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Добірка наукової літератури з теми "Viscous flow Mathematical models"

Автор: Grafiati

Опубліковано: 4 червня 2021

Оновлено: 11 лютого 2022

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Статті в журналах з теми "Viscous flow Mathematical models"

Masuko, Akira, Yasushi Shirose, Yasunori Ando, and Masafumi Kawai. "Numerical Simulation of Viscous Flow around a Series of Mathematical Ship Models." Journal of the Society of Naval Architects of Japan 1987, no. 162 (1987): 1–10. http://dx.doi.org/10.2534/jjasnaoe1968.1987.162_1.

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Toxopeus, Serge L. "Deriving mathematical manoeuvring models for bare ship hulls using viscous flow calculations." Journal of Marine Science and Technology 14, no. 1 (July 23, 2008): 30–38. http://dx.doi.org/10.1007/s00773-008-0002-9.

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Aripov, M. M., J. SH Rajabov, and SH R. Settiev. "About one of the mathematical models of viscous flow incompressible fluid above sandy bottom." Journal of Physics: Conference Series 1902, no. 1 (May 1, 2021): 012001. http://dx.doi.org/10.1088/1742-6596/1902/1/012001.

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Howell, P. D. "Models for thin viscous sheets." European Journal of Applied Mathematics 7, no. 4 (August 1996): 321–43. http://dx.doi.org/10.1017/s0956792500002400.

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Leading-order equations governing the dynamics of a two-dimensional thin viscous sheet are derived. The inclusion of inertia effects is found to result in an ill-posed model when the sheet is compressed, and the resulting paradox is resolved by rescaling the equations over new length-and timescales which depend on the Reynolds number of the flow and the aspect ratio of the sheet. Physically this implies a dominant lengthscale for transverse displacements during viscous buckling. The theory is generalized to give new models for fully three-dimensional sheets.

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PATEL, L. K., and LAKSHMI S. DESAI. "PLANE SYMMETRIC VISCOUS-FLUID COSMOLOGICAL MODELS WITH HEAT FLUX." International Journal of Modern Physics D 03, no. 03 (September 1994): 639–45. http://dx.doi.org/10.1142/s0218271894000770.

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A class of nonstatic inhomogeneous plane-symmetric solutions of Einstein field equations is obtained. The source for these solutions is a viscous fluid with heat flow. The fluid flow is irrotational and it has nonzero expansion, shear and acceleration. All these solutions have a big-bang singularity. The matter-free limit of the solutions is the well-known Kasner vacuum solution. Some physical features of the solutions are briefly discussed.

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Krusteva, Ekaterina D., Stefan Y. Radoslavov, and Zdravko I. Diankov. "Modelling the Seepage of Groundwater: Application of the Viscous Analogy and Numerical Methods." Applied Rheology 9, no. 4 (August 1, 1999): 165–71. http://dx.doi.org/10.1515/arh-2009-0012.

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Abstract The application of the viscous analogy, known as the Hele-Show model, for seepage investigation is demonstrated in the paper. The changes in the viscous properties of the model fluid (glycerine) resulting from the changes of the atmospheric conditions - temperature and humidity, have been taken under consideration as factors influencing the flow discharge in the model. A method has been substantiated for the exact quantitative comparison of discharges obtained under different boundary conditions of the seepage process using parallel rheological measurements of the model fluid. The results from the viscous and mathematical models are compared for a particular two-dimensional seepage process - the operation of a horizontal drainage. The complete coincidence of these results, proves the good grounds of the method as well as its applicability as a test method for the development of mathematical models.

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Nazarov, Serdar, Muhammetberdi Rakhimov, and Gurbanyaz Khekimov. "Linearization of the Navier-Stokes equations." E3S Web of Conferences 216 (2020): 01060. http://dx.doi.org/10.1051/e3sconf/202021601060.

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This paper studies mathematical models of the heat transfer process of a viscous incompressible fluid. Optimal control methods are used to solve the problem of optimal modeling. Questions of linearization of the Navier-Stokes equation for a plane fluid flow are considered. The optimal modes (optimal functional dependencies) of the pump and heating device are found depending on the fluid flow rate.

