Relevant bibliographies by topics / Coriolis number

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

Academic literature on the topic 'Coriolis number'

Author: Grafiati
Published: 28 June 2021
Last updated: 13 February 2022

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Journal articles on the topic "Coriolis number"

1

Cho, H. C., and F. C. Chou. "Rivulet Instability with Effect of Coriolis Force." Journal of Mechanics 22, no. 3 (September 2006): 221–27. http://dx.doi.org/10.1017/s1727719100000861.

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AbstractThe effect of Coriolis force on the rivulet (fingering) instability, the onset of rivulet phenomena during spin coating, is investigated by flow visualization experiments incorporating with dimensional analysis. This study demonstrates that the Coriolis force will affect significantly the critical radius of rivulet instability and the deflection angle of instability rivulet. For the cases of low Bond number, the effect of Coriolis force is a stabilizing factor, and the dimensionless critical radius increases slightly with increasing rotational Reynolds number Reω. In the case of high Bond number, the effect of Coriolis force becomes a destabilizing factor while Reω < 1, and a characteristic length is found by balancing the viscous force with the surface tension. For Reω > 1, the radial Corilois force, which is always pointing inward, plays a stabilizing role with magnitude Reω2.
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Khiri, Rachid. "Coriolis effect on convection for a low Prandtl number fluid." International Journal of Non-Linear Mechanics 39, no. 4 (June 2004): 593–604. http://dx.doi.org/10.1016/s0020-7462(02)00225-1.

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Nakabayashi, Koichi, and Osami Kitoh. "Low Reynolds number fully developed two-dimensional turbulent channel flow with system rotation." Journal of Fluid Mechanics 315 (May 25, 1996): 1–29. http://dx.doi.org/10.1017/s0022112096002303.

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Theoretical and experimental studies have been performed on fully developed twodimensional turbulent channel flows in the low Reynolds number range that are subjected to system rotation. The turbulence is affected by the Coriolis force and the low Reynolds number simultaneously. Using dimensional analysis, the relevant parameters of this flow are found to be Reynolds number Re* = u*D/v (u* is the friction velocity, D the channel half-width) and Ωv/u2* (Ω is the angular velocity of the channel) for the inner region, and Re* and ΩD/u* for the core region. Employing these parameters, changes of skin friction coefficients and velocity profiles compared to nonrotating flow can be reasonably well understood. A Coriolis region where the Coriolis force effect predominates is shown to exist in addition to conventional regions such as viscous and buffer regions. A flow regime diagram that indicates ranges of these regions as a function of Re* and |Ω|v/u2* is given from which the overall flow structure in a rotating channel can be obtained.Experiments have been made in the range of 56 ≤ Re* ≤ 310 and -0.0057 ≤ Ωv/u2* ≤ 0.0030 (these values correspond to Re = 2UmD/v from 1700 to 10000 and rotation number R0 = 2|Ω|D/Um up to 0.055; Um is bulk mean velocity). The characteristic features of velocity profiles and the variation of skin friction coefficients are discussed in relation to the theoretical considerations.
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Ivers, D. J., A. Jackson, and D. Winch. "Enumeration, orthogonality and completeness of the incompressible Coriolis modes in a sphere." Journal of Fluid Mechanics 766 (February 4, 2015): 468–98. http://dx.doi.org/10.1017/jfm.2015.27.

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AbstractWe consider incompressible flows in the rapid-rotation limit of small Rossby number and vanishing Ekman number, in a bounded volume with a rigid impenetrable rotating boundary. Physically the flows are inviscid, almost rigid rotations. We interpret the Coriolis force, modified by a pressure gradient, as a linear operator acting on smooth inviscid incompressible flows in the volume. The eigenfunctions of the Coriolis operator $\boldsymbol{{\mathcal{C}}}$ so defined are the inertial modes (including any Rossby modes) and geostrophic modes of the rotating volume. We show $\boldsymbol{{\mathcal{C}}}$ is a bounded operator and that $-\text{i}\boldsymbol{{\mathcal{C}}}$ is symmetric, so that the Coriolis modes of different frequencies are orthogonal. We prove that the space of incompressible polynomial flows of degree $N$ or less in a sphere is invariant under $\boldsymbol{{\mathcal{C}}}$. The symmetry of $-\text{i}\boldsymbol{{\mathcal{C}}}$ thus implies the Coriolis operator is non-defective on the finite-dimensional space of spherical polynomial flows. This enables us to enumerate the Coriolis modes, and to establish their completeness using the Weierstrass polynomial approximation theorem. The fundamental tool, which is required to establish invariance of spherical polynomial flows under $\boldsymbol{{\mathcal{C}}}$ and completeness, is that the solution of the polynomial Poisson–Neumann problem, i.e. Poisson’s equation with a Neumann boundary condition and polynomial data, in a sphere is a polynomial. We also enumerate the Coriolis modes in a sphere, with careful consideration of the geostrophic modes, directly from the known analytic solutions.
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Kumar, Vivek, and Martin Anklin. "Numerical simulations of Coriolis flow meters for low Reynolds number flows." MAPAN 26, no. 3 (September 2011): 225–35. http://dx.doi.org/10.1007/s12647-011-0021-6.

