczne modelowanie procesów mieszania kąpieli metalowej w reaktorach metalurgicznych. Kraków: AGH, 1998.

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Davis, Cabell S. Biological/physical modeling of upper ocean processes. Woods Hole, Mass: Woods Hole Oceanographic Institution, 1994.

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Jiang, L. Y. Turbulent mixing in supersonic high-temperature exhaust jets. North York, Ont: Institute for Aerospace Studies, University of Toronto, 1996.

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Wells, Judith R. A laboratory study of localized boundary mixing in a rotating stratified fluid. Cambridge, Mass: Massachusetts Institute of Technology, 2003.

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Manoa), ʻAha Hulikoʻa Hawaiian Winter Workshop (5th 1989 University of Hawaii at. Parameterization of small-scale processes: Proceedings, ʾAha Hulikoʾa Hawaiian Winter Workshop, University of Hawaii at Manoa, January 17-20, 1989. Honolulu, Hawaii: Hawaii Institute of Geophysics, 1989.

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Bondarenko, A. L. Techenii͡a︡ Kaspiĭskogo mori͡a︡ i formirovanie poli͡a︡ solenosti vod Severnogo Kaspii͡a︡. Moskva: Nauka, 1993.

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A, Cornell John. A primer on experiments with mixtures. Hoboken, N.J: Wiley, 2011.

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Book chapters on the topic "Mixing – Mathematical models"

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Lim, Hyunkyung, Yan Yu, James Glimm, and David H. Sharp. "Mathematical, Physical and Numerical Principles Essential for Models of Turbulent Mixing." In Nonlinear Conservation Laws and Applications, 405–13. Boston, MA: Springer US, 2011. http://dx.doi.org/10.1007/978-1-4419-9554-4_23.

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Brauer, Fred, Carlos Castillo-Chavez, and Zhilan Feng. "Models with Heterogeneous Mixing." In Texts in Applied Mathematics, 179–227. New York, NY: Springer New York, 2019. http://dx.doi.org/10.1007/978-1-4939-9828-9_5.

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Klingbeil, Knut, Hans Burchard, Sergey Danilov, Claus Goetz, and Armin Iske. "Reducing Spurious Diapycnal Mixing in Ocean Models." In Mathematics of Planet Earth, 245–86. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-05704-6_8.

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Britton, Tom, and Etienne Pardoux. "Chapter 3 A General Two-Level Mixing Model." In Lecture Notes in Mathematics, 159–213. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-30900-8_7.

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Stoellinger, Michael, Denis Efimov, and Dirk Roekaerts. "Monte Carlo Simulations of Turbulent Non-premixed Combustion using a Velocity Conditioned Mixing Model." In Mathematical Engineering, 143–74. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-18206-3_7.

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Uçar, Sümeyra, Necati Özdemir, and Zakia Hammouch. "A Fractional Mixing Propagation Model of Computer Viruses and Countermeasures Involving Mittag-Leffler Type Kernel." In 4th International Conference on Computational Mathematics and Engineering Sciences (CMES-2019), 186–99. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-39112-6_13.

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Cooke, Kenneth L., Donald A. Allers, and Carlos Castillo-Chavez. "Mixing Patterns in Models of AIDS." In Mathematical population dynamics, 297–309. CRC Press, 2020. http://dx.doi.org/10.1201/9781003072706-24.

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Verma, Shashi Kant, S. L. Sinha, and D. K. Chandraker. "Selection of Appropriate Turbulance Model in Fuel Bundle of Nuclear Energy." In Soft Computing Techniques and Applications in Mechanical Engineering, 249–66. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-3035-0.ch012.

