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| 10. |
- af Klinteberg, Ludvig, et al.
(author)
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An explicit Eulerian method for multiphase flow with contact line dynamics and insoluble surfactant
- 2014
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In: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 101, s. 50-63
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Journal article (peer-reviewed)abstract
- The flow behavior of many multiphase flow applications is greatly influenced by wetting properties and the presence of surfactants. We present a numerical method for two-phase flow with insoluble surfactants and contact line dynamics in two dimensions. The method is based on decomposing the interface between two fluids into segments, which are explicitly represented on a local Eulerian grid. It provides a natural framework for treating the surfactant concentration equation, which is solved locally on each segment. An accurate numerical method for the coupled interface/surfactant system is given. The system is coupled to the Navier-Stokes equations through the immersed boundary method, and we discuss the issue of force regularization in wetting problems, when the interface touches the boundary of the domain. We use the method to illustrate how the presence of surfactants influences the behavior of free and wetting drops.
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| 11. |
- Ahmed, Z., et al.
(author)
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Turbulent bubbly channel flows : Effects of soluble surfactant and viscoelasticity
- 2020
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In: Computers & Fluids. - : Elsevier Ltd. - 0045-7930 .- 1879-0747. ; 212
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Journal article (peer-reviewed)abstract
- Interface-resolved direct numerical simulations are performed to examine the combined effects of soluble surfactant and viscoelasticity on the structure of a bubbly turbulent channel flow. The incompressible flow equations are solved fully coupled with the FENE-P viscoelastic model and the equations governing interfacial and bulk surfactant concentrations. The latter coupling is achieved through a non-linear equation of state which relates the surface tension to the surfactant concentration at the interface. The two-fluid Navier-Stokes equations are solved using a front-tracking method, augmented with a very efficient FFT-based pressure projection method that allows for massively parallel simulations of turbulent flows. It is found that, for the surfactant-free case, bubbles move toward the wall due to inertial lift force, resulting in formation of wall layers and a significant decrease in the flow rate. Conversely, a high-enough concentration of surfactant changes the direction of lateral migration of bubbles, i.e., the contaminated bubbles move toward the core region and spread out across the channel. When viscoelasticity is considered, viscoelastic stresses counteract the Marangoni stresses, promoting formation of bubbly wall-layers and consequently strong decrease in the flow rate. The formation of bubble wall-layers for combined case depends on the interplay of the inertial and elastic, and Marangoni forces.
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| 12. |
- Alenius, Emma
(author)
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Mode switching in a thick orifice jet, an LES and dynamic mode decomposition approach
- 2014
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In: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 90, s. 101-112
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Journal article (peer-reviewed)abstract
- The dynamics of a confined thick orifice plate jet, at Mach 0.4, are studied with dynamic mode decomposition (DMD), of the velocity from a large eddy simulation (LES). The jet exhibits strong periodic structures, due to an initially laminar shear layer, and a non-deterministic switching is observed between an axisymmetric and an azimuthal jet mode. The DMD captures the shape of these structures as different dynamic modes, but (by definition) not their true time-evolution. In order to study the time-evolution of semi-periodic structures in the flow, such as the jet modes that come and go in time, it is suggested to use DMD for identifying the shape of the structures and then calculate time-coefficients for them, by expressing the velocity field as a linear combination of the most important dynamic modes. These time-coefficients are then shown to capture the physics of the flow; they oscillate at the frequency of the corresponding mode, within an envelope with a non-deterministically varying period, representing the mode switching. Additionally, a time variation of the strength of the jet, represented by mode zero, is found to be related to this switching.
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| 13. |
- Arlov, Dragana, et al.
(author)
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Numerical simulation of a gas-liquid Rushton stirred reactor - LES and LPT
- 2008
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In: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 37:7, s. 793-801
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Conference paper (peer-reviewed)abstract
- Simulations of aerated stirred reactor is performed using a combination of large eddy simulation (LES) and Lagrangian particle tracking (LPT). A single impeller Rushton turbine is positioned at the center of the reactor and air is introduced at the bottom through a circular sparger. Effects of the gas volume flow, stirrer speed and sparger dimension are investigated. The results show that the time averaged liquid velocities in radial and tangential directions decrease with increasing gas volume fraction. In the axial direction, the gas redirects the radial jet upwards, breaking the symmetry of the ring vortices. Especially, for a narrower sparger, a more concentrated tilt upwards is observed with a larger region of negative axial velocity. Although, low aeration number is used, the periodicity from the impeller is decreasing and interfering with the creation of the trailing vortex pair. The gas dispersion increases with decreasing the sparger diameter.
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| 14. |
- Bale, Rahul, et al.
(author)
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Stencil Penalty approach based constraint immersed boundary method
- 2020
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In: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 2000, s. 104457-
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Journal article (peer-reviewed)abstract
- The constraint-based immersed boundary (cIB) method has been shown to be accurate between low and moderate Reynolds number (Re) flows when the immersed body constraint is imposed as a volumetric constraint force. When the IB is modelled as a zero-thickness interface, where it is no longer possible to model a volumetric constraint force, we found that cIB is not able to produce accurate results. The main source of inaccuracies in the cIB method is the distribution of the pressure field around the IB surface. An IB surface results in a jump in the pressure field across the IB. Evaluation of the discrete gradient of pressure close to the IB leads to a pressure gradient that does not satisfy the Neumann boundary condition for pressure at the IB. Furthermore, a non-zero discrete pressure gradient on the IB results in spurious flow at grid points close to the IB. We present a novel numerical formulation which adapts the cIB formulation for ‘zero-thickness’ immersed bodies. In order to impose the Neumann boundary condition on pressure on the IB more accurately, we introduce an additional body force to the momentum equation. A WENO based stencil penalization technique is used to define the new force term. Due to the more accurate imposition on the Neumann pressure boundary condition on the IB, spurious flow is reduced and the accuracy of no penetration velocity boundary condition on the IB is improved.
