Direct Numerical Simulation of Mixing of a Passive in Decaying Turbulence

1999 ◽  
Author(s):  
P. Deb ◽  
Pradip Majumdar
Keyword(s):  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Scalar Dissipation ◽  
Step Method ◽  
Fractional Step Method ◽  
Mixing Processes ◽  
Turbulent Reactive Flows ◽  
Decaying Turbulence

Abstract Research on turbulent mixing processes is of great interest to those working on turbulent-reactive flows. In this paper, a detailed study has been performed for the evolution of scalar fields of different initial integral scales in decaying, homogeneous and isotropic turbulence using DNS technique. Passive scalar mixing in a cubical decaying, homogeneous, isotropic turbulence field is considered. The three-dimensional incompressible Navier-Stokes equations together with scalar equation are solved using Fractional Step Method. The convective and diffusive terms in governing equations are discretised by Compact Finite Difference Scheme. The 32 × 32 × 32 uniform staggered grids are used. The present simulation is performed at Taylor Reynolds number of 28.83. In this paper, the evolution of scalar RMS and scalar dissipation rate for different integral length scales has been presented. The initial velocity vector and Probability Density Function (PDF) of scalar at different eddy turn over time have also been presented.

Effect of Schmidt number on small-scale passive scalar turbulence

2003 ◽  
Vol 56 (6) ◽  
pp. 615-632 ◽  
Author(s):  
RA Antonia ◽  
P Orlandi
Keyword(s):  
Turbulent Flows ◽  
Schmidt Number ◽  
Isotropic Turbulence ◽  
Passive Scalar ◽  
Scalar Dissipation ◽  
Small Scale ◽  
Homogeneous Isotropic Turbulence ◽  
Passive Scalars ◽  
First Case ◽  
Decaying Turbulence

Previous reviews of the behavior of passive scalars which are convected and mixed by turbulent flows have focused primarily on the case when the Prandtl number Pr, or more generally, the Schmidt number Sc is around 1. The present review considers the extra effects which arise when Sc differs from 1. It focuses mainly on information obtained from direct numerical simulations of homogeneous isotropic turbulence which either decays or is maintained in steady state. The first case is of interest since it has attracted significant theoretical attention and can be related to decaying turbulence downstream of a grid. Topics covered in the review include spectra and structure functions of the scalar, the topology and isotropy of the small-scale scalar field, as well as the correlation between the fluctuating rate of strain and the scalar dissipation rate. In each case, the emphasis is on the dependence with respect to Sc. There are as yet unexplained differences between results on forced and unforced simulations of homogeneous isotropic turbulence. There are 144 references cited in this review article.

Dynamic interaction of multiple buoyant jets

2012 ◽  
Vol 708 ◽  
pp. 539-575 ◽  
Author(s):  
Adrian C. H. Lai ◽  
Joseph H. W. Lee
Keyword(s):  
Stokes Equations ◽  
Dynamic Pressure ◽  
Unit Length ◽  
Iterative Solution ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Dynamic Interaction ◽  
Ambient Conditions ◽  
Buoyant Jet ◽  
Buoyant Jets

AbstractAn array of closely spaced round buoyant jets interact dynamically due to the pressure field induced by jet entrainment. Mutual jet attraction can result in a significant change in jet trajectories. Jet merging also leads to overlapping of the passive scalar fields associated with the individual jets, resulting in mixing characteristics that are drastically different from those of an independent free jet. A general semi-analytical model for the dynamic interaction of multiple buoyant jets in stagnant ambient conditions is proposed. The external irrotational flow field induced by the buoyant jets is computed by a distribution of point sinks with strength equal to the entrainment per unit length along the unknown jet trajectories and accounting for boundary effects. The buoyant jet trajectories are then determined by an iterative solution of an integral buoyant jet model by tracking the changes in the external entrainment flow and dynamic pressure fields. The velocity and concentration fields of the jet group are obtained by momentum or kinetic energy superposition for merged jets and plumes, respectively. The modelling approach is supported by numerical solution of the Reynolds-averaged Navier–Stokes equations. The model shows that jet merging and mixing can be significantly affected by jet interactions. Model predictions of the multiple jet trajectories, merging height, as well as the centreline velocity and concentration of the buoyant jet group are in good agreement with experimental data for: (i) a clustered momentum jet group; (ii) a turbulent plume pair; and (iii) a rosette buoyant jet group. Dynamic interactions between a jet group are shown to decrease with the addition of an ambient cross-flow.