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This chapter presents an overview of various types of turbulence model and their effect on thermal-hydraulic characteristics of nuclear fuel bundle, both past and present using Computational Fluid Dynamic (CFD) approach. It includes the mathematical definition related to fuel bundle in nuclear energy. The various types of geometrical arrangement like Pressurized Water Reactor (PWR), Boiling Water Reactor (BWR), etc., are stressed. The solution procedures that are applicable to the various reactor types are introduced here and presented in detail for different types of turbulence models. Study of these characteristics enables the student to appreciate the effect of the different types of turbulence models on turbulent mixing and related phenomena. Finally, recommendations of turbulence model for rod bundle are finalized. The inclusion of related references provides a starting point for the interested reader / researchers /industrialists.
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Diekmann, Odo, Hans Heesterbeek, and Tom Britton. "Other indicators of severity." In Mathematical Tools for Understanding Infectious Disease Dynamics. Princeton University Press, 2012. http://dx.doi.org/10.23943/princeton/9780691155395.003.0008.

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This chapter is devoted to the initial real-time growth rate r, the probability of a major outbreak, the final size, and the endemic level, in structured populations, with special attention for computational simplifications in the case of separable mixing. Chapter 7 studied the basic reproduction number R₀ for epidemic models in populations manifesting various forms of heterogeneity. It was illustrated that R₀ depends on the transmission parameters, contact rates, the infectious period and on the community structure. The importance of R₀ lies in the fact that an epidemic can, and will in the deterministic setting, take off only if R₀ > 1, a characteristic referred to as supercritical. In a community having births or immigration of susceptibles, this also means that the disease can become endemic. If the parameters and community are such that R₀ < 1 (or R₀ = 1), we are in the subcritical (critical) regime and an epidemic outbreak cannot occur. The chapter examines important supplementary characteristic features and shows how they depend on the different parameters of the model.
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Chhabra, Kaval, Divesh Agrawal, and Saladi S. V. Subbarao. "Modeling of Polypropylene Modified Bitumen Mix Design Results Using Regression Analysis." In Handbook of Research on Manufacturing Process Modeling and Optimization Strategies, 256–75. IGI Global, 2017. http://dx.doi.org/10.4018/978-1-5225-2440-3.ch012.

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This study investigates the effects of mixing Polypropylene waste plastics in the bituminous mix for the design of Flexible Pavement. Since, obtaining Marshall Test results from the bituminous mix is time-consuming, so if the practitioners measure the values of stability and flow by mechanical testing, other computations can be done by applying simple mathematical calculations. So, this study carried out stability and flow tests on different specimens made with varying bitumen and polypropylene plastic content. From the initial test results, the optimum bitumen and plastic contents are found. Further, the test results obtained from Marshall Test are modelled by identifying various input variables, which are various physical properties of the mix such as plastic content, bitumen content, air voids and unit weight. The regression modeling framework is adopted in this study to predict the Marshall stability and flow value. Since the developed models have yielded good results, these can be effectively used in parameter estimation, and thus aids the future researchers.
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Conference papers on the topic "Mixing – Mathematical models"

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Maskal, Alan B., and Fatih Aydogan. "Mathematical Models of Spacer Grids." In 2016 24th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/icone24-60098.