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Ali, Azhar, Dil Nawaz Khan Marwat, and Saleem Asghar. "Viscous flow over a stretching (shrinking) and porous cylinder of non-uniform radius." Advances in Mechanical Engineering 11, no. 9 (September 2019): 168781401987984. http://dx.doi.org/10.1177/1687814019879842.

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The classical models of viscous flows and heat transfer are reformulated in this article. The physical problem describes flow and heat transfer over a stretching (shrinking) and porous cylinder of non-uniform radius. The mathematical model is presented in the form of new equations and dimensionless parameters by means of reframing techniques. A porous and heated cylinder of a non-uniform diameter is stretched (shrunk) with variable stretching (shrinking) velocities. The governing equations and their physical geometrical perspectives are summarized into simplest boundary value ordinary differential equations. A set of unseen, generalized, and convenient transformations are used to solve the complex problem. The current formulation accumulates all the previous models of axisymmetric flow and heat transfer toward stretching (shrinking) and porous cylinder presented in the literature and prevails over all such models. The current model can be easily transformed into classical simulations for particular values of the parameters. The problem is solved numerically and the results were compared with the benchmark solutions. Velocity, temperature, skin friction coefficient, and Nusselt number profiles are plotted and analyzed for different values of the parameters. Moreover, coupling effects of all parameters are seen on flow and heat transfer characteristics and new results are explored and discussed.

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Nazarov, Serdar, Muhammetberdi Rakhimov, and Gurbanyaz Khekimov. "Optimal modeling of the heat transfer of a viscous incompressible liquid." E3S Web of Conferences 216 (2020): 01059. http://dx.doi.org/10.1051/e3sconf/202021601059.

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This paper discusses mathematical models of the heat transfer process of a viscous incompressible fluid. Optimal control methods are used to solve the problem of optimal modeling. Questions of linearization of the Navier - Stokes equation are considered. The optimal modes (optimal functional dependencies) of the pump and heating device are found depending on the fluid flow rate.

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Socolowsky, Jürgen. "On the Nusselt Solution of a Nonisothermal Two-Fluid Inclined Film Flow." International Journal of Mathematics and Mathematical Sciences 2009 (2009): 1–8. http://dx.doi.org/10.1155/2009/981983.

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Nonisothermal viscous two-fluid flows occur in numerous kinds of coating devices. The corresponding mathematical models often represent two-dimensional free boundary value problems for the Navier-Stokes equations or their modifications. In the present paper we are concerned with a particular problem of coupled heat and mass transfer. Marangoni convection is incorporated, too. The solvability of a corresponding stationary problem is discussed. The obtained results generalize previous results for a similar isothermal problem.

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Дисертації з теми "Viscous flow Mathematical models"

Stokes, Yvonne Marie. "Very Viscous Flows Driven by Gravity with particular application to Slumping of Molten Glass." Title page, contents and abstract only, 1998. http://thesis.library.adelaide.edu.au/public/adt-SUA20020724.171358.

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Bibliography: leaves 247-257. Electronic publication; Full text available in PDF format; abstract in HTML format. This thesis examines the flow of very viscous Newtonian fluids driven by gravity, with emphasis on the lumping of molten glass into a mould, as in the manufacture of optical components, which are in turn used to manufacture ophthalmic lenses. Electronic reproduction.[Australia] :Australian Digital Theses Program,2001.

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Marshall, David D. "Extending the functionalities of Cartesian grid solvers : viscous effects modeling and MPI parallelization." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/11999.

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Rossi, Louis Frank, and Louis Frank Rossi. "A spreading blob vortex method for viscous bounded flows." Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186562.