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Chan, Kwing L. "‘Negative’ surface differential rotation in stars having low Coriolis numbers (slow rotation or high turbulence)." Proceedings of the International Astronomical Union 5, S264 (August 2009): 219–21. http://dx.doi.org/10.1017/s1743921309992663.

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AbstractA general picture of differential rotation in cool stars is that they are ‘solar-like’, with the equator spinning faster than the poles. Such surface differential rotation profiles have also been demonstrated by some three-dimensional simulations. In our numerical investigation of rotating convection (both regional and global), we found that this picture is not universally applicable. The equator may spin substantially slower than the poles (Ωequator − Ωpole)/Ω can reach −50%). The key parameter that determines the transition in behavior is the Coriolis number (inverse Rossby number). ‘Negative’ differential rotation of the equator (relative to the mean rotation) occurs if the Coriolis number is below a critical value.
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Eley, R., C. H. J. Fox, and S. McWilliam. "The dynamics of a vibrating-ring multi-axis rate gyroscope." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 214, no. 12 (December 1, 2000): 1503–13. http://dx.doi.org/10.1243/0954406001523443.

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A novel, multi-axis rate sensor based on the vibration properties of a ring structure is presented. Vibrating ring structures have been used successfully to detect rates applied about the axis perpendicular to the plane of the ring using Coriolis coupling between in-plane displacements. The presented multi-axis sensor is capable of detecting rate applied about three mutually perpendicular axes using Coriolis coupling between in-plane and out-of-plane displacements. The steady state amplitude of the induced displacements are proportional to the applied rate. Coriolis coupling is only present for certain combinations of in-plane and out-of-plane displacement patterns, which allows a number of feasible concepts for two- and three-axis rate sensitivity.
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Oke, Abayomi S., Winifred N. Mutuku, Mark Kimathi, and Isaac L. Animasaun. "Insight into the dynamics of non-Newtonian Casson fluid over a rotating non-uniform surface subject to Coriolis force." Nonlinear Engineering 9, no. 1 (October 13, 2020): 398–411. http://dx.doi.org/10.1515/nleng-2020-0025.

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AbstractCasson fluid model is the most accurate mathematical expression for investigating the dynamics of fluids with non-zero plastic dynamic viscosity like that of blood. Despite huge number of published articles on the transport phenomenon, there is no report on the increasing effects of the Coriolis force. This report presents the significance of increasing not only the Coriolis force and reducing plastic dynamic viscosity, but also the Prandtl number and buoyancy forces on the motion of non-Newtonian Casson fluid over the rotating non-uniform surface. The relevant body forces are derived and incorporated into the Navier-Stokes equations to obtain appropriate equations for the flow of Newtonian Casson fluid under the action of Coriolis force. The governing equations are non-dimensionalized using Blasius similarity variables to reduce the nonlinear partial differential equations to nonlinear ordinary differential equations. The resulting system of nonlinear ordinary differential equations is solved using the Runge-Kutta-Gills method with the Shooting technique, and the results depicted graphically. An increase in Coriolis force and non-Newtonian parameter decreases the velocity profile in the x-direction, causes a dual effect on the shear stress, increases the temperature profiles, and increases the velocity profile in the z-direction.
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Riahi, D. H. "The effect of Coriolis force on nonlinear convection in a porous medium." International Journal of Mathematics and Mathematical Sciences 17, no. 3 (1994): 515–36. http://dx.doi.org/10.1155/s0161171294000761.

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Nonlinear convection in a porous medium and rotating about vertical axis is studied in this paper. An upper bound to the heat flux is calculated by the method initiated first by Howard [6] for the case of infinite Prandtl number.ForTa≪0(1), the rotational effect is not significant. For0(1)≪Ta≪0(RlogR), the Nusselt number decreases with increasingTafor a given Rayleigh numberR. The flow has always a finite number of modes, but with increasingTain this region, the number of modes decreases. The functional dependence of the Nusselt number onRandTais found to have discontinuities as the number of modesN*reduces toN*−1. For0(RlogR)≪Ta≪0(R), the Nusselt number is proportional toRTa(logRTa). The stabilizing effect of rotation is so strong that the optimal solution has left with only one horizontal mode. ForTa=0(R), the Nusselt number becomes0(1)and the convection is inhibited entirely by rotation forTa>1π2R.
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Chan, Kwing L. "A finite-difference convective model for Jupiter's equatorial jet." Proceedings of the International Astronomical Union 2, S239 (August 2006): 230–32. http://dx.doi.org/10.1017/s174392130700049x.

