Relevant bibliographies by topics / Vorticity Transport Equation

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

Academic literature on the topic 'Vorticity Transport Equation'

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Published: 6 September 2023

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Journal articles on the topic "Vorticity Transport Equation"

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Eldho, T. I., and D. L. Young. "Two-Dimensional Incompressible Viscous Flow Simulation Using Velocity-Vorticity Dual Reciprocity Boundary Element Method." Journal of Mechanics 20, no. 3 (September 2004): 177–85. http://dx.doi.org/10.1017/s1727719100003397.

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AbstractThis paper describes a computational model based on the dual reciprocity boundary element method (DRBEM) for the solution of two-dimensional incompressible viscous flow problems. The model is based on the Navier-Stokes equations in velocity-vorticity variables. The model includes the solution of vorticity transport equation for vorticity whose solenoidal vorticity components are obtained by solving Poisson equations involving the velocity and vorticity components. Both the Poisson equations and the vorticity transport equations are solved iteratively using DRBEM and combined to determine the velocity and vorticity vectors. In DRBEM, all source terms, advective terms and time dependent terms are converted into boundary integrals and hence the computational domain of the problem reduces by one. Internal points are considered wherever solution is required. The model has been applied to simulate two-dimensional incompressible viscous flow problems with low Reynolds (Re) number in a typical square cavity. Results are obtained and compared with other models. The DRBEM model has been found to be reasonable and satisfactory.
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ESCHER, JOACHIM, and MARCUS WUNSCH. "RESTRICTIONS ON THE GEOMETRY OF THE PERIODIC VORTICITY EQUATION." Communications in Contemporary Mathematics 14, no. 03 (June 2012): 1250016. http://dx.doi.org/10.1142/s0219199712500162.

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We prove that several evolution equations arising as mathematical models for fluid motion cannot be realized as metric Euler equations on the Lie group DIFF∞(𝕊1) of all smooth and orientation-preserving diffeomorphisms on the circle. These include the quasi-geostrophic model equation, cf. [A. Córdoba, D. Córdoba and M. A. Fontelos, Formation of singularities for a transport equation with nonlocal velocity, Ann. of Math. 162 (2005) 1377–1389], the axisymmetric Euler flow in ℝd (see [H. Okamoto and J. Zhu, Some similarity solutions of the Navier–Stokes equations and related topics, Taiwanese J. Math. 4 (2000) 65–103]), and De Gregorio's vorticity model equation as introduced in [S. De Gregorio, On a one-dimensional model for the three-dimensional vorticity equation, J. Stat. Phys. 59 (1990) 1251–1263].
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Lo, D. C., T. Liao, D. L. Young, and M. H. Gou. "Velocity-Vorticity Formulation for 2D Natural Convection in an Inclined Cavity by the DQ Method." Journal of Mechanics 23, no. 3 (September 2007): 261–68. http://dx.doi.org/10.1017/s1727719100001301.

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AbstractThe aim of this paper attempts to apply the differential quadrature (DQ) method for solving two-dimensional natural convection in an inclined cavity. The velocity-vorticity formulation is used to represent the mass, momentum, and energy conservations of the fluid medium in an inclined cavity. We employ a coupled technique for four field variables involving two velocities, one vorticity and one temperature components. In this method, the velocity Poisson equation, continuity equation, vorticity transport equation and energy equation are all solved as a coupled system of equations so as to we are capable of predicting four field variables accurately. The main advantage of present approach is that coupling the velocity and the vorticity equations allows the determination of the boundary values implicitly without requiring the explicit specification of the vorticity values at the boundary walls. A natural convection in a cavity with different angle of inclinations for Rayleigh number equal to 103, 104, 105 and 106 and H/L aspect ratios varying from 1 to 3 is investigated. It is shown that with the use of the present algorithm the benchmark results for temperature and flow fields could be obtained using a coarse mesh grid.
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Ponta, Fernando L. "Kinematic Laplacian Equation Method: A Velocity-Vorticity Formulation for the Navier-Stokes Equations." Journal of Applied Mechanics 73, no. 6 (February 4, 2006): 1031–38. http://dx.doi.org/10.1115/1.2198245.