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| 15. |
- Bartuschat, D., et al.
(author)
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Two computational models for simulating the tumbling motion of elongated particles in fluids
- 2016
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In: Computers & Fluids. - : Elsevier. - 0045-7930 .- 1879-0747. ; 127, s. 17-35
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Journal article (peer-reviewed)abstract
- Suspensions with fiber-like particles in the low Reynolds number regime are modeled by two different approaches that both use a Lagrangian representation of individual particles. The first method is the well-established formulation based on Stokes flow that is formulated as integral equations. It uses a slender body approximation for the fibers to represent the interaction between them directly without explicitly computing the flow field. The second is a new technique using the 3D lattice Boltzmann method on parallel supercomputers. Here the flow computation is coupled to a computational model of the dynamics of rigid bodies using fluid-structure interaction techniques. Both methods can be applied to simulate fibers in fluid flow. They are carefully validated and compared against each other, exposing systematically their strengths and weaknesses regarding their accuracy, the computational cost, and possible model extensions.
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| 16. |
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| 17. |
- Brändle de Motta, J. C., et al.
(author)
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Assessment of numerical methods for fully resolved simulations of particle-laden turbulent flows
- 2019
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In: Computers & Fluids. - : Elsevier Ltd. - 0045-7930 .- 1879-0747. ; 179, s. 1-14
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Journal article (peer-reviewed)abstract
- During the last decade, many approaches for resolved-particle simulation (RPS) have been developed for numerical studies of finite-size particle-laden turbulent flows. In this paper, three RPS approaches are compared for a particle-laden decaying turbulence case. These methods are, the Volume-of-Fluid Lagrangian method, based on the viscosity penalty method (VoF-Lag); a direct forcing Immersed Boundary Method, based on a regularized delta function approach for the fluid/solid coupling (IBM); and the Bounce Back scheme developed for Lattice Boltzmann method (LBM-BB). The physics and the numerical performances of the methods are analyzed. Modulation of turbulence is observed for all the methods, with a faster decay of turbulent kinetic energy compared to the single-phase case. Lagrangian particle statistics, such as the velocity probability density function and the velocity autocorrelation function, show minor differences among the three methods. However, major differences between the codes are observed in the evolution of the particle kinetic energy. These differences are related to the treatment of the initial condition when the particles are inserted in an initially single-phase turbulence. The averaged particle/fluid slip velocity is also analyzed, showing similar behavior as compared to the results referred in the literature. The computational performances of the different methods differ significantly. The VoF-Lag method appears to be computationally most expensive. Indeed, this method is not adapted to turbulent cases. The IBM and LBM-BB implementations show very good scaling.
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| 18. |
- Burman, Erik, et al.
(author)
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Cut finite elements for convection in fractured domains
- 2019
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In: Computers & Fluids. - : Elsevier. - 0045-7930 .- 1879-0747. ; 179, s. 728-736
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Journal article (peer-reviewed)abstract
- We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain, which is a union of manifolds of different dimensions such that a d dimensional component always resides on the boundary of a d+1 dimensional component. This type of domain can for instance be used to model porous media with embedded fractures that may intersect. The convection problem is formulated in a compact form suitable for analysis using natural abstract directional derivative and divergence operators. The cut finite element method is posed on a fixed background mesh that covers the domain and the manifolds are allowed to cut through a fixed background mesh in an arbitrary way. We consider a simple method based on continuous piecewise linear elements together with weak enforcement of the coupling conditions and stabilization. We prove a priori error estimates and present illustrating numerical examples.
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| 19. |
- Caraeni, D., et al.
(author)
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Compact third-order multidimensional upwind discretization for steady and unsteady flow simulations
- 2005
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In: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 34:05-apr, s. 419-441
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Journal article (peer-reviewed)abstract
- We propose a new third-order multidimensional upwind algorithm for the solution of the flow equations on tetrahedral cells unstructured grids. This algorithm has a compact stencil (cell-based computations) and uses a finite element idea when computing the residual over the cell to achieve its third-order (spatial) accuracy. The construction of the new scheme is presented. The asymptotic accuracy for steady or unsteady, inviscid or viscous flow situations is proved using numerical experiments. The new high-order discretization proves to have excellent parallel scalability. Our studies show the advantages of the new compact third-order scheme when compared with the classical second-order multidimensional upwind schemes.
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| 20. |
- Dalla Barba, Federico, et al.