Numerical Simulation of Solitary Wave Using the Fully Lagrangian Method of Moving Particle Semi Implicit

2014 ◽  
Author(s):  
Mohammad Amin Nabian ◽  
Leila Farhadi
Keyword(s):  
Numerical Simulation ◽  
Free Surface ◽  
Solitary Wave ◽  
Stokes Equations ◽  
Rock Avalanche ◽  
Water Tank ◽  
Step Method ◽  
Fractional Step Method ◽  
Time Step ◽  
Moving Particle

A mesh-less numerical approach, called the moving particle semi implicit method (MPS), is presented to solve inviscid Navier-Stokes equations in a fully Lagrangian form using a fractional step method. This method consists of splitting each time step in two steps. The fluid is represented with particles and the motion of each particle is calculated through interactions with neighboring particles by means of a kernel function. In this paper, the MPS method is used to simulate a dynamic system consisting of a heavy box sinking vertically into a water tank, known as Scott Russell’s wave generator problem. This problem is an example of a falling rock avalanche into natural or artificial reservoirs. The box sinks into water tank and as a result the water is heaved up to form a solitary wave and a reverse plunging wave which forms a vortex. This vortex follows the solitary wave down the water tank. The good agreement between the numerical simulation and the analytical solution confirms the accuracy of the model. This proves the applicability of the present model in simulating complex free surface problems. The number of particles on free surface is presented as an indicator of stability of the model.

Use of Immersed Boundary Method for the Analysis of Electro-Osmotic Flow Generated by a Pair of Cylindrical Electrodes in a Micro-Cavity

2008 ◽  
Author(s):  
Dolfred V. Fernandes ◽  
Sangmo Kang ◽  
Yong K. Suh
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Ionic Concentration ◽  
Ion Concentration ◽  
Dimensional Case ◽  
Immersed Boundary ◽  
Bench Mark ◽  
Step Method ◽  
Fractional Step Method ◽  
Micro Cavity

The bulk motion of an aqueous solution induced by the application of DC electric field is studied numerically. The physical model consists of a micro-cavity with two completely polarizable cylindrical electrodes. The electric double layer (EDL) model coupled with Navier-Stokes equations governing the electroosmotic flow has been described. The Nernst-Planck model uses two extra equations for the prediction of ion concentration. We employed IB (immersed boundary) technique for the implementation of boundary conditions and semi-implicit fractional-step method for solving the governing equations. A new method is described for implementing concentration boundary conditions on the electrodes. The bench mark problems, driven cavity flow and flow over a cylnder were used for the validation of our present code. The numerical results are compared with the analytical results obtained using Gouy-Chapman-Stern model for the one dimensional case. For the two dimensional case the flow field and the ionic concentration distributions obtained shows that the electoosmotic effect is predominant in the thin region around the electrode.

Passive-scalar wake behind a line source in grid turbulence

2000 ◽  
Vol 416 ◽  
pp. 117-149 ◽  
Author(s):  
D. LIVESCU ◽  
F. A. JABERI ◽  
C. K. MADNIA
Keyword(s):  
Line Source ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Transport Equations ◽  
Source Size ◽  
Scalar Dissipation ◽  
Grid Turbulence ◽  
Scalar Flux ◽  
Convective Regime ◽  
Scalar Variance