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The fuel rods in Pressurized Water Reactor (PWR) and Boiling Water Reactor (BWR) cores are supported by spacer grids. Even though spacer grids add to the pressure loss in the reactor core, spacer grids have several benefits in Light Water Reactors (LWRs). Some of these benefits are: (i) increasing the turbulence at the bottom of the reactor core for better heat transfer in single phase region of the LWRs, (ii) improving the departure nucleate boiling ratio results for PWRs, and (iii) improving critical power ratio (CPR) values by increasing the thickness of film in annular flow regime in the top section of the reactor core of BWRs. Several mathematical models have been developed for single and two phase pressure loss across the grid spacer. Almost all of them significantly depend on Reynolds Number. Spacer designs have evolved (incorporating mixing vanes, springs, dimples, etc), resulting in the complexity of the analysis across the grid, all the models have been compared not only theoretically but also quantitatively. For the quantitative comparisons, this work compares the results of mathematical spacer models with experimental data of BWR Full Size Fine Mesh Bundle Tests (BFBT). The experimental data of BFBT provides very detailed experimental results for pressure drop by using several different boundary condition and detailed pressure drop measurements. Since one CT-scanner was used at the bundle exit and three X-ray densitometers were used for the chordal average void distribution at different elevations to generate the BFBT results, detailed two phase parameters have been measured in BFBT database. Two bundle types of BFBT, the current 8×8 type and the high burn-up 8×8 type, were simulated. Three combinations of radial and axial power shapes were tested: 1) beginning of cycle (BOC) radial power pattern/cosine axial power shape (the C2A pattern); 2) end of cycle (EOC) radial power pattern/cosine axial power shape (C2B pattern); and 3) beginning of cycle radial power pattern/inlet peaked axial power shape (C3 pattern) in BFBT. The pressure drop in BFBT database was measured in both single-phase flow and two-phase flow conditions that cover the normal operational behavior. BFBT database gives the three combinations of high burnup assemblies with different radial and axial power shapes, namely C2A, C2B and C3, which were utilized in the critical power measurements. There are two types of spacers in this program — ferrule type and grid type. Therefore, detailed experimental data of BFBT was used for analyzing mathematical models of spacer grid for various boundary conditions of BWR in this paper. It was observed and discussed that pressure drop values due to spacer models can be significantly different.
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MORISHITA, YOSUKE, DAISUKE SANNOHE, TATSUYA OSAWA, TOMOYA TANAKA, and TARO NAKAMURA. "DERIVATION OF MATHEMATICAL MODELS OF THE PERISTALTIC CRAWLING ROBOT FOR MAINTENANCE OF A MIXING TANK." In Proceedings of the 16th International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814525534_0035.

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Basara, Branislav, Ales Alajbegovic, and Decan Beader. "Calculation of Flow in Mixing Vessels With Various Turbulence Models." In ASME 2004 Heat Transfer/Fluids Engineering Summer Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/ht-fed2004-56260.

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The paper presents calculations of flow in a mixing vessel stirred by a six-blade Rushton impeller. Mathematical model used in computations is based on the ensemble averaged conservation equations. An efficient finite-volume method based on unstructured grids with rotating sliding parts composed of arbitrary polyhedral elements is used together with various turbulence models. Besides the standard k-ε model which served as a reference, k-ε-v2 model (Durbin, 1995) and the recently proposed hybrid EVM/RSM turbulence model (Basara & Jakirlic, 2003) were used in the calculations. The main aim of the paper is to investigate if more advanced turbulence models are needed for this type of CFD applications. The results are compared with the available experimental data.
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Jaskulski, Maciej, Artur Lewandowski, and Ireneusz Zbiciński. "Mathematical modeling of moisture evaporation in co-current foam spray drying." In 21st International Drying Symposium. Valencia: Universitat Politècnica València, 2018. http://dx.doi.org/10.4995/ids2018.2018.7252.

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Two models of foam drying are presented in the paper: single droplet drying and perfect mixing of phases spray drying models to describe mechanism of drying of droplet containing bubble. Analysis of drying curves shows that in constant drying rate period and in the falling drying rate period, evaporation rate decreases due to particle shrinkage and increasing of resistance of moisture diffusion inside the solid crust. Increase of gas pressure in the bubble might cause particle breakage. Slight differences between theoretical and experimental results caused by disregarding broken particles in the simulations proves accuracy of the developed model. Keywords: spray drying, modeling, foamed materials, particle morphology
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Pease, Leonard F., and Judith Ann Bamberger. "Attached Jet Velocity Profiles in Mixing Tanks." In ASME 2020 Fluids Engineering Division Summer Meeting collocated with the ASME 2020 Heat Transfer Summer Conference and the ASME 2020 18th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/fedsm2020-20220.