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AbstractWe present results of a numerical model for studying the dynamics of Jupiter's equatorial jet. The computed domain is a piece of spherical shell around the equator. The bulk of the region is convective, with a thin radiative layer at the top. The shell is spinning fast, with a Coriolis number = ΩL/V on the order of 50. A prominent super-rotating equatorial jet is generated, and secondary alternating jets appear in the higher latitudes. The roles of terms in the zonal momentum equation are analyzed. Since both the Reynolds number and the Taylor number are large, the viscous terms are small. The zonal momentum balance is primarily between the Coriolis and the Reynolds stress terms.
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Dissertations / Theses on the topic "Coriolis number"

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Lewis, Tanat. "Numerical simulation of buoyancy-induced flow in a sealed rotating cavity." Thesis, University of Bath, 1999. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.285311.

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Bourouiba, Lydia. "Numerical and theoretical study of homogeneous rotating turbulence." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=115861.

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The Coriolis force has a subtle, but significant impact on the dynamics of geophysical and astrophysical flows. The Rossby number, Ro, is the nondimensional parameter measuring the relative strength of the Coriolis term to the nonlinear advection terms in the equations of motion. When the rotation is strong, Ro goes to zero and three-dimensional flows are observed to two-dimensionalize. The broad aim of this work is to examine the effect of the strength of rotation on the nonlinear dynamics of turbulent homogeneous flows. Our approach is to decompose the rotating turbulent flow modes into two classes: the zero-frequency 2-dimensional (2D) modes; and the high-frequency inertial waves (3D).
First, using numerical simulations of decaying turbulence over a large range of Ro we identified three regimes. The large Ro regime is similar to non-rotating, isotropic turbulence. The intermediate Ro regime shows strong 3D-to-2D energy transfers and asymmetry between cyclones (corotating) and anticyclones (couter-rotating), whereas at small Ro regime these features are much reduced.
We then studied discreteness effects and constructed a kinematic model to quantify the threshold of nonlinear broadening below which the 2D-3D interactions critical to the intermediate Ro regime are not captured. These results allow for the improvement of numerical studies of rotating turbulence and refine the comparison between results obtained in finite domains and theoretical results derived in unbounded domains.
Using equilibrium statistical mechanics, we examined the hypothesis of decoupling predicted in the small Ro regime. We identified a threshold time, t☆ = 2/Ro2, after which the asymptotic decoupling regime is no longer valid. Beyond t ☆, we show that the quasi-invariants of the decoupled model continue to constrain the system on the short timescales.
We found that the intermediate Ro regime is also present in forced turbulence and that interactions responsible for it are nonlocal. We explain a steep slope obtained in the 2D energy spectrum by a downscale enstrophy transfer. The energy of the 2D modes is observed to accumulate in the largest scales of the domain in the long-time limit. This is reminiscent of the "condensation" observed in classical forced 2D flows and magnetohydrodynamics.
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Šuráň, David. "Vliv nastavitelných vestaveb v savce turbiny na charakteristiku a tlakové pulzace." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-444634.

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This master’s thesis deals with the draft tube and its optimization for various operating conditions. The research investigates the theoretical description and function of the draft tube and explains known methods of suppressing pressure pulsation so far. In the computational part, the author proposes a new method and designs optimal geometry of adjustable installations (ribs) for the draft tube. Finally, the comparison with the default geometry without ribs is performed.
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Haugen, Christina G. M. "Numerical Investigation of Thermal Performance for Rotating High Aspect Ratio Serpentine Passages." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1412698677.

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Do, Minh Hieu. "Analyse mathématique de schémas volume finis pour la simulation des écoulements quasi-géostrophiques à bas nombre de Froude." Thesis, Sorbonne Paris Cité, 2017. http://www.theses.fr/2017USPCD087/document.