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In this dissertation, I introduce a vortex method that is generally applicable to any two-dimensional, incompressible flow with or without boundaries. This method is deterministic, accurate, convergent, naturally adaptive, geometry independent and fully localized. For viscous flows, the vorticity distribution of each vortex element must evolve in addition to following a Lagrangian trajectory. My method relies upon an idea called core spreading. Core spreading is inconsistent by itself, but I have corrected it with a deterministic process known as "vortex fission" where one "fat" vortex is replaced by several "thinner" ones. Also, I examine rigorously a method for merging many blobs into one. This process maintains smaller problem sizes thus boosting the efficiency of the vortex method. To prove that this corrected core spreading method will converge uniformly, I adapted a continuous formalism to this grid-free scheme. This convergence theory does not rely on any form of grid. I only examine the linear problem where the flow field is specified, and treat the full nonlinear problem as a perturbation of the linear problem. The estimated rate of convergence is demonstrated to be sharp in several examples. Boundary conditions are approximated indirectly. The boundary is decomposed into a collection of small linear segments. I solve the no-slip and no-normal flow conditions simultaneously by superimposing a potential flow and injecting vorticity from the boundary consistent with the unsteady Rayleigh problem. Finally, the ultimate test for this new method is to simulate the wall jet. The simulations produce a dipole instability along the wall as observed in water tank and wind tunnel experiments and predicted by linear stability analysis. Moreover, the wavelength and height of these simulations agree quantitatively with experimental observations.

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Kim, Goo. "A vorticity-velocity approach for three-dimensional unsteady viscous flow over wings." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/12123.

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Huang, Lingyan, and 黃凌燕. "Mass transport due to surface waves in a water-mud system." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B35380457.

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Vantzos, Orestis. "Mathematical Modeling of Charged Liquid Droplets: Numerical Simulation and Stability Analysis." Thesis, University of North Texas, 2006. https://digital.library.unt.edu/ark:/67531/metadc5240/.

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The goal of this thesis is to study of the evolution of 3D electrically charged liquid droplets of fluid evolving under the influence of surface tension and electrostatic forces. In the first part of the thesis, an appropriate mathematical model of the problem is introduced and the linear stability analysis is developed by perturbing a sphere with spherical harmonics. In the second part, the numerical solution of the problem is described with the use of the boundary elements method (BEM) on an adaptive mesh of triangular elements. The numerical method is validated by comparison with exact solutions. Finally, various numerical results are presented. These include neck formation in droplets, the evolution of surfaces with holes, singularity formation on droplets with various symmetries and numerical evidence that oblate spheroids are unstable.

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Sirino, Thiago. "Estudo numérico da influência da viscosidade no desempenho de uma bomba centrífuga submersa." Universidade Tecnológica Federal do Paraná, 2013. http://repositorio.utfpr.edu.br/jspui/handle/1/880.

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Petrobrás; ANP; UTFPR; LACIT<br>Bombas centrífugas submersas têm sido cada vez mais utilizadas comométodo de elevação artificial para a produção de óleos em campos marítimos profundos. O bombeio de fluidos com viscosidades significativamente diferentes a da água gera um desempenho da bomba distinto ao do apresentado no seu catálogo, com uma queda de rendimento da mesma, assim sendo, a influência da viscosidade do fluido no desempenho em uma bomba centrífuga submersa tem recebido muita atenção há alguns anos. Neste cenário, no presente trabalho foi realizada a simulação numérica do escoamento monofásico, newtoniano, incompressível e isotérmico no rotor e difusor de uma bomba centrífuga submersa utilizando o programa de dinâmica de fluidos computacional ANSYS CFX. As simulações numéricas foram realizadas para um estágio de uma BCS de três estágios para escoamentos envolvendo fluidos com viscosidades variando de 1 a 1020 cP. A partir dos resultados numéricos obtidos foram elaboradas as curvas para a altura de elevação da bomba e eficiência e comparados contra dados experimentais obtidos por Amaral (2007). Também foi realizada uma análise do padrão do escoamento no rotor e difusor com o objetivo de avaliar o comportamento dos campos de velocidade e pressão, a intensidade turbulenta e o aparecimento de recirculações para a BCS operando fora da faixa de operação ótima. Alem disso foi analisada a degradação do desempenho da bomba em função da viscosidade do fluido de trabalho, e foram utilizados números adimensionais como parâmetros para quantificar essa degradação.<br>This work presents a numerical analysis on the influence of viscosity on the performance of a semi-axial electrical submersible pump (ESP) such as the ones used in offshore petroleum production. A single stage composed of an impeller with seven blades and a diffuser with seven vanes is considered. Flow simulations for water and other fluids with viscosity ranging from 60 to 1020 cP were performed with the aid of Computational Fluid Dynamics, and both design and off-design flow rates and impeller speeds were investigated. The numerical model was compared with experimental measurements of the static pressure difference on a given stage of a three-stage ESP system. Results showed good agreement between the numerical and the measured pressure difference values. As a main objective, the pump performance degradation relative to viscosity is analyzed for several conditions regarding design and off-design operation. The flow field pattern associated with the effect of viscosity is also analyzed. Studying the pump performance degradation cause by viscosity, especially for off-design operation like this work is also intended, is a current and ongoing demand in offshore petroleum production. In association with that, understanding the flow field pattern for those scenarios, which seems to be very particular for each pump, should help to contribute to the related literature in this field.

