Sinking, merging and stationary plumes in a coupled chemotaxis-fluid model: a high-resolution numerical approach

2012 ◽  
Vol 694 ◽  
pp. 155-190 ◽  
Author(s):  
A. Chertock ◽  
K. Fellner ◽  
A. Kurganov ◽  
A. Lorz ◽  
P. A. Markowich
Keyword(s):  
High Resolution ◽  
Stokes Equations ◽  
Fluid Model ◽  
Numerical Approach ◽  
Navier Stokes ◽  
High Concentration ◽  
Fluid System ◽  
Concentration Layer ◽  
High Concentrations ◽  
Chemotaxis System

AbstractAquatic bacteria like Bacillus subtilis are heavier than water yet they are able to swim up an oxygen gradient and concentrate in a layer below the water surface, which will undergo Rayleigh–Taylor-type instabilities for sufficiently high concentrations. In the literature, a simplified chemotaxis–fluid system has been proposed as a model for bio-convection in modestly diluted cell suspensions. It couples a convective chemotaxis system for the oxygen-consuming and oxytactic bacteria with the incompressible Navier–Stokes equations subject to a gravitational force proportional to the relative surplus of the cell density compared to the water density. In this paper, we derive a high-resolution vorticity-based hybrid finite-volume finite-difference scheme, which allows us to investigate the nonlinear dynamics of a two-dimensional chemotaxis–fluid system with boundary conditions matching an experiment of Hillesdon et al. (Bull. Math. Biol., vol. 57, 1995, pp. 299–344). We present selected numerical examples, which illustrate (i) the formation of sinking plumes, (ii) the possible merging of neighbouring plumes and (iii) the convergence towards numerically stable stationary plumes. The examples with stable stationary plumes show how the surface-directed oxytaxis continuously feeds cells into a high-concentration layer near the surface, from where the fluid flow (recurring upwards in the space between the plumes) transports the cells into the plumes, where then gravity makes the cells sink and constitutes the driving force in maintaining the fluid convection and, thus, in shaping the plumes into (numerically) stable stationary states. Our numerical method is fully capable of solving the coupled chemotaxis–fluid system and enabling a full exploration of its dynamics, which cannot be done in a linearised framework.

scholarly journals Two- and Three-Dimensional Numerical Experiments Representing Two Limiting Cases of an In-Line Pair of Finger Seal Components

2003 ◽  
Vol 9 (3) ◽  
pp. 171-179 ◽  
Author(s):  
M. J. Braun ◽  
V. V. Kudriavtsev ◽  
B. M. Steinetz ◽  
M. P. Proctor
Keyword(s):  
Solid Mechanics ◽  
Stokes Equations ◽  
Fluid Model ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Navier Stokes ◽  
Line Pair ◽  
Navier Stokes Equations ◽  
Flowing Fluid ◽  
Elemental Component

The work presented here concerns the numerical development and simulation of the flow, pressure patterns, and motion of a pair of fingers arranged one behind the other and axially aligned in line. The fingers represent the basic elemental component of a finger seal and form a tight seal around the rotor. Yet their flexibility allows compliance with rotor motion and, in a passive-adaptive mode, compliance with the hydrodynamic forces induced by the flowing fluid. Although this article does not treat the actual staggered configuration of a finger seal, the in-line arrangement represents a first step toward that final goal. The numerical two-dimensional (axial-radial) and three-dimensional results presented herein were obtained using a commercial package (CFD-ACE+). Both models use an integrated numerical approach, which couples the hydrodynamic fluid model based on Navier-Stokes equations to the solid mechanics code that models the compliance of the fingers.

scholarly journals Analysis of a Decoupled Time-Stepping Scheme for Evolutionary Micropolar Fluid Flows

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
S. S. Ravindran
Keyword(s):  
Micropolar Fluid ◽  
Stokes Equations ◽  
Fluid Model ◽  
Navier Stokes ◽  
Optimal Order ◽  
Step Size ◽  
Time Step ◽  
Order Error ◽  
Time Step Size ◽  
Time Stepping

Micropolar fluid model consists of Navier-Stokes equations and microrotational velocity equations describing the dynamics of flows in which microstructure of fluid is important. In this paper, we propose and analyze a decoupled time-stepping algorithm for the evolutionary micropolar flow. The proposed method requires solving only one uncoupled Navier-Stokes and one microrotation subphysics problem per time step. We derive optimal order error estimates in suitable norms without assuming any stability condition or time step size restriction.

scholarly journals Choice and Limits of a Fluid Model for the Numerical Study in Dynamic Fluid Structure Interaction Problems

2003 ◽  
Author(s):  
Jean Franc¸ois Sigrist ◽  
Christian Laine ◽  
Dominique Lemoine ◽  
Bernard Peseux
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Model ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Linear Solution ◽  
Fluid Structure ◽  
Design Engineers ◽  
Inviscid Incompressible Fluid ◽  
Basic Fluid