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The shallow water system plays an important role in the numerical simulation of oceanic models, coastal flows and dam-break floods. Several kinds of source terms can be taken into account in this model, such as the influence of bottom topography, Manning friction effects and Coriolis force. For large scale oceanic phenomena, the Coriolis force due to the Earth’s rotation plays a central role since the atmospheric or oceanic circulations are frequently observed around the so-called geostrophic equilibrium which corresponds to the balance between the pressure gradient and the Coriolis source term. The ability of numerical schemes to well capture the lake at rest, has been widely studied. However, the geostrophic equilibrium issue, including the divergence free constraint on the velocity, is much more complex and only few works have been devoted to its preservation. In this manuscript, we design finite volume schemes that preserve the discrete geostrophic equilibriuminordertoimprovesignificantlytheaccuracyofnumericalsimulationsofperturbations around this equilibrium. We first develop collocated and staggered schemes on rectangular and triangular meshes for a linearized model of the original shallow water system. The crucial common point of the various methods is to adapt and combine several strategies known as the Apparent Topography, the Low Mach and the Divergence Penalisation methods, in order to handle correctly the numerical diffusions involved in the schemes on different cell geometries, so that they do not destroy geostrophic equilibria. Finally, we extend these strategies to the non-linear case and show convincing numerical results
Le système de Saint-Venant joue un rôle important dans la simulation de modèles océaniques, d’écoulements côtiers et de ruptures de barrages. Plusieurs sortes de termes sources peuvent être pris en compte dans ce modèle, comme la topographie, les effets de friction de Manning et la force de Coriolis. Celle-ci joue un rôle central dans les phénomènes à grande échelle spatiale car les circulations atmosphériques ou océaniques sont souvent observées autour de l’équilibre géostrophique qui correspond à l’équilibre du gradient de pression et de cette force. La capacité des schémas numériques à bien reproduire le lac au repos a été largement étudiée; en revanche, la question de l’équilibre géostrophique (incluant la contrainte de vitesse à divergence nulle) est beaucoup plus complexe et peu de travaux lui ont été consacrés. Dans cette thèse, nous concevons des schémas volumes finis qui préservent les équilibres géostrophiques discrets dans le but d’améliorer significativement la précision des simulations numériques de perturbations autour de ces équilibres. Nous développons tout d’abord des schémas colocalisés et décalés sur des maillages rectangulaires ou triangulaires pour une linéarisation du modèle d’origine. Le point commun décisif de ces méthodes est d’adapter et de combiner les stratégies dites "topographie apparente", "bas Mach" et "pénalisation de divergence" pour contrôler l’effet de la diffusion numérique contenue dans les schémas, de telle sorte qu’elle ne détruise pas les équilibres géostrophiques. Enfin, nous étendons ces stratégies au cas non-linéaire et montrons des résultats prometteurs
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Sleiti, Ahmad Khalaf. "EFFECT OF CORIOLIS AND CENTRIFUGAL FORCES ON TURBULENCE AND TRANSPORT AT HIGH ROTATION AND BUOYANCY NUMBERS." Doctoral diss., University of Central Florida, 2004. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/4408.

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This study attempts to understand one of the most fundamental and challenging problems in fluid flow and heat transfer for rotating machines. The study focuses on gas turbines and electric generators for high temperature and high energy density applications, respectively, both which employ rotating cooling channels so that materials do not fail under high temperature and high stress environment. Prediction of fluid flow and heat transfer inside internal cooling channels that rotate at high rotation number and high density ratio similar to those that are existing in turbine blades and generator rotors is the main focus of this study. Both smooth-wall and rib-roughened channels are considered here. Rotation, buoyancy, bends, ribs and boundary conditions affect the flow inside theses channels. Ribs are introduced inside internal cooling channel in order to enhance the heat transfer rate. The use of ribs causes rapid increase in the supply pressure, which is already limited in a turbine or a generator and requires high cost for manufacturing. Hence careful optimization is needed to justify the use of ribs. Increasing rotation number (Ro) is another approach to increase heat transfer rate to values that are comparable to those achieved by introduction of ribs. One objective of this research is to study and compare theses two approaches in order to decide the optimum range of application and a possible replacement of the high-cost and complex ribs by increasing Ro. A fully computational approach is employed in this study. On the basis of comparison between two-equation (k-[epsilon] and k-[omega]) and RSM turbulence models, against limited available experimental data, it is concluded that the two-equation turbulence models cannot predict the anisotropic turbulent flow field and heat transfer correctly, while RSM showed improved prediction. For the near wall region, two approaches with standard wall functions and enhanced near wall treatment were investigated. The enhanced near wall approach showed superior results to the standard wall functions approach. Thus RSM with enhanced near wall treatment is validated against available experimental data (which are primarily at low rotation and buoyancy numbers). The model was then used for cases with high Ro (as much as 1.29) and high-density ratios (DR) (up to 0.4). Particular attention is given to how turbulence intensity, Reynolds stresses and transport are affected by Coriolis and buoyancy/centrifugal forces caused by high levels of Ro and DR. Variations of flow total pressure along the rotating channel are also predicted. The results obtained are explained in view of physical interpretation of Coriolis and centrifugal forces. Investigation of channels with smooth and with rib-roughened walls that are rotating about an orthogonal axis showed that increasing Ro always enhances turbulence and the heat transfer rate, while at high Ro, increasing DR although causes higher turbulence activity but does not necessarily increase Nu and in some locations even decreases Nu. The increasing thermal boundary layer thickness near walls is the possible reason for this behavior of Nu. The heat transfer enhancement for smooth-wall cases correlates linearly with Ro (with other parameters are kept constant) and hence it is possible to derive linear correlation for the increase in Nu as a function of Ro. Investigation of channels with rib-roughened walls that rotate about orthogonal axis showed that 4-side-average Nur correlates with Ro linearly, where a linear correlation for Nur/Nus as a function of Ro is derived. It is also observed that the heat transfer rate on smooth-wall channel can be enhanced rapidly by increasing Ro to values that are comparable to the enhancement due to the introduction of ribs inside internal cooling channels. This observation suggests that ribs may be unnecessary in high-speed machines, and has tremendous implications for possible cost savings in these machines. In square channels that rotate about parallel axis, the heat transfer rate enhances with Ro on three surfaces of the square channel and decreases on the inner surface (that is the one closest to the axis of rotation). However, the four-sides average Nu increases with Ro. Increasing wall heat flux at high Ro does not necessarily increase Nu on walls although higher turbulence activity is observed. This study examines the rich interplay of physics under the simultaneous actions of Coriolis and centrifugal/buoyancy forces in one of the most challenging internal flow configurations. Several important conclusions are reached from this computational study that may have far-reaching implications on how turbine blades and generator rotors are currently designed. Since the computation study in not validated for high Ro cases, these important results call for a experimental investigation.
Ph.D.
Department of Mechanical, Materials and Aerospace Engineering
Engineering and Computer Science
Mechanical, Materials and Aerospace Engineering
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Books on the topic "Coriolis number"