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In this work, a novel procedure to solve the Navier-Stokes equations in the vorticity-velocity formulation is presented. The vorticity transport equation is solved as an ordinary differential equation (ODE) problem on each node of the spatial discretization. Evaluation of the right-hand side of the ODE system is computed from the spatial solution for the velocity field provided by a new partial differential equation expression called the kinematic Laplacian equation (KLE). This complete decoupling of the two variables in a vorticity-in-time/velocity-in-space split algorithm reduces the number of unknowns to solve in the time-integration process and also favors the use of advanced ODE algorithms, enhancing the efficiency and robustness of time integration. The issue of the imposition of vorticity boundary conditions is addressed, and details of the implementation of the KLE by isoparametric finite element discretization are given. Validation results of the KLE method applied to the study of the classical case of a circular cylinder in impulsive-started pure-translational steady motion are presented. The problem is solved at several Reynolds numbers in the range 5<Re<180 comparing numerical results with experimental measurements and flow visualization plates. Finally, a recent result from a study on periodic vortex-array structures produced in the wake of forced-oscillating cylinders is included.
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Wen, Jiangang, and Philip L. F. Liu. "Mass transport under partially reflected waves in a rectangular channel." Journal of Fluid Mechanics 266 (May 10, 1994): 121–45. http://dx.doi.org/10.1017/s0022112094000959.

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Mass transport under partially reflected waves in a rectangular channel is studied. The effects of sidewalls on the mass transport velocity pattern are the focus of this paper. The mass transport velocity is governed by a nonlinear transport equation for the second-order mean vorticity and the continuity equation of the Eulerian mean velocity. The wave slope, ka, and the Stokes boundary-layer thickness, k (ν/σ)½, are assumed to be of the same order of magnitude. Therefore convection and diffusion are equally important. For the three-dimensional problem, the generation of second-order vorticity due to stretching and rotation of a vorticity line is also included. With appropriate boundary conditions derived from the Stokes boundary layers adjacent to the free surface, the sidewalls and the bottom, the boundary value problem is solved by a vorticity-vector potential formulation; the mass transport is, in gneral, represented by the sum of the gradient of a scalar potential and the curl of a vector potential. In the present case, however, the scalar potential is trivial and is set equal to zero. Because the physical problem is periodic in the streamwise direction (the direction of wave propagation), a Fourier spectral method is used to solve for the vorticity, the scalar potential and the vector potential. Numerical solutions are obtained for different reflection coefficients, wave slopes, and channel cross-sectional geometry.
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Swaters, Gordon E. "A perturbation theory for the solitary-drift-vortex solutions of the Hasegawa-Mima equation." Journal of Plasma Physics 41, no. 3 (June 1989): 523–39. http://dx.doi.org/10.1017/s0022377800014069.

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A multiple-scales adiabatic perturbation theory is presented describing the adiabatic dissipation of the solitary vortex-pair solutions of the Hasegawa-Mima equation. The vortex parameter transport equations are derived as solvability conditions for the asymptotic expansion and are identical with the transport equations previously derived by Aburdzhaniya et al. (1987) using an energy- and enstrophy-conservation balance procedure. The theoretical results are compared with high-resolution numerical simulations. Global properties such as the decay in the enstrophy and energy are accurately reproduced. Local properties such as the position of the centre of the vortex pair, decay of the extrema in the vorticity and stream-function fields, and the dilation of the vortex dipole are also in good agreement. In addition, time series of vorticity–stream-function scatter diagrams for the numerical simulations are presented to verify the adiabatic ansatz.
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Hu, Running, Xinliang Li, and Changping Yu. "Effects of the Coriolis force in inhomogeneous rotating turbulence." Physics of Fluids 34, no. 3 (March 2022): 035108. http://dx.doi.org/10.1063/5.0084098.