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Abstract Free jets have been studied in detail over much of the last century, but the theory for offset and attached jets remains incomplete. Attached jets differ from free jets in that they lose momentum to nearby surfaces, attenuating their velocities. The velocity profiles of free circular jets are nearly Gaussian, with quantitative mathematical descriptions derived from first principles by Goertler and Tollmien (Rajaratnam, 1976). In contrast, mathematical descriptions of three-dimensional attached jets from circular nozzles remain much less mature. Agelin-Chaab and Tachie (2011) used particle imaging velocimetry of a three-dimensional attached jet to show that the scaled velocity decays with scaled distance from the nozzle with a power law exponent between −1.15 and −1.20, which is larger in magnitude than that of a free jet. However, quantitative analytical expressions for the velocity profiles of attached jets similar to those of free jets remain elusive. This paper addresses this critical gap. Here we evaluate the velocity profiles of three-dimensional offset jets emerging from circular nozzles that become attached jets. These jets lose momentum due to interactions with nearby surfaces and are important to evaluating flows in mixing vessels and to suspending solids and trapped gases in radioactive waste tanks. Despite the importance of attached jets, prior insight has been purely experimental, limited to overly simplistic analytical models, or restricted to computationally expensive computational fluid dynamics case studies. We compare the expression of Verhoff (1963) to experimental results to find reasonable quantitative agreement. As stated by Agelin-Chaab and Tachie (2011), “detailed velocity measurements of 3D offset jets are rare.” Such remains the case. This study adds to the literature by providing information at two additional Reynolds numbers (1.43 · 106 and 1.87 · 106) and evaluating simple but accurate expressions for velocity profiles. These Reynolds numbers and corresponding velocities are higher, typically orders of magnitude higher, than other reports. The semi-empirical stream wise velocity profile perpendicular to the surface proposed by Verhoff (1963) is in approximate agreement with these velocity profiles, which is surprising because these attached jets are three-dimensional instead of two-dimensional as evaluated by Verhoff. However, additional work is necessary to fully describe these profiles quantitatively.
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Pease, Leonard F., Arich J. L. Fuher, Judith Ann Bamberger, and Michael J. Minette. "A Test of Steady State Erosion Models." In ASME 2018 5th Joint US-European Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/fedsm2018-83392.

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Here we ask the question: how well is the erosion of particle beds in vessels with curved bottoms at industrial scale flow rates represented by models of radial wall jets traversing flat surfaces using the critical shear stress for erosion from the Shields diagram? This mathematical construction has been used successfully to predict the functional forms for the extent of erosion with time using two dimensionless fitting parameters (Pease, et al., 2017). However, the direct prediction of the curves without fitting and scaling has not been tested quantitatively. Here we evaluate the radial wall jet models of Poreh, et al., (1967) and Rajaratnam (1976) and the expressions for the Shields diagram by Paphitis (2001) and Cao, Pender, and Meng (2006). The use of two models for each element accounts for uncertainty in model selection. The data selected to benchmark these models was obtained in a geometrically scaled version of an industrial scale mixing vessel with 12 jets arrayed in a double ring configuration (Meyer, et al., 2012). These particular jets were operated continuously with observations at steady-state, providing a direct comparison between the long-time erosion fronts and these proposed long-time solutions (i.e., where the applied shear stress equals the critical shear stress for erosion) without interference from transients or parameters that affect transients (e.g., the particle bed thickness). We find experimentally that the extent of the erosion depends significantly on the vessel curvature. Even so, we also find that all of these formulations significantly over predict the extent of erosion observed experimentally. A discussion of model features that may be modified to revise the theory into quantitative agreement is presented.
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Borissov, Anatoli, and James J. McCoy. "Supersonic Injection of Gaseous Fuel Described as Possible Solution for NOx Emissions From Large-Bore Gas Engines." In ASME 2002 Internal Combustion Engine Division Spring Technical Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/ices2002-448.

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Both physical and mathematical models were built to describe the main processes in large-bore gas engines. Based on the detail modeling and analysis of cylinder airflow, fuel injection, mixing, combustion and NOx generation, it was possible to pinpoint the problem of abnormal NOx production, even for lean mixtures, that occurs in these engines. In addition, analysis of the experimental data of jet mixing using high-speed photographic evidence, as well as engine performance data, has helped in the understanding of the mixing process. This has resulted in the development of a new way of the mixing of fuel and air utilizing multiple-nozzle supersonic injection. The fuel injection system is designed to optimize the mixing of the methane fuel with the air in the cylinder of a large bore natural gas engine. The design goals of low-pressure (<130 psi), all-electronic valve actuation, and optimal mixing were all achieved with a unique valve/nozzle arrangement. Later, a laser induced fluorescence method was used to take high-speed photographs of the development of the fuel jet exiting the newly developed supersonic electronic fuel injector (SSEFI). This result, together with the results of numerous experimental testing of SSEFI on different engines (GMVH-6, GMW-10, V-250, UTC-165) are presented as evidence of the success of the SSEFI application for the improvement of engine performance, engine control and NOx reduction.
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Tang, Gongyue, Chun Yang, and Yee Cheong Lam. "Joule Heating Induced Heat Transfer and Its Effects on Electrokinetic Mixing in T-Shape Microfluidic Channels." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35136.