(author)
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An interface capturing method for liquid-gas flows at low-Mach number
- 2021
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In: Computers & Fluids. - : Elsevier Ltd. - 0045-7930 .- 1879-0747. ; 216
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Journal article (peer-reviewed)abstract
- Multiphase, compressible and viscous flows are of crucial importance in a wide range of scientific and engineering problems. Despite the large effort paid in the last decades to develop accurate and efficient numerical techniques to address this kind of problems, current models need to be further improved to address realistic applications. In this context, we propose a numerical approach to the simulation of multiphase, viscous flows where a compressible and an incompressible phase interact in the low-Mach number regime. In this frame, acoustics are neglected but large density variations of the compressible phase can be accounted for as well as heat transfer, convection and diffusion processes. The problem is addressed in a fully Eulerian framework exploiting a low-Mach number asymptotic expansion of the Navier-Stokes equations. A Volume of Fluid approach (VOF) is used to capture the liquid-gas interface, built on top of a massive parallel solver, second order accurate both in time and space. The second-order-pressure term is treated implicitly and the resulting pressure equation is solved with the eigenexpansion method employing a robust and novel formulation. We provide a detailed and complete description of the theoretical approach together with information about the numerical technique and implementation details. Results of benchmarking tests are provided for five different test cases.
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| 21. |
- Delorme, Yann T., et al.
(author)
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A simple and efficient incompressible Navier-Stokes solver for unsteady complex geometry flows on truncated domains
- 2017
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In: Computers & Fluids. - : Elsevier. - 0045-7930 .- 1879-0747. ; 150, s. 84-94
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Journal article (peer-reviewed)abstract
- Incompressible Navier-Stokes solvers based on the projection method often require an expensive numerical solution of a Poisson equation for a pressure-like variable. This often involves linear system solvers based on iterative and multigrid methods which may limit the ability to scale to large numbers of processors. The artificial compressibility method (ACM) [6] introduces a time derivative of the pressure into the incompressible form of the continuity equation creating a coupled closed hyperbolic system that does not require a Poisson equation solution and allows for explicit time-marching and localized stencil numerical methods. Such a scheme should theoretically scale well on large numbers of CPUs, GPU'€™s, or hybrid CPU-GPU architectures. The original ACM was only valid for steady flows and dual-time stepping was often used for time-accurate simulations. Recently, Clausen [7] has proposed the entropically damped artificial compressibility (EDAC) method which is applicable to both steady and unsteady flows without the need for dual-time stepping. The EDAC scheme was successfully tested with both a finite-difference MacCormack'€™s method for the two-dimensional lid driven cavity and periodic double shear layer problem and a finite-element method for flow over a square cylinder, with scaling studies on the latter to large numbers of processors. In this study, we discretize the EDAC formulation with a new optimized high-order centered finite-difference scheme and an explicit fourth-order Runge-€“Kutta method. This is combined with an immersed boundary method to efficiently treat complex geometries and a new robust outflow boundary condition to enable higher Reynolds number simulations on truncated domains. Validation studies for the Taylor-€“Green Vortex problem and the lid driven cavity problem in both 2D and 3D are presented. An eddy viscosity subgrid-scale model is used to enable large eddy simulations for the 3D cases. Finally, an application to flow over a sphere is presented to highlight the boundary condition and performance comparisons to a traditional incompressible Navier-€“Stokes solver is shown for the 3D lid driven cavity. Overall, the combined EDAC formulation and discretization is shown to be both effective and affordable.
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| 22. |
- Docampo-Sánchez, J., et al.
(author)
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Enhancing accuracy with a convolution filter : What works and why!
- 2020
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In: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 213, s. 104727-104727
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Journal article (peer-reviewed)abstract
- In this paper we present a simplified discussion of the Smoothness-Increasing Accuracy-Conserving (SIAC) filter. We demonstrate the importance of appropriately initializing the data in order to be able to extract higher orders of accuracy by comparing the nodal and modal forms of a discontinuous Galerkin approximation applied to a simplified cubic polynomial. Using the modal form, we are able to exactly reproduce the cubic polynomial, whereas this reconstruction does not occur using the nodal form. Furthermore, we tie the ability of the filter to extract extra accuracy to its accurate wave propagation properties.
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| 23. |
- Du, Lin, et al.
(author)
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Effect of flapping frequency on aerodynamics of wing in freely hovering flight
- 2015
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In: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 117, s. 79-87
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Journal article (peer-reviewed)abstract
- The two-dimensional incompressible Navier-Stokes equations are solved using the immersed boundary method. The wing is driven to translate in the horizontal direction and rotate periodically to emulate the wing motion of a fruit fly in normal hovering flight, while the motion in the vertical direction responds passively to the action of the wing aerodynamic lift and weight of the insect body. The insect body is modeled by a point mass. It is shown that flapping wing cannot produce required lift to maintain stable hovering flight in specified range with low flapping frequencies, if the insect weight is equivalent to the averaged wing lift in one cycle on the assumption of zero vertical velocity. The vertical velocity influences the instantaneous angle of attack of the hovering wing, which results in the variation in aerodynamics of the wing. The insect may experience fluctuating hovering flight with a reduced weight when the flapping frequency is low. The fluctuating amplitude decreases with increasing flapping frequency. The efficiency of hovering flight is also a problem of concern.
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| 24. |
- Evegren, Philip, et al.