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The effects of the Coriolis force in inhomogeneous rotating turbulence are studied in the paper. Linear analyses and numerical simulations both reveal that energy is transported to the slowly rotating fields, and the energy distribution is proportional to [Formula: see text]. The scale energy is almost spatially self-similar, and the inverse cascade is reduced by inhomogeneous rotation. The corresponding evolution equation of the scale energy, i.e., the generalized Kolmogorov equation, is calculated to study the scale transport process in the presence of inhomogeneity. The equation is reduced to twice the energy transport equation at sufficiently large scales, which is verified by numerical results. In addition, the results reveal the dominant role of the corresponding pressure of the Coriolis force in the spatial energy transport. An extra turbulent convention effect in r-space solely in slowly rotating fields is also recognized. It can be associated with the small-scale structures with strong negative vorticity, whose formation mechanism is similar to rotating condensates. Finally, by vortex dynamic analyses, we find that the corresponding pressure of the Coriolis force transports energy by vorticity tube shrinking and thickening. The effects of the Coriolis force can be divided into two components: one is related to the gradient of rotation, and the other is associated with the strength of rotation.
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Brown, Richard E., and Andrew J. Line. "Efficient High-Resolution Wake Modeling Using the Vorticity Transport Equation." AIAA Journal 43, no. 7 (July 2005): 1434–43. http://dx.doi.org/10.2514/1.13679.

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Marn, Jure, and Ivan Catton. "Analysis of Flow Induced Vibration Using the Vorticity Transport Equation." Journal of Fluids Engineering 115, no. 3 (September 1, 1993): 485–92. http://dx.doi.org/10.1115/1.2910164.

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Crossflow induced vibrations are the subject of this work. The analysis is two dimensional. The governing equations for fluid motion are solved using linearized perturbation theory and coupled with the equations of motion for cylinders to yield the threshold of dynamic instability for an array of cylinders. Parametric analysis is performed to determine the lowest instability threshold for a rotated square array and correlations are developed relating the dominant parameters. The results are compared with theoretical and experimental data for similar arrays and the discrepancies are discussed.
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Halpern, Federico D., Ronald E. Waltz, and Tess N. Bernard. "Drift-ordered fluid vorticity equation with energy consistency." Physics of Plasmas 30, no. 3 (March 2023): 032302. http://dx.doi.org/10.1063/5.0135158.

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Although drift-ordered fluid models are widely applied in tokamak edge turbulence simulations, the models used are acknowledged not to conserve energy or even electrical charge. The present paper aims to remove many of the existing pitfalls in drift-fluid models, however, with the objective of finding a solution simple enough to be implemented in numerical applications. Our main result is an improved version of the drift-Braginskii equations involving a generalized vorticity function. In the new drift-Braginskii system, the quasi-neutrality condition translates into a transport equation for a generalized vorticity, expressed in conservation form, and related to the total mass-weighted circulation. It is found that kinetic energy conservation can be achieved if the polarization flow is defined recursively. The resulting model conserves the kinetic energy associated with [Formula: see text] and diamagnetic flows and retains the associated perpendicular kinetic energy flux.
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Dissertations / Theses on the topic "Vorticity Transport Equation"

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Koh, Yang-Moon. "Numerical solution of three-dimensional vorticity transport equations." Thesis, Imperial College London, 1987. http://hdl.handle.net/10044/1/46971.

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Sastrapradja, Debbie. "Rayleigh streaming simulation using the vorticity transport equation." 2004. http://etda.libraries.psu.edu/theses/approved/WorldWideIndex/ETD-702/index.html.

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Vinod, Kumar B. G. "Co-operative Destabilization of a Flat Plate Boundary Layer by a Free Stream Convecting Vortex and Wall Suction/Blowing." Thesis, 2007. https://etd.iisc.ac.in/handle/2005/4627.