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In this paper, we report numerical and experimental studies of the Joule heating-induced heat transfer in fabricated T-shape microfluidic channels. We have developed comprehensive 3D mathematical models describing the temperature development due to Joule heating and its effects on electrokinetic flow. The models consist of a set of governing equations including the Poisson-Boltzmann equation for the electric double layer potential profiles, the Laplace equation for the applied electric field, the modified Navier-Stokes equations for the electrokinetic flow field, and the energy equations for the Joule heating induced conjugated temperature distributions in both the liquid and the channel walls. Specifically, the Joule number is introduced to characterize Joule heating, to account for the effects of the electric field strength, electrolyte concentration, channel dimension, and heat transfer coefficient outside channel surface. As the thermophysical and electrical properties including the liquid dielectric constant, viscosity and electric conductivity are temperature-dependent, these governing equations are strongly coupled. We therefore have used the finite volume based CFD method to numerically solve the coupled governing equations. The numerical simulations show that the Joule heating effect is more significant for the microfluidic system with a larger Joule number and/or a lower thermal conductivity of substrates. It is found that the presence of Joule heating makes the electroosmotic flow deviate from its normal “plug-like” profiles, and cause different mixing characteristics. The T-shape microfluidic channels were fabricated using rapid prototyping techniques, including the Photolithography technique for the master fabrication and the Soft Lithography technique for the channel replication. A rhodamine B based thermometry technique, was used for direct “in-channel” measurements of liquid solution temperature distributions in microfluidic channels, fabricated by the PDMS/PDMS and Glass/PDMS substrates. The experimental results were compared with the numerical simulations, and reasonable agreement was found.
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Nuzhnov, Yu V. "The Method of Autonomous Statistical Modeling ASMTurb and its Testing on the Example of Classical Turbulent Flows." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-36355.

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A physical designation of the method of autonomous statistical modeling turbulent flows (ASMTurb method with consideration of external intermittency) and its testing are presented. The method is tested on the example of constructing of mathematical models for self-similar turbulent shear flows such as: I-the two-stream plane mixing layer; II-the outer region of the boundary layer on the wall; III-the far wake behind a cross-streamlined cylinder; IV-the axisymmetric submerged jet. Test results are presented in the form calculating the main conditional and total statistical averages applied to self-similar region of turbulent flows. It is shown that the ASMTurb models which constructed here are more accurate and more detailed than RANS models. A comparison is made between predictions and known experimental data for energy-containing structure of turbulent flow and excellent agreements are noted.
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Killion, Jesse D., and Srinivas Garimella. "Liquid Films Falling Over Horizontal Tube Banks: Deviations From Idealized Flow Patterns and Implications for Heat and Mass Transfer." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-33223.

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Liquid films falling over banks of internally cooled horizontal tubes are often used to absorb mass from a surrounding vapor. This arrangement is particularly suitable for absorption processes where the vapor has a high heat of absorption and where high transfer rates and low pressure drops are required, as is the case of absorption heat pumps and other chemical processes. When the liquid film presents a significant resistance to heat and mass transfer, understanding the motion of the film is critical. However, mathematical models of these types of systems in the literature have generally made use of many simplifying assumptions about the behavior of the falling liquid. The formation, detachment, and impact of droplets and the associated waves and film disturbances can all affect the mixing of the liquid and can enhance transfer rates accordingly. The objective of this paper is to identify and visually document these deviations from idealized film behavior and discuss their implications on the heat and mass transfer processes, which are important to consider in the development of mechanistic models of the absorption process.
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