scholarly journals On the settling of small grains in dusty discs: analysis and formulae

2020 ◽  
Vol 494 (4) ◽  
pp. 5134-5147
Author(s):  
Guillaume Laibe ◽  
Charles-Edouard Bréhier ◽  
Maxime Lombart
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Asymptotic Expansions ◽  
Dust Grains ◽  
Correlation Times ◽  
Small Grains ◽  
Balance Of Forces ◽  
Finite Correlation

ABSTRACT Instruments achieve sharper and finer observations of micrometre-in-size dust grains in the top layers of young stellar discs. To provide accurate models, we revisit the theory of dust settling for small grains, when gas stratification, dust inertia, and finite correlation times for the turbulence should be handled simultaneously. We start from a balance of forces and derive distributions at steady state. Asymptotic expansions require caution since limits do not commute. In particular, non-physical bumpy distributions appear when turbulence is purely diffusive. This excludes very short correlation times for real discs, as predicted by numerical simulations.

scholarly journals Temperature Fluctuations and Evolution of Dust Grains in Dense Interstellar Clouds

1987 ◽  
Vol 115 ◽  
pp. 88-89
Author(s):  
S. Aiello ◽  
B. Barsella ◽  
C. Cecchi-Pestellini ◽  
F. Ferrini ◽  
F. Mencaraglia ◽  
...  
Keyword(s):  
Steady State ◽  
Interstellar Medium ◽  
State Energy ◽  
Temperature Fluctuations ◽  
Interstellar Extinction ◽  
Incident Radiation ◽  
Dust Grains ◽  
Interstellar Clouds ◽  
Large Fluctuations ◽  
Small Grains

Interstellar extinction studies (Chlewicki et al, 1984), as well as IR observations (Sellgren et al, 1983) require the presence in the interstellar medium of a substantial number of small (a≲0.01 μm) dust grains. The temperature of such small grains is subjected, because of their small steady-state energy, to large fluctuations as they absorb photons from the incident radiation, which could prevent the accretion on such grains (Greenberg and Hong, 1974).

A Consistent Implementation of Inelastic Material Models into Steady State Rolling

2016 ◽  
Vol 44 (3) ◽  
pp. 174-190 ◽  
Author(s):  
Mario A. Garcia ◽  
Michael Kaliske ◽  
Jin Wang ◽  
Grama Bhashyam
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Viscoelastic Material ◽  
Rolling Contact ◽  
Arbitrary Lagrangian Eulerian ◽  
Ale Formulation ◽  
Inelastic Material ◽  
Material Formulation ◽  
Steady State Rolling ◽  
Efficient Alternative

ABSTRACT Rolling contact is an important aspect in tire design, and reliable numerical simulations are required in order to improve the tire layout, performance, and safety. This includes the consideration of as many significant characteristics of the materials as possible. An example is found in the nonlinear and inelastic properties of the rubber compounds. For numerical simulations of tires, steady state rolling is an efficient alternative to standard transient analyses, and this work makes use of an Arbitrary Lagrangian Eulerian (ALE) formulation for the computation of the inertia contribution. Since the reference configuration is neither attached to the material nor fixed in space, handling history variables of inelastic materials becomes a complex task. A standard viscoelastic material approach is implemented. In the inelastic steady state rolling case, one location in the cross-section depends on all material locations on its circumferential ring. A consistent linearization is formulated taking into account the contribution of all finite elements connected in the hoop direction. As an outcome of this approach, the number of nonzero values in the general stiffness matrix increases, producing a more populated matrix that has to be solved. This implementation is done in the commercial finite element code ANSYS. Numerical results confirm the reliability and capabilities of the linearization for the steady state viscoelastic material formulation. A discussion on the results obtained, important remarks, and an outlook on further research conclude this work.

scholarly journals Spatiotemporal Patterns Formed by a Discrete Nutrient-Phytoplankton Model with Time Delay

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Feifan Zhang ◽  
Wenjiao Zhou ◽  
Lei Yao ◽  
Xuanwen Wu ◽  
Huayong Zhang
Keyword(s):  
Steady State ◽  
Time Delay ◽  
Numerical Simulations ◽  
Functional Response ◽  
Bifurcation Analysis ◽  
Discrete Model ◽  
Continuous Model ◽  
Spatiotemporal Patterns ◽  
Homogeneous Steady State ◽  
Simulation Results

In this research, a continuous nutrient-phytoplankton model with time delay and Michaelis–Menten functional response is discretized to a spatiotemporal discrete model. Around the homogeneous steady state of the discrete model, Neimark–Sacker bifurcation and Turing bifurcation analysis are investigated. Based on the bifurcation analysis, numerical simulations are carried out on the formation of spatiotemporal patterns. Simulation results show that the diffusion of phytoplankton and nutrients can induce the formation of Turing-like patterns, while time delay can also induce the formation of cloud-like pattern by Neimark–Sacker bifurcation. Compared with the results generated by the continuous model, more types of patterns are obtained and are compared with real observed patterns.