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The stability of wall bounded shear layer at subcritical Reynolds number disturbed by a freestream convecting vortex and unsteady suction/blowing at the wall was studied. A counterclockwise line vortex was convected parallel to the plate in the direction of the free-stream, slower than the free-stream velocity and well outside the boundary layer. Simultaneously, unsteady periodic suction/blowing of the identical uid was introduced near the leading edge on the plate through a narrow slit. The incompressible unsteady problem was modelled using the vorticity stream function formulation with appropriate boundary conditions. The solution was obtained numerically. A sixth-order compact difference. scheme has been used for convection terms of the vorticity transport equation, first-order Euler for time marching and second order central differences for the stream function Poisson equation. Simulations were performed for a range of vortex strengths (􀀀 = 0, 4.5, 6.75 and 9.0) and peak velocity of suction/blowing (vmax = 0, 0:005U1, 0:01U1 and 0:05U1). This study advances previous investigations of the response to convected vortices alone. Here, a cooperative instability has been found, and the mechanism of destabilization has also been revealed. It is due to the appearance of a thin, internal shear layer originating at the leading edge, stretching downstream and lying within the boundary layer. This shear layer is susceptible to inviscid instability and sheds vortices over the plate. In the presence of unsteady periodic suction/blowing, the shear layer was found oscillating in the frequency which is equal to that of suction/blowing and strong shedding was observed resulting in multiple separation bubbles on the plate. The response was strongly dependent on the intensity of suction/blowing, strength of the vortex and height of the vortex from the plate. In case of a strong vortex the shedding of shear layer was quick and separation bubble was formed nearer to the leading edge. In case of a weak vortex the shedding got delayed and separation bubble was observed away from the leading edge. When the suction/blowing intensity was strong, the shedding was quicker and multiple bubbles were appearing on the plate. Suction/blowing alone could not induce any separation because of the absence of the internal shear layer.
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Book chapters on the topic "Vorticity Transport Equation"

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Pozrikidis, C. "Equation of motion and vorticity transport." In Fluid Dynamics, 252–305. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4757-3323-5_6.

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Pozrikidis, C. "Equation of motion and vorticity transport." In Fluid Dynamics, 361–417. Boston, MA: Springer US, 2016. http://dx.doi.org/10.1007/978-1-4899-7991-9_6.

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Pozrikidis, Constantine. "Equation of Motion and Vorticity Transport." In Fluid Dynamics, 308–59. Boston, MA: Springer US, 2009. http://dx.doi.org/10.1007/978-0-387-95871-2_6.

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Alemseged Worku, Nahom. "Basics of Fluid Dynamics." In Computational Overview of Fluid Structure Interaction. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.96312.

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In this chapter, studies on basic properties of fluids are conducted. Mathematical and scientific backgrounds that helps sprint well into studies on fluid mechanics is provided. The Reynolds Transport theorem and its derivation is presented. The well-known Conservation laws, Conservation of Mass, Conservation of Momentum and Conservation of Energy, which are the foundation of almost all Engineering mechanics simulation are derived from Reynolds transport theorem and through intuition. The Navier–Stokes equation for incompressible flows are fully derived consequently. To help with the solution of the Navier–Stokes equation, the velocity and pressure terms Navier–Stokes equation are reduced into a vorticity stream function. Classification of basic types of Partial differential equations and their corresponding properties is discussed. Finally, classification of different types of flows and their corresponding characteristics in relation to their corresponding type of PDEs are discussed.
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De Padova, Diana, and Michele Mossa. "Hydrodynamics of Regular Breaking Wave." In Geophysics and Ocean Waves Studies [Working Title]. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.94449.