(author)
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Pulsating flow and mass transfer in an asymmetric system of bifurcations
- 2011
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In: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 49:1, s. 46-61
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Journal article (peer-reviewed)abstract
- Pulsating flow through bifurcations are of general interest. In the human body such flows are also very common; for example in blood vessels and the respiratory tract. The characteristics of the flow in arteries have been related to the process of atherogenesis, based on the observation that the initial manifestation of the process is observed at certain common locations, i.e., near bifurcations in vessels of certain size. Inspite of these observations there is no direct understanding between the flow itself and the pathological process. In fact, the flow itself is rather complex since it is unsteady and transitional. The paper considers both unsteady- and steady-flow through a three generation system of (non-symmetric) bifurcations. The geometry consists of a 90 degrees. bifurcation followed by two sets of consecutive symmetric bifurcations. The aim of the paper is to investigate the effects of the bifurcations on the flow and mass transport in such a geometrical configuration that is often found in physiological situations. Additionally, the effects of different inlet velocity conditions have been considered. The different inlet conditions are aimed at studying the sensitivity to variations of inflow conditions; variations found under normal physiological conditions. The results show that the geometrical asymmetry affects the velocity distribution even after a second bifurcation downstream. Two generations down this asymmetry does not have a significant effect any-more. The different inlet conditions affect the flow to the next generation of branches during parts of the cycle. At peak flow and further downstream in the system the effects are negligible. It is also found that over a cycle the mass flow distribution through the outlets can be affected by the inlet velocity conditions. The distribution of a passive scalar is not uniform but depends on the inlet conditions and the Schmidt number (i.e., molecular diffusion).
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| 25. |
- Fernandez, David C. Del Rey, et al.
(author)
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Entropy-stable p-nonconforming discretizations with the summation-by-parts property for the compressible Navier-Stokes equations
- 2020
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In: Computers & Fluids. - : PERGAMON-ELSEVIER SCIENCE LTD. - 0045-7930 .- 1879-0747. ; 210
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Journal article (peer-reviewed)abstract
- The entropy-conservative/stable, curvilinear, nonconforming, p-refinement algorithm for hyperbolic conservation laws of Del Rey Fernandez et al. (2019) is extended from the compressible Euler equations to the compressible Navier-Stokes equations. A simple and flexible coupling procedure with planar interpolation operators between adjoining nonconforming elements is used. Curvilinear volume metric terms are numerically approximated via a minimization procedure and satisfy the discrete geometric conservation law conditions. Distinct curvilinear surface metrics are used on the adjoining interfaces to construct the interface coupling terms, thereby localizing the discrete geometric conservation law constraints to each individual element. The resulting scheme is entropy conservative/stable, element-wise conservative, and freestream preserving. Viscous interface dissipation operators that retain the entropy stability of the base scheme are developed. The accuracy and stability of the resulting numerical scheme are shown to be comparable to those of the original conforming scheme in Carpenter et al. (2014) and Parsani et al. (2016), i.e., this scheme achieves similar to p 1/2 convergence on geometrically high-order distorted element grids; this is demonstrated in the context of the viscous shock problem, the Taylor-Green vortex problem at a Reynolds number of Re = 1, 600, and a subsonic turbulent flow past a sphere at Re = 2, 000. (C) 2020 Published by Elsevier Ltd.
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| 26. |
- Frungieri, Graziano, et al.
(author)
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Heavy and light inertial particle aggregates in homogeneous isotropic turbulence : A study on breakup and stress statistics
- 2023
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In: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 263
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Journal article (peer-reviewed)abstract
- The breakup of inertial, solid aggregates in an incompressible, homogeneous and isotropic three-dimensional turbulent flow is studied by means of a direct numerical simulation, and by a Lagrangian tracking of the aggregates at varying Stokes number and fluid-to-particle density ratio. Within the point-particle approximation of the Maxey–Riley–Gatignol equations of motion, we analyze the statistics of the time series of shear and drag stresses, which are here both deemed as responsible for aggregate breakup. We observe that, regardless of the Stokes number, the shear stresses produced by the turbulent velocity gradients similarly impact the breakup statistics of inertial and neutrally buoyant aggregates, and dictate the breakup rate of loose aggregates. When the density ratio is different from unity, drag stresses become dominant and are seen to be able to cause to breakup of also the most resistant aggregates. A transition from a shear-dominated to a drag-dominated breakup regime is observed, and a power-law is seen to well describe the breakup rate of loose aggregates regardless of their inertia. The present work assesses the role of shear and drag stresses on aggregate breakup and computes breakup rates to be possibly used in population balance models.
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| 27. |
- Grosshans, Holger, et al.
(author)
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Enhanced liquid-gas mixing due to pulsating injection
- 2015
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In: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 107, s. 196-204
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Journal article (peer-reviewed)abstract
- This paper considers the effects of intermittent injection of a liquid jet or spray on the initial break-up and mixing of one fluid with the surrounding ambient fluid. The aim of the analysis is to describe the physical process and indicate the mechanisms that control the mixing under different flow conditions (time-dependent injection and its frequency relative to the time scales of the flow) and fluid properties (density ratio), Schmidt number for a single phase case which is studied for comparison, or the Weber number for the two-phase cases. The computations use Large Eddy Simulation (LES) to account for turbulence, and either Volume Of Fluid (VOF) for the initial break-up or Lagrangian Particle Tracking (LPT) with droplet break-up model in the case of liquid droplets injected into the ambient gas. The results show that, depending on the physical properties of the liquid and ambient gas, the initial break-up and turbulent mixing can be enhanced substantially with intermittent injection. The numerical modeling is validated by recovering key results of experimental and analytical works. It can be observed that a main effect during the mixing is the suction of ambient fluid at the tail of the injected liquid, which depends on the fluid properties. Increased injection frequency shows to increase the mixing significantly during the initial transient phase.
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| 28. |
- Grosshans, H., et al.
