Incompressible Fluid Dynamics Research Articles

Transient Dynamic Modeling and Analysis of Complex Parachute Inflation with Fixed Payload

The inflation process of a special parachute with slots and a fixed payload is investigated using a multimaterial arbitrary Lagrangian-Euler–coupled numerical approach, which considers fluid-structure interaction within the LS-DYNA nonlinear analysis code. The transient dynamic solver is set up using a Lagrangian-Euler penalty method, and a numerical simulation of the slot parachute design that considers permeability is performed. The inflation characteristics of a slot parachute at different initial velocities are analyzed. The three-dimensional simulation results for the inflation are validated by comparing with the airdrop test results. Finally, the incompressible fluid dynamics and the evolution of vortexes during the opening process are analyzed. The results demonstrate the following. This slot parachute can rapidly attain a steady state after fully inflating without any obvious canopy breathing. The stress distribution near the slots is obviously higher than the average level across the canopy surface. A symmetrically counterrotated vortex couple appears at the top of the parachute, which then extrudes to asymmetry until the couple separates and is brushed off by the airflow.

Numerical comparison of hybridized discontinuous Galerkin and finite volume methods for incompressible flow

SUMMARYIn this study, a hybridizable discontinuous Galerkin method is presented for solving the incompressible Navier–Stokes equation. In our formulation, the convective part is linearized using a Picard iteration, for which there exists a necessary criterion for convergence. We show that our novel hybridized implementation can be used as an alternative method for solving a range of problems in the field of incompressible fluid dynamics. We demonstrate this by comparing the performance of our method with standard finite volume solvers, specifically the well‐established finite volume method of second order in space, such as the icoFoam and simpleFoam of the OpenFOAM package for three typical fluid problems. These are the Taylor–Green vortex, the 180‐degree fence case and the DFG benchmark. Our careful comparison yields convincing evidence for the use of hybridizable discontinuous Galerkin method as a competitive alternative because of their high accuracy and better stability properties. Copyright © 2014 John Wiley & Sons, Ltd.

An integrated multiphysics model for friction stir welding of 6061 Aluminum alloy

This article presents a new, combined ‘integrated’- ‘multiphysics’ model of friction stir welding (FSW) where a set of governing equations from non-Newtonian incompressible fluid dynamics, conductive and convective heat transfer, and plain stress solid mechanics have been coupled for calculating the process variables and material behaviour both during and after welding. More specifically, regarding the multiphysics feature, the model is capable of simultaneously predicting the local distribution, location and magnitude of maximum temperature, strain, and strain rate fields around the tool pin during the process; while for the integrated (post-analysis) part, the above predictions have been used to study the microstructure and residual stress field of welded parts within the same developed code. A slip/stick condition between the tool and workpiece, friction and deformation heat source, convection and conduction heat transfer in the workpiece, a solid mechanics-based viscosity definition, and the Zener-Hollomon- based rigid-viscoplastic material properties with solidus cut-off temperature and empirical softening regime have been employed. In order to validate all the predicted variables collectively, the model has been compared to a series of published case studies on individual/limited set of variables, as well as in-house experiments on FSW of aluminum 6061.

Velocity pick-up and discharge coefficient for round orifices with cross flow at inlet

This study investigates the flow through round orifices with cross flow at the inlet. Emphasis is placed on the change in tangential velocity component for orifices with low L/ D. A definition of velocity pick-up is developed based on the orifice exit to cross-flow tangential velocity ratio. Steady, incompressible, and 3D computational fluid dynamics models with the SST [Formula: see text] turbulent model are employed to calculate orifice flows with different geometrical and flow conditions. Stationary orifices and axial orifices in a rotating disk are considered. Computational fluid dynamics solutions are compared with experimental results and published correlations for discharge coefficients, and good agreement is generally demonstrated. It is found that the non-dimensional velocity pick-up depends strongly on the ratio of characteristic times for flow to travel across the orifice in the tangential direction and that for the flow to pass through the orifice. A correlation of velocity pick-up as a function of this ratio is given.