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Turbulence and undertow currents play an important role in surf-zone mixing and transport processes; therefore, their study is fundamental for the understanding of nearshore dynamics and the related planning and management of coastal engineering activities. Pioneering studies qualitatively described the features of breakers in the outer region of the surf zone. More detailed information on the velocity field under spilling and plunging breakers can be found in experimental works, where single-point measurement techniques, such as Hot Wire Anemometry and Laser Doppler Anemometry (LDA), were used to provide maps of the flow field in a time-averaged or ensemble-averaged sense. Moreover, the advent of non-intrusive measuring techniques, such as Particle Image Velocimetry (PIV) provided accurate and detailed instantaneous spatial maps of the flow field. However, by correlating spatial gradients of the measured velocity components, the instantaneous vorticity maps could be deduced. Moreover, the difficulties of measuring velocity due to the existence of air bubbles entrained by the plunging jet have hindered many experimental studies on wave breaking encouraging the development of numerical model as useful tool to assisting in the interpretation and even the discovery of new phenomena. Therefore, the development of an WCSPH method using the RANS equations coupled with a two-equation k–ε model for turbulent stresses has been employed to study of the turbulence and vorticity distributions in in the breaking region observing that these two aspects greatly influence many coastal processes, such as undertow currents, sediment transport and action on maritime structures.
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Nurgaliev, Ildus Saetgalievich. "Solar Energy in Agro-Ecologic Micrometeorology Measurements." In Handbook of Research on Renewable Energy and Electric Resources for Sustainable Rural Development, 141–48. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-3867-7.ch006.

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New approach to the measurements in agro-ecologic micrometeorology is suggested on the bases of renewable solar panels for energy supply to instruments at the remote sites and new turbulent model of the flow of the gases. Analytical dynamic model of the turbulent multi-component flow in the three-layer boundary system is presented. Turbulence is simulated by the non-zero vorticity, but not only. Other mathematical aspects of the turbulence are an introducing new model of the material point and considering a torsion of their trajectories. The generalized advection-diffusion-reaction equation is derived for an arbitrary number of components in the flow. The flows in the layers are objects for matching requirements on the boundaries between the layers. Different types of transport mechanisms are dominant on the different levels of the layers and space scales. The same models of mass and energy transfer are instrumental in simulation rural electrification concepts in general on the bases renewable sources.
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Ji, Yong, and Xi Chen. "Vorticity Transports in Wall Turbulent Flow Under Spanwise Wall Jet Forcing and Blowing-Suction Control." In Advances in Transdisciplinary Engineering. IOS Press, 2022. http://dx.doi.org/10.3233/atde220051.

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This study investigates vorticity transports in wall turbulent flow under blowing-suction (BS) and spanwise opposed wall jet forcing (SOJF) control via direct numerical simulation of the Navier-Stokes equation. For combining SOJF and BS control, the drag reduction can achieve maximum value about 33% – obviously larger than individual control (18% for SOJF and 27% for BS). Following Ji et al. [1], the mean spanwise vorticity(Ωz), the vorticity fluctuation transports in spanwise direction(−v′ωz′) and normal direction(w′ωy′) are investigated. Results support our previous conclusion that the frictional drag is considerably contributed by the transports of vorticity fluctuations. A triple decomposition (mean, coherent and random) shows that the role of the random −v′′ωz′′ is drag adding, but other terms – random w′′ωy′′ and the coherent −ṽω̃z and w̃ω̃y transports – are all drag decreasing.
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Kaimal, J. C., and J. J. Finnigan. "Spectra and Cospectra Over Flat Uniform Terrain." In Atmospheric Boundary Layer Flows. Oxford University Press, 1994. http://dx.doi.org/10.1093/oso/9780195062397.003.0005.