(author)
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Sensitivity of VOF simulations of the liquid jet breakup to physical and numerical parameters
- 2016
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In: Computers & Fluids. - : Elsevier. - 0045-7930 .- 1879-0747. ; 136, s. 312-323
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Journal article (peer-reviewed)abstract
- In this paper the characteristics of the primary breakup of a liquid jet is analyzed numerically. We applied the Volumes of Fluids (VOF) approach utilizing the Direction Averaged Curvature (DAC) model, to estimate the interface curvature, and the Direction Averaged Normal (DAN) model, to propagate the interface. While being used for the first time to predict liquid atomization, this methodology showed a high accuracy. The influence of varying the fluid properties, namely liquid-gas density and viscosity ratio, and injection conditions is discussed related to the required grid resolution. Resulting droplet sizes are compared to distributions obtained through the One-Dimensional Turbulence (ODT) model.
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| 29. |
- Hoffman, Johan, et al.
(author)
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Unicorn : Parallel adaptive finite element simulation of turbulent flow and fluid-structure interaction for deforming domains and complex geometry
- 2013
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In: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 80:SI, s. 310-319
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Journal article (peer-reviewed)abstract
- We present a framework for adaptive finite element computation of turbulent flow and fluid structure interaction, with focus on general algorithms that allow for complex geometry and deforming domains. We give basic models and finite element discretization methods, adaptive algorithms and strategies for efficient parallel implementation. To illustrate the capabilities of the computational framework, we show a number of application examples from aerodynamics, aero-acoustics, biomedicine and geophysics. The computational tools are free to download open source as Unicorn, and as a high performance branch of the finite element problem solving environment DOLFIN, both part of the FEniCS project.
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| 30. |
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| 31. |
- Jansson, Niclas, 1983-, et al.
(author)
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Neko: A modern, portable, and scalable framework for high-fidelity computational fluid dynamics
- 2024
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In: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 275, s. 106243-106243
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Journal article (peer-reviewed)abstract
- Computational fluid dynamics (CFD), in particular applied to turbulent flows, is a research area with great engineering and fundamental physical interest. However, already at moderately high Reynolds numbers the computational cost becomes prohibitive as the range of active spatial and temporal scales is quickly widening. Specifically scale-resolving simulations, including large-eddy simulation (LES) and direct numerical simulations (DNS), thus need to rely on modern efficient numerical methods and corresponding software implementations. Recent trends and advancements, including more diverse and heterogeneous hardware in High-Performance Computing (HPC), are challenging software developers in their pursuit for good performance and numerical stability. The well-known maxim “software outlives hardware” may no longer necessarily hold true, and developers are today forced to re-factor their codebases to leverage these powerful new systems. In this paper, we present Neko, a new portable framework for high-order spectral element discretization, targeting turbulent flows in moderately complex geometries. Neko is fully available as open software. Unlike prior works, Neko adopts a modern object-oriented approach in Fortran 2008, allowing multi-tier abstractions of the solver stack and facilitating hardware backends ranging from general-purpose processors (CPUs) down to exotic vector processors and FPGAs. We show that Neko’s performance and accuracy are comparable to NekRS, and thus on-par with Nek5000’s successor on modern CPU machines. Furthermore, we develop a performance model, which we use to discuss challenges and opportunities for high-order solvers on emerging hardware
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| 32. |
- Khatri, Shilpa, et al.
(author)
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A numerical method for two phase flows with insoluble surfactants
- 2011
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In: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 49:1, s. 150-165
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Journal article (peer-reviewed)abstract
- In many practical multiphase flow problems, i.e. treatment of gas emboli and various microfluidic applications, the effect of interfacial surfactants, or surface reacting agents, on the surface tension between the fluids is important. The surfactant concentration on an interface separating the fluids can be modeled with a time dependent differential equation defined on the moving and deforming interface. The equations for the location of the interface and the surfactant concentration on the interface are coupled with the Navier-Stokes equations. These equations include the singular surface tension forces from the interface on the fluid, which depend on the interfacial surfactant concentration. A new accurate and inexpensive numerical method for simulating the evolution of insoluble surfactants is presented in this paper. It is based on an explicit yet Eulerian discretization of the interface, which for two dimensional flows allows for the use of uniform one dimensional grids to discretize the equation for the interfacial surfactant concentration. A finite difference method is used to solve the Navier-Stokes equations on a regular grid with the forces from the interface spread to this grid using a regularized delta function. The timestepping is based on a Strang splitting approach. Drop deformation in shear flows in two dimensions is considered. Specifically, the effect of surfactant concentration on the deformation of the drops is studied for different sets of flow parameters.
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| 33. |
- Kierkegaard, Axel, et al.
(author)
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Flow field eigenmode decompositions in aeroacoustics
- 2010
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In: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 39:2, s. 338-344
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Journal article (peer-reviewed)abstract
- In this paper an efficient method to study sound generation processes in low Mach number flows is presented. We apply the methodology on a two-dimensional flow over a cavity with smoothed corners. Instead of the full flow field obtained from, for example a Direct Numerical Simulation (DNS), we use a reduced model based on global modes to obtain the aeroacoustic sources. Global modes are eigenmodes to the Navier-Stokes equations, linearized about a steady base flow. In a reduced model the perturbations from a steady state are approximated by a linear combination of the eigenmodes. The time dependence is determined by the corresponding eigenvalues. Curie's equation is used to calculate the acoustic field, and by studying the source terms in Curie's equation, mechanisms for sources of sound are identified. Results of acoustic pressure in the far-field and source strengths for different superpositions of eigenmodes are presented.
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| 34. |
- Kopriva, David A, et al.