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Cummings, Linda Jane. "Free boundary models in viscous flow." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.339364.

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Goble, Brian Dean. "A truncation error injection approach to viscous-inviscid interaction." Diss., The University of Arizona, 1988. http://hdl.handle.net/10150/184318.

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A numerical procedure is presented which uses the truncation error injection methodology to efficiently achieve accurate approximations to complex problems having disparate length scales in the context of solving viscous, transonic flow over an airfoil. The truncation error distribution is estimated using the solution on a coarse grid. Local fine grids are formed which improve the resolution in regions of large truncation error. A fast fourth-order accurate scheme is presented for interpolating and relating the solutions between the generalized curvilinear coordinate systems of the local and global grids. It is shown that accurate solutions can be obtained on a global coarse grid with correction information obtained on local fine grids, which may or may not be topologically similar to the global grid as long as they are capable of resolving the local length scale. Dirichlet boundary conditions for the local grid yield the best results. The scheme also serves as the basis of a local refinement technique wherein a grid local to the nose of an airfoil is used to resolve a supersonic zone terminated by a shock and its interaction with a turbulent boundary layer. The solution on the local grid reveals details of the shock structure and a jet-like flow emanating from the root of the normal shock in the shock boundary layer interaction zone.

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Garthwaite, Matthew Campbell. "Deformation of Tibet : InSAR analysis and viscous flow models." Thesis, University of Leeds, 2011. http://etheses.whiterose.ac.uk/2611/.

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The Tibetan plateau in central Asia is a prime example of the distributed deformation that occurs in the lithosphere as a result of continental collision. Large scale lithospheric deformation can be estimated using viscous continuum models that balance the vertical stress induced by lateral variations of potential energy, and horizontal stress induced by tectonic boundary forces. I find that the 2-dimensional Thin Viscous Sheet (TVS) model gives a good approximation to deformation during continental collision, providing that the indenter half-width is greater than the lithospheric thickness. However even when this ratio approaches one, reasonable correspondence exists when the strain-rate exponent (n) of the rheological constitutive law is ≤ 3. By applying the TVS to model the contemporary deformation of Asia, I find that the first order features of the geodetically-determined velocity field can be explained. Models which can best predict the observed velocity field have n between 2 and 5 Argand numbers of between 1 and 4, and the strength of the Tibetan plateau and Tien Shan is between 3 and 8 times weaker than the foreland regions. Models with these parameters give a value of FL = 7-15x1012 N m-1 for the vertically integrated horizontal driving force on the Himalayan arc. I describe the π-rate method for determining slow linear deformation rates from Interferometric Synthetic Aperture Radar (InSAR) observations and validate it using synthetic data. When using real data, the π-rate method out-performs the conventional stacking method. The RMS difference between the two methods and observed GPS measurements are 3.7 and 7.1 mm/yr for π-rate and stacking respectively. I used the ~rate method to determine the interseismic velocity field across the Tibetan plateau in an approximately north-south orientated, ~1000 km-long swath using ESA Envisat data spanning a period of 6.23 years. The resulting InSAR rate map indicates a factor of 2 variation in the magnitude of line-of-sight (LOS) velocity between the latitudes of 29-40oN. Significant localisation of deformation around mapped fault zones is not observed. A deviation of up to 8 mm/yr in LOS between the InSAR rate map and GPS-derived horizontal velocity field suggests either ~8 mm/yr of vertical uplift, an additional ~20 mm/yr of eastward motion, or a combination of horizontal and vertical motion that has not been measured using horizontal-component campaign GPS data. Comparison of InSAR and GPS observations with predictions of kinematic block and viscous continuum models suggests that the latter provides a more useful description for large-scale continental deformation.