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Turbulent flows like those in the atmospheric boundary layer can be thought of as a superposition of eddies—coherent patterns of velocity, vorticity, and pressure— spread over a wide range of sizes. These eddies interact continuously with the mean flow, from which they derive their energy, and also with each other. The large “energy-containing” eddies, which contain most of the kinetic energy and are responsible for most of the transport in the turbulence, arise through instabilities in the background flow. The random forcing that provokes these instabilities is provided by the existing turbulence. This is the process represented in the production terms of the turbulent kinetic energy equation (1.59) in Chapter 1. The energy-containing eddies themselves are also subject to instabilities, which in their case are provoked by other eddies. This imposes upon them a finite lifetime before they too break up into yet smaller eddies. This process is repeated at all scales until the eddies become sufficiently small that viscosity can affect them directly and convert their kinetic energy to internal energy (heat). The action of viscosity is captured in the dissipation term of the turbulent kinetic energy equation. The second-moment budget equations presented in Chapter 1, of which (1.59) is one example, describe the summed behavior of all the eddies in the turbulent flow. To understand the conversion of mean kinetic energy into turbulent kinetic energy in the large eddies, the handing down of this energy to eddies of smaller and smaller scale in an “eddy cascade” process, and its ultimate conversion to heat by viscosity, we must isolate the different scales of turbulent motion and separately observe their behavior. Taking Fourier spectra and cospectra of the turbulence offers a convenient way of doing this. The spectral representation associates with each scale of motion the amount of kinetic energy, variance, or eddy flux it contributes to the whole and provides a new and invaluable perspective on boundary layer structure. The spectrum of boundary layer fluctuations covers a range of more than five decades: millimeters to kilometers in spatial scales and fractions of a second to hours in temporal scales.
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Salmon, Rick. "Introduction to Geophysical Fluid Dynamics." In Lectures on Geophysical Fluid Dynamics. Oxford University Press, 1998. http://dx.doi.org/10.1093/oso/9780195108088.003.0005.

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This second chapter offers a brief introduction to geophysical fluid dynamics—the dynamics of rotating, stratified flows. We start with the shallow water equations, which govern columnar motion in a thin layer of homogeneous fluid. Roughly speaking, the solutions of the shallow-water equations comprise two types of motion: ageostrophic motions, including inertia-gravity waves, on the one hand, and nearly geostrophic motions on the other. In rapidly rotating flow, these two types of motion may, in some sense, decouple. We seek simpler equations that describe only the nearly geostrophic motion. The simplest such equations are the quasigeostrophic equations. In the quasigcostrophic equations, potential vorticity plays the key role: The potential vorticity completely determines the velocity field that transports it, thereby controlling the whole dynamics. We begin by generalizing our previously derived fluid equations to a rotating coordinate frame.
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Conference papers on the topic "Vorticity Transport Equation"

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Rasheed, Maan A., Alla Tareq Balasim, and Ali F. Jameel. "Some results for the vorticity transport equation by using A.D.I scheme." In THE 4TH INNOVATION AND ANALYTICS CONFERENCE & EXHIBITION (IACE 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5121068.

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Gharakhani, Adrin. "A High-Order Flux Reconstruction Method for 2-D Vorticity Transport." In ASME 2021 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/fedsm2021-63196.

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Abstract A compact high-order finite difference method on unstructured meshes is developed for discretization of the unsteady vorticity transport equations (VTE) for 2-D incompressible flow. The algorithm is based on the Flux Reconstruction Method of Huynh [1, 2], extended to evaluate a Poisson equation for the streamfunction to enforce the kinematic relationship between the velocity and vorticity fields while satisfying the continuity equation. Unlike other finite difference methods for the VTE, where the wall vorticity is approximated by finite differencing the second wall-normal derivative of the streamfunction, the new method applies a Neumann boundary condition for the diffusion of vorticity such that it cancels the slip velocity resulting from the solution of the Poisson equation for the streamfunction. This yields a wall vorticity with order of accuracy consistent with that of the overall solution. In this paper, the high-order VTE solver is formulated and results presented to demonstrate the accuracy and convergence rate of the Poisson solution, as well as the VTE solver using benchmark problems of 2-D flow in lid-driven cavity and backward facing step channel at various Reynolds numbers.
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Kaldellis, J., D. Douvikas, and K. D. Papailiou. "A Secondary Flow Calculation Method Based on the Meridional Vorticity Transport Equation." In ASME 1988 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1988. http://dx.doi.org/10.1115/88-gt-260.