(author)
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A provably stable discontinuous Galerkin spectral element approximation for moving hexahedral meshes
- 2016
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In: Computers & Fluids. - : Elsevier. - 0045-7930 .- 1879-0747. ; 139, s. 148-160
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Journal article (peer-reviewed)abstract
- We design a novel provably stable discontinuous Galerkin spectral element (DGSEM) approximation to solve systems of conservation laws on moving domains. To incorporate the motion of the domain, we use an arbitrary Lagrangian-Eulerian formulation to map the governing equations to a fixed reference domain. The approximation is made stable by a discretization of a skew-symmetric formulation of the problem. We prove that the discrete approximation is stable, conservative and, for constant coefficient problems, maintains the free- stream preservation property. We also provide details on how to add the new skew-symmetric ALE approximation to an existing discontinuous Galerkin spectral element code. Lastly, we provide numerical support of the theoretical results.
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| 35. |
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| 36. |
- Laurén, Fredrik, 1990-, et al.
(author)
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Practical Inlet Boundary Conditions for Internal Flow Calculations
- 2018
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In: Computers & Fluids. - : Elsevier. - 0045-7930 .- 1879-0747. ; 175, s. 159-166
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Journal article (peer-reviewed)abstract
- To impose boundary conditions, data at the boundaries must be known, and consequently measurements of the imposed quantities must be available. In this paper, we consider the two most commonly used inflow boundary conditions with available data for internal flow calculations: the specification of the total temperature and total pressure. We use the energy method to prove that the specification of the total temperature and the total pressure together with the tangential velocity at an inflow boundary lead to well-posedness for the linearized compressible Euler equations. Next, these equations are discretized in space using high-order finite-difference operators on summation-by-parts form, and the boundary conditions are weakly imposed. The resulting numerical scheme is proven to be stable and the implementation of the corresponding nonlinear scheme is verified with the method of manufactured solutions. We also derive the spectrum for the continuous and discrete problems and show how to predict the convergence rate to steady state. Finally, nonlinear steady-state computations are performed, and they confirm the predicted convergence rates.
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| 37. |
- Lokatt, Mikaela, et al.
(author)
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Finite-volume scheme for the solution of integral boundary layer equations
- 2016
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In: Computers & Fluids. - : Elsevier. - 0045-7930 .- 1879-0747. ; 132, s. 62-71
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Journal article (peer-reviewed)abstract
- An unstructured-mesh finite-volume formulation for the solution of systems of steady conservation laws on embedded surfaces is presented. The formulation is invariant to the choice of local tangential coordinate systems and is stabilized by a novel up-winding scheme applicable also to mixed-hyperbolic systems. The formulation results in a system of non-linear equations which is solved by a quasi-Newton method. While the finite volume scheme is applicable to a range of conservation laws, it is here implemented for the solution of the integral boundary layer equations, as a first step in developing a fully coupled viscous-inviscid interaction method. For validation purposes, integral boundary layer quantities computed using a minimal set of three-dimensional turbulent integral boundary layer equations are compared to experimental data and an established computer code for two-dimensional problems. The validation shows that the proposed formulation is stable, yields a well-conditioned global Jacobian, is conservative on curved surfaces and invariant to rotation as well as convergent with regard to mesh refinement.
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| 38. |
- Lokatt, Mikaela, et al.
(author)
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Robust viscous-inviscid interaction scheme for application on unstructured meshes
- 2017
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In: Computers & Fluids. - : Elsevier. - 0045-7930 .- 1879-0747. ; 145, s. 37-51
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Journal article (peer-reviewed)abstract
- A coupled viscous-inviscid interaction scheme combining the continuity equation for potential flow with the three-dimensional integral boundary layer equations is presented. The inviscid problem is discretized by a finite-element approach whereas an upwind-biased finite-volume scheme is employed for the boundary layer equations. The discretization is applicable to unstructured tetrahedral-triangular meshes and results in a sparse system of non-linear equations which is solved by a Newton-type method. The mathematical reasons for the singularities commonly associated with the integral boundary layer equations in separated flow regions are analyzed and the connection between the mathematical singularities and the numerical ill-conditioning is discussed. It is shown that, by a suitable choice of closure relations, it is possible to obtain a boundary layer model free from numerical ill-conditioning in separated flow regions. The accuracy of the coupled viscous-inviscid model is investigated in a number of test cases including transitional and mildly separated flow over two different natural laminar flow airfoils and three-dimensional flow over a swept wing. It is concluded that the coupled method is able to provide reasonably accurate predictions of viscous and inviscid flow field quantities for the investigated cases.
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| 39. |
- Marin, Oana, et al.
(author)
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A highly accurate boundary treatment for confined Stokes flow
- 2012
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In: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 66, s. 215-230
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Journal article (peer-reviewed)abstract
- Fluid flow phenomena in the Stokesian regime abounds in nature as well as in microfluidic applications. Discretizations based on boundary integral formulations for such flow problems allow for a reduction in dimensionality but have to deal with dense matrices and the numerical evaluation of integrals with singular kernels. The focus of this paper is the discretization of wall confinements, and specifically the numerical treatment of flat solid boundaries (walls), for which a set of high-order quadrature rules that accurately integrate the singular kernel of the Stokes equations are developed. Discretizing by Nystrom's method, the accuracy of the numerical integration determines the accuracy of the solution of the boundary integral equations, and a higher order quadrature method yields a large gain in accuracy at negligible cost. The structure of the resulting submatrix associated with each wall is exploited in order to substantially reduce the memory usage. The expected convergence of the quadrature rules is validated through numerical tests, and this boundary treatment is further applied to the classical problem of a sedimenting sphere in the vicinity of solid walls.