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Книги з теми "Viscous flow Mathematical models"

Laminar viscous flow. New York: Springer, 1995.

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Numerical computation of compressible and viscous flow. Reston, Virginia: American Institute of Aeronautics and Astronautics, Inc., 2014.

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Rose, M. E. Numerical methods for incompressible viscous flows with engineering aplications. Norfolk, Va: Department of Mechanical Engineering & Mechanics, College of Engineering & Technology, Old Dominion University, 1988.

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Pao, Yih-Ho. Time-dependent viscous incompressible flow past a finite flat plate. [Seattle, Wash.]: Boeing Scientific Research Laboratories, Flight Sciences Laboratory, 1986.

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Pao, Yih-Ho. Time-dependent viscous incompressible flow past a finite flat plate. [Seattle, Wash.]: Boeing Scientific Research Laboratories, Flight Sciences Laboratory, 1986.

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Bielski, W. Nonstationary flows of viscous fluids through porous elastic media: Homogenization method. Warszawa: Institute of Geophysics, Polish Academy of Sciences, 2005.

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Lliboutry, Luis. Very slow flows of solids: Basics of modeling in geodynamics and glaciology. Dordrecht: Martinus Nijhoff, 1987.

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Bartel, Robert E. Prediction of transonic vortex flows using linear and nonlinear turbulent eddy viscosity models. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 2000.

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Introduction to the numerical analysis of incompressible viscous flows. Philadelphia: Society for Industrial and Applied Mathematics, 2008.

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Golovachov, Yuri P. Numerical simulation of viscous shock layer flows. Dordrecht: Kluwer Academic Publishers, 1995.

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Частини книг з теми "Viscous flow Mathematical models"

Chetverushkin, Boris N., and Eugene V. Shilnikov. "Unsteady Viscous Flow Simulation Based on QGD System." In Mathematical Models of Non-Linear Excitations, Transfer, Dynamics, and Control in Condensed Systems and Other Media, 137–46. Boston, MA: Springer US, 1999. http://dx.doi.org/10.1007/978-1-4615-4799-0_11.

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Abels, Helmut, and Harald Garcke. "Weak Solutions and Diffuse Interface Models for IncompressibleTwo-Phase Flows." In Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 1267–327. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-13344-7_29.

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Abels, Helmut, and Harald Garcke. "Weak Solutions and Diffuse Interface Models for Incompressible Two-Phase Flows." In Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 1–60. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-10151-4_29-1.

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Azevedo, A. V., and D. Marchesin. "Multiple Viscous Profile Riemann Solutions in Mixed Elliptic-Hyperbolic Models for Flow in Porous Media." In The IMA Volumes in Mathematics and Its Applications, 1–17. New York, NY: Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4613-9049-7_1.

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Aupoix, B. "Experimental Validation of Hypersonic Viscous Flow Models." In New Trends in Instrumentation for Hypersonic Research, 41–50. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1828-6_4.

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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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Kobayashi, K., Y. Ohura, and K. Onishi. "Computer Programme KYOKAI.F for Viscous and Thermal Fluid Flow Problems." In Mathematical and Computational Aspects, 579–92. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-662-21908-9_39.

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Colli, Pierluigi, Gianni Gilardi, and Jürgen Sprekels. "Nonlocal Phase Field Models of Viscous Cahn–Hilliard Type." In CIM Series in Mathematical Sciences, 71–100. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-33116-0_3.