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A secondary flow calculation method is presented in this work, which makes use of the meridional vorticity transport equation. Circumferentially mean flow quantities are calculated using an inverse procedure. The method makes use of the mean kinetic energy integral equation and calculates simultaneously hub and tip secondary flow development. Emphasis is placed upon the use of a coherent two-zone model and particular care is taken in order to describe adequately the flow inside an unbounded (external), semi-bounded (annulus) and fully-bounded (bladed) space. The velocity field, the losses and the defect forces receive particular attention. Comparison between theoretical and experimental results is presented.
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Sastrapradja, Debbie. "Rayleigh streaming simulation in a cylindrical tube using the vorticity transport equation." In INNOVATIONS IN NONLINEAR ACOUSTICS: ISNA17 - 17th International Symposium on Nonlinear Acoustics including the International Sonic Boom Forum. AIP, 2006. http://dx.doi.org/10.1063/1.2210396.

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Dalton, Charles, and Wu Zheng. "Numerical Solutions of a Viscous Uniform Approach Flow Past Square and Diamond Cylinders." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-32287.

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Numerical results are presented for a uniform approach flow past square and diamond cylinders, with and without rounded corners, at Reynolds numbers of 250 and 1000. This unsteady viscous flow problem is formulated by the 2-D Navier-Stokes equations in vorticity and stream-function form on body-fitted coordinates and solved by a finite-difference method. Second-order Adams-Bashforth and central-difference schemes are used to discretize the vorticity transport equation while a third-order upwinding scheme is incorporated to represent the nonlinear convective terms. A grid generation technique is applied to provide an efficient mesh system for the flow. The elliptic partial differential equation for stream-function and vorticity in the transformed plane is solved by the multigrid iteration method. The Strouhal number and the average in-line force coefficients agree very well with the experimental and previous numerical values. The vortex structures and the evolution of vortex shedding are illustrated by vorticity contours. Rounding the corners of the square and diamond cylinders produced a noticeable decrease on the calculated drag and lift coefficients.
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Yazdani, Miad, and Yasmin Khakpour. "Vortex Transport in Separating Flows and Role of Vortical Structures in Reynolds Stress Production and Distribution." In ASME 2005 Fluids Engineering Division Summer Meeting. ASMEDC, 2005. http://dx.doi.org/10.1115/fedsm2005-77005.

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In this paper we will present some approaches on Reynolds stress production by vortex transport phenomena and nonlinear vorticity generation in momentum equation. First of all we represent a history of recent works to describe how fluid particle motions can be associated with Reynolds stress through either displacement or acceleration terms. In the next section we will describe how vortex stretching causes the Reynolds stress production and what is the dominant effect near and far from the boundary where viscous effects have to be considered. On the other hand, some vortex considered methodologies such as those synthesize boundary layer, as a collection of vortical objects seem to be inappropriate in general flow configuration. Therefore, there must be a moderate consideration in which both vortex and momentum transports come into account as it is done in LES. Furthermore since there exist open questions on Reynolds stress distribution in complex flows such as those with separation, our particular attention is paid to such effects due to vortical structures in separating flows. Further discussions include turbulence development caused by either vortex stretching or gradient terms that is determined by predominant conditions. However, it is seen that at the beginning, vorticity generators in Navier-Stokes equation contribute to dissipation effect. In addition, since such contribution corresponds to vorticity alignment, we investigate maximum vortex aligning and the effects of which causes the deviation of such alignment. The paper provides theoretical and numerical comparisons, where in the former, the vortical structure role is taken into account.
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He, J., and B. Q. Zhang. "The Local Analytic Numerical Method for the Double Vortex Combustor Flow." In ASME 1985 Beijing International Gas Turbine Symposium and Exposition. American Society of Mechanical Engineers, 1985. http://dx.doi.org/10.1115/85-igt-110.