The structure and development of the scalar wake produced by a single line source are studied in decaying isotropic turbulence. The incompressible Navier–Stokes and the passive-scalar transport equations are solved via direct numerical simulations (DNS). The velocity and the scalar fields are generated by simulating Warhaft's (1984) experiment. The results for mean and r.m.s. scalar statistics are in good agreement with those obtained from the experiment. The structure of the scalar wake is examined first. At initial times, most of the contribution to the scalar variance is due to the flapping of the wake around the centreline. Near the end of the turbulent convective regime, the wake develops internal structure and the contribution of the flapping component to the scalar variance becomes negligible. The influence of the source size on the development of the scalar wake has been examined for source sizes ranging from the Kolmogorov microscale to the integral scale. After an initial development time, the half-widths of mean and scalar r.m.s. wakes grow at rates independent of the source size. The mixing in the scalar wake is studied by analysing the evolution of the terms in the transport equations for mean, scalar flux, variance, and scalar dissipation. The DNS results are used to test two types of closures for the mean and the scalar variance equations. For the time range simulated, the gradient diffusion model for the scalar flux and the commonly used scalar dissipation model are not supported by the DNS data. On the other hand, the model based on the unconditional probability density function (PDF) method predicts the scalar flux reasonably well near the end of the turbulent convective regime for the highest Reynolds number examined. The scalar source size does not significantly influence the models' predictions, although it appears that the time-scale ratio of mechanical dissipation to scalar dissipation approaches an asymptotic value earlier for larger source sizes.

scholarly journals A divergence free fractional step method for the Navier-Stokes equations on non-staggered grids

2010 ◽  
Vol 51 ◽  
pp. 654 ◽  
Author(s):  
Steven William Armfield ◽  
Nicholas Williamson ◽  
Michael Kirkpatrick ◽  
Robert Street
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Fractional Step ◽  
Step Method ◽  
Fractional Step Method ◽  
Navier Stokes Equations ◽  
Staggered Grids ◽  
Divergence Free

Micro-structure and Lagrangian statistics of the scalar field with a mean gradient in isotropic turbulence

2003 ◽  
Vol 474 ◽  
pp. 193-225 ◽  
Author(s):  
G. BRETHOUWER ◽  
J. C. R. HUNT ◽  
F. T. M. NIEUWSTADT
Keyword(s):  
Scalar Field ◽  
Isotropic Turbulence ◽  
Numerical Study ◽  
Compressive Strain ◽  
Scalar Fields ◽  
Scalar Dissipation ◽  
Small Scale ◽  
Length Scale ◽  
Random Forcing ◽  
Kolmogorov Length Scale

This paper presents an analysis and numerical study of the relations between the small-scale velocity and scalar fields in fully developed isotropic turbulence with random forcing of the large scales and with an imposed constant mean scalar gradient. Simulations have been performed for a range of Reynolds numbers from Reλ = 22 to 130 and Schmidt numbers from Sc = 1/25 to 144.The simulations show that for all values of Sc [ges ] 0.1 steep scalar gradients are concentrated in intermittently distributed sheet-like structures with a thickness approximately equal to the Batchelor length scale η/Sc½ with η the Kolmogorov length scale. We observe that these sheets or cliffs are preferentially aligned perpendicular to the direction of the mean scalar gradient. Due to this preferential orientation of the cliffs the small-scale scalar field is anisotropic and this is an example of direct coupling between the large- and small-scale fluctuations in a turbulent field. The numerical simulations also show that the steep cliffs are formed by straining motions that compress the scalar field along the imposed mean scalar gradient in a very short time period, proportional to the Kolmogorov time scale. This is valid for the whole range of Sc. The generation of these concentration gradients is amplified by rotation of the scalar gradient in the direction of compressive strain. The combination of high strain rate and the alignment results in a large increase of the scalar gradient and therefore in a large scalar dissipation rate.These results of our numerical study are discussed in the context of experimental results (Warhaft 2000) and kinematic simulations (Holzer & Siggia 1994). The theoretical arguments developed here follow from earlier work of Batchelor & Townsend (1956), Betchov (1956) and Dresselhaus & Tabor (1991).

Sign in / Sign up

Export Citation Format

Share Document