Considerations of Blood Properties, Outlet Boundary Conditions and Energy Loss Approaches in Computational Fluid Dynamics Modeling

Despite recent development of computational fluid dynamics (CFD) research, analysis of computational fluid dynamics of cerebral vessels has several limitations. Although blood is a non-Newtonian fluid, velocity and pressure fields were computed under the assumptions of incompressible, laminar, steady-state flows and Newtonian fluid dynamics. The pulsatile nature of blood flow is not properly applied in inlet and outlet boundaries. Therefore, we present these technical limitations and discuss the possible solution by comparing the theoretical and computational studies.

Preface to special issue on mathematics of social systems

This special issue is an outgrowth of a minisyposium titled ``Mathematics of Social Systems" held at the 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications, held in Orlando, FL in July 2012. Presenters from that session were invited to submit papers that were reviewed using the usual procedures of the DCDS journals, along with additional authors from the field. Mathematics has already had a significant impact on basic research involving fundamental problems in physical sciences, biological sciences, computer science and engineering. Examples include understanding of the equations of incompressible fluid dynamics, shock wave theory and compressible gas dynamics, ocean modeling, algorithms for image processing and compressive sensing, and biological problems such as models for invasive species, spread of disease, and more recently systems biology for modeling of complex organisms and complex patterns of disease. This impact has yet to come to fruition in a comprehensive way for complex social behavior. While computational models such as agent-based systems and well-known statistical methods are widely used in the social sciences, applied mathematics has not to date had a core impact in the social sciences at the level that it achieves in the physical and life sciences. However in recent years we have seen a growth of work in this direction and ensuing new mathematics problems that must be tackled to understand such problems. Technical approaches include ideas from statistical physics, nonlinear partial differential equations of all types, statistics and inverse problems, and stochastic processes and social network models. The collection of papers presented in this issue provides a backdrop of the current state of the art results in this developing new research area in applied mathematics. The body of work encompasses many of the challenges in understanding these discrete complex systems and their related continuum approximations. <br><br> For more information please click the “Full Text” above.

Simulation for Wind Pressure of Pedestrian Bridge Induced by Main Line Train

Wind pressure of pedestrian bridge induced by main line train has been investigated using numerical simulation. Based on time-filtered Reynolds Averaged Navier-Stokes equations, meanwhile, the RNG k-ε turbulent model is selected to close the equations, the three-dimensional incompressible unsteady flow computational fluid dynamics model have been established by commercial software FLUENT. The distribution of wind pressure and the time histories of wind pressure on surface of the bottom of bridge are obtained, moreover, the characteristics of variation process are summarized.

Simulation on Torpedo Unsteady Hydrodynamic with the Movement in the Longitudinal Plane

The unsteady hydrodynamic accurate calculation is the premise of submerged body trajectory design and maneuverability design. Calculation model of submerged body unsteady hydrodynamic with the movement in the longitudinal plane was established, which based on unsteady three-dimensional incompressible fluid dynamics theory. Variable speed translational and variable angular velocity of the pitching motion in the longitudinal plane of submerged body was achieved by dynamic mesh method. The unsteady hydrodynamic could be obtained by model under the premise of good quality grid by the results. Modeling methods can learn from other similar problems, which has engineering application value.

Multiscale Modeling of Membrane Rearrangement, Drainage, and Rupture in Evolving Foams

Modeling the physics of foams and foamlike materials, such as soapy froths, fire retardants, and lightweight crash-absorbent structures, presents challenges, because of the vastly different time and space scales involved. By separating and coupling these disparate scales, we have designed a multiscale framework to model dry foam dynamics. This leads to a predictive and flexible computational methodology linking, with a few simplifying assumptions, foam drainage, rupture, and topological rearrangement, to coupled interface-fluid motion under surface tension, gravity, and incompressible fluid dynamics. Our computed results match theoretical analyses and experimentally observed physical effects, including thin-film drainage and interference, and are used to study bubble rupture cascades and macroscopic rearrangement. The developed multiscale model allows quantitative computation of complex foam evolution phenomena.

Localization of point vortices under curvature perturbations

We discuss the effect of curvature on the dynamics of a two-dimensional inviscid incompressible fluid with initial vorticity concentrated in N small disjoint regions, that is, the classical point vortex system. We recall some results about point vortex dynamics on simply connected surfaces with constant curvature K, that is, plane, spherical, and hyperbolic surfaces. We show that the effect of curvature can be treated as a smooth perturbation to the Green's function of the equation related to the stream function in the planar case. Then we obtain as a main result that the localization property of point vortices, already proved for the plane, is preserved also under the effect of curvature perturbation.