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Yuan, S. P. A near-wall Reynolds-stress closure without wall normals. [Washington, DC: National Aeronautics and Space Administration, 1997.

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C, So Ronald M., and United States. National Aeronautics and Space Administration., eds. A near-wall Reynolds-stress closure without wall normals: Final report ... under grant number NAG-1-1772. Tempe, Ariz: College of Engineering and Applied Sciences, Arizona State University, 1997.

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C, So Ronald M., and United States. National Aeronautics and Space Administration., eds. A near-wall Reynolds-stress closure without wall normals: Final report ... under grant number NAG-1-1772. Tempe, Ariz: College of Engineering and Applied Sciences, Arizona State University, 1997.

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C, So Ronald M., and United States. National Aeronautics and Space Administration., eds. A near-wall Reynolds-stress closure without wall normals: Final report ... under grant number NAG-1-1772. Tempe, Ariz: College of Engineering and Applied Sciences, Arizona State University, 1997.

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C, So Ronald M., and United States. National Aeronautics and Space Administration., eds. A near-wall Reynolds-stress closure without wall normals: Final report ... under grant number NAG-1-1772. Tempe, Ariz: College of Engineering and Applied Sciences, Arizona State University, 1997.

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C, So Ronald M., and United States. National Aeronautics and Space Administration., eds. A near-wall Reynolds-stress closure without wall normals: Under grant NAG1-1772. [Washington, DC: National Aeronautics and Space Administration, 1997.

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C, So Ronald M., and United States. National Aeronautics and Space Administration., eds. A near-wall Reynolds-stress closure without wall normals: Under grant NAG1-1772. [Washington, DC: National Aeronautics and Space Administration, 1997.

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A near-wall Reynolds-stress closure without wall normals: Under grant NAG1-1772. [Washington, DC: National Aeronautics and Space Administration, 1997.

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A near-wall Reynolds-stress closure without wall normals: Under grant NAG1-1772. [Washington, DC: National Aeronautics and Space Administration, 1997.

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Book chapters on the topic "Coriolis number"

1

Chemin, Jean-Yves, Benoit Desjardins, Isabelle Gallagher, and Emmanuel Grenier. "Stability of Horizontal Boundary Layers." In Mathematical Geophysics. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198571339.003.0016.

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Let us now detail the stability properties of an Ekman layer introduced in Part I, page 11. First we will recall how to compute the critical Reynolds number. Then we will describe briefly what happens at larger Reynolds numbers. The first step in the study of the stability of the Ekman layer is to consider the linear stability of a pure Ekman spiral of the form where U∞ is the velocity away from the layer and ζ is the rescaled vertical component ζ = x3/√εν. The corresponding Reynolds number is Let us consider the Navier–Stokes–Coriolis equations, linearized around uE The problem is now to study the (linear) stability of the 0 solution of the system (LNSCε). If u=0 is stable we say that uE is linearly stable, if not we say that it is linearly unstable. Numerical results show that u=0 is stable if and only if Re<Rec where Rec can be evaluated numerically. Up to now there is no mathematical proof of this fact, and it is only possible to prove that 0 is linearly stable for Re<Re1 and unstable for Re>Re2 with Re1<Rec<Re2, Re1 being obtained by energy estimates and Re2 by a perturbative analysis of the case Re=∞. We would like to emphasize that the numerical results are very reliable and can be considered as definitive results, since as we will see below, the stability analysis can be reduced to the study of a system of ordinary differential equations posed on the half-space, with boundary conditions on both ends, a system which can be studied arbitrarily precisely, even on desktop computers (first computations were done in the 1960s by Lilly).
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Chemin, Jean-Yves, Benoit Desjardins, Isabelle Gallagher, and Emmanuel Grenier. "Other Systems." In Mathematical Geophysics. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198571339.003.0017.