This paper is related to the study of a nuclear propulsion reactor prototype for the French Navy. This prototype is built on ground and is to be dimensioned toward seismic loading. The dynamic analysis takes the coupled fluid structure analysis into account. The basic fluid models used by design engineers are inviscid incompressible or compressible. The fluid can be described in a bidimensional by slice or a three-dimensional approach. A numerical study is carried out on a generic problem for the linear FSI dynamic problem. The results of this study are presented and discussed. As a conclusion, the three-dimensional inviscid incompressible fluid appears to be the best compromise between the description of physical phenomena and the cost of modeling. The geometry of the reactor is such that large displacements of the structure in the fluid can occur. Therefore, the linearity hypothesis might not be longer valid. The case of large amplitude imposed oscillating motion of a cylinder in a confined fluid is numerically studied. A CFD code is used to investigate the fluid behavior solving the NAVIER-STOKES equations. The forces induced on the cylinder by the fluid are computed and compared to the linear solution. The limit of the linear model can then be exhibited.

scholarly journals Models for water steam condensing flows

2012 ◽  
Vol 33 (1) ◽  
pp. 67-86
Author(s):  
Włodzimierz Wróblewski ◽  
Sławomir Dykas ◽  
Tadeusz Chmielniak
Keyword(s):  
Stokes Equations ◽  
Fluid Model ◽  
Vapour Phase ◽  
Separate Flow ◽  
Navier Stokes ◽  
Governing Equations ◽  
State Equations ◽  
Water Steam ◽  
Condensing Flows ◽  
Two Fluid Model

Models for water steam condensing flows The paper presents a description of selected models dedicated to steam condensing flow modelling. The models are implemented into an in-house computational fluid dynamics code that has been successfully applied to wet steam flow calculation for many years now. All models use the same condensation model that has been validated against the majority of available experimental data. The state equations for vapour and liquid water, the physical model as well as the numerical techniques of solution to flow governing equations have been presented. For the single-fluid model, the Reynolds-averaged Navier-Stokes equations for vapour/liquid mixture are solved, whereas the two-fluid model solves separate flow governing equations for the compressible, viscous and turbulent vapour phase and for the compressible and inviscid liquid phase. All described models have been compared with relation to the flow through the Laval nozzle.

Heat and Mass Transfer Porous Medium Saturated with Compressible Fluid with Boundary Domain Integral Method

2008 ◽  
Vol 273-276 ◽  
pp. 808-813 ◽  
Author(s):  
Janja Kramer ◽  
Renata Jecl ◽  
Leo Škerget
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Heat And Mass Transfer ◽  
Compressible Fluid ◽  
Integral Method ◽  
Stokes Equations ◽  
Numerical Approach ◽  
Momentum Equation ◽  
Navier Stokes ◽  
Domain Integral

A numerical approach to solve a problem of combined heat and mass transfer in porous medium saturated with compressible fluid is presented. Transport phenomena in porous media is described using the modified Navier-Stokes equations, where for the governing momentum equation the Brinkman extended Darcy formulation is used. Governing equations are solved with the Boundary Domain Integral Method, which is an extension of classical Boundary Element Method.

Effects of Non-Dimensional Parameters on Formation and Break Up of Cylindrical Droplets

2004 ◽  
Author(s):  
Mohammad Taeibi-Rahni ◽  
Shervin Sharafatmand
Keyword(s):  
Stokes Equations ◽  
Fluid Model ◽  
Time Dependent ◽  
Navier Stokes ◽  
Ohnesorge Number ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Dimensional Parameters ◽  
Break Up ◽  
Eotvos Number

The consistent behavior of non-dimensional parameters on the formation and break up of large cylindrical droplets has been studied by direct numerical simulations (DNS). A one-fluid model with a finite difference method and an advanced front tracking scheme was employed to solve unsteady, incompressible, viscous, immiscible, multi-fluid, two-dimensional Navier-Stokes equations. This time dependent study allows investigation of evolution of the droplets in different cases. For moderate values of Atwood number (AT), increasing Eotvos number (Eo) explicitly increases the deformation rate in both phenomena. Otherwise, raising the Ohnesorge number (Oh) basically amplifies the viscous effects.

Dynamics of Pulsed Jet in Crossflow

2007 ◽  
Author(s):  
M. Arienti ◽  
M. C. Soteriou
Keyword(s):  
Stokes Equations ◽  
Near Field ◽  
Numerical Approach ◽  
Mie Scattering ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Pulsed Jet ◽  
Jet In Crossflow ◽  
Lagrangian Equations ◽  
Phase Doppler Interferometry

We examine the effect of time-dependent forcing on jet-in-crossflow atomization in the case of pulsed liquid injection and uniform crossflow. The dynamics of the jet is captured by a numerical approach that blends interface tracking of the liquid surface with an empirical description of the atomization process. The unsteady Reynolds-Averaged Navier-Stokes equations for the gas and the continuous (i.e., preceding breakup) liquid phase are solved simultaneously with the Lagrangian equations for the droplet trajectories. This approach captures the near field transient due to the opening (closing) of the fuel valve, as well as the convective delay of the spray in the far field. Validation is carried out with Phase Doppler Interferometry (PDI) and Mie scattering measurements at standard conditions for pulsed jets of water and ethanol in crossflow air. The discussion is focused on the shape of the convecting spray pulse and on the trends due to variations in crossflow and jet velocities.

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