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A new hyperbolic function discretization equation for two dimensional Navier-Stokes equation in the stream function vorticity from is derived. The basic idea of this method is to integrat the total flux of the general variable ϕ in the differential equations, then incorporate the local analytic solutions in hyperbolic function for the one-dimensional linearized transport equation. The hyperbolic discretization (HD) scheme can more accurately represent the conservation and transport properties of the governing equation. The method is tested in a range of Reynolds number (Re=100~2000) using the viscous incompressible flow in a square cavity. It is proved that the HD scheme is stable for moderately high Reynolds number and accurate even for coarse grids. After some proper extension, the method is applied to predict the flow field in a new type combustor with air blast double-vortex and obtained some useful results.
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Wu, Chunlin, and Spyros A. Kinnas. "Laminar and Turbulent Flow Past a Hydrofoil Predicted by a Distributed Vorticity Method." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-18867.

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Abstract A distributed viscous vorticity equation (VISVE) method is presented in this work to simulate the laminar and turbulent flow past a hydrofoil. The current method is proved to be more computationally efficient and spatially compact than RANS (Reynolds-Averaged Navier-Stokes) methods since this method does not require unperturbed far-field boundary conditions, which leads to a small computational domain, a small number of mesh cells, and consequently much less simulation time. To model the turbulent flow, a synchronous coupling scheme is implemented so that the VISVE method can resolve the turbulent flow by considering the eddy viscosity in the vorticity transport equation, and the eddy viscosity is obtained by coupling VISVE with the existing turbulence model of OpenFOAM, via synchronous communication. The proposed VISVE method is applied to simulate both the laminar flow at moderate Reynolds numbers and turbulent flow at high Reynolds numbers past a hydrofoil. The velocity and vorticity calculated by the coupling method agree well with the results obtained by a RANS method.
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9

Barmpalias, K. G., A. I. Kalfas, N. Chokani, and R. S. Abhari. "The Dynamics of the Vorticity Field in a Low Solidity Axial Turbine." In ASME Turbo Expo 2008: Power for Land, Sea, and Air. ASMEDC, 2008. http://dx.doi.org/10.1115/gt2008-51142.

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A current trend in turbomachinery design is the use of low solidity axial turbines that can generate a given power with fewer blades. However, due to the higher turning of the flow, relative to a high solidity turbine, there is an increase in secondary flows and their associated losses. In order to increase the efficiency of these more highly loaded stages, an improved understanding of the mechanisms related to the development, evolution and unsteady interaction of the secondary flows is required. An experimental investigation of the unsteady vorticity field in highly loaded stages of a research turbine is presented here. The research turbine facility is equipped with a two-stage axial turbine that is representative of the high-pressure section of a steam turbine. Steady and unsteady area measurements are performed, with the use of miniature pneumatic and fast response aerodynamic probes, in closely spaced planes at the exits of each blade row. In addition to the 3D total pressure flowfield, the multi-plane measurements allow the full three-dimensional time-resolved vorticity and velocity fields to be determined. These measurements are then used to describe the development, evolution and unsteady interaction of the secondary flows and loss generation. Particular emphasis is given to the vortex stretching term of the vorticity transport equation, which gives new insight into the vortex tilting and stretching that is associated with the secondary loss generation.
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10

Mochizuki, Shinsuke, Seiji Yamada, and Hideo Osaka. "Reynolds Stress Field of a Stronger Wall Jet Managed by a Streamwise Vortex: Effect of Periodic Perturbation." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45228.

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Six Reynolds stress components were studied experimentally to understand evolution of streamwise vortex and a plane wall jet. It is seen that periodic perturbation are able to modify non-isotropic Reynolds stress field involved in the transport equation for streamwise vorticity. Modified Reynolds stress field accelerates development of vortex radius in spanwise direction. Interaction between streamwise vortex and spanwise eddies in the outer layer of the plane wall jet strengthen both velocity and length scales of large-scale eddies and increase streamwise momentum flux in enhancement of entrainment process.
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Reports on the topic "Vorticity Transport Equation"

1

Lung, Tyler B., Phil Roe, and Nathaniel R. Morgan. Vorticity Preserving Flux Corrected Transport Scheme for the Acoustic Equations. Office of Scientific and Technical Information (OSTI), August 2012. http://dx.doi.org/10.2172/1048874.

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