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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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Тези доповідей конференцій з теми "Viscous flow Mathematical models"

Boretti, A. A. "Compressible, Turbulent, Viscous Flow Computations for Blade Aerodynamic and Heat Transfer." In ASME 1996 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-gt-178.

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The paper presents a computer code for steady and unsteady, three-dimensional, compressible, turbulent, viscous flow simulations. The mathematical model is based on the Favre-averaged Navier-Stokes conservation equations, closed by a statistical model of turbulence. Turbulence effects are represented by using a low Reynolds number K-ω model. The numerical model makes use of a finite difference approximation in generalized coordinates for space discretization. The solution of time-dependent, three-dimensional, non-homogeneous, partial differential equations is obtained by solving, in a prescribed, symmetric pattern, three time-dependent, one-dimensional, homogeneous partial differential equations, representing convection and diffusion along each generalized coordinate direction, and one ordinary differential equation, representing generation and destruction. An explicit, multi-step, dissipative, Runge-Kutta scheme is finally adopted for time discretization. The code is applied to simulate the flow through a linear cascade of turbine rotor blades, where detailed experimental data are available. Blade aerodynamic and heat transfer are computed, at variable Reynolds and Mach numbers and turbulence levels, and compared with experimental data. While the aerodynamic prediction is relatively unaffected by the properties of both mathematical and numerical models, the heat transfer prediction proves to be extremely sensitive to models details. Low Reynolds number K-ω turbulence models theoretically reproduce laminar, turbulent and transitional boundary layers. However, their practical use in a Navier-Stokes code does not allow to entirely capture the effects of turbulence intensity and Mach and Reynolds numbers on blade heat transfer.

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Wanderley, Juan B. V., and Carlos Levi. "Free Surface Viscous Flow Around a Ship Model." In 25th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/omae2006-92165.

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The present stage of viscous flow numerical analysis combined with computer technology latest advances made viable the mathematical treatment of many robust and complex engineering problems of practical interest. Some numerical problems which solutions would be just unthinkable not more than ten years ago may be now dealt with in a reliable and fairly accurate manner. A truly example of this kind of problem would be the calculation of hydrodynamic loads acting on yawing ships. The solution of such a problem raises practical interest due to applications, for instance, as in the case of stationary FPSO/FSO ships facing sea currents, commonly used in offshore deep-water oil production. In the present solution, the complete incompressible Navier–Stokes (N-S) equations are solved by means of an algorithm that applies the Beam and Warming [1] approximated factorization scheme to simulate the flow around a Wigley’s hull. The numerical code was implemented using Message Passage Interface (MPI) and can be run in a cluster with an arbitrary number of computers. The good agreement with other numerical and experimental data obtained from the literature and high efficiency of the algorithm indicated its potential to be used as an effective tool in ship design.

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Wang, X. Sheldon. "A Simplified Model of Flow-Induced Oscillations of Collapsible Tubes Conveying Viscous Fluids." In ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/pvp2006-icpvt-11-93851.

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In this paper, a simple mathematical model is formulated to study the static and dynamic instabilities of collapsible tubes conveying viscous fluids. The governing equations of motion for the pipe are derived under small deformation assumptions with the consideration of fluid frictional forces and inertia effects. In the case of steady flow, both buckling and flutter instabilities can be predicted based on the real and imaginary parts of the eigenvalues. In the case of pulsatile flow, the Bolotin method is employed to identify the dynamic stability regions.

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Bhuiyan, A. S., M. R. Biswas, Ilias Kotsireas, Roderick Melnik, and Brian West. "Effects of Pressure Stress Work and Viscous Dissipation in Mixed Convection Flow Along a Vertical Flat Plate." In ADVANCES IN MATHEMATICAL AND COMPUTATIONAL METHODS: ADDRESSING MODERN CHALLENGES OF SCIENCE, TECHNOLOGY, AND SOCIETY. AIP, 2011. http://dx.doi.org/10.1063/1.3663449.

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Fomin, Sergei A., Konstantin G. Kornev, Chris Wolter, Jon Young, and Tyler Brandenburg. "Mathematical Modeling of the Polymer Rotational Molding." In ASME/JSME 2007 5th Joint Fluids Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/fedsm2007-37619.