Large-Time Dynamics of Incompressible Fluid on a Sphere

Large-Time Dynamics of Incompressible Fluid on a Sphere

Inverse problem for Navier-Stokes systems with finite-dimensional overdetermination

We consider an inverse problem for an evolution equation with a quadratic nonlinearity. In this problem, one should find the right-hand side belonging at each time to a finitedimensional subspace on the basis of the given projection of the solution onto that subspace. We prove the time-nonlocal solvability of the inverse problem. Under the condition of additional regularity of the original data and a sufficiently large dimension of the observation subspace, we show that the solution of the inverse problem is unique and more smooth. By way of application, we consider the inverse problem for the three-dimensional Navier-Stokes equations describing the dynamics of a viscous incompressible fluid.

Unstructured overset incompressible computational fluid dynamics for unsteady wind turbine simulations

ABSTRACTOverset computational fluid dynamics (CFD) methods are the most sophisticated methods currently available to predict the unsteady motion of wind turbine blades without the need for additional simplifications or restrictions on the turbine operational conditions. An unstructured implementation of the governing equations of motion permits rapid modeling of the salient components, such as nacelles, towers and other localized obstructions of interest. A time‐accurate incompressible formulation accelerates the convergence of the solution, in addition to eliminating the need for low‐Mach number preconditioning, which can be problematic and computationally expensive for time‐accurate simulations. The use of a hybrid Reynolds‐averaged Navier–Stokes/large eddy simulation (RANS/LES) turbulence method is observed to improve the prediction and extent of separation, as well as integrated performance variables for stalled rotors under fully turbulent conditions. Copyright © 2012 John Wiley &amp; Sons, Ltd.

The h-principle and equations of fluid dynamics

In this note we survey some recent results for the Euler equations in compressible and incompressible fluid dynamics. The main point of all these theorems is the surprising fact that a suitable variant of Gromov's h-principle holds in several cases.

The ℎ-principle and the equations of fluid dynamics

In this note we survey some recent results for the Euler equations in compressible and incompressible fluid dynamics. The main point of all these theorems is the surprising fact that a suitable variant of Gromov’s h h -principle holds in several cases.

Numerical prediction of heat transfer and pressure drop in three-dimensional channels with alternated opposed ribs

Nusselt numbers and friction factor of a ribbed channel have been calculated for several Reynolds numbers and geometric parameters, by the mean of three-dimensional incompressible computational fluid dynamics. The geometry is a rectangular duct with streamwise-periodic transverse rectangular ribs, alternated on its two smaller walls. Reynolds numbers from 75 to 2000 have been investigated. Pressure drop is found to increase monotonically with Re, whereas heat transfer is enhanced only when Re is greater than a critical value. Heat transfer enhancement interpretations, such as the interruption of developed thermal boundary layers and vortex shedding phenomena are discussed.

On the existence and uniqueness of solution to problems of fluid dynamics on a sphere

Orthogonal projectors and fractional derivatives on a two-dimensional unit sphere are introduced. Hilbert and Banach spaces of smooth functions on the sphere and some embedding assertions are given. The unique solvability of a nonstationary problem of vortex dynamics of viscous incompressible fluid on a rotating sphere is shown. The existence of a weak solution to stationary problem is proved too, and a condition guaranteeing the uniqueness of solution is also given.

Surface Tension of Multi-phase Flow with Multiple Junctions Governed by the Variational Principle

We explore a computational model of an incompressible fluid with a multi-phase field in three-dimensional Euclidean space. By investigating an incompressible fluid with a two-phase field geometrically, we reformulate the expression of the surface tension for the two-phase field found by Lafaurie, Nardone, Scardovelli, Zaleski and Zanetti (J. Comp. Phys. \vol{113} \yr{1994} \pages{134-147}) as a variational problem related to an infinite dimensional Lie group, the volume-preserving diffeomorphism. The variational principle to the action integral with the surface energy reproduces their Euler equation of the two-phase field with the surface tension. Since the surface energy of multiple interfaces even with singularities is not difficult to be evaluated in general and the variational formulation works for every action integral, the new formulation enables us to extend their expression to that of a multi-phase ($N$-phase, $N\ge2$) flow and to obtain a novel Euler equation with the surface tension of the multi-phase field. The obtained Euler equation governs the equation of motion of the multi-phase field with different surface tension coefficients without any difficulties for the singularities at multiple junctions. In other words, we unify the theory of multi-phase fields which express low dimensional interface geometry and the theory of the incompressible fluid dynamics on the infinite dimensional geometry as a variational problem. We apply the equation to the contact angle problems at triple junctions. We computed the fluid dynamics for a two-phase field with a wall numerically and show the numerical computational results that for given surface tension coefficients, the contact angles are generated by the surface tension as results of balances of the kinematic energy and the surface energy.