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| 40. |
- Mattsson, Ken, et al.
(author)
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High-order accurate computations for unsteady aerodynamics
- 2007
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In: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 36:3, s. 636-649
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Journal article (peer-reviewed)abstract
- A high-order accurate finite difference scheme is used to perform numerical studies on the benefit of high-order methods. The main advantage of the present technique is the possibility to prove stability for the linearized Euler equations on a multi-block domain, including the boundary conditions. The result is a robust high-order scheme for realistic applications. Convergence studies are presented, verifying design order of accuracy and the superior efficiency of high-order methods for applications dominated by wave propagation. Furthermore, numerical computations of a more complex problem, a vortex-airfoil interaction, show that high-order methods are necessary to capture the significant flow features for transient problems and realistic grid resolutions. This methodology is easy to parallelize due to the multi-block capability. Indeed, we show that the speedup of our numerical method scales almost linearly with the number of processors.
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| 41. |
- Mukha, Timofey, 1988, et al.
(author)
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Predictive accuracy of wall-modelled large-eddy simulation on unstructured grids
- 2021
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In: Computers and Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 221
-
Journal article (peer-reviewed)abstract
- The predictive accuracy of wall-modelled LES is influenced by a combination of the subgrid model, the wall model, the numerical dissipation induced primarily by the convective numerical scheme, and also by the density and topology of the computational grid. The latter factor is of particular importance for industrial flow problems, where unstructured grids are typically employed due to the necessity to handle complex geometries. Here, a systematic simulation-based study is presented, investigating the effect of grid-cell type on the predictive accuracy of wall-modelled LES in the framework of a general-purpose finite-volume solver. Following standard practice for meshing near-wall regions, it is proposed to use prismatic cells. Three candidate shapes for the base of the prisms are considered: a triangle, a quadrilateral, and an arbitrary polygon. The cell-centre distance is proposed as a metric to determine the spatial resolution of grids with different cell types. The simulation campaign covers two test cases with attached boundary layers: fully-developed turbulent channel flow, and a zero-pressure-gradient flat-plate turbulent boundary layer. A grid construction strategy is employed, which adapts the grid metric to the outer length scale of the boundary layer. The results are compared with DNS data concerning mean wall shear stress and profiles of flow statistics. The principle outcome is that unstructured simulations may provide the same accuracy as simulations on structured orthogonal hexahedral grids. The choice of base shape of the near-wall cells has a significant impact on the computational cost, but in terms of accuracy appears to be a factor of secondary importance.
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| 42. |
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| 43. |
- Mukha, Timofey, et al.
(author)
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The generation of turbulent inflow boundary conditions using precursor channel flow simulations
- 2017
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In: Computers & Fluids. - : Elsevier Ltd. - 0045-7930 .- 1879-0747. ; 156, s. 21-33
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Journal article (peer-reviewed)abstract
- The use of a precursor simulation of fully developed turbulent channel flow for the generation of turbulent boundary layer (TBL) inflow data is investigated. Based on the desired properties of the TBL, a complete procedure is described for how to specify the precursor simulation. The key feature of the specification is to match the momentum thickness of the precursor to that of the inflow TBL. The inflow data is then constructed from time- and space-dependent flow data in a cross-plane of the precursor. The proposed procedure removes the need to rescale the flow data and thus violate the governing equations, as is common practice in other state-of-the-art inflow generation methods for TBLs. The adaption length of the generated TBL is investigated using wall-resolved large-eddy simulation (WRLES) for a zero-pressure gradient (ZPG-) TBL, with a momentum thickness Reynolds number in the interval 830–2 400. The results are compared with a solution obtained using a standard rescaling procedure for the inflow data. The adaption length is shown to be similar for the two methods. Practical differences and advantages of the proposed of method, as compared to other inflow generation techniques, are assessed. These involve the role of the auxiliary simulation, channel flow in the present case, in the overall computational procedure, as well as data handling, initial transients and adaption lengths.
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| 44. |
- Muld, Tomas W., et al.
(author)
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Flow structures around a high-speed train extracted using Proper Orthogonal Decomposition and Dynamic Mode Decomposition
- 2012
-
In: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 57, s. 87-97
-
Journal article (peer-reviewed)abstract
- In this paper, Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) are used to extract the most dominant flow structures of a simulated flow in the wake of a high-speed train model, the Aerodynamic Train Model (ATM). The use of decomposition methods to successfully identify dominant flow structures for an engineering geometry is achieved by using a flow field simulated with the Detached Eddy Simulation model (DES), which is a turbulence model enabling time accurate solutions of the flows around engineering geometries. This paper also examines the convergence of the POD and DMD modes for this case. It is found that the most dominant DMD mode needs a longer sample time to converge than the most dominant POD mode. A comparison between the modes from the two different decomposition methods shows that the second and third POD modes correspond to the same flow structure as the second DMD mode. This is confirmed both by investigating the spectral content of the POD mode coefficients, and by comparing the spatial modes. The flow structure associated with these modes is identified as being vortex shedding. The identification is performed by reconstructing the flow field using the mean flow and the second DMD mode. A second flow structure, a bending of the counter-rotating vortices, is also identified. Identifying this flow structure is achieved by reconstructing the flow field with the mean flow and the fourth and fifth POD modes.
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| 45. |
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| 46. |
- Nair, Vineeth, et al.