EFFECT OF WATER CURRENT ON UNDERWATER GLIDER VELOCITY AND RANGE

2016 ◽  
Vol 78 (10-4) ◽  
Author(s):  
Muhammad Yasar Javaid ◽  
Mark Ovinis ◽  
Fakhruldin Mohd Hashim ◽  
Adi Maimun ◽  
Yasser M. Ahmed ◽  
...  
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Relative Motion ◽  
Water Current ◽  
Underwater Glider ◽  
Water Currents ◽  
Effect Of Water ◽  
Actuation System ◽  
Autonomous Underwater Glider

An autonomous underwater glider speed and range is influenced by water currents. This is compounded by a weak actuation system for controlling its movement. In this work, the effects of water currents on the speed and range of an underwater glider at steady state glide conditions are investigated. Extensive numerical simulations have been performed to determine the speed and range of a glider with and without water current at different net buoyancies. The results show that the effect of water current on the glider speed and range depends on the current relative motion and direction. In the presence of water current, for a given glide angle, glide speed can be increased by increasing the net buoyancy of the glider.

scholarly journals Identification of the Essential Features of the Transient Amplification of Mistuned Systems

2020 ◽  
Author(s):  
Luigi Carassale ◽  
Vincent Denoël ◽  
Carlos Martel ◽  
Lars Panning-von Scheidt
Keyword(s):  
Linear System ◽  
Numerical Simulations ◽  
Mechanical System ◽  
Asymptotic Expansions ◽  
Damping Ratio ◽  
Multiple Scale ◽  
Analytic Solutions ◽  
Sweep Rate ◽  
Scale Method ◽  
Complex Manner

Abstract The dynamic behavior of bladed disks in resonance crossing has been intensively investigated in the community of turbomachinery, addressing the attention to (1) the transienttype response that appear when the resonance is crossed with a finite sweep rate and (2) the localization of the vibration in the disk due to the blade mistuning. In real conditions, the two mentioned effects coexist and can interact in a complex manner. This paper investigates the problem by means of analytic solutions obtained through asymptotic expansions, as well as numerical simulations. The mechanical system is assumed as simple as possible: a 2-dof linear system defined through the three parameters: damping ratio ξ, frequency mistuning Δ, rotor acceleration Ω˙. The analytic solutions are calculated through the multiple-scale method.

Dynamics of Dual-Cell Series Miura-Ori Structures With Different Types of Inter-Cell Connections

2021 ◽  
Author(s):  
Hai Zhou ◽  
Haiping Wu ◽  
Jian Xu ◽  
Hongbin Fang
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Theoretical Basis ◽  
Initial Conditions ◽  
Cell Structure ◽  
Dynamic Responses ◽  
Complex Environment ◽  
Current State ◽  
Different Types ◽  
Cell Series

Abstract Origami-inspired structures and materials have shown remarkable properties and performances originating from the intricate geometries of folding. Origami folding could be a dynamic process and origami structures could possess rich dynamic characteristics under external excitations. However, the current state of dynamics of origami has mostly focused on the dynamics of a single cell. This research has performed numerical simulations on multi-stable dual-cell series Miura-Ori structures with different types of inter-cell connections based on a dynamic model that does not neglect in-plane mass. We introduce a concept of equivalent constraint stiffness k* to distinguish different types of inter-cell connections. Results of numerical simulations reveal the multi-stable dual-cell structure will exhibit a variety of complex nonlinear dynamic responses with the increasing of connection stiffness because of the deeper energy well it has. The connection stiffness has a strong effect on the steady-state dynamic responses under different excitation amplitudes and a variety of initial conditions. This effect makes us able to adjust the dynamic behaviors of dual-cell series Miura-Ori structure to our needs in a complex environment. Furthermore, the results of this research could provide us a theoretical basis for the dynamics of origami folding and serve as guidelines for designing dynamic applications of origami metastructures and metamaterials.