SPONTANEOUS CURRENT-LAYER FRAGMENTATION AND CASCADING RECONNECTION IN SOLAR FLARES. I. MODEL AND ANALYSIS

Magnetic reconnection is commonly considered as a mechanism of solar (eruptive) flares. A deeper study of this scenario reveals, however, a number of open issues. Among them is the fundamental question, how the magnetic energy is transferred from large, accumulation scales to plasma scales where its actual dissipation takes place. In order to investigate this transfer over a broad range of scales we address this question by means of a high-resolution MHD simulation. The simulation results indicate that the magnetic-energy transfer to small scales is realized via a cascade of consecutive smaller and smaller flux-ropes (plasmoids), in analogy with the vortex-tube cascade in (incompressible) fluid dynamics. Both tearing and (driven) "fragmenting coalescence" processes are equally important for the consecutive fragmentation of the magnetic field (and associated current density) to smaller elements. At the later stages a dynamic balance between tearing and coalescence processes reveals a steady (power-law) scaling typical for cascading processes. It is shown that cascading reconnection also addresses other open issues in solar flare research such as the duality between the regular large-scale picture of (eruptive) flares and the observed signatures of fragmented (chaotic) energy release, as well as the huge number of accelerated particles. Indeed, spontaneous current-layer fragmentation and formation of multiple channelised dissipative/acceleration regions embedded in the current layer appears to be intrinsic to the cascading process. The multiple small-scale current sheets may also facilitate the acceleration of a large number of particles. The structure, distribution and dynamics of the embedded potential acceleration regions in a current layer fragmented by cascading reconnection are studied and discussed.

Non-linear asymptotic stability for the through-passing flows of inviscid incompressible fluid

The paper addresses the dynamics of inviscid incompressible fluid confined within bounded domain with the inflow and outflow of fluid through certain parts of the boundary. This system is non-conservative essentially since the fluxes of energy and vorticity through the flow boundary are not equal to zero. Therefore, the dynamics of such flows should demonstrate the generic non-conservative phenomena such as the asymptotic stability of the equilibria, the onset of instability or the excitation of the self-oscillations, etc. These phenomena are studied extensively for the flows of the viscous fluids but not for the inviscid ones. In this paper, we prove a sufficient condition for the non-linear asymptotic stability of the inviscid steady flows. In this paper, we consider the flows of inviscid incompressible fluid through a given domain thereby assuming that the fluid is allowed to come in and out the flow domain through the prescribed parts of its boundary. Such sort of boundaries and the related fluid flows are referred to as open ones. The relevant examples are the flows through the finite ducts or pipes with the inflow of fluid at one end and outflow on the other end. In the case of open boundaries, the inviscid fluid represent a non-conservative system. The violation of the conservation laws takes place since the inflow and outflow of fluid supplies to and withdraws from the flow both energy and vorticity. The withdrawal can be considered as some sort of dissipation. Therefore, the dynamics of open flows should demonstrate the generic non-conservative phenomena such as the asymptotic stability of the equilibria, the onset of the instability or excitation of the self-oscillations, etc. These features are quite new for the dynamics of inviscid fluid though they are investigated widely for the Navier-Stokes and allied equations. Generally, the result of the withdrawal-supplying competition depends on boundary conditions at the flow inlet and outlet and the withdrawal dominates sometimes. For example, Morgulis and Yudovich (11) have pointed out wide classes of 2D open flows admitting the decreasing Liapunov functionals. Their construction employs the Arnold stability approach. Later on, Gallaire and Chomaz (7) examined the effect of the boundary conditions on the inviscid swirling flows through the finite pipes. Among other