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The methods developed in this book can be applied to various physical systems. We will not detail all the possible applications and will only quote three systems arising in magnetohydrodynamics (MHD) and meteorology, namely conducting fluids in a strong external “large scale” magnetic field, a classical MHD system with high rotation, and the quasigeostrophic limit. The main theorems of this book can be extended to these situations. The theory of rotating fluids is very close to the theory of conducting fluids in a strong magnetic field. Namely the Lorenz force and the Coriolis force have almost the same form, up to Ohm’s law. The common feature is that these phenomena appear as singular perturbation skew-symmetric operators. The simplest equations in MHD are Navier–Stokes equations coupled with Ohm’s law and the Lorenz force where ∇φ is the electric field, j the current, and e the direction of the imposed magnetic field. In this case ε is called the Hartmann number. In physical situations, like the geodynamo (study of the magnetic field of the Earth), it is really small, of order 10−5–10−10, much smaller than the Rossby number. These equations are the simplest model in geomagnetism and in particular in the geodynamo. As ε→0 the flow tends to become independent of x3. This is not valid near boundaries. For horizontal boundaries, Hartmann layers play the role of Ekman layers and in the layer the velocity is given by The critical Reynolds number for linear instability is very high, of order Rec ∼ 104. The main reason is that there is no inflexion point in the boundary layer profile (10.1.2), therefore it is harder to destabilize than the Ekman layer since the Hartmann profile is linearly stable for the inviscid model associated with (10.1.1). As for Ekman layers, Hartmann layers are stable for Re<Rec and unstable for Re>Rec. There is also something similar to Ekman pumping, which is responsible for friction and energy dissipation. Vertical layers are simpler than for rotating fluids since there is only one layer, of size (εν)1/4. We refer to for physical studies.
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Conference papers on the topic "Coriolis number"

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Hsieh-chen, HSIEH-CHEN, and Tim Colonius. "Coriolis Effect on Dynamic Stall in a Vertical Axis Wind Turbine at Moderate Reynolds Number." In 32nd AIAA Applied Aerodynamics Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2014. http://dx.doi.org/10.2514/6.2014-3140.

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Elyyan, Mohammad A., and Danesh K. Tafti. "Effect of Coriolis Forces in a Rotating Channel With Dimples and Protrusions." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-66677.

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The use of dimple-protrusions for internal cooling of rotating turbine blades has been investigated. A channel with dimple imprint diameter to channel height ratio (H/D = 1.0), dimple depth to channel height ratio (δ/H = 0.2), spanwise and streamwise pitch to channel height ratios (P/H = S/H = 1.62) was modeled. Four rotation numbers; Rob = 0.0, 0.15, 0.39, and 0.64, at nominal flow Reynolds number, ReH = 10000, were investigated to quantify the effect of Coriolis forces on the flow structure and heat transfer in the channel. Under the influence of rotation, the leading (protrusion) side of the channel showed weaker flow impingement, larger wakes and delayed flow reattachment with increasing rotation number. The trailing (dimple) side experienced a smaller recirculation region inside the dimple and stronger flow ejection from the dimple cavity with increasing rotation. Secondary flow structures in the cross-section played a major role in transporting momentum away from the trailing side at high rotation numbers and limiting heat transfer augmentation. While heat transfer augmentation on the trailing side increases by over 90% at Rob = 0.64, overall Nusselt number and friction coefficient augmentation ratios decrease from 2.5 to 2.05, and 5.74 to 4.78, respectively, as rotation increased from Rob = 0 to Rob = 0.64.
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3

You, Haoliang, Haiwang Li, Ruquan You, Zhi Tao, and Jincheng Shi. "Experimental Investigations of Turbulent Flow in a Rotating Ribbed Channel in Terms of the Effect of Coriolis Force." In ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/gt2019-90757.

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Abstract In the current work, the effect of Coriolis force is considered in a rotating rectangular rib-roughened channel. Time-resolved PIV (Particle Image Velocimetry) was used to measure the flow field. The Reynolds number is fixed at 10000, and the rotation numbers range from 0 to 0.52. The ribs obstruct the channel by 10%. The mean velocity fields and Reynolds shear stress fields are obtained. Due to the effect of Coriolis force, the flow fields are different between leading and trailing side. Furthermore, the vortex and the reattachment are also investigated. Based on the results, it can be inferred that Coriolis force plays a significant effect on the vortices. Coriolis force enlarges the vortex near the leading side, but suppresses the vortex near the trailing side. An interesting phenomenon has been found. Because of the Coriolis force pointing to the trailing side, the main stream is supposed to be pushed to the trailing side. But the results show that a velocity deficit appears near the trailing side. This phenomenon indicates that the Coriolis force is not the only force affecting the flow, but the secondary flow is also an important factor that cannot be ignored in a rotating ribbed channel.
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4

Kikuyama, Koji, Yutaka Hasegawa, Takashi Yokoi, and Masashi Hirota. "Effects of Coriolis Force on Instability of Laminar Boundary Layer on a Concave Surface." In ASME 1994 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/94-gt-287.