(author)
-
Inspecting sound sources in an orifice-jet flow using Lagrangian coherent structures
- 2016
-
In: Computers & Fluids. - : Elsevier. - 0045-7930 .- 1879-0747. ; 140, s. 397-405
-
Journal article (peer-reviewed)abstract
- A novel method is proposed to identify flow structures responsible for sound generation in confined flow past an inhibitor. Velocity fields obtained using Large Eddy Simulations (LES) are post-processed to compute the Finite Time Lyapunov Exponent (FTLE) field, the ridges of which in backward time represent an approximation to Lagrangian Coherent Structures (LCS), the structures that organize transport in the flow field. The flow-field is first decomposed using dynamic mode decomposition (DMD), and the organizing centers or vortices at the significant DMD frequencies are extracted. The results are then compared with the lambda(2) criterion. Features such as shear layer roll-up and development of secondary instabilities are more clearly visible in the FTLE field than with the lambda(2) criterion.
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| 47. |
- Nchupang, Mojalefa P., et al.
(author)
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A provably stable and high-order accurate finite difference approximation for the incompressible boundary layer equations
- 2023
-
In: Computers & Fluids. - : PERGAMON-ELSEVIER SCIENCE LTD. - 0045-7930 .- 1879-0747. ; 267
-
Journal article (peer-reviewed)abstract
- In this article we develop a high order accurate method to solve the incompressible boundary layer equations in a provably stable manner. We first derive continuous energy estimates, and then proceed to the discrete setting. We formulate the discrete approximation using high-order finite difference methods on summation-by-parts form and implement the boundary conditions weakly using the simultaneous approximation term method. By applying the discrete energy method and imitating the continuous analysis, the discrete estimate that resembles the continuous counterpart is obtained proving stability. We also show that these newly derived boundary conditions removes the singularities associated with the null-space of the nonlinear discrete spatial operator. Numerical experiments that verifies the high-order accuracy of the scheme and coincides with the theoretical results are presented. The numerical results are compared with the well-known Blasius similarity solution as well as that resulting from the solution of the incompressible Navier–Stokes equations.
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| 48. |
- Nobis, Harrison, et al.
(author)
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Topology optimization of unsteady flows using the spectral element method
- 2022
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In: Computers & Fluids. - : Elsevier. - 0045-7930 .- 1879-0747. ; 239
-
Journal article (peer-reviewed)abstract
- We investigate the applicability of a high-order Spectral Element Method (SEM) to density based topology optimization of unsteady flows in two dimensions. Direct Numerical Simulations (DNS) are conducted relying on Brinkman penalization to describe the presence of solid within the domain. The optimization procedure uses the adjoint-variable method to compute gradients and a checkpointing strategy to reduce storage requirements. A nonlinear filtering strategy is used to both enforce a minimum length scale and to provide smoothing across the fluid-solid interface, preventing Gibbs oscillations. This method has been successfully applied to the design of a channel bend and an oscillating pump, and demonstrates good agreement with body fitted meshes. The precise design of the pump is shown to depend on the initial material distribution. However, the underlying topology and pumping mechanism is the same. The effect of a minimum length scale has been studied, revealing it to be a necessary regularization constraint for the oscillating pump to produce meaningful designs. The combination of SEM and density based optimization offer some unique challenges which are addressed and discussed, namely a lack of explicit boundary tracking exacerbated by the interface smoothing. Nevertheless, SEM can achieve equivalent levels of precision to traditional finite element methods, while requiring fewer degrees of freedom. Hence, the use of SEM addresses the two major bottlenecks associated with optimizing unsteady flows: computation cost and data storage.
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| 49. |
- Nordström, Jan, et al.
(author)
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A hybrid method for unsteady inviscid fluid flow
- 2009
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In: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 38:4, s. 875-882
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Journal article (peer-reviewed)abstract
- We show how a stable and accurate hybrid procedure for fluid flow can be constructed. Two separate solvers, one using high order finite difference methods and another using the node-centered unstructured finite volume method are coupled in a truly stable way. The two flow solvers run independently and receive and send information from each other by using a third coupling code. Exact solutions to the Euler equations are used to verify the accuracy and stability of the new computational procedure. We also demonstrate the capability of the new procedure in a calculation of the flow in and around a model of a coral.
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| 50. |
- Nordström, Jan, et al.
(author)
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Conjugate heat transfer for the unsteady compressible Navier–Stokes equations using a multi-block coupling
- 2013
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In: Computers & Fluids. - : Elsevier. - 0045-7930 .- 1879-0747. ; 72, s. 20-29
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Journal article (peer-reviewed)abstract
- This paper deals with conjugate heat transfer problems for the time-dependent compressible Navier–Stokes equations. One way to model conjugate heat transfer is to couple the Navier–Stokes equations in the fluid with the heat equation in the solid. This requires two different physics solvers. Another way is to let the Navier–Stokes equations govern the heat transfer in both the solid and in the fluid. This simplifies calculations since the same physics solver can be used everywhere.We show by energy estimates that the continuous problem is well-posed when imposing continuity of temperature and heat fluxes by using a modified L2-equivalent norm. The equations are discretized using finite difference on summation-by-parts form with boundary- and interface conditions imposed weakly by the simultaneous approximation term. It is proven that the scheme is energy stable in the modified norm for any order of accuracy.We also show what is required for obtaining the same solution as when the unsteady compressible Navier–Stokes equations are coupled to the heat equation. The differences between the two coupling techniques are discussed theoretically as well as studied numerically, and it is shown that they are indeed small.
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