Swirling flow states in finite-length diverging or contracting circular pipes

2017 ◽  
Vol 819 ◽  
pp. 678-712 ◽  
Author(s):  
Zvi Rusak ◽  
Yuxin Zhang ◽  
Harry Lee ◽  
Shixiao Wang
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Finite Length ◽  
Vortex Breakdown ◽  
Steady States ◽  
Inviscid Limit ◽  
Circular Pipes ◽  
Outlet Flow ◽  
Separation Zones ◽  
Steady State Solutions

The dynamics of inviscid-limit, incompressible and axisymmetric swirling flows in finite-length, diverging or contracting, long circular pipes is studied through global analysis techniques and numerical simulations. The inlet flow is described by the profiles of the circumferential and axial velocity together with a fixed azimuthal vorticity while the outlet flow is characterized by a state with zero radial velocity. A mathematical model that is based on the Squire–Long equation (SLE) is formulated to identify steady-state solutions of the problem with special conditions to describe states with separation zones. The problem is then reduced to the columnar (axially-independent) SLE, with centreline and wall conditions for the solution of the outlet flow streamfunction. The solution of the columnar SLE problem gives rise to the existence of four types of solutions. The SLE problem is then solved numerically using a special procedure to capture states with vortex-breakdown or wall-separation zones. Numerical simulations based on the unsteady vorticity circulation equations are also conducted and show correlation between time-asymptotic states and steady states according to the SLE and the columnar SLE problems. The simulations also shed light on the stability of the various steady states. The uniqueness of steady-state solutions in a certain range of swirl is proven analytically and demonstrated numerically. The computed results provide the bifurcation diagrams of steady states in terms of the incoming swirl ratio and size of pipe divergence or contraction. Critical swirls for the first appearance of the various types of states are identified. The results show that pipe divergence promotes the appearance of vortex-breakdown states at lower levels of the incoming swirl while pipe contraction delays the appearance of vortex breakdown to higher levels of swirl and promotes the formation of wall-separation states.

Numerical simulations of non-stationary distributions of electrochemical potentials in SOFC

2017 ◽  
Vol 34 (6) ◽  
pp. 1956-1988 ◽  
Author(s):  
Mayu Muramatsu ◽  
Keiji Yashiro ◽  
Tatsuya Kawada ◽  
Kenjiro Tarada
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Chemical Potential ◽  
Simulation Method ◽  
Open Circuit ◽  
Operating Conditions ◽  
Stationary Distributions ◽  
Experimental Conditions ◽  
Content Type ◽  
Numerical Examples

Purpose The purpose of this study is to develop a simulation method to calculate non-stationary distributions of the chemical potential of oxygen in a solid oxide fuel cell (SOFC) under operation. Design/methodology/approach The initial-boundary value problem was appropriately formulated and the appropriate boundary conditions were implemented so that the problem of non-stationary behavior of SOFC can be solved in accordance with actual operational and typical experimental conditions. The dependencies of the material properties on the temperature and partial pressure of oxygen were also elaborately introduced to realize actual material responses. The capability of the proposed simulation method was demonstrated under arbitrary operating conditions. Findings The steady state calculated with the open circuit voltage condition was conformable with the analytical solution. In addition, the transient states of the spatial distributions of potentials and currents under the voltage- and current-controlled conditions were successfully differentiated, even though they eventually became the same steady state. Furthermore, the effects of dense materials assumed for interconnects and current collectors were found to not be influential. It is thus safe to conclude that the proposed method enables us to simulate any type of transient simulations regardless of controlling conditions. Practical implications Although only uniaxial models were tested in the numerical examples in this paper, the proposed method is applicable for arbitrary shapes of SOFC cells. Originality/value The value of this paper is that adequate numerical simulations by the proposed method properly captured the electrochemical transient transport phenomena in SOFC under various operational conditions, and that the applicability was confirmed by some numerical examples.

scholarly journals Alternating direction implicit type preconditioners for the steady state inhomogeneous Vlasov equation

2017 ◽  
Vol 83 (1) ◽  
Author(s):  
Markus Gasteiger ◽  
Lukas Einkemmer ◽  
Alexander Ostermann ◽  
David Tskhakaya
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Vlasov Equation ◽  
Numerical Solutions ◽  
Splitting Method ◽  
Time Integration ◽  
Computational Effort ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Wide Range

The purpose of the current work is to find numerical solutions of the steady state inhomogeneous Vlasov equation. This problem has a wide range of applications in the kinetic simulation of non-thermal plasmas. However, the direct application of either time stepping schemes or iterative methods (such as Krylov-based methods such as the generalized minimal residual method (GMRES) or relaxation schemes) is computationally expensive. In the former case the slowest time scale in the system forces us to perform a long time integration while in the latter case a large number of iterations is required. In this paper we propose a preconditioner based on an alternating direction implicit type splitting method. This preconditioner is then combined with both GMRES and Richardson iteration. The resulting numerical schemes scale almost ideally (i.e. the computational effort is proportional to the number of grid points). Numerical simulations conducted show that this can result in a speed-up of close to two orders of magnitude (even for intermediate grid sizes) with respect to the unpreconditioned case. In addition, we discuss the characteristics of these numerical methods and show the results for a number of numerical simulations.

Sign in / Sign up

Export Citation Format

Share Document