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Stability of laminar boundary layer having a mean velocity of Pohlhausen type was studied by solving numerically the perturbation equations when the boundary layer is subject to curvature and Coriolis force. When the channel rotates so that the Coriolis force acts toward the concave wall, the Taylor-Görtler vortices are generated on a concave surface with a weaker curvature than that in the stationary condition because of the instability effects of the Coriolis force. Vortices are suppressed and the critical Görtler number is increased when the Coriolis force acts opposite to the centrifugal force due to the wall curvature. Over a wide range of rotation rate, vortices with scales as large as the boundary layer thickness are easily generated.
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Abdel-Wahab, Samer, and Danesh K. Tafti. "Large Eddy Simulation of Flow and Heat Transfer in a 90° Ribbed Duct With Rotation: Effect of Coriolis and Centrifugal Buoyancy Forces." In ASME Turbo Expo 2004: Power for Land, Sea, and Air. ASMEDC, 2004. http://dx.doi.org/10.1115/gt2004-53799.

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Results from large eddy simulations (LES) of fully developed flow in a 90° ribbed duct are presented with rib pitch-to-height ratio P/e = 10 and a rib height-to-hydraulic-diameter ratio e/Dh = 0.1. Three rotation numbers Ro = 0.18, 0.36 and 0.68 are studied at a nominal Reynolds number based on bulk velocity of 20,000. Centrifugal buoyancy effects are included at two Richardson numbers of Ri = 12, 28 (Buoyancy number, Bo = 0.12 and 0.30) for each rotation case. Buoyancy strengthens the secondary flow cells in the duct cross-section which leads to an increase of 20% to 30% in heat transfer augmentation at the smooth walls over and above the effect of Coriolis forces. Buoyancy also accentuates the augmentation of turbulence near the trailing wall of the duct and increases the heat transfer augmentation ratio 10% to 20% over the action of Coriolis forces alone. However, it does not have any significant effect at the leading side of the duct. The overall effect of buoyancy on heat transfer augmentation for the ribbed duct is found to be less than 10% over the effect of Coriolis forces alone. Friction on the other hand is augmented 15% to 20% at the highest buoyancy number studied. Comparison with available experiments in the literature show excellent agreement.
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Mayo, Ignacio, Tony Arts, Julien Clinckemaillie, and Aude Lahalle. "Spatially Resolved Heat Transfer Coefficient in a Rib-Roughened Channel Under Coriolis Effects." In ASME Turbo Expo 2013: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/gt2013-94506.

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Heat transfer in a magnified rotating ribbed channel is studied by means of liquid crystal thermometry. The test section consists of four Plexiglas walls, forming a rectangular cross section, mounted on a large rotating disk together with the complete necessary measurement chain. The investigated wall is equipped with ribs perpendicular to the main flow direction, it is heated in such a way to achieve a uniform heat flux boundary condition. Facing the need of two-dimensional experimental heat transfer data, tets were carried out in order to quantify the convective heat transfer distribution on the wall between two consecutive ribs under rotating conditions. Different Rotation numbers (0, 0.06, 0.11 and 0.17) were tested at a Reynolds number of 15,000. For the selected heat flux and rotation rates, and based on previous aerodynamic and thermal investigations presented in open literature, no effect of buoyancy is expected, while the Coriolis forces play an important role in the determination of heat transfer. The rotating cases were performed in both senses of rotation in order to allow the studied wall to act as both a trailing and a leading side. At the highest Rotation number, the results confirm that heat transfer is enhanced up to 17% along the trailing side compared with the non-rotating case. This is due to the secondary flows and shear layer instability instigated by the Coriolis forces. On the other hand, heat transfer on the leading side is reduced up to 19% at the highest rotation number; this is caused by the stabilization of the shear layer and the contribution of the secondary flows.
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7

Govender, Saneshan, and Peter Vadasz. "On the Effect of Mechanical and Thermal Anisotropy on the Stability of Gravity Driven Convection in Rotating Porous Media." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-79029.

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We investigate Rayleigh-Benard convection in a porous layer subjected to gravitational and Coriolis body forces, when the fluid and solid phases are not in local thermodynamic equilibrium. The Darcy model (extended to include Coriolis effects and anisotropic permeability) is used to describe the flow whilst the two-equation model is used for the energy equation (for the solid and fluid phases separately). The linear stability theory is used to evaluate the critical Rayleigh number for the onset of convection and the effect of both thermal and mechanical anisotropy on the critical Rayleigh number is discussed.
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8

Yang, Li, Kartikeya Tyagi, Srinath Ekkad, and Jing Ren. "Influence of Rotation on Heat Transfer in a Two-Pass Channel With Impingement Under High Reynolds Number." In ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/gt2015-42871.