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We study the rimming flow of a viscoelastic film on the inner surface of a horizontal rotating cylinder. Simple lubrication theory is applied assuming that the Reynolds number is small and the liquid film is thin. For the steady-state flow of the Upper-Convected Maxwell (UCM) fluid the mathematical model reduces to a first order nonlinear ODE for the film thickness. We show that the liquid viscoelasticity changes the flow structure. In particular, the singularity observed for viscous liquids within the same lubrication approximation can be eliminated due liquid elasticity. We performed a detailed numeric analysis of the model and revealed some criticality regimes which are specific only for viscoelastic liquids.

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Okafor, Charles, Patrick Verdin, and Phill Hart. "CFD Investigation of Downhole Natural Gas Separation Efficiency in the Churn Flow Regime." In SPE Gulf Coast Section Electric Submersible Pumps Symposium. SPE, 2021. http://dx.doi.org/10.2118/204509-ms.

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Abstract Downhole Natural Gas Separation Efficiency (NGSE) is flow regime dependent, and current analytical models in certain conditions lack accuracy. Downhole NGSE was investigated through 3D Computational Fluid Dynamics (CFD) transient simulations for pumping wells in the Churn flow regime. The Volume of Fluid (VOF) multiphase model was considered along with the k – ε turbulence model for most simulations. A mesh independence study was performed, and the final model results validated against experimental data, showing an average error of less than 6 %. Numerical simulation results showed that the steady state assumption used by current mathematical models for churn flow can be inaccurate. Several key parameters affecting the NGSE were identified, and suggestions for key improvements to the widely used mathematical formulations for viscous flow provided. Sensitivity studies were conducted on fluid/geometric parameters and operating conditions, to gain a better understanding of the influence of each parameter on NGSE. These are important results as they equip the ESP engineer with additional knowledge to maximise the NGSE from design stage to pumping operations.

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Nakate, Prajakta, Domenico Lahaye, Cornelis Vuik, and Marco Talice. "Systematic Development and Mesh Sensitivity Analysis of a Mathematical Model for an Anode Baking Furnace." In ASME 2018 5th Joint US-European Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/fedsm2018-83131.

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The anode baking process is developed and improved since the 1980s due to its importance in Aluminium industry. The process is characterized by multiple physical phenomena including turbulent flow, combustion process, conjugate heat transfer, and radiation. In order to obtain an efficient process with regards to quality of anodes, soot-free combustion, reduction of NOx and minimization of energy, a mathematical model can be developed. A mathematical model describes the physical phenomena and provides a deeper understanding of the process. Turbulent flow is one of the important physical phenomena in an anode baking process. In the present work, isothermal turbulent flow is studied in detail with respect to two turbulence models in COMSOL Multiphysics software. The difference between wall boundary conditions for these models and their sensitivity towards the boundary layer mesh is investigated. A dimen-sionless distance in viscous scale units is used as a parameter for comparison of models with and without a boundary layer mesh. The investigation suggests that the boundary layer mesh for both turbulence models increase the accuracy of flow field near walls. Moreover, it is observed that along with the accuracy, the numerical convergence of Spalart-Allmaras turbulence model in COMSOL Multiphysics is highly sensitive to the boundary layer mesh. Therefore, development of converged Spalart-Allmaras model for the complete geometry is difficult due to the necessity of refined mesh. Whereas, the numerical convergence of k-ε model in COMSOL Multiphysics is less sensitive to the dimen-sionless viscous scale unit distance. A converged solution of the complete geometry k-ε model is feasible to obtain even with less refined mesh at the boundary. However, a comparison of a developed solution of k-ε model with another simulation environment indicates differences which enhance the requirement of having converged Spalart-Allmaras model for complete geometry.

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Pereira, Filipe S., Guilherme Vaz, Luís Eça, and Sébastien Lemaire. "On the Numerical Prediction of Transitional Flows With Reynolds-Averaged Navier-Stokes and Scale-Resolving Simulation Models." In ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/omae2016-54414.