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Effect of rotation on turbine blade internal cooling is an important factor in gas turbine cooling systems. In order to minimize the impact from the Coriolis force, cooling structures with less rotation-dependent cooling effectiveness are needed. This study presents an impingement design in a two pass channel to reduce impact of rotational forces on non-uniform heat transfer behavior inside these complex channels. A Transient Liquid Crystal(TLC) method was employed to obtain local heat transfer coefficient measurements in a rotating environment. The channel Reynolds number based on the channel diameter ranges from 25,000 to 100,000. The rotation number ranges from 0 to 0.14. A series of computational simulations with the SST model were also utilized to understand the flow field behavior that impacts the heat transfer distributions on the walls. A 1-D correlation of zone averaged Nusselt number distribution was derived from the measurements. Results show that rotation reduces the heat transfer on both sides of the impingement, which is due to the Coriolis force and the pressure redistribution. The local change in the present study is about 25%. Rotation significantly enhances the heat transfer near the closed end because of the centrifugal force and the ‘pumping’ effect. Within the parameters of this test, the magnitude of enhancement is 25% to 75%. Compared to U-bended two pass channel, impingement channel has advantages in the upstream channel and the end region, but performance is not beneficial on the leading side of the downstream channel.
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Chang, Shyy Woei, Tong-Minn Liou, Wen-Hsien Yeh, and Jui-Hung Hung. "Heat Transfer in a Radially Rotating Square-Sectioned Duct With Two Opposite Walls Roughened by 45° Staggered Ribs." In ASME Turbo Expo 2006: Power for Land, Sea, and Air. ASMEDC, 2006. http://dx.doi.org/10.1115/gt2006-90153.

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This paper describes an experimental study of heat transfer in a radially rotating square duct with two opposite walls roughened by 45° staggered ribs. Air coolant flows radially outward in the test channel with experiments to be undertaken that match the actual engine conditions. Laboratory-scale heat transfer measurements along centerlines of two rib-roughened surfaces are performed with Reynolds number (Re), rotation number (Ro) and density ratio (Δρ/ρ) in the ranges of 7500–15000, 0–1.8 and 0.076–0.294. The experimental rig permits the heat transfer study with the rotation number considerably higher than those studied in other researches to date. The rotational influences on cooling performance of the rib-roughened channel due to Coriolis forces and rotating buoyancy are studied. A selection of experimental data illustrates the individual and interactive impacts of Re, Ro and buoyancy number on local heat transfer. A number of experimental-based observations reveal that the Coriolis force and rotating buoyancy interact to modify heat transfer even if the rib induced secondary flows persist in the rotating channel. Local heat transfer ratios between rotating and static channels along the centerlines of stable and unstable rib-roughened surfaces with Ro varying from 0.1 to 1.8 are in the ranges of 0.6–1.6 and 1–2.2 respectively. Empirical correlations for periodic flow regions are developed to permit the evaluation of interactive and individual effects of rib-flows, convective inertial force, Coriolis force and rotating buoyancy on heat transfer.
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10

Singh, Prashant, and Srinath V. Ekkad. "Experimental Investigation of Rotating Rib Roughened Two-Pass Square Duct With Two Different Channel Orientations." In ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gt2017-64225.

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Effects of rotation on heat transfer on leading and trailing sides of gas turbine blades has been extensively studied in the past. It has been established for typical two-pass channel that radially outward flow (first pass) has higher heat transfer on trailing side and lower heat transfer on leading side and vice versa for radially inward flow (second pass). Rotation induces three forces on the coolant flow — Coriolis, Centrifugal and Buoyancy forces. The direction of Coriolis force depends on the relative angle between the coolant flow and the rotation direction, because of which the direction of Coriolis force is different in individual passes — which in turn results in non-uniform distribution of high heat transfer regions on leading and trailing walls. The present study is focused on utilizing the Coriolis force favorably in both the passes by rotating the typical arrangement of two-pass channels by 90°. Firstly, smooth two pass duct (Model A-smooth) having typical arrangement of coolant flow and rotation direction is studied. The second configuration is the corresponding ribbed channel (Model A-ribbed) featuring V-shaped ribs on both leading and trailing walls. The rib-height-to-channel hydraulic diameter ratio was 0.125, rib pitch-to-rib height ratio was 8, and channel aspect ratio was unity. Model B was obtained by rotating the Model A by 90° and changing the coolant inlet port as well. Model B had three configurations — (a) smooth duct, (b) single sided ribbed duct, and (c) double sided ribbed duct. Detailed heat transfer coefficients were measured by transient liquid crystal thermography under rotating conditions. In order to match the direction of Buoyancy force as it exists in actual engines, colder air was passed during the transient experiment. The heat transfer experiments were carried out at a Reynolds number of 20000 and Rotation numbers of 0, 0.05 and 0.1. The Nusselt numbers have been reported in two forms, (a) normalized with respect to Dittus-Boelter correlation for developed turbulent flow in circular duct, (b) normalized with corresponding Nusselt number obtained from smooth channel experiments. The effects of Coriolis force and centrifugal force on heat transfer has been discussed in detail. A new model has been proposed based on the understanding and findings of the present study, which has positive effects of rotation on both leading and trailing walls.
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