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The present work investigates the transitional flow around a smooth circular cylinder at Reynolds number Re = 140,000. The flow is resolved using the viscous-flow solver ReFRESCO, and distinct mathematical models are applied to assess their ability to handle transitional flows. The selected mathematical models are the Reynolds-Averaged Navier-Stokes equations (RANS), Scale-Adaptive Simulation (SAS), Delayed Detached-Eddy Simulation (DDES), eXtra Large-Eddy Simulation (XLES) and Partially-Averaged Navier-Stokes (PANS) equations. The RANS equations are supplemented with the k–ω Shear-Stress Transport (SST) with and without the Local Correlation Transition Model (LCTM). The numerical simulations are carried out using structured grids ranging from 9.32 × 104 to 2.24 × 107 cells, and a dimensionless time-step of 1.50 × 10−3. As expected, the outcome demonstrates that transition from laminar to turbulent regime is incorrectly predicted by the k–ω SST model. Transition occurs upstream of the flow separation, which is typical of the supercritical regime and so the flow physics is incorrectly modelled. Naturally, all Scale-Resolving Simulation (SRS) models that rely on RANS to solve the boundary-layer, called hybrid models, will exhibit a similar trend. On the other hand, mathematical models capable to resolve part of the turbulence field in the boundary layer (PANS) lead to a better agreement with the experimental data. Furthermore, the k–ω SST LCTM is also able to improve the modelling accuracy when compared to the k–ω SST. Therefore, it might be a valuable engineering tool if its computational demands are considered (in the RANS context). Therefore, the results confirm that the choice of the most appropriate mathematical model for the simulation of turbulent flows is not straightforward and it may depend on the details of the flow physics.

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Giles, Michael, and Robert Haimes. "Validation of a Numerical Method for Unsteady Flow Calculations." In ASME 1991 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/91-gt-271.

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This paper describes and validates a numerical method for the calculation of unsteady inviscid and viscous flows. A companion paper compares experimental measurements of unsteady heat transfer on a transonic rotor with the corresponding computational results. The mathematical model is the Reynolds-averaged unsteady Navier-Stokes equations for a compressible ideal gas. Quasi-three-dimensionality is included through the use of a variable streamtube thickness. The numerical algorithm is unusual in two respects: a) for reasons of efficiency and flexibility it uses a hybrid Navier-Stokes/Euler method, and b) to allow for the computation of stator/rotor combinations with arbitrary pitch ratio a novel space-time coordinate transformation is used. Several test cases are presented to validate the performance of the computer program, UNSFLO. These include: a) unsteady, inviscid flat plate cascade flows, b) steady and unsteady, viscous flat plate cascade flows, c) steady turbine heat transfer and loss prediction. In the first two sets of cases comparisons are made with theory, and in the third the comparison is with experimental data.

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Escandón, Juan P., and David A. Torres. "Analysis of Combined Electroosmotic and Pressure Driven Flow of Multilayer Immiscible Fluids in a Narrow Capillary." In ASME 2019 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/imece2019-10466.

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Abstract This paper presents the analytical solution of a combined electroosmotic and pressure driven flow of multilayer immiscible fluids in a narrow capillary. The mathematical model is based in the Poisson-Boltzmann equation and the modified Navier-Stokes equations. In the steady-state analysis, we consider different conditions at the interfaces between the fluids as potential differences, surface charge densities and electro-viscous stresses balances, which are discussed in detail. Results show the transport phenomena coupled in the description of velocity distribution, by the analyzing of the dimensionless parameters obtained, such as: potential differences, surface charge densities, electrokinetic parameters, term involving the external pressure gradient, ratios of viscosity and of dielectric permittivity. Here, the presence of a net electric charges balance at the interfaces breaks the continuity of the electric potential distributions and viscous shear stresses, modifying the flow field; thus, the electrical conditions established at the interfaces play an important role on the flow behavior. The present work, in which the velocity field is described, aims to be an important contribution in the development of theoretical models that provide a better understanding about labs-on-a